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Material Information
- Title:
- Precipitation in nickel-aluminum-molybdenum superalloys
- Creator:
- Kersker, Michael Miller, 1948-
- Publisher:
- University of Florida
- Publication Date:
- 1986
- Language:
- English
- Physical Description:
- viii, 202 leaves : ill. ; 28 cm.
Subjects
- Subjects / Keywords:
- Alloys ( jstor )
Conceptual lattices ( jstor )
Crystals ( jstor )
Cubes ( jstor )
Diffraction patterns ( jstor )
Lattice parameters ( jstor )
Precipitates ( jstor )
Precipitation ( jstor )
Superlattices ( jstor )
Wave diffraction ( jstor )
Dissertations, Academic -- Materials Science and Engineering -- UF
Electron precipitation ( lcsh )
Heat resistant alloys ( lcsh )
Materials Science and Engineering thesis, Ph.D.
Notes
- Thesis:
- Thesis (Ph.D.)--University of Florida, 1986.
- Bibliography:
- Bibliography: leaves 185-190.
- General Note:
- Typescript.
- General Note:
- Vita.
- Statement of Responsibility:
- by Michael Miller Kersker.
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- University of Florida
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- University of Florida
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- Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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15539055 ( OCLC )
AEK9766 ( NOTIS )
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- UFIR:
- Institutional Repository at the University of Florida (IR@UF)
- UFETD:
- University of Florida Theses & Dissertations
- IUF:
- University of Florida
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PRECIPITATION IN
NICKEL-ALUMINUM-MOLYBDENUM SUPERALLOYS
By
MICHAEL MILLER KERSKER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1986
ACKNOWLEDGEMENTS
Special thanks are given to John J. Hren, my mentor
and advisor. I am especially grateful that he is as
stubborn as I. The assistance of Scott Walck, my
colleague and friend, in handling the logistics and
mechanics of my dissertation, is especially appreciated.
The continued support of Dr. E. Aigeltinger is sincerely
acknowledged. I am also grateful to Drs. Kenik, Bentley,
Lehman, and Carpenter for their generous assistance during
my visits to the Oak Ridge National Laboratory. For the
perserverance and persistence of my wife, Janice, I am
most endebted.
I am also indebted to Pratt and Whitney Government
Products Division, West Palm Beach, for providing the
necessary funding to see this project through to
completion, to the SHARE programs at ORNL for the generous
use of their instruments and expertise, and to the
Department of Materials Science and Engineering at the
University of Florida for providing the education,
training, and constant devotion to excellence in research
that have directed my career and scientific character.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS.................................... ii
ABSTRACT ....................................... .. vii
CHAPTER
1 INTRODUCTION..................... ........1
2 BACKGROUND ............ ....... .. ... ... ... 7
2.1 Phase Diagrams ......................7
2.1.1 Binary Phase Diagrams......... 7
2.1.1.1 Ni-Mo................7
2.1.1.2 Ni-Al............ 9
2.1.1.3 Ni-W................. 9
2.1.1.4 Ni-Ta...............12
2.1.2 Ternary
2.1.2.1
2.1.2.2
2.1.2.3
Diagrams ............. 12
Ni-Al-Mo............12
Ni-Al-Ta............14
Ni-Al-W.............16
2.2 Binary Phases...................... 16
2.2.1 Ni-Mo...
2.2.1.1
2.2.1.2
2.2.1.3
2.2.1.4
2.2.2 Ni-W....
2.2.2.1
2.2.2.2
2.2.2.3
2.2.2.4
................... 16
Ni4Mo............... 18
Ni3Mo...............20
Ni2Mo...... ........ 20
Ni-Mo. ..............23
..................... 23
Ni4W ...............24
Ni3W .................24
Ni2W ................24
NiW ................. 24
2.2.3 Domain Variants/Antiphase
Boundaries..................25
2.2.3.1 Ni4x(Dla)...........25
2.2.3.2 Ni3x(D022). .....27
2.2.3.3 Ni2x(Pt2Mo).........29
2.2.4 SRO in Ni-x Binaries.........29
2.2.5 Ordering Reactions and Kinetics....31
2.2.5.1 Binary Alloys.............31
2.2.5.2 Ternary Alloys ...........35
2.2.6 Ni-Al Ni3A1.....................36
2.3 Diffraction Patterns: NixMo Phases/
Ni3Al .....................................40
2.3.1 DO22 Reciprocal Lattice............40
2.3.2 Dla/Pt2Mo/L12 Reciprocal Lattices..42
2.3.3 SRO (1, 1/2, 0) Scattering.........46
2.3.4 Variant Imaging...................46
2.3.4.1 DO22: Ni3Mo...............47
2.3.4.2 Dla: Ni4Mo.................47
2.3.4.3 Pt2Mo: Ni2Mo..............51
3 EXPERIMENTAL PROCEDURE........................ 53
3.1 Composition............................ .. 53
3.2 Heat Treatments.......................... 54
3.3 Characterization: Methods of Analysis....55
4 SPECIAL METHODS................................. 61
4.1 Convergent Beam Electron Diffraction
(CBED) Methods............................61
4.1.1 Experimental Technique.............. 63
4.1.2 HOLZ Lines (High Order Laue
Zone Lines)........................ 66
4.1.3 Indexing HOLZ Lines................ 72
4.1.4 Lattice Parameter Changes...........89
4.1.5 The Effect of Strain and
Non-Cubicity on Pattern Symmetry...91
4.2 Energy Dispersive Methods.................97
5 RESULTS ...................... .............. 106
5.1 Microstructural Characterization.........106
5.1.1 As Extruded RSR 197 and RSR 209
Alloys............................ .106
5.1.2 RSR 197-As Solution Heat Treated
and Quenched......................106
5.1.3 General Microstructural Features..111
5.1.4 RSR 197 Aging....................111
5.1.4.1 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours.................... 111
5.1.4.2 Lattice imaging of D022
and Dla Phases ............ 127
5.1.4.3 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours ....... ........... .132
5.1.4.4 Solution Heat Treated,
Quenched and Aged at
870 C for up to 100
Hours ....... ......... ... 134
5.1.4.5 Aging Summary RSR 197...140
5.1.5 RSR 209 As Solution Heat
Treated and Quenched............... 142
5.1.6 RSR 209 Aging.....................142
5.1.6.1 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours...................... 142
5.1.6.2 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours .............. ......145
5.1.6.3 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours........... .. ...... 149
5.1.6.4 Aging Summary RSR 209...152
5.1.7 Special Aging/Special Alloys.......153
5.1.7.1 Alloy #17 Solution
Heat Treated, Quenched
and Aged at 760 C for
100 Hours................153
5.1.7.2 Alloy #17 Solution
Heat Treated, Quenched
and Aged at 870 C for
100 Hours................. 153
5.1.7.3 RSR 197 Solution Heat
Treated, Quenched and
Aged at 870 C for 1 Hour,
Furnace Cooled to 760 C
and Aged for 100 Hours at
760 C........ ............ 156
5.1.7.4 RSR 185 Solution Heat
Treated at 1315 C and
Water Quenched.............156
5.2 X-Ray Diffraction Measurements............ 156
5.3 Convergent Beam Measurements ..............161
5.4 Energy Dispersive X-Ray Measurements....167
5.5 Microhardness Measurements.............. 167
6 DISCUSSION AND CONCLUSIONS................... 170
6.1 Metastable NixMo Phase
Formation: Effects of Chemistry
and Microstructure.......................... 170
6.2 Precipitation in RSR 197................176
6.3 Precipitation in RSR 209................179
6.4 Mechanical Response to Aging............179
6.5 Convergent Beam/X-Ray Diffraction.......181
6.6 Conclusions.............................183
REFERENCES. .................. .......................... 185
APPENDICES
A HOLZ PATTERN CALCULATION.....................191
B INTERPLANAR ANGLES...........................199
BIOGRAPHICAL SKETCH.................................... 201
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
PRECIPITATION IN
NICKEL-ALUMINUM-MOLYBDENUM SUPERALLOYS
By
Michael Miller Kersker
August, 1986
Chairman: John J. Hren
Major Department: Materials Science and Engineering
The precipitation of 420 phases, common in the NiMo
binary system, is also observed in Ni-Al-Mo-(x)
superalloys. Two such superalloys, where x is Ta or W,
were characterized, after aging, using a variety of
electron microscopy methods.
The 420 type NixMo phases that precipitate during
aging depend strongly on the partitioning of the
quaternary elements. The DO22 and Dla phases predominate
in the Ta containing quaternary. The strain between the
gamma prime precipitates is sufficient to suppress the
nucleation of specific DO22 (Ni3Mo) variants, in turn
affecting the subsequent coarsening behavior of the Dla
phase. The crystallographic similarity of these two
phases is demonstrated by simultaneously imaging the
lattices of the two phases at common interfaces. The
predominant NixMo precipitate in the W bearing quaternary
is Pt2Mo (Ni2Mo), though D022 and Dla can be present
concurrent with the Pt2Mo.
When aged at temperatures above the solvi for the
NixMo phases, equilibrium NiMo and equilibrium Mo phases
precipitate, the former in the Ta containing alloy, the
latter in the W containing alloy. The presence of these
phases is in general agreement with the expected phase
equilibria predicted by the phase diagram.
Convergent beam electron diffraction, one of the
methods used in the characterization of the alloys, is
shown to have sufficient sensitivity for lattice parameter
variations to qualitatively measure the difference in
partitioning of the quaternary additions to the gamma
prime and gamma phases of both quaternary alloys. The
method is compared to x-ray diffraction results and
confirmed by energy dispersive x-ray analysis. In
addition to the measurement of partitioning, the fine
spatial resolution of the convergent beam method makes it
ideal for the measurement of other factors that are
reflected in lattice parameter changes -- strain, for
example. Simple equations are developed for the indexing
of HOLZ line patterns and for the measurement of lattice
parameters and uniform strain. Examples are given using
the superalloys characterized in this study.
viii
CHAPTER 1
INTRODUCTION
No single factor in jet engine design has been as
important as the development of high strength, high
temperature alloys for the hot turbine section of the
engine. This development has proceeded over the
relatively short period from the early 1930's, the early
development days of the jet engine, to the present. These
high strength, high temperature alloys had to maintain
their strength at very high temperatures under very high
load conditions yet still maintain close dimensional
tolerances so that thrust levels would not deteriorate
significantly with time. They had to be capable of
withstanding extremes in thermal cycling and had to resist
degradation under the most severe of hot corrosion
environments. It is no wonder these materials were and
are referred to as superalloys.
Alloy development has proceeded in superalloy systems
as it has historically proceeded in other metallurgical
systems -- empirical trial and test. In this approach
numerous alloys are prepared, fabricated, heat treated,
and tested. The winners are selected based on their
property responses. Compositional tolerances are
determined based again on desirable property limits.
It is especially fortunate that considerable
microstructural analysis of successful (and unsuccessful)
alloys has accompanied this standard approach to alloy
design. The property-microstructure relationships
developed as a result of correlations made following this
approach have been instrumental in elucidating many of the
known strengthening mechanisms that are now known to
contribute to both high and low temperature strength in
metals. These mechanisms include, among others,
1) precipitation strengthening, 2) solid solution
strengthening, 3) order strengthening, and 4) dispersion
strengthening. An alphabet of elements may be required to
activate these mechanisms and alloys such as TRWNASAVIA
(composition, at.%: Ni-61.0, Cr-6.1, Co-7.5, Mo-2.0,
W-5.8, Ta-9.0, Cb-.5, Al-0.4, Ti-l.0, C-0.13, B-0.02,
Zr-0.13, Re-0.5, and Hf-0.4) were developed seemingly as
confirmation of the old superalloy adage, "The more stuff
we put in, the better it is."
Though TRWNASAVIA is an extreme example of maximizing
desirable properties based on intentional additions (the
alloy contains 1/7 of all known naturally occurring
elements), many other superalloys also contain a large
number of intentionally added elements. These superalloy
compositions are often based on the Ni-Al system. The
microstructure of this "average" Ni based superalloy
consists of essentially three distinct microstructural
features. The first is the matrix, which is usually
disordered FCC nickel and can contain numerous elements in
solution. Secondly, there are incoherent precipitates
which can include the carbides, nitrides, and Ni bearing
phases, phases like sigma phase (Sims and Hagel, 1972).
Thirdly, there are the coherent phases which are normally
ordered superlattices of the disordered FCC matrix. The
major FCC ordered phase in such Ni-Al alloys is Ni3Al, an
L12 superlattice also known as gamma prime. This is
normally the strengthening phase in Ni-Al alloys. When
refractory metals are added to Ni-Al alloys, other
coherent phases can also be present as either the minor
precipitate or as the major strengthening precipitate,
e.g., D022 phase in In 718 (Quist et al., 1971; Cozar and
Pineau, 1973).
Alloys under development at Pratt and Whitney
Government Products Division in West Palm Beach, Florida,
are also based on the Ni-Al system. They are similar to
the ternary alloy WAZ-20-Ds (Sims and Hagel, 1972), but
additionally contain small quaternary additions of Ta and
W. A host of unforeseen solid state reactions proceeds
during low temperature heat treating of the Pratt and
Whitney superalloys (Aigeltinger and Kersker, 1981;
Aigeltinger, Kersker, and Hren, 1979). These reactions
are very similar to those in the Ni-Mo binary system.
Much effort in studying Ni rich, Ni-Mo binary alloys has
been devoted to describing the transition from the
disordered state to the ordered state, typically a
transition through the short range ordered state. Very
elegant theories dealing with the nucleation of these
phases have been developed.
These metastable phases can be found in alloys of the
ternary Ni-Mo-Al system, and also in the Pratt and Whitney
quaternary alloys (Aigeltinger, Kersker, and Hren, 1979).
They are not present at the high temperatures normally
encountered in the turbine section of an engine, at
temperatures in the range of 1100 C, and therefore do not
contribute to high temperature strength in such Ni based
ternary and quaternary alloys. Nevertheless, certain
aspects of their microstructures suggest that they might
still contribute to alloy strength at lower than normal
turbine operating temperatures.
The metastable phases investigated here are of the
type NixMo, where x can be 2, 3 or 4. They are coherent
with the FCC matrix which is a Ni rich solution in the
above superalloys. They may be present at temperatures of
700 degrees C and lower for very long times (Martin,
1982), and may delay the precipitation of the equilibrium
phases that would be predicted from the equilibrium phase
diagram.
Though there are similarities in the precipitation of
these NixMo metastable phases among the binary, ternary,
and quaternary alloys described earlier, there are
5
differences, chemistries aside, between the Ni-Mo binaries
and Ni-Mo-Al-(x) alloys, most importantly the presence in
the ternaries and quaternaries of primary gamma prime
phase. Could this gamma prime phase affect the
precipitation behavior of the Nix(Mo,x) phases which
precipitate from gamma solution? Would the physical
constraints imposed by the gamma prime precipitate affect
the "equilibrium" structure of these precipitates after
coarsening? What would be the effect of the quaternary
additions on the metastable precipitation behavior of
these alloys? Would these quaternary additions have any
effect on the gamma prime phase?
In order to answer questions such as these, it was
necessary to characterize the Pratt and Whitney alloys in
a way that such information could be directed towards
answering these questions. The study was to focus on the
use of the electron microscope. The advantage offered by
this instrument in studying fine scale precipitation
phenomena are trivially obvious, copiously documented, and
relatively straightforward. Some microstructural
measurements, however, are not easily accomplished in the
microscope -- the measurement of local composition or the
measurement of local lattice parameters, for example.
These applications were in their infancy and had, for the
most part, not as yet been directed toward practical
problem solving in materials science.
This dissertation is about the various phases, both
stable and metastable, that form in the quaternary
Ni-Mo-Al-(Ta or W) alloys. It is about their
crystallography and about various aspects of the alloys'
microstructure that could affect this crystallography. It
is additionally an electron microscope study devoted in
part to exploring methods for studying these phases.
Chapter 2 introduces the reader to the various binary
metastable phases that occur in the alloys and
additionally to theories dealing with their formation. A
brief background in the Ni-Al system will also be
developed. Chapter 3 outlines the alloys, experiments,
and experimental methods chosen for this study. Chapter 4
develops the necessary background in certain special
methods that were employed to study critical features of
the superalloy microstructure. These methods include
convergent beam diffraction and energy dispersive x-ray
analysis. Chapter 5 reports on the results of the
experiments described in Chapter 3. The dissertation
concludes with Chapter 6, a discussion of the results with
the conclusions and inferences therefrom.
CHAPTER 2
BACKGROUND
This chapter will provide the background necessary to
understand the crystallography and precipitate types that
will be described in detail in Chapter 5. It additionally
provides some seminal ideas on nucleation mechanisms for
the ordered nonequilibrium coherent phases that will be
shown to precipitate in the otherwise disordered gamma
matrix. All the known equilibrium phases are also
described and the relevant phase diagrams presented.
Interpretation of the diffraction patterns of the NixMo
coherent phases is explained last.
2.1 Phase Diagrams
2.1.1 Binary Phase Diagrams
2.1.1.1 Ni-Mo
The binary Ni-Mo equilibrium phase diagram is shown
in Figure 2.1 (Hansen, 1958). This diagram has been
recently confirmed by Heijnegen and Rieck (1973). Three
equilibrium intermetallic phases can occur: Ni4Mo, a Dla
superlattice, Ni3Mo, an orthorhombic phase, and NiMo, an
orthorhombic phase. Only NiMo is ever at equilibrium with
the liquid.
WEIGHT PERCENT NICKEL
Mo 0.1 02 0.3 04 0.5 0 6 0.7 0.8 0.9 N.
LuLLLUJ XNi
Figure 2.1
Ni-Mo binary equilibrium phase diagram
(after Hansen, 1958).
The Ni4Mo and Ni3Mo phases are the result of solid-solid
transformations. There is no true order-disorder
transition temperature for either of them. The Ni4Mo
phase is formed by a peritectoid reaction between gamma
and Ni3Mo: gamma + Ni3Mo <> Ni4Mo, at 875 C. The Ni3Mo
phase also forms by peritectoid reaction at 910 C; gamma +
NiMo 0=) Ni3Mo. Above 900 C an alloy of composition Ni4Mo
will be wholly in the gamma disordered FCC region. An
alloy of Ni3Mo stoichiometry will be a solid solution
above 1135 C.
2.1.1.2 Ni-Al
Figure 2.2 is the equilibrium diagram for the Ni-Al
system (Hansen, 1958). This diagram has been more
recently confirmed by Taylor and Doyle (1972). Two phases
exist on the Ni rich side of the diagram. They are AlNi,
a congruently melting compound, and Ni3Al, an ordered L12
superlattice phase commonly referred to as gamma prime.
Gamma prime is formed eutectically with gamma (solid
solution Ni and Al) at 1385 C. No solid state reactions
occur in this system at lower temperatures.
2.1.1.3 Ni-W
The Ni-W binary diagram as modified by Walsh and
Donachie (1973) is shown in Figure 2.3 (Moffatt, 1977).
The modified diagram includes the intermetallics NiW and
NiW2.
A1-Ni
WEIGHT PERCENT NICKEL
Al 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ni
LaaUui XNi
Figure 2.2 Ni-Al binary equilibrium phase diagram
(after Hansen, 1958).
11
WEIGHT % W
Ni 20 4050 60 70 75 80 85 90 95 W
1800
Z z 2
L IQ ,
1510 (W)
1500 1510 LI. + (W)
14 1 1500 4
17.5 20.7 99.1
S 1453 (NL) + (W)
L 1200-
:D 10o30 < T 1093
S-100 1010
ul 900-
0-
L (Ni)
600.
(Ni4W) (NiW) (NiW,)
+ + +
300. (NiW) (NmW,) (W)
$
Ni. 10 20 30 40 50 60 70 80 90 W
ATOM % W
Figure 2.3 Ni-W binary equilibrium phase diagram
(after Moffatt, 1977).
The intermetallic Ni4W forms by the peritectoid reaction
Ni + NiW <=)Ni4W at 970 C. The crystal structure of Ni4W
is isostructural with Ni4Mo (Epremian and Harker, 1949).
Note the absence of any phase comparable to Ni3Mo.
2.1.1.4 Ni-Ta
The Ni-Ta diagram as given by Shunk (1969) has been
modified to include the low temperature NigTa
intermetallic by Larson et al. (1970). It is shown in
Figure 2.4 (Moffatt, 1977). The Ni8Ta intermetallic forms
sluggishly by peritectoid reaction with Ni3Ta and Ni. It
is reported to be F.C.T. The Ni3Ta phase has been found
to be monoclinic with a possible orthorhombic variant
(TiCo3 type), or as a tetragonal D04 superlattice (TiAl3
type). The phase is thus not isostructural with either
Ni3Mo D022 or with orthorhombic equilibrium Ni3Mo.
2.1.2 Ternary Diagrams
2.1.2.1 Ni-Al-Mo
High temperature Ni-Mo-Al isotherms show a
quasibinary eutectic between the NiAl and Mo phases
(Bagaryatski and Ivanovskaya, 1960). This allows the
diagram to be conveniently split in two at a line
connecting the NiAl and Mo phase fields. At the time this
investigation was originally begun, the Ni-rich low
temperature phase equilibria of this ternary system were
WEIGHT % Ta
60 70 75 80 85
ouuU. N 2998
d d 2
2500. z z z ,
1 1 1 -
0(Ta)
,' LI..
1453 LI 1785
St/1360 1420
3 1545 1570
1500 1
J 15.4 ....... A 1320
0 (Ni)/ ( 38)
j N ji) I '<13-0
1000- (N) 1320
tY-Ni T(c,
570 NTa NiTa NiTa
500 1- + + +
S d NiTa N iTa I (Ta)
o ; I j
Ni 10 20 30 40 50 60 70 80 90 Ta
ATOM % Ta
Figure 2.4 Ni-Ta binary equilibrium phase diagram
(after Moffatt, 1977).
in question. Guard and Smith (1959-1960) reported the
presence of a ternary compound at 1000 C on the Ni-rich
side of the diagram. This phase was included in a
subsequently derived equilibrium diagram by Aigeltinger et
al. (1978). No other investigator has reported the
presence of a ternary Ni-Mo-Al compound (Bagaryatski and
Ivanovskaya, 1960; Virkar & Raman, 1969; Raman and
Schubert, 1965; Pryakhina et al., 1971; Miracle et al.,
1984).
Aigeltinger et al. (1978), Loomis et al. (1972), and
recently Miracle et al. (1984), extend the maximum
solubility of Mo in Ni3A1 to 6.0 at. % Mo, a value much
higher than that previously reported by Guard and Smith
(1959-1960), Bagaryatski and Ivanovskaya (1960), Virkar
and Raman (1969), Raman and Schubert (1965), and Pryakhina
et al. (1971). Miracle et al. (1984) also report an
additional class II reaction at 1090 C involving gamma,
gamma prime, NiMo, and Mo. This reaction brings gamma
prime, gamma, and NiMo into equilibrium at lower
temperatures. This class II reaction was previously
unreported. A 1000 C isotherm from their work is compared
with the 600 C section from Pryakhina et al. (1971) in
Figure 2.5.
2.1.2.2 Ni-Al-Ta
The Ni-rich side of this diagram has recently been
reviewed by Nash and West (1979). They confirm the
MO
a.
N( 4At If)
f/i -/ / A/
Nt()I / 80 I O M ,' tf Mo ZO Mo
c MONV4 Ay/i.3 N, ,am %"O
b.
Figure 2.5 Ternary Ni-Al-Mo isotherms;
a.) 1038 C (after Miracle et al., 1984)
and b.) 600 C (after Pryakhina et al.,
1971).
presence of the ternary phase Ni6TaAl, and also NigTa.
The former phase is hexagonal and is not isostructural
with any Ni-Mo-Al phase. According to their 1000 C
section, Ta can substitute for Al up to 8.0 at.% in gamma
prime (Ni3Al). It is soluble to approximately 10.0 at.%
at 1250 C.
2.1.2.3 Ni-Al-W
This diagram has been recently determined by Nash et
al. (1983). A 1250 C isotherm from their work is shown in
Figure 2.6. No ternary phase is shown in the isotherm,
nor is a ternary phase reported at temperatures as low as
1000 C. The diagram is qualitatively very similar to the
Ni-Mo-Al ternary diagram shown in Figure 2.5b.
2.2 Binary Phases
2.2.1 Ni-Mo
In addition to the equilibrium phases mentioned in
the previous section, there are intermediate metastable
phases that can precipitate from Ni rich solutions of
Ni-Mo binaries. The practical limit of Mo solubility in
Ni is about 27 atomic percent. Molybdenum in excess of
this amount cannot be put into solution. If a Ni-Mo
binary of 27.0 at.% or less Mo is quenched from a
temperature high enough for the alloy to have been a
/b"
u-
Ni "- --------
20 40 60
W, at.-*/.
Figure 2.6 Ternary Ni-Al-W 1250 C isotherm;
(after Nash et al., 1983).
single phase solid solution, and subsequently heat treated
below the solvus temperature for that particular
as-quenched composition, intermediate metastable phases
may precipitate instead of the equilibrium phases
predicted by the equilibrium phase diagram. These phases
are Ni2Mo, a Pt2Mo superlattice; Ni3Mo, as a D022 phase
rather than the equilibrium orthorhombic phase; and/or
Ni4Mo, the previously described binary equilibrium phase
which can exist as a metastable phase at certain Ni-Mo
compositions.
2.2.1.1 Ni4Mo
The Ni4Mo phase is a BCT structure derived from the
disordered FCC lattice. Its lattice parameters as a BCT
cell are a' = b' = 5.727 Angstroms, c' = 3.566 Angstroms.
The BCT unit cell can be derived from the FCC parent by
using the following transformation:
XA' = 1/2 (311+A2); A2' = 1/2 (-A1+312); A3' = A3,
where Al, A2, and A3 are the lattice vectors for FCC and
Al', A2', and A3' are the vectors from the BCT unit cell
(Mishra, 1979). The c axis of the Dla undergoes a
contraction of 1.2% during the transformation from
disordered FCC to ordered Dla. Hence, A3' is only
approximately equal to A3. A convenient way to visualize
the Ni4Mo structure is to consider the ordering of Mo on
* o \*o 0o^ o Y P,.O
o \ o o
*0 Mo Open circles: atoms in first and
third layers
S Ni Closed circles: atoms in second
layer
Figure 2.7 Two dimensional representation of Dla
stacking showing 1.) FCC unit cell ( ),
2.) Dla unit cell (-- -), and 3.) 420 FCC
stacking sequence (----).
every fifth 420 plane of the FCC parent lattice (Okamoto
and Thomas, 1971), as described in Figure 2.7. This
stacking sequence is pertinent. With slight variation it
can also describe the stacking sequences of both Ni2Mo
Pt2Mo and Ni3Mo DO22. It also simplifies the
visualization of the diffraction patterns for these
phases, c.f., section 2.3.4.2.
2.2.1.2 Ni3Mo
The Ni3Mo phase exists stoichiometrically as both an
orthorhombic equilibrium phase, where a = 5.064 Angstroms,
b = 4.448 Angstroms, and c = 4.224 Angstroms, and as a
metastable DO22 superlattice phase where a' = b' = 3.560
Angstroms, and c' = 7.12 Angstroms. Note that
c(FCC)=c'/2=3.560 Angstroms. The orthorhombic structure
was determined by Saito and Beck (1959) and was shown to
be isostructural with Cu3Ti. The DO22 phase is an
equilibrium phase in the Ni-V system (Tanner, 1968). In
the Ni-Mo system it is not. Figure 2.8a shows the D022
tetragonal cell. The prominent 420 planes of Mo are now
separated by three 420 planes of Ni instead of four Ni
planes as in Ni4Mo. Figure 2.8b describes this packing.
2.2.1.3 Ni2Mo
The Ni2Mo phase was first discovered by Saburi et al.
(1969). It is a Pt2Mo type superlattice, as shown in
ta
C
Mo
S Ni
Q c8~-
~~0 -~
c~cp~--0-
cih
Figure 2.8
C
The Ni3Mo DO22 phase;
a.) Ni3Mo DO22 unit cell and
b.) two dimensional representation
of Figure 2.8a. showing 1.) FCC unit
cell (- ), 2.) D022 unit cell
(----), and 3.) 420 FCC stacking
sequence (- ---).
o 0
0o
O^
0'
/
0
0 *
0'0
Figure 2.9
The Ni2Mo D022 phase;
a.) Ni2Mo Pt2Mo unit cell and b.) two
dimensional representation of Figure
2.9a showing 1.) FCC unit cell ( ),
2.) Pt2Mo unit cell (- -), and 3.) 420
FCC stacking sequence (-- -).
Q'a
c
mat----
C'
-- k
/C
O0
00
Figure 2.9a, with lattice constants a' = 2.588 Angstroms,
b' = 7.674 Angstroms, and c' = 3.618 Angstroms. It is
again best described in relation to the FCC lattice. Here
the stacking sequence is 420 planes of Mo separated by two
420 planes of Ni. This stacking is shown in Figure 2.9b.
The Pt2Mo phase is stable in the Ni-V system (Tanner,
1972).
2.2.1.4 NiMo
The equilibrium delta NiMo phase is orthorhombic with
lattice constants a = 9.107 Angstroms, b = 9.107
Angstroms, and c = 8.852 Angstroms (Shoemaker and
Shoemaker, 1963; Shoemaker et al., 1960). This phase has
deleterious effects on the mechanical behavior of Ni-Mo-Al
superalloys (its crystal structure is very similar to
structures for the embrittling sigma phases) and the
conditions under which it will form in ternary and higher
order alloys should be more extensively studied now that
its deleterious effect on mechanical properties is better
understood.
2.2.2 Ni-W
According to the published phase diagram shown in
Figure 2.3, a NiW alloy of Ni4W stoichiometry cannot be
put into solid solution. However, a NiW alloy of 20 at.%
W or less quenched from above the peritectoid reaction
temperature and subsequently aged below this temperature
will decompose in a fashion similar to the decomposition
of the Ni-Mo alloys and will produce Ni-W phases similar
to those described in Section 2.2.1 (Mishra, 1979). For
example, Ni3W D022 and Ni2W Pt2Mo phases are observed
during the decomposition of quenched and aged Ni4W
stoichiometric alloys (Mishra, 1979). These metastable
NixW phases are crystallographically identical to the
NixMo phases described in Section 2.2.1.
2.2.2.1 Ni4W
The Ni4W is a Dla superlattice with lattice parameters
a' = b' = 5.730 Angstroms and c' = 3.553 Angstroms. This
structure can be derived from the FCC alpha matrix with a
slight tetragonal distortion; here c'/c = .98. It is
isostructural and presumably isomorphous with Ni4Mo.
2.2.2.2 Ni3W
This phase is crystallographically identical to Ni3Mo
D022 (see Section 2.2.1.2).
2.2.2.3 Ni2W
This phase is crystallographically identical to Ni2Mo
Pt2Mo (see Section 2.2.1.3).
2.2.2.4 NiW
Equilibrium NiW is an orthorhombic phase (Walsh and
Donachie, 1973) with lattice constants a = 7.76, b =
12.48, and c = 7.10. All of these phases and the relevant
Ni-Ta phases are summarized in Table 2.1.
2.2.3 Domain Variants/Antiphase Boundaries
The phases just described exhibit wide variability in
both the crystallographic habits which they can take and
in the interfaces that result from domain impingement.
When these different variants come into contact out of
phase, domain boundaries are created. These interfaces
are known as antiphase boundaries. Common to all of the
ordered precipitates previously described are 1)
translational antiphase boundaries, 2) antiparallel twin
boundaries, 3) perpendicular twin boundaries, and 4)
dissociated antiphase boundaries. The permissible
variants and three of the four antiphase boundary types
are described in the following sections.
2.2.3.1 Ni4x (Dla)
Thirty different variants can form in this structure
(Harker, 1944). First, the tetrad (c) axis can be
parallel to any one of the three cube axes of the parent
lattice. Second, the a axis of the Ni4x lattice can be
rotated clockwise or counterclockwise relative to the FCC
cube axis. Third, the origin can be shifted, allowing
five independent variants (one x and 4 Ni) to exist.
There are thus 3x2x5 = 30 domain orientations. Ruedl et
al. (1968) have reviewed the three domain boundaries that
Table 2.1 -- Structural Data
Crystal Structure
Lattice
Parameter (A)
Ni-Mo
Ni4Mo
Ni3Mo
Ni3Mo
Ni2Mo
NiMo
Ni-W
NiTa
Ni4W
Ni3W
Ni2W
NiW
Ni8Ta
Ni3Ta
NiAl
Ni3Al
NiTaAl
Ni6TaAl
BCT/10 atoms
BCT/8 atoms
OR/8 atoms
BCO/6 atoms
OR/--
BCT/10 atoms
BCT/8 atoms
BCO/6 atoms
OR/--
Tetr./ --
Ortho/Tetr.
Cubic/4 atoms
Hex./--
Dla
D022
Cu3Ti
Pt2Mo
Orthorhombic
Dla
DO22
Pt2Mo
Orthorhombic
Orth./D024
L12
Ni3Ti 5.112
Lattice
5.727
3.566
5.064
2.588
9.107
5.730
7.76
7.67
5.10
3.60
5.727
3.566
4.448
7.674
9.107
5.730
12.48
7.67
4.42
3.60
c
3.566
7.132
4.224
3.618
8.852
3.553
7.10
3.48
4.24
3.60
8.357
M
are possible in Ni4Mo. They would be similar in all Dla
structures. They are 1) translational antiphase
boundaries (TAPB), 2) antiparallel twin boundaries (ATB),
and 3) perpendicular twin boundaries (PT).
A translation APB results when the domains have
parallel axes but the origins are shifted by a lattice
translation vector. Figure 2.10 shows one of four
possible TAPB in Ni4x. The lattice translation vector is
1/5 [130]. The other three vectors are 1/5 [210], 1/10
[135], and 1/10 [3T5].
The antiparallel twin boundary results when two
contiguous domains have their tetrad axes antiparallel.
The possible twinning planes are of the type 200, 020, and
270, relative to the parent lattice. An APT boundary with
200 twinning plane is shown in Figure 2.11.
A perpendicular twin results when the c axis of the
ordered domains aligns with two different axes of the FCC
cube. The lattices are not continuous across the
interface, unlike the other two boundaries. This occurs
in Ni4x because c/c' is not an integer (see Section
2.2.1.2). Combinations of all three interfaces are
possible.
2.2.3.2 Ni3x (D022)
The D022 phase can form twelve variants. The c axis
of the crystal may lie along any one of the FCC cube
axes.
Figure 2.10 A translation antiphase boundary in the
Dla structure. The lattice translation
vector (----- ) is 1/5 (130). This vector
is in the plane of the figure.
Figure 2.11 An antiparallel twin boundary in the
Dla structure. The twinning plane in
FCC coordinates is the (200).
Four origins are possible for each orientation. Thus,
3x4 = 12 variants exist. TAPB and PT interfaces can
result (Ruedl et al., 1968).
2.2.3.3 Ni2x (Pt2Mo)
Eighteen different variants can exist. The
orthorhombic cell can have six relationships with respect
to the FCC unit cell. Each domain may have three
different origins. There are thus 6x3 = 18 variants
possible. TAPB, ATB, and PT boundaries have been reported
for the Pt2Mo superlattice Ni2V (Tanner, 1972).
2.2.4 SRO in Ni-x Binaries
The Nix binary alloys can also exhibit short range
order (SRO). Briefly, SRO in binary alloys is a local
arrangement of atoms in which an A atom has a greater
preference for another unlike atom, say a B atom, than for
another A atom. The presence of diffuse (1, 1/2, 0)
maxima in both x-ray and electron diffraction patterns has
been offered as evidence for the existence of short range
order in Ni-Mo and Ni-W alloys.
Considerable controversy exists over the explanation
of this diffuse (1, 1/2, 0) scattering. These scattered
intensities can be calculated from a model of statistical
arrangements of atoms in which statistical short range
order is maintained, that is, a model in which there is a
higher probability of finding a B atom next to an A atom
than there is of finding a B atom next to another B atom.
This model is the statistical-mechanical model originally
proposed by Clapp and Moss (1966, 1968a, 1968b). It is
derived from classical descriptions of SRO.
The scattered intensities can also be derived from a
model in which very small long range ordered (LRO) regions
within the normally disordered matrix diffract to produce
the diffuse maxima. This is the microdomain model,
originally proposed by Spruiell and Stansbury (1965).
They used x-ray diffraction to study the phenomenon in
Ni-Mo alloys. Ruedl et al. (1968) used dark field
electron microscopy to image these small LRO domains.
They found, as did Das and Thomas (1974), Okamoto and
Thomas (1971), and Das et al. (1973), that the microdomain
model could explain the very fine precipitate that they
were able to image using the (1, 1/2, 0) diffuse
reflections. Similarly, deRidder et al. (1976) proposed a
cluster model which describes clusters of atoms with
simple polyhedral arrangements. The polyhedral clusters
so described are actually prototypes of long range order,
though they can also be considered as most probable
arrangements and hence statistical. In addition to
explaining diffuse maxima at the (1, 1/2, 0) positions,
these clusters can explain other diffuse maxima in
electron diffraction patterns of Ni-Mo binary alloys.
The former statistical model implies that the short
range ordered structure will probably not be the same as
the structure of the long range ordered phases that will
ultimately precipitate. In the microdomain model, the
short range ordered structure may be the same as the final
long range ordered structure since the model structure is
in fact merely a microcell of the final long range ordered
cell.
2.2.5 Ordering Reactions and Kinetics
2.2.5.1 Binary Alloys
Ni-20% Mo. This composition corresponds to
stoichiometric Ni4Mo. Saburi et al. (1969) used electron
microscopy to study the ordering kinetics of a Ni-20% Mo
binary alloy quenched from solid solution and aged at 800
C. They conclude that the ordering process is
heterogeneous. Long range ordered domains of Ni4Mo
nucleate in the matrix and grow with time. Domain
impingement is characterized by numerous perpendicular
twin plates. Chakravarti et al. (1970) used both TEM and
FIM (Field Ion Microscopy) to study the ordering of Ni-20%
Mo from solid solution. At 700 C they report that the
transformation is wholly homogeneous. A fine, mottled
"tweed" structure develops with aging times of up to and
less than three hours. After three hours, heterogeneous
precipitation of Ni4Mo is observed along grain
boundaries. Ling and Starke (1971) used x-ray line
broadening techniques to calculate LRO parameters, domain
size, and microstrains in similarly aged material. Their
conclusions support those of Chakravarti et al. (1970).
Das and Thomas (1974) used TEM to study ordering at
650 C. After eight hours at 650 C they found diffraction
evidence for the existence of Ni2Mo and Ni4Mo. They
explain the presence of Ni2Mo as being due to
nonconservative antiphase boundaries on (420) planes of
Ni4Mo. The regions of APB thus formed correspond to small
ordered regions of Ni2Mo within the Ni4Mo ordered layers.
Above 650 C, there was no evidence of Ni2Mo
precipitation. Only Ni4Mo precipitated.
Ni-25% Mo. Yamamoto et al. (1970) were the first to
study the structural changes during aging of a
stoichiometric Ni3Mo binary alloy rapidly quenched from
1100 C. At 860 C, both Ni2Mo and Ni4Mo precipitate from
the disordered matrix. These phases are subsequently
consumed by the growth of the ordered orthorhombic Ni3Mo
phase which nucleates at grain boundaries. Following this
work, Das and Thomas (1974) aged a quenched stoichiometric
Ni3Mo alloy at 650 C. They hoped, by aging at this lower
temperature, to reduce the nucleation kinetics so that the
earlier stages of decomposition (which were presumably
missed in the work of Yamamoto et al.) could be studied.
They confirm the results of Yamamoto et al. (1970), i.e.,
the presence of both Ni2Mo and Ni4Mo during the initial
stages of ordering. In this study the Ni2Mo existed as a
discreet phase, unlike the Ni2Mo in the Ni4Mo aging study,
which Das and Thomas (1974) presume occurred as the result
of the formation of a non-conservative AFB.
Van Tendeloo et al. (1975) have summarized their work
on Ni-25% Mo alloys and the works of the others as
follows: at 800 C, the Ni3Mo ordering (decomposition)
follows the sequence FCC SRO D022 Ni4Mo/Ni2Mo HCP
- Ni3Mo orthorhombic. In their work, the D022 phase forms
only when the quench from solid solution is especially
fast. From this observation they presume that the D022
phase precedes the precipitation of both the Ni2Mo and
Ni4Mo phases, and further, that this DO22 precipitation
was not reported by any of the other previous
investigators because the alloys were not quenched fast
enough in the previous studies. Nevertheless, both the
work of Van Tendeloo et al. (1975) and the work of Das et
al. (1973) show that the stabilization of D022 at the
Ni3Mo stoichiometry is especially difficult.
Ni-lO% Mo. The first work in an off stoichiometric
alloy was that of Spruiell and Stansbury (1965) who
proposed to have found SRO in their x-ray study of
quenched Ni-10% Mo. The diffuse maxima they detected at
(1, 1/2, 0) positions were retained for aging times of up
to 100 hours at a temperature of 450 C, and though these
maxima sharpened with time, no superlattice ever
developed.
Ni-17% Mo. Nesbit and Laughlin (1978) studied off
stoichiometric Ni-16.7% Mo. Two mechanisms of ordering
are suggested from their study:
1. the ordered phase (Ni4Mo) may form
heterogeneously from the disordered
supersaturated solid solution by heterogeneous
nucleation, or
2. the ordered Ni4Mo phase may form homogeneously
throughout the gamma matrix by one of the
following mechanisms:
a. spinodal clustering followed by ordering
within the solute region,
b. spinodal ordering, and
c. continuous ordering in which the final
equilibrium structure evolves continuously
from a low amplitude quasi-homogeneous
concentration wave.
Their results show that ordering at 750 C takes place
by the homogeneous nucleation of Ni4Mo. At 700 C,
reasonable evidence exists for the mechanism to be
spinodal ordering. Continuous ordering is not plausible
since the SRO maxima do not correspond to maxima in the
long range ordered state. They did not age at a high
enough temperature to draw any conclusion about the
possibility of heterogeneous nucleation of Ni4Mo.
2.2.5.2 Ternary Alloys
Yamamoto et al. (1970) studied the effects on the
precipitation behavior of the NixMo of small ternary
additions of Ta to stoichiometric Ni3Mo. They found that
the DO22 phase was formed in the alloy containing 5 at.%
Ta. Van Tendeloo et al. (1975) and Das et al. (1973) were
not able to stabilize the D022 phase in binary Ni-25%
alloys. In aged ternary alloys containing 2 at.% and less
Ta, no D022 phase was detected. The diffuse scattering at
the (1, 1/2, 0) positions in electron diffraction patterns
was characteristically present, but no DO22 superlattice
spots developed during aging. They speculate that other
elements might stabilize D022 phase, for example, Ti and
Nb. These are similar to Ta in that the atomic radius of
each is larger than the atomic radius of the Mo. Elements
which might not stabilize D022 are presumed therefore to
be V, Fe, and Co, even though Ni3V as D022 is the stable
precipitate in the Ni-V system (Section 2.2.1.2). These
atoms are of smaller atomic radius than Mo. No evidence
is offered to support these speculations.
Martin (1982) has recently studied the effects of
additions of Al, Ta, and W to Ni3Mo stoichiometric alloys
on the nucleation and growth of NixMo metastable phases.
His explanations for the precipitation of phases in these
alloys follow closely those of deFontaine (1975), deRidder
et al. (1976), Chevalier and Stobbs (1979), and
originally, Clapp and Moss (1966, 1968a, 1968b). His
findings show that the transformation from the SRO ordered
state to the long range ordered one is as follows.
Initially the Pt2Mo phase forms in all the ternary
alloys. In the Al containing alloy, the Pt2Mo
precipitates concurrently with D022. In the W containing
alloy, D022 is not stabilized. All three NixMo metastable
phases can co-exist in the Al bearing ternary, but only
Ni2Mo and Ni4Mo in the Ta and W containing one. The final
ordered state in all three cases is the equilibrium
orthorhombic Ni3Mo phase, which heterogeneously nucleates
at grain boundaries and subsequently consumes the body of
the grain. The presence of Ta greatly accelerates the
kinetics of the formation of this final, equilibrium
phase.
2.2.6 Ni-Al Ni3Al
Nickel-Aluminum alloys that would be candidates for
superalloy applications are generally two phase alloys
consisting of gamma phase, the disordered FCC matrix, and
gamma prime phase, an L12 superlattice of the FCC matrix
corresponding to the approximate stoichiometric
composition Ni3Al. The crystal structure of this compound
is shown in Figure 2.12.
When small volume fractions of gamma prime are
precipitated from gamma solid solution, that is, when the
alloy is relatively lean in Al, the gamma prime will first
I
Figure 2.12
b
SAl
O Ni
The Ni3Al unit cell.
J~
appear as fine, spherical precipitate (Weatherly, 1973).
This spherical morphology will change as the lattice
mismatch between the gamma prime and gamma matrix
changes. The spherical precipitates occur for mismatches
of -0.3% above which cube morphologies predominate,
independent of size or volume fraction of gamma prime
(Merrick, 1978). When gamma prime precipitates as cubes,
the cube habit is (100) gamma//(100) gamma prime.
When the gamma prime precipitate size is small
(100-300 Angstroms), the coherency of the precipitate is
not lost and can be maintained by a tetragonal distortion
at the matrix/precipitate interface (Merrick, 1978). When
coherency is lost, the lattice mismatch between the two
phases can be accommodated by a dislocation network. This
network has been characterized for Ni based superalloys by
Lasalmonie and Strudel (1975). Since the morphology of
the gamma prime is a sensitive function of lattice
mismatch, it follows that this mismatch can be varied by
making alloy additions to the binary alloy which will
partition preferentially to one or the other of the two
predominant phases. In pure binary alloys, Phillips
reports this lattice mismatch at 0.53% (Phillips, 1966).
In ternary and higher order alloys, the mismatch is widely
variable due to elemental partitioning differences between
the two phases.
Gamma prime is a unique intermetallic phase. Its
major contributions to strength are the result of both
antiphase boundary formation and modulus strengthening
(Sims and Hagel, 1972). The strength of the gamma prime
increases with temperature, an anomaly not yet fully
explained. The phase also remains fully ordered to very
high temperatures (Pope and Garin, 1977).
In the early stages of gamma prime precipitation in
Ni-Al alloys, side band satellites in x-ray powder
diffraction patterns appear. These satellites were first
thought to correspond to periodic modulations in structure
(Kelly and Nicholson, 1963). These presumed modulations
lead to the speculation that the mechanism of Ni-Al
decomposition was spinodal. Cahn (1961) originally
suggested this possibility. The data of Corey et al.
(1973) and Gentry and Fine (1972) suggest that this
mechanism is possible at high supersaturations. Faulkner
and Ralph (1972) studied the early stages of precipitation
in a more dilute Ni-Al 6.5 wt.% alloy using FIM and
conclude that the spinodal ordering mechanism is
unlikely. They suggest that the sidebands are due to
particle morphology changes during the early stages of
decomposition.
The nucleation of the gamma prime could not likely
explain the "macro" order in the microstructure, the large
uniformly sized and distributed gamma prime precipitates
that are present in the alloys studied here. Ardell et
al. (1966) explain this ordered microstructure with a
model which explains the gamma prime alignment and uniform
size by considering the coarsening behavior of gamma prime
precipitates under the influences of mutual elastic
interactions between the coarsening gamma prime
precipitates. Ardell's model provides the most reasonable
explanation for the development of the microstructures in
alloys like those discussed in Chapter 5 of this
dissertation.
2.3 Diffraction Patterns: NixMo Phases/Ni3Al
The reciprocal lattices of the various NixMo phases
can be constructed easily based on the crystallography of
each precipitate type. Since it is easiest to relate the
diffraction patterns of each to the parent FCC lattice,
(here the disordered gamma phase), this will be done for
the D022 Ni3Mo phase. The other diffraction patterns were
similarly constructed.
2.3.1 D922 Reciprocal Lattice
The DO22 is a tetragonal cell with atom positions at
Mo (000), (1/2, 1/2, 1/2);
Ni (1/2, 1/2, 0), (1/2, 0, 1/4), (1/2, 0, 3/4)
(0, 1/2, 1/4), (0, 0, 1/2), (0, 1/2, 3/4).
The structure factor can then be written as the summation:
F= Mof(l+exp(Tri(h+k+l)) + Nif[(exp(rri(h+k)) +
exp(Tri(1)) + exp(Tri(h+1/2)) + e(i(k+/2)) +
exp(TTi(h+31/2)) + exp(rri(k+31/2))].
Table 2.2 -- Structure Factor Values
F
B+ if 1 = 2(n+l), n even OR
A if 1 = 2n
A
A
B if
A if
B if
A if
1 = 2(n+l)
1 = 2n
1 = 2(n+l)
1 = 2n
hkl
EO
00
SE
EE
EO
0EE
0O
0O
00
OE
EO
00
0O
00
00
00
EO
OE
* A = 2fMo + 6fNi
+ B = 2fMo 2fNi
Substitution of values for h, k, and 1 yields the series
of values for F in Table 2.2
The D022 reciprocal lattice constructed using those
values of F listed in Table 2.2 is shown in Figure 2.13a.
The lattice is constructed using D022 coordinates and
compared to a corresponding FCC construction in the two
dimensional B = [100] and B = [001] sections shown in
Figure 2.13b. Note that both the (020) and (200) of the
D022 correspond to the (020) and the (200) of the parent
FCC lattice since a/2 FCC = a/2D022. Also, the (004) D022
= 1/4(2a) (the "A" indices from Table 2.2) = a/2 FCC. The
fundamental reflections of the D022 are then in the same
reciprocal lattice positions as the fundamental FCC
reflections. The (011), (022), etc. of the D022 are 1/4
multiples of the FCC (042). This makes the Mo rich (011)
planes of the D022 structure the (042) Mo rich planes of
the FCC parent lattice.
2.3.2 Dla/Pt2Mo/L12 Reciprocal Lattices
Similar constructions result in the reciprocal
lattices of Ni4Mo and Ni2Mo, shown respectively in Figures
2.14 and 2.15, both lattices in FCC coordinates. The
reciprocal lattice of the FCC ordered gamma prime is shown
in Figure 2.16.
* Fundamental
0 Superlattice
0013
*011
000 020
000 020
0
0 0:
110
.200 220
Figure 2.13 The D022 phase;
a.) the reciprocal lattice for the D022
phase and b.) B=[010] left, [001 right,
D022 left, FCC right.
*%(042)
%(2 /4(042)
411/2((3421
*1/4(042) *
000 042
004 024
0I A&
200 220
022
Fundamental
E Superlattice
Figure 2.14 The reciprocal lattice for Dla.
^^^-^ 0
IIr
w Ii
0
020
o0 Fundamental
Superlattice
Figure 2.15 The reciprocal lattice for Pt2Mo.
000
L
ooo 200 W Fundamental
SSuperlattice
Figure 2.16 The reciprocal lattice for the L12
structure.
2.3.3 SRO (1, 1/2, 0) Scattering
In Ni-Mo binary alloys, SRO is characterized by
diffuse scattering at the (1, 1/2, 0) positions. (All g
vectors will subsequently be defined in FCC coordinates.)
Diffraction patterns of (1, 1/2, 0) SRO for B = [100] and
B = [112] are shown in Figure 2.19a. Characteristic of
this scattering is the absence of any true superlattice
reflection, for example, the (100) and (011) reflections
of either the D022 or the L12 superlattices. Because
gamma prime phase is always present in the alloys studied
here, any selected area diffraction pattern will always
contain L12 superlattice reflections. Discriminating
between the D022 superlattice reflections and scattering
at (1, 1/2, 0) SRO positions with superimposed L12
superlattice reflections is difficult. There are two ways
to differentiate SRO from the L12 and DO22 superlattices,
both of which are discussed in Chapter 5.
2.3.4 Variant Imaging
In section 2.2.3 of this chapter, a plethora of
possible variants for each precipitate were given. As
should be readily apparent from the reciprocal lattice
constructions of this section, only certain of these
variants are imagable with the electron microscope. Many
of the aforementioned antiphase boundaries are
indistinguishable.
2.3.4.1. D022: Ni3Mo
There are three easily differentiated variants in the
D022 structure, each corresponding to the c axis of the
D022 being parallel to one of the cube axes of the parent
FCC lattice. This is shown in Figure 2.17a. All three
variants may be visible simultaneously. Indexed [001] and
[T12] diffraction patterns are shown in Figure 2.19b.
2.3.4.2 Dla: Ni4Mo
Six distinguishable variants of Ni4Mo are possible.
These correspond to the tetrad axis of the Dla being
parallel to the parent FCC cube axes (three variants) and
further, the a axis of the Ni4Mo rotated cw or ccw about
the c axis relative to each FCC cube axis. Only two of
the six distinguishable variants will be visible along any
B = 100 imaging condition. These two are the single
axis clockwise and counterclockwise rotated variants shown
in Figure 2.18a. The B=[100] indexed diffraction pattern
corresponding to these two real space variants is shown in
Figure 2.18b. Indexed B = [001] and B = [112] Ni4Mo
diffraction patterns are shown in Figure 2.19c.
02
A
II Il
A V
Alll i
020
SFundamental
& Superlattice
b.
Figure 2.17 The D022 phase;
a.) DO22 variants along FCC axes
and b.) B = Cl00] SADP with variants.
o e 0 0 0 *\ 0
0 o o o0 o o\0 o
o *\o o 0 o 0 o
S0 O\ o \0 0 0 )-
0o 0\o 0 o o
00 o o D o
0 0/ 0 /
o */o
0o 0 *
eo wo
o0 *'
*0/Z 0
o/0 o
B
.*o */o 0
o / o
o /e o 's o
o,0 o0o0
Figure 2.18
The Dia phase;
a.) Dla variants along FCC axes and
b.) B = [100] SADP with variants.
*o 0 \ 0
0 0 \0
oCre o
* 0 *e
0~\
402
0 .
420
**
*" *
000 200
000 200
020 420
000
0 E
000 [
OO
402
/-
/
A U
000
(3 0 a 0
00
000
020
* *0
27 0
000
zZU 402
0 0 A
So 0, 0
402
/*
,,m m B
-p
212
-p i Et
00
000
d.
* Fundamental
a Superlattice
Figure 2.19
Indexed B = [001] and B = [112]
reciprocal lattice sections of
a.) (1, 1/2, 0) S.R.O., b.) DO22,
c.) Dla, and d.) Pt2Mo.
2.3.4.3 Pt2Mo: Ni2Mo
In Ni2Mo, the imaging conditions are identical to
those for Ni4Mo. The c axis of the superlattice may be
parallel to one of the cube directions in the FCC parent.
As in Dla, there are two orientation possibilities per
cube axis, as shown in Figure 2.20a. The real space
lattice and the corresponding B=[001] indexed diffraction
pattern are shown in Figures 2.20a and 2.20b. Indexed B =
[001] and B = [112] diffraction patterns are shown in
Figure 2.19d.
All of the above phases may be present
simultaneously. When this happens, all of the diffraction
patterns overlap.
a.
O o 0/ C)/.0 /0 0/* 0
0 *o 04 ,,o o,* o 0 o
*o?1 oOoo oa0o
o 0,o oW"o 0'0 0 o0.r
So 'O u o'g o O & o'e
A
002
B A
m a
Figure 2.20
* O0\ 0 0o 0O o0 s
* oo o* oOoB* O
o'o* CO- o o oO* o
B
022
0
The Pt2Mo phase;
a.) Pt2Mo variants along FCC axes.
A and B can exist along each axis.
b.) B = [100] SADP with variants.
CHAPTER 3
EXPERIMENTAL PROCEDURE
3.1 Composition
Two major alloy compositions were chosen for this
investigation. They both represent potentially attractive
alloys for gas turbine blade applications. These two
alloys are designated as RSR 197 and RSR 209. They are
prepared by a powder metallurgy process developed at Pratt
and Whitney Aircraft Government Products Division. They
are two of a multitude of experimental alloys under
development for future high temperature turbine blade
materials. The RSR in the alloy designation is an acronym
for a rapid solidification process to be described
subsequently. The numbers 197 and 209 are arbitrary
numbers representative of the sequence in which the alloys
were prepared. The composition of these two alloys is
given in Table 3.1.
In the RSR process, the desired alloy is melted under
inert conditions (under argon gas) and allowed to impinge
in the molten state onto a rapidly rotating disc (Holiday
et al., 1978). The resulting spherical liquid metal
droplets are quenched in a stream of cooled He gas. The
powder is collected and canned under inert conditions.
In addition to alloys 197 and 209, an additional
ternary alloy was prepared by arc melting rather than by
the RSR process. The composition of this ternary, alloy
#17, was chosen as being representative of a compromise
ternary composition between the composition of RSR 197 and
RSR 209 (Table 3.1). The Ta and W were, of course, not
present in the ternary alloy.
Alloy 185, an alloy similar to RSR 209, was used for
only one experiment. Its composition is given in Table
3.1.
3.2 Heat Treatments
The canned RSR 197 and RSR 209 alloys were soaked at
1315 degrees C for four hours and extruded as bar at an
extrusion ratio of 43/1 at 1200 C. The extruded bars were
subjected to the various heat treatments described in
Figure 3.1. The heat treatments were conducted in a
vacuum furnace accurate to + 5 C. The times and
temperatures for these thermal treatments were chosen
based on the times and temperatures for aging binary Ni-Mo
alloys described in Chapter 2. The processing variables
are summarized in Figure 3.1.
The arc melted sample and an RSR 185 sample were
encapsulated in evacuated and He backfilled quartz tubing
prior to thermal treatment. The arc melted samples were
wrapped in four nines pure Ni foil to prevent reaction
with the quartz tube during solution heat treating and
aging. The arc melted samples were solution treated at
1315 C for four hours in a tube furnace and water quenched
upon completion of the solution treatment. RSR 185 was
prepared for electron microscopy directly after quenching
(Martin, 1982). Alloy #17 was re-encapsulated, as above,
and subsequently aged in a second tube furnace. The aging
practice is described in Table 3.1. Samples were water
quenched upon completion of aging.
3.3 Characterization: Methods of Analysis
Longitudinal slices were taken from the bar centers
of the extruded RSR alloys and from the center of the
sliced button, alloy #17, mechanically thinned to 130
microns, and jet polished in a solution of 80% methanol,
20% perchloric acid until perforated. The foil for the
RSR 185 alloy was prepared by Martin as described by
Martin (1982). Foils thus prepared were examined in a
Philips 301 Scanning Transmission Electron Microscope
(STEM) and in a special Philips 400 STEM. This latter
microscope is equipped with a field emission gun which
allows small, high intensity beams to be used in the TEM
mode. Special operating features of this microscope are
described in Section 4.1.1 of Chapter 4.
Four different electron diffraction methods were used
to generate the diffraction patterns shown and discussed
in Chapters 4 and 5. They are 1) selected area
diffraction (SAD), 2) Riecke method C-2 aperture limited
microdiffraction, 3) convergent beam diffraction, and 4)
convergent beam microdiffraction.
If the sample area selected by the selected area
aperture was reasonably strain free, that is, free of
buckling and bending, then the selected area diffraction
mode was used to generate large area diffraction
patterns. The area defined by the aperture was minimally
3 square microns. If this method could not be used
because of buckling and bending, the Riecke method
(Warren, 1979) was used. The area defined by this method
is much smaller than that defined by the selected area
method, about 0.6 square microns. This area is too small
to be representative of the sample as a whole. The above
two methods produce diffraction patterns that are similar
in appearance and application. They both produce fine
diffraction spots in the diffraction patterns and are thus
amenable to the detection of subtle scattering effects.
Convergent beam diffraction is a spatially localized
diffraction method. Only hundreds of square Angstroms are
analyzed. The diffraction pattern consists of large discs
rather than diffraction spots. Subtle diffraction effects
are usually masked by the elastic intensity distributions
in these discs. The elastic information in the discs
makes the convergent beam method uniquely suitable for
other purposes, however. These are reviewed in the
following chapter.
Convergent beam microdiffraction is also a spatially
localized diffraction method. Again, only hundreds of
square Angstroms are analyzed. The diffraction pattern
consists of discs rather than spots. These discs are
quite small in comparison to normal CBED discs and may be
dimensionally comparable to the spots seen in selected
area and Riecke patterns. If subtle diffraction effects
are present, they will not be masked if this diffraction
method is used.
In addition to electron diffraction, the electron
microscopes were used to produce bright field, dark field,
and lattice images. The 400 FEG instrument was also used,
in conjunction with a KEVEX energy dispersive x-ray
detector and a DEC 1103 minicomputer, as an analytical
x-ray system for x-ray analysis of the RSR alloys. The
data reduction scheme for quantification was developed by
Zaluzec (1978). Details of these analyses are discussed
in the following chapter.
To test the accuracy and applicability of the
convergent beam diffraction method for the measurement of
local lattice parameters, the lattice parameters of the
RSR alloys were measured using x-ray diffraction. The
58
measurements were made with a General Electric horizonal
main protractor diffractometer using Ni filtered Cu
K-alpha radiation. Data thus generated were also used to
measure the lattice mismatch between the gamma and gamma
prime phase in the RSR alloys.
Rockwell C microhardness measurements were made on
most of the RSR aged alloys. Six hardness values from
each sample were recorded.
ARC MELTED
BUTTON
Air
Quench
Solution heat
treat 1315 C, 2 hr.
Air Quench
Age/Hours
Air Quench
Solution Heat
treat 1315 C, 4 hr.
Cold Water
........ Quench
Age
760 C, 100 hr.
870 C, 1 hr.
Cold Water
Quench
Figure 3.1 Processing Variables
Cool
Table 3.1 -- Alloy Compositions
RSR 197
at% wt%
73.9
5.8
14.3
6.0
.015
RSR 209
at% wt%
74.0
15.0
9.0
2.0
72.6
6.8
14.4
6.1
.015
RSR 185
at% wt%
73.8 72.6
15.0 6.7
9.0 14.4
2.0 6.0
.2 -
76.0
13.0
9.0
2.0
#17
at% wt%
77.0
14.0
9.0
CHAPTER 4
SPECIAL METHODS
This chapter will explain the methods used to measure
the partitioning of elements to the gamma and gamma prime
phases. The convergent beam diffraction method is one
method described extensively in this chapter. Simple
equations are developed which aid in interpreting the
patterns and further allow simulated patterns of
experimental patterns to be generated. The results of the
lattice parameter measurements and strain measurements
made using the CBED method are given in Chapter Five.
Chapter Four also includes a brief section on energy
dispersive analysis, specifically as it relates to the
characterization of the alloys analyzed in this study.
4.1 Convergent Beam Electron Diffraction
(CBED)Methods
A convergent beam electron diffraction pattern is
similar to a selected area diffraction pattern with one
major and self-defining difference: a convergent beam
pattern uses a focused beam with a large convergence
angle to define the area from which the diffraction
pattern will be taken. Beam convergence angles generally
range between 2 x 10-3 rads to 20 x 10-3 rads. The
resulting pattern consists of a number of diffracted
discs, each disc corresponding to a diffracted beam.
The selected area diffraction pattern is formed using
a large beam that is essentially parallel. The area from
which the diffraction pattern is taken is defined by an
aperture, the selected area aperture. Beam convergence is
usually on the order of 1 x 10-4 rads. The resulting
pattern consists of diffraction spots. Each spot
corresponds to a diffracted beam.
The convergent beam electron diffraction (CBED)
pattern is usually formed in the back focal plane of the
objective lens, just as is the diffraction pattern in the
selected area diffraction mode (Steeds, 1979). The CBED
pattern contains a wealth of information about the
crystallography of the diffracting crystal, in many cases
much more information than is contained in the selected
area diffraction pattern. This information appears in the
discs of the pattern and can be used in 1) identification
of the diffracting crystal's point and space groups
(Buxton et al., 1976), 2) identification of Burgers
vectors (Carpenter and Spence, 1982), 3) the measurement
of local lattice parameters (Jones et al., 1977), 4) the
measurement of foil thickness (Kelly et al., 1975),
and 5) the measurement of uniform lattice strain (Steeds,
1979).
4.1.1 Experimental Technique
There are a number of methods for forming the
convergent probe. The most common method in modern STEM
instruments is to use the STEM "spot" mode to translate
the already convergent probe to the area from which the
pattern will be taken. In the STEM mode, the imaging and
projector lenses are already configured to form a
diffraction pattern. Convergence in the probe is
controlled by the selection of a suitable second condenser
aperture. Suitable is defined as the maximum aperture
size that will still give discreet, non-overlapping discs
in the diffraction patterns. The covergence angle alpha
is defined as the angle subtended by the radius of the
disc. Choice of the proper aperture size will obviously
depend on the lattice parameter and orientation of the
crystal from which the pattern will be taken.
Even more simply, the probe may be focused directly
in the TEM mode, a situation which yields acceptable beam
convergence but usually with large probe sizes. Once the
probe has been focused using the condenser controls, the
proper lens excitations to image the diffraction pattern
are selected, usually by selecting the diffraction mode of
the instrument, and a CBED pattern results.
Alternatively, the objective lens may be overexcited
in the TEM mode (a situation that approximates a STEM
condition), and the probe then focused with the second
condenser lens. The resulting probe will be smaller than
a conventional TEM probe, but generally, depending on the
amount of overexcitation, larger than the standard STEM
probe (Steeds, 1979). Under this condition, the
diffraction pattern appears in the imaging plane of the
objective lens rather than in the back focal plane. The
lens optics for this condition cannot be found in standard
texts. The reader is referred to Olsen and Goodman (1979)
for details.
The method chosen for this investigation uses the
focused TEM probe. The beam convergence is controlled by
the size of the second condenser aperture. After
selection and centering of the proper C-2 aperture, the
diffraction mode of the instrument is selected and the
condenser lens is brought to crossover. The result is a
focused convergent beam and the image will be a focused
convergent beam diffraction pattern. The beam is not
imagable under this condition. As the beam is focused
(as the condenser lense is brought to crossover), the
second condenser aperture will become visible as a disc in
the diffraction pattern and a bright field image of the
sample will appear in the central transmitted disc of the
pattern. Dark field images corresponding to the various
crystal diffracting conditions will appear in the
diffracted discs. As focus is more closely approached,
the magnification of the images in the discs will increase
until, at focus, the magnification in the discs reaches
infinity. By watching the image "blow-up" in the disc,
the exact location of the beam on the sample can be
monitored. This technique is referred to as the shadow
technique (Steeds, 1979). The image in the transmitted
disc is the shadow image. This method is the only sure
way to eliminate diffraction error that is generally
present if the probe is focused in the imaging mode
rather than in the diffraction mode, as just described.
(Diffraction error is the noncoincidence of the probe
position in the imaging and diffraction modes
respectively.) If the probe is formed by overexciting the
objective lens, the resulting out of focus image is the
shadow image. There is thus no diffraction error if this
latter technique is used to form the convergent probe.
Diffraction error is not a serious problem and can be
easily eliminated. In any event, it does not affect the
information that is present in the pattern, only the area
from which the information is taken. This information is
usually confined to the discs of the diffraction pattern.
There can be considerable detail in both the diffracted
and transmitted discs, depending on the diffracting
conditions under which the pattern is formed.
The applications of this information to materials
science were discussed earlier in this chapter. The
information in the discs includes 1) HOLZ (High Order Laue
Zone) lines, for lattice parameter measurements and for
pattern symmetry determinations, 2) Pendellosung Fringes,
used in making foil thickness determinations, 3) the
shadow image, used for tilting the sample and placing the
beam, and 4) dynamical features (absences and excesses)
that reveal detailed information about the crystal space
group for crystal symmetry and space group
determinations. Since HOLZ lines were used extensively in
this study, they are described in more detail below.
4.1.2 HOLZ Lines (High Order Laue Zone Lines)
A HOLZ line is a locus of diffracted beams. It is
the result of elastic scattering from Laue zones beyond
the zero order zone. HOLZ lines are analogous to Kikuchi
lines in two respects. First, they are a Bragg
diffraction phenomenon, and second, they result in lines
rather than diffraction spots. Like Kikuchi lines, the
spacing between the HOLZ lines in the diffracting disc and
the transmitted disc represents the spacing of the planes
that are responsible for Bragg diffraction in the HOLZ.
It is only necessary to index the discs that are
diffracting in the HOLZ to determine which lines in the
ZOLZ (Zero Order Laue Zone) correspond to these
diffracting discs. Any HOLZ line in the ZOLZ will
be parallel to its counterpart in the HOLZ, analogous to
excess and defect lines in Kikuchi patterns. It is the
HOLZ lines in the ZOLZ that are used for most HOLZ line
measurements.
An example of what one expects to see in a
transmitted disc containing HOLZ lines is shown in Figure
4.1. The lines in the disc (labelled a in the figure) are
the HOLZ lines. The lines outside the discs but seen as
continuations of the HOLZ lines (labelled b in the figure)
are the Kikuchi lines. The Kikuchi lines extend across
the transmitted disc, thus overlapping the HOLZ lines in
the disc.
The clarity and contrast of the HOLZ line patterns
and the accuracy of the HOLZ line positions are dependent
on at least five factors. First, there are limitations to
the thickness of the diffracting crystal (Jones et al.,
1977). This thickness should usually be on the order of
100-200 nm. If the crystal is much thicker, excessive
diffuse scattering in the ZOLZ will attenuate the HOLZ
lines entirely; if much thinner, no HOLZ lines will be
present at all.
Second, the energy loss as the beam is transmitted
through the sample added to the inherent energy spread of
electron sources (i.e., W filament, LaB6, or FEG) can
affect the accuracy of the line position. This energy
loss will affect the thickness of the HOLZ line, reducing
the accuracy to which it can be measured. Foil
thickness can also affect the HOLZ line thickness (Jones
et al., 1977).
Third, tilting the crystal away from normal
perpendicular incidence means a different thickness may be
encountered across the diameter of the beam with a
consequent change in intensity across the pattern.
(Recall that the beam is convergent.) This is not usually
a problem since only the intensity, not the actual line
position, is affected.
Fourth, the distortion in the pattern introduced by
the objective lens can affect the accuracy of direct
measurements in the Higher Order zone (Ecob et al.,
1981). Since one almost always uses zone axis patterns to
generate HOLZ information, the final tilt necessary to
obtain an exact zone axis pattern can be accomplished by
tilting the beam rather than tilting the sample. This
tilting can be done in two ways. The beam can be tilted
electronically using the deflector system of the
instrument, or the beam can be tilted by displacing the
second condenser aperture. Either of these procedures is
easier than tilting the sample using the goniometer
controls of the microscope stage. However, a beam
entering the objective lens off axis is subject to the
inherent spherical abberation effects of the lens. The
abberation increases with increasing off axis angle,
degrading the accuracy of the pattern. For this reason it
is best to tilt the sample as close to the exact zone
axis orientation as possible using the goniometer tilt
controls, rather than tilting the beam. This will not in
itself completely eliminate the spherical abberation
effect since diffracted beams from the higher order zones
must enter the lens at large angles anyway. It is thus
more accurate to use the HOLZ line in the transmitted disc
than its counterpart in the HOLZ ring. The subsequent
image forming lenses of the instrument will also impart
radial and spiral distortion to the diffraction pattern.
These distortions are minimized on the optical axis of the
instrument.
Fifth, the ubiquitous presence of carbonaceous matter
both in the microscope and on the sample surface can lead
to contamination spikes at the specimen/beam interface
with a consequent attenuation of the beam current, a loss
in spatial resolution due to scattering, and the
introduction of astigmatism into the beam due to
charging. All of these are undesirable. Methods for
reducing contamination have been reviewed elsewhere (Hren,
1979). Contamination and its effects were minimized in
this study by using the minimum practical time to focus
the diffraction pattern, to tilt to the proper
orientation, to determine the exposure time for each
pattern, and to record the image.
In consideration of the above effects, the following
procedure for obtaining HOLZ patterns is recommended:
1. The crystal should be tilted to the approximate
zone axis using the shadow technique. This greatly
simplifies tilting in polycrystalline samples.
2. An area in the crystal that is the proper
thickness for good HOLZ line formation should be found.
3. The sample should be in focus at the eucentric
position. These two conditions will insure that the
objective lens excitation is constant for every pattern
thus standardizing both the camera length and the
convergence angle for each pattern.
4. The condenser aperture should be centered.
5. The sample should be tilted to the exact zone
axis, again using the shadow image technique.
(By iterating between 5 and 3, a good zone axis
pattern can be obtained.)
6. The spot exposure meter should be used to
determine the proper exposure time for recording the
diffraction pattern.
Under the above conditions, only STEM and focused
TEM probes should be used for generating the convergent
beam. If a convergent probe is formed using the
overexcited objective lens method, the sample must still
be at the eucentric position, but since the image will not
be focused, the objective lens current must be recorded
so that it may be reproduced for each subsequent pattern.
4.1.3 Indexing HOLZ Lines
There area a number of ways to index HOLZ lines
(Steeds, 1979; Ecob et al., 1981). The approach taken in
this study is somewhat different from the approach
described in the above references in that the actual HOLZ
diffracting conditions are calculated. This method gives
a more intuitive feel for HOLZ detail and permits a more
rapid indexing of the patterns. The subsequent use of the
HOLZ lines for lattice parameter measurements is similar
to that developed by Jones et al. (1977).
To calculate the HOLZ line positions, one need only
determine the intersections of the Ewald sphere with the
reciprocal lattice beyond the zero order zone of the
reciprocal lattice. The equations necessary to do this
for a cubic crystal are presented below.
Let h, k, 1 be the Miller indices of
planes in the diffracting crystal.
These will also define the g vector for
the diffraction pattern.
Let a be the lattice parameter of the
material.
Let U, V, W be the idices of the beam
direction, B, in the crystal. These
indices are, by convention, given in
crystal coordinates. They are also
taken as antiparallel to the actual beam
direction in the instrument.
In reciprocal space, the center of the Ewald sphere for
the cubic crystal will be at
UR/IBI, VR/IBI, and WR/IBI, where R = / .
Values of h, k, 1 which satisfy the following equation are
simultaneous solutions to the intersection of the Ewald
sphere with the reciprocal lattice:
(h/a UR/IBI)2 + (k/a VR/IBI)2 + (1/a WR/IBI)2 = R2.
Expansion and rearrangement of this equation yield
h2+k2+12 + R2(U2+V2+W2) 2(hU+kV+lW) R = R2.
a (U2+V2+W2) a TB
This can be simplified to
h2+k2+12 = 2 g-B. (1)
This equation says that the sum of the squares of the
planar indices of a diffracting plane is equal to a
constant for a given electron accelerating potential,
lattice parameter, beam direction and cubic Bravais
lattice type.
To solve the equation, one must know the microscope
accelerating potential, the approximate lattice parameter
of the examined crystal, and the beam direction in the
crystal. The accelerating potential is never known to
great accuracy. When only relative and comparative
lattice parameter measurements are to be made, this
uncertainty cancels. The lattice parameter can be
approximately derived from either a calibrated selected
area diffraction pattern, or from a calibrated CBED
pattern. The beam direction must be known.
To solve equation (1), only the value of g-B needs to
be derived (we assume here that the other information is
at hand). The values of g-B will depend on the specific
cubic Bravais lattice.
For an FCC crystal, as for both the matrix and the
gamma prime phase in the RSR alloys, diffraction pattern
planar indices cannot be mixed. The three values of g in
g'B will thus be all odd or all even. Indices for the
beam direction can be reduced to three combinations of
terms: B is odd, odd, odd; B is odd, even, even; and B is
odd, odd, even. The following cases are constructed to
show values for the dot products of unmixed g indices and
the three combinations of B terms given above.
Case 1) B h,k,l Case 2) B h,k,l Case 3) B h,k,l
0 0 E 0o E 0 0 E
O0 E EE E 0 E
OO E EE E EE E
The first case will be used as an example. If B is all
odd, for example, B = (111>, the individual terms in the
dot product of this B and an odd set of g indices will
contain all odd terms. The algebraic sum of all odd terms
is odd. For this case, g.B can equal one, since one is an
odd term. The results in Case 2 are the same. For
Case 3, the algebraic sum will always be even. For this
case, g'B will equal two. These results can be
generalized as follows: if U+V+W = even, g-B will
equal two. If U+V+W = odd, g-B will equal one. This
calculation applies only to the first order zone.
Most of the CBED patterns in this study were taken
from the gamma prime phase, an L12 superlattice. In such
a superlattice, the superlattice reflections appear in the
forbidden positions for FCC. The true first order Laue
zone for U+V+W = even will consist only of superlattice
reflections. The first zone can be clearly seen in Figure
4.2, a B = (114> CBED pattern of the gamma prime phase in
alloy RSR 197. These superlattice reflections are usually
too weak to give HOLZ lines in the central disc. Only the
HOLZ lines from the B = (114> "second" order zone were
used in this study. This "second" zone will hereafter be
referred to as the first order zone (FOLZ) since it in
fact corresponds to the first order zone for a typical FCC
crystal.
An alternate way of deriving the preceding result is
through construction of the Ewald sphere and geometrical
solution of the intersection with the reciprocal lattice.
With reference to Figure 4.3,
the angle 0 equals 9' by similar triangles.
Then Sin 9' = H/Igl/2R and Sin 9' = H/Igl.
Combining these two equations gives g2 = 2RH.
By definition, g2 = l/d2 = (h2+k2+12)/ao2.
Substituting for igl2 gives h2+k2+12 = 2a2 RH.
H can be shown to equal (g-B/a )(U2+V2+W2)1/2.
Therefore, h2+k2+12 = (2aR/IBI)(g.B).
At this point, both the graphical and calculated
methods yield a solution that is valid for a single beam
direction only. Neither method has included the effect of
the beam convergence. There are numerical methods for
including this convergence (Warren, 1979). An alternate
way is to calculate an upper and lower limit of h2+k2+12
values for a given beam convergence angle. This approach
provides a useful and intuitive estimate of the
convergence effect. It has the shortcoming of slightly
overestimating this effect. A more rigorous method is
described in a following section.
For a given IBI, g*B = I|glIBI'cose.
Let K2 = K1 (g-B) where K1 = 2aR/IB[.
Terms ao, R, and B are as previously defined.
Then K2 = |g12 = [g.B/(IBlcose)]2
and e = cos-1 (g.B/(IBI)(K2)1/2).
Two limiting values of h2+k2+12 (limiting values of
k2), can now be calculated:
K21 = (Bg)
LT BIcos(+.J2
K22 = (B g)2
LIBIcose-TT9 ,
where ( is the convergence angle.
Values of h2+k2+12 between these limiting K2 values will
define a plane (h,k,l) that will diffract in the FOLZ. As
an example, consider the solution to a CBED pattern from
the gamma prime phase of RSR 197. The approximate
constants for substitution into the equations are
ao = 3.56,
R = 27.07 (100 keV electrons),
B = (114>,
and alpha = 2.5 x 10-3 rads.
The calculated values of K21 and K22 are 101 and 82,
respectively. Any plane h, k, 1 with values of h2+k2+12
between 82 and 101 which also satisfies the g-b = 2
criterion will diffract under Bragg conditions and will
thus yield a FOLZ line in the transmitted disc. Possible
values are given in Table 4.1.
The value of K2 for the zero convergence case is the
exact Bragg solution. It is seldom an integer. If its
value were an integer, a set of conditions could be
achieved that would yield some set of FOLZ lines directly
through the center of the pattern. For example, for the
case just calculated, h2+k2+12 = 90.713. This value is
very close to the exact solution for h2+k2+12 (h=9, k=3,
1=1) = 91.0. The (931) lines should pass almost directly
through the center of the transmitted disc. They could be
made to pass directly through the center by either
increasing the alloy lattice parameter from 3.560 to 3.571
Angstroms, or by changing the accelerating potential
of the microscope to adjust the wavelength. This latter
can now be done to great accuracy in most modern STEM
equipment.
The advantage of having all of one type of line
passing directly through the center of the pattern is
explained below. If it were possible to have all of one
line type (the (9311 lines for a B =(114)pattern) in the
center of the pattern, a reference microscope operating
potential could then be defined for that particular
lattice parameter. For a material of different lattice
parameter, the difference in accelerating potential
required to bring the lines to the center of the pattern
compared to the reference would be proportional to the
difference in lattice parameter between the two materials
(Steeds, 1979). To measure a change in lattice parameter
in this way, one would merely note the change in
accelerating potential required to achieve identical
patterns in the central disc.
To more rigorously solve the effect of beam
convergence on HOLZ line formation, the Bragg angle and
the actual angle the beam makes with each specific HOLZ
diffracting plane must be determined. For example, for B
= (114>, a = 3.56, and R = 27.07 (100 kV electrons), the
calculated value for h2+k2+12 using equation (1) is
90.713. Because this number is not an integer, the Bragg
condition in the first order zone is not satisfied for B =
(114>. Consider a second beam direction B'. If B' were
Table 4.1 HOLZ Planes
hkl
h2+k2+12
=2
No
g'B
Yes
X
Indices for B=[114]
751 571
773
860 680
913 193 931 391
1002 0102
75
83
99
99
107
80
84
96
100
104
83
71
107
99
100
104
108
inclined slighty to B (Fig. 4.4), it might be possible for
B' to satisfy the Bragg condition for the above value of
h2+k2+12. Fortnuately, it is not necessary to calculate
the indices of B'. One first calculates the Bragg angles
for the planes that can diffract in the FOLZ (those planes
listed in Table 4.1) and then calculates the actual angle
these planes make with the given beam direction, in this
case, the (114). If the difference between theta a, the
angle the low index beam makes with the plane, and theta
b, the calculated Bragg angle for that plane, is less than
alpha, the angle of convergence, then that diffracting
plane will produce a FOLZ line. This situation is
described in Figure 4.5. If theta a and theta b are both
plotted against h2+k2+l2, the two intersecting curves in
Figure 4.5 result. Note that the two curves intersect at
the value of h2+k2+12 calculated from the equation. Any
convergence angle up to 4.8 mrad can be superimposed onto
this figure and the resulting range of h2+k2+12 values
determined. For an alpha of 2.5 x 10-3 rads, this range
of values is 100 to 83, a slightly smaller range than
determined by the first method.
Once the range of h2+k2+12 values has been determined
and the actual indices assigned as in Table 4.1, it is a
simple matter to index any pattern for the FCC crystal.
One first indexes the zero order Laue zone (ZOLZ) in the
normal way (Edington, 1976). This zero order indexed
pattern is shown in Figure 4.6 for a [114] CBED pattern
ea-eb
B'
V
A= Alpha, the convergence angle
0b= Bragg angle
0 = Calculated angle between B and
diffracting plane
Figure 4.4 Method for determining HOLZ line formation
limits for a given convergence angle.
+ 2 2 2=
C h2+k2+1 2=90.713
+ co
88 .
756 ..... .
2.4 2.5 2.6 2.7 2.8 2.9 3. 3.1 3.2
Degrees
Figure 4.5 Plot of data for 100 KV, a=3.56
Angstroms, B=(114), from Figure 4.4.
from the FCC gamma prime phase. One then calculates the
angles between the planes represented by any zero order
indexed spot and the FOLZ reflections listed in Table
4.1. The indexed spots in the FOLZ using the calculated
angles are shown in Figure 4.6. The indexing in the FOLZ
must be consistent with the indexing in the ZOLZ. Once
the FOLZ reflections have been indexed, the HOLZ lines in
the central spot can be indexed. The lines in the pattern
center are parallel to the lines through the FOLZ discs,
as illustrated in Figure 4.7.
One advantage to indexing patterns from the
calculations is that the line pattern in the central spot
can be indexed directly without first indexing the
reflections in the HOLZ. An indexing of a B = [114] line
pattern is shown in Figure 4.8. To index in this way, one
first identifies the line types using Table 4.1. Next,
one finds the lowest symmetry line, if it exists, and
indexes it. This is easily done in this pattern for the
773 line. One then finds the next lowest symmetry lines
and indexes them, and so on. The sign of the vector cross
product between these lines must be consistent with the
choice of beam direction. The direction of g can be
determined from Table 1. The remaining lines are then
indexed using the calculated interplanar angles (Figure
4.6). The angles measured between HOLZ lines are slightly
different from the calculated values. In addition to
normal measurement error, these measured angles are
projected from the higher order zone onto the zero order
zone and are different from the calculated ones. The
difference is explained in Appendix B.
Once the FOLZ has been indexed, FOLZ line positions
in the transmitted disc can be used to determine relative
lattice parameter differences and can be used to measure
small symmetry differences due to crystallographic changes
as a result of alloying, strain, or transformation.
4.1.4 Lattice Parameter Changes
The easiest way to visualize the changes in the FOLZ
line position in the central spot that accompany changes
in lattice parameter is to look at a few examples of
patterns to see what happens when the lattice parameter is
varied. Figure 4.9a illustrates a case where the lattice
parameter of a diffracting crystal is such that at 100 kV,
the four 931 lines in a B = (114) pattern pass exactly
through the center of the transmitted disc. This is
equivalent to saying that the Bragg condition is satisfied
for g = (931) when B = (114). For this to be true, the
lattice parameter of the crystal must be exactly 3.5712
Angstroms. If the lattice parameter is greater than this,
a pattern like that shown in Figure 4.9b will result. If
the lattice parameter is less than 3.5712 Angstroms, the
pattern will look like Figure 4.8c. The shaded area in
the figure outlines the symmetry changes. This change is
exaggerated compared to the micrographs. The calculations
required to determine the line positions of the patterns
are summarized in Appendix A.
Since only a relative change in lattice parameter can
be realistically measured, measuring this relative change
involves measuring and quantifying changes in the HOLZ
line positions from one pattern to the next. This is
easily and most accurately accomplished by using HOLZ
lines that both intersect at shallow angles, and most
desirably, that move in opposite directions to one another
when the lattice parameter is varied. Distances between
intersections are then measured and these distances
ratioed for different values of absolute lattice
parameter. Figure 4.10 is a plot of the ratio a/b versus
relative change in lattice parameter. Parameters a and b
are defined in Figure 4.9. The calculation of the values
for Figure 4.10 is given in Appendix A.
4.1.5 The Effect of Strain and Non-Cubicity on
Pattern Symmetry
If a previously cubic crystal is nonisotropically
strained or has become noncubic due to transformation or
change in order, the CBED pattern will reflect this change
by a reduction in the symmetry of the HOLZ line pattern.
The CBED technique is especially sensitive, theoretically
capable of detecting changes in lattice parameter on the
order of two parts in ten thousand at 100 kV (Steeds,
3.60
.59
E .58
o
S-
+,
ca .57
S.56
E
r .55
S.-
r0
rl-
S.54
-m,-
r .53
.52
.51
3.50
RATIO a/b
Figure 4.10 Plot of lattice parameter verses the
ratio of a to b (a and b defined in
Figure 4.9).
1979). This would of course apply to nonsymmetrical
changes in lattice parameter as well. The magnitude of
these nonsymmetrical changes can be deduced by measuring
the change in HOLZ line positions as the lattice parameter
changes, described in the preceding section.
Again, the easiest way to visualize the effects of
crystal asymmetry is to look at a few examples of CBED
HOLZ patterns to see how this asymmetry affects HOLZ line
position. The direction of shift of the lines will depend
on the orientation of the now noncubic crystal with
respect to the beam direction. For example, if the
expansion or contraction is along the c axis, the c
direction defined as being parallel to the beam, the
symmetry of the pattern changes very little. If the beam
is a parallel to either of the a or b cube axes, the
change in symmetry is very marked, as shown in Figures
4.11a, 4.11b, and 4.11c. The method for calculating these
HOLZ line patterns is explained in Appendix A.
It is not straightforward to differentiate symmetry
changes from lattice parameter changes to arrive at a
measure of both lattice parameter and loss of cubicity.
Ecob et al. (1981) simulated CBED HOLZ line patterns to
measure the lattice parameter differences in gamma/gamma
prime alloys, and to measure the changes in symmetry of
the gamma prime phase after recrystallization. The
simulations were then compared to actual patterns.
Numerous trial and error iterations would usually
a.
Figure 4.11
The effect of non-symmetrial changes in
the lattice parameter on the symmetry of the
transmitted HOLZ pattern; a.) a, b, and c
3.5713 Angstroms, b.) a, b, and c 3.5713
Angstroms, and c.) a = 3.5713, b and c a.
The mirror symmetry in the pattern has been
lost. The mirror is perpendicular to this
caption.
provide an adequate match. They used the B = (111>
pattern to make these measurements. This pattern is a
simple one to analyze because of the threefold symmetry in
the ZOLZ transmitted disc. This pattern could not be used
in the study of the Pratt and Whitney alloys, however,
because of the microstructural scale in these alloys.
When the sample is in a B = (11) orientation, the gamma
prime precipitates usually overlap either the gamma phase
or the gamma phase and another gamma prime precipitate.
The result is either a highly distorted HOLZ pattern or no
pattern at all. If B = (114>, the beam is more closely
parallel to the 100 direction; 19 degrees from the B =
(100> direction. Eades (1977) used this orientation to
study the gamma/gamma prime mismatch in In-100, a Ni-based
superalloy. The B = (114> CBED pattern can be used to
measure both lattice parameter and noncubicity. The
method is outlined in Appendix A.
The B = <111> pattern has been used recently by
Braski (1982) and by Lin (1984) to measure lattice
parameter change in ordered alloys. In both cases, the
microscope accelerating voltage was continuously variable,
meaning that the HOLZ line positions in these patterns
could be varied. Because the B = 111) pattern in a cubic
material always exhibits either sixfold or threefold
symmetry, it is always possible to find three FOLZ lines
that can be made to pass directly through the center of a
CBED pattern, and hence intersect at a point in the
center of the pattern. If a lattice parameter measurement
is to be made using the relative voltage differences
required to go from one three line point intersection to
another three line point intersection, this measurement
cannot be accurate if any noncubicity is present. Braski
alluded to the nonacceptability of using the B = (114)
patterns for his measurements because of the sensitivity
of this pattern for noncubic effects. All patterns are
sensitive to strain effects.
There should be other CBED zone axis patterns that
could be used to make the measurements for which the B =
(114> pattern was used in this study. The B = <100>
pattern would be the most crystallographically sensible.
There is no gamma/gamma prime overlap along this
direction.
Using equation (1), it is simple to calculate the
expected HOLZ for B = (001>.
At 100 kV:
R = 27.07,
ao = 3.56 Angstroms,
B = <001>,
g*B = 1, and
h2+k2+12 = 193.
The Bragg angle for this FOLZ ring is about 4.2 degrees at
100 kV. This means the FOLZ will be 8.4 degrees from the
center of the pattern, far from the transmitted spot and
hence possibly too weak to give strong FOLZ lines in the
central spot.
If the accelerating potential of the microscope is
lowered, the FOLZ ring will move in toward the center of
the pattern. The scattering amplitude increases as the
ring moves in and the diffracted intensity consequently
increases (Steeds, 1979).
4.2 Energy Dispersive Methods
The use of energy dispersive x-ray analysis is a well
established means of characterizing the compositions of
materials on a microscale (Goldstein, 1979). The effects
of various experimental variables on the accuracy and
precision of the final EDS results are of paramount
importance. These effects have been reviewed extensively
elsewhere (Zaluzec, 1979). They are summarized here as 1)
instrument related, 2) specimen related, and 3) data
reduction related. Care must be taken in defining the
effects of all three if an accurate result is to be
obtained.
Consider first the instrument and its effects.
Microscopes of the late 1970's vintage are generally less
than perfect experimental benches for x-ray
microanalysis. In unmodified instruments, many
uncollimated electrons and x-rays make their way to the
specimen environment where they then contribute to the
x-ray signals that are supposed to be generated only by
the local interaction of the specimen and the beam. These
stray electrons and x-rays can be mostly eliminated by
proper specimen shielding and by proper design of the
column. The 400T STEM at Oak Ridge National Lab is
properly modified to minimize spurious x-ray fluorescence
through the use of top hat condenser apertures, and to
reduce sprayed, uncollimated electrons through the use of
spray apertures below the condenser lenses. Hole counts
are consequently low, in the neighborhood of 1 to 2
percent of the total elemental counts when the beam is on
the sample. A hole count spectrum was always accumulated
for each specimen and subtracted from each specimen
generated spectrum before any subsequent curve fitting and
peak deconvolution (Zaluzec, 1979).
The specimen related effects are more difficult to
assess. These effects are primarily due to absorption of
specimen generated x-rays by the specimen itself. The
most common method for quantitative analysis in the
analytical TEM follows the Cliff-Lorimer equation (Cliff
and Lorimer, 1972). This equation relates the ratio of
the concentrations of unknowns in the sample to the ratios
of the beam generated x-ray itensities:
CA/CB = (K) IA/IB.
The major assumption in the equation is that the k term,
the proportionality constant, is independent of the
specimen thickness. This assumption is not valid
in the alloys that were characterized in this study.
The proportionality constant can either be measured,
in which case the standard from which it is measured must
satisfy a criterion called the "thin film criterion," a
criterion that defines the maximum thickness of the
standard, or the constant can be calculated. Both of
these methods are outlined by Goldstein (1979) and Zalusec
(1979). It is primarily the effect of thickness on the k
term in the Cliff-Lorimer equation that defines the
specimen related effects. This thickness effect is a very
serious problem in Ni-Al alloys. The aluminum x-rays are
preferentially absorbed by the Ni, to the extent that the
thin film criterion in Ni-Mo-Al of RSR composition is not
satisfied for thicknesses in excess of about 600
Angstroms.
The ternary alloy #17 will be used as an example of
how thickness affects quantitation. A large beam was used
in an attempt to measure a "bulk" composition of the
alloy. The results are summarized below:
Nominal Composition Ni Mo Al
wt.% 78.5 15.0 6.5
at.% 77.0 9.0 14.0
X-Ray Results
No thickness correction wt.% 79.2 15.6 5.22
No thickness correction at.% 79.1 9.5 11.3
1000 Angstrom correction wt.% 78.8 15.5 5.6
|
| Full Text |
PRECIPITATION IN
NICKEL-ALUMINUM-MOLYBDENUM SUPERALLOYS
By
MICHAEL MILLER KERSKER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1986
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii
ABSTRACT vii
CHAPTER
1 INTRODUCTION 1
2 BACKGROUND 7
2.1 Phase Diagrams 7
2.1.1 Binary Phase Diagrams 7
2.1.1.1 Ni-Mo 7
2.1.1.2 Ni-Al 9
2.1.1.3 Ni-W 9
2.1.1.4 Ni-Ta 12
2.1.2 Ternary Diagrams 12
2.1.2.1 Ni-Al-Mo 12
2.1.2.2 Ni-Al-Ta 14
2.1.2.3 Ni-Al-W 16
2.2 Binary Phases 16
2.2.1 Ni-Mo 16
2.2.1.1 N4M0 18
2.2.1.2 N3M0 20
2.2.1.3 N2M0 20
2.2.1.4 Ni-Mo... 23
2.2.2 Ni-W 23
2.2.2.1 N4W 24
2.2.2.2 Ni3W 24
2.2.2.3 Ni£W 24
2.2.2.4 NiW 24
2.2.3 Domain Variants/Antiphase
Boundaries 25
2.2.3.1 N4X (Dla) 25
2.2.3.2 Ni3x(D022> 27
2.2.3.3 Ni2x(Pt2Mo) 29
2.2.4 SRO in Ni-x Binaries 29
111
ACKNOWLEDGEMENTS
Special thanks are given to John J. Hren, my mentor
and advisor. I am especially grateful that he is as
stubborn as I. The assistance of Scott Walck, my
colleague and friend, in handling the logistics and
mechanics of my dissertation, is especially appreciated.
The continued support of Dr. E. Aigeltinger is sincerely
acknowledged. I am also grateful to Drs. Kenik, Bentley,
Lehman, and Carpenter for their generous assistance during
my visits to the Oak Ridge National Laboratory. For the
perserverance and persistance of my wife, Janice, I am
most endebted.
I am also indebted to Pratt and Whitney Government
Products Division, West Palm Beach, for providing the
necessary funding to see this project through to
completion, to the SHARE programs at ORNL for the generous
use of their instruments and expertise, and to the
Department of Materials Science and Engineering at the
University of Florida for providing the education,
training, and constant devotion to excellence in research
that have directed my career and scientific character.
2.2.5 Ordering Reactions and Kinetics .... 31
2.2.5.1 Binary Alloys 31
2.2.5.2 Ternary Alloys 35
2.2.6 Ni-Al N3AI 36
2.3 Diffraction Patterns: NixMo Phases/
N3AI 40
2.3.1 DO22 Reciprocal Lattice 40
2.3.2 Dla/Pt2Mo/Ll2 Reciprocal Lattices..42
2.3.3 SRO (1, 1/2, 0) Scattering 46
2.3.4 Variant Imaging 46
2.3.4.1 DO22: N3M0 47
2.3.4.2 Da: N4M0 47
2.3.4.3 Pt2Mo: N2M0 51
3 EXPERIMENTAL PROCEDURE 53
3.1 Composition 53
3.2 Heat Treatments 54
3.3 Characterization: Methods of Analysis ....55
4 SPECIAL METHODS 61
4.1 Convergent Beam Electron Diffraction
(CBED) Methods 61
4.1.1 Experimental Technique 63
4.1.2 HOLZ Lines (High Order Laue
Zone Lines) 66
4.1.3 Indexing HOLZ Lines 72
4.1.4 Lattice Parameter Changes 89
4.1.5 The Effect of Strain and
Non-Cubicity on Pattern Symmetry... 91
4.2 Energy Dispersive Methods 97
5 RESULTS 106
5.1Microstructural Characterization 106
5.1.1 As Extruded RSR 197 and RSR 209
Alloys 106
5.1.2 RSR 197-As Solution Heat Treated
and Quenched 106
5.1.3 General Microstructural Features..Ill
5.1.4 RSR 197 Aging Ill
5.1.4.1Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours Ill
IV
5.1.4.2 Lattice imaging of D022
and Dla Phases 127
5.1.4.3 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours 132
5.1.4.4 Solution Heat Treated,
Quenched and Aged at
870 C for up to 100
Hours 134
5.1.4.5 Aging Summary RSR 197...140
5.1.5 RSR 209 As Solution Heat
Treated and Quenched 142
5.1.6 RSR 209 Aging 142
5.1.6.1 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours 142
5.1.6.2 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours 145
5.1.6.3 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours 149
5.1.6.4 Aging Summary RSR 209...152
5.1.7 Special Aging/Special Alloys 153
5.1.7.1 Alloy ?/17 Solution
Heat Treated, Quenched
and Aged at 760 C for
100 Hours 153
5.1.7.2 Alloy //17 Solution
Heat Treated, Quenched
and Aged at 870 C for
100 Hours 153
5.1.7.3 RSR 197 Solution Heat
Treated, Quenched and
Aged at 870 C for 1 Hour,
Furnace Cooled to 760 C
and Aged for 100 Hours at
760 C 156
5.1.7.4 RSR 185 Solution Heat
Treated at 1315 C and
Water Quenched 156
5.2 X-Ray Diffraction Measurements 156
5.3 Convergent Beam Measurements 161
V
5.4 Energy Dispersive X-Ray Measurements ....167
5.5 Microhardness Measurements 167
6 DISCUSSION AND CONCLUSIONS 170
6.1 Metastable NixMo Phase
Formation: Effects of Chemistry
and Microstructure 170
6.2 Precipitation in RSR 197 176
6.3 Precipitation in RSR 209 179
6.4 Mechanical Response to Aging 179
6.5 Convergent Beam/X-Ray Diffraction 181
6.6 Conclusions 183
REFERENCES 185
APPENDICES
A HOLZ PATTERN CALCULATION 191
B INTERPLANAR ANGLES 199
BIOGRAPHICAL SKETCH 201
vi
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
PRECIPITATION IN
NICKEL-ALUMINUM-MOLYBDENUM SUPERALLOYS
By
Michael Miller Kersker
August, 1986
Chairman: John J. Hren
Major Department: Materials Science and Engineering
The precipitation of 420 phases, common in the NiMo
binary system, is also observed in Ni-Al-Mo-(x)
superalloys. Two such superalloys, where x is Ta or W,
were characterized, after aging, using a variety of
electron microscopy methods.
The 420 type NixMo phases that precipitate during
aging depend strongly on the partitioning of the
quaternary elements. The DO22 and Dla phases predominate
in the Ta containing quaternary. The strain between the
gamma prime precipitates is sufficient to suppress the
nucleation of specific DO22 (N3M0) variants, in turn
affecting the subsequent coarsening behavior of the Dla
phase. The crystallographic similarity of these two
VI1
phases is demonstrated by simultaneously imaging the
lattices of the two phases at common interfaces. The
predominant NixMo precipitate in the W bearing quaternary
is Pt2Mo (N2M0), though DO22 and Dla can be present
concurrent with the Pt2Mo.
When aged at temperatures above the solvi for the
NixMo phases, equilibrium NiMo and equilibrium Mo phases
precipitate, the former in the Ta containing alloy, the
latter in the W containing alloy. The presence of these
phases is in general agreement with the expected phase
equilibria predicted by the phase diagram.
Convergent beam electron diffraction, one of the
methods used in the characterization of the alloys, is
shown to have sufficient sensitivity for lattice parameter
variations to qualitatively measure the difference in
partitioning of the quaternary additions to the gamma
prime and gamma phases of both quaternary alloys. The
method is compared to x-ray diffraction results and
confirmed by energy dispersive x-ray analysis. In
addition to the measurement of partitioning, the fine
spatial resolution of the convergent beam method makes it
ideal for the measurement of other factors that are
reflected in lattice parameter changes -- strain, for
example. Simple equations are developed for the indexing
of HOLZ line patterns and for the measurement of lattice
parameters and uniform strain. Examples are given using
the superalloys characterized in this study.
Vlll
CHAPTER 1
INTRODUCTION
No single factor in jet engine design has been as
important as the development of high strength, high
temperature alloys for the hot turbine section of the
engine. This development has proceeded over the
relatively short period from the early 1930's, the early
development days of the jet engine, to the present. These
high strength, high temperature alloys had to maintain
their strength at very high temperatures under very high
load conditions yet still maintain close dimensional
tolerances so that thrust levels would not deteriorate
significantly with time. They had to be capable of
withstanding extremes in thermal cycling and had to resist
degradation under the most severe of hot corrosion
environments. It is no wonder these materials were and
are referred to as superalloys.
Alloy development has proceeded in superalloy systems
as it has historically proceeded in other metallurgical
systems -- empirical trial and test. In this approach
numerous alloys are prepared, fabricated, heat treated,
and tested. The winners are selected based on their
property responses. Compositional tolerances are
determined based again on desirable property limits.
1
2
It is especially fortunate that considerable
microstructural analysis of successful (and unsuccessful)
alloys has accompanied this standard approach to alloy
design. The property-microstructure relationships
developed as a result of correlations made following this
approach have been instrumental in elucidating many of the
known strengthening mechanisms that are now known to
contribute to both high and low temperature strength in
metals. These mechanisms include, among others,
1) precipitation strengthening, 2) solid solution
strengthening, 3) order strengthening, and 4) dispersion
strengthening. An alphabet of elements may be required to
activate these mechanisms and alloys such as TRWNASAVIA
(composition, at.%: Ni-61.0, Cr-6.1, Co-7.5, Mo-2.0,
W-5.8, Ta-9.0, Cb-.5, Al-0.4, Ti-1.0, C-0.13, B-0.02,
Zr-0.13, Re-0.5, and Hf-0.4) were developed seemingly as
confirmation of the old superalloy adage, "The more stuff
we put in, the better it is."
Though TRWNASAVIA is an extreme example of maximizing
desirable properties based on intentional additions (the
alloy contains 1/7 of all known naturally occurring
elements), many other superalloys also contain a large
number of intentionally added elements. These superalloy
compositions are often based on the Ni-Al system. The
microstructure of this "average" Ni based superalloy
consists of essentially three distinct microstructural
features. The first is the matrix, which is usually
3
disordered FCC nickel and can contain numerous elements in
solution. Secondly, there are incoherent precipitates
which can include the carbides, nitrides, and Ni bearing
phases, phases like sigma phase (Sims and Hagel, 1972).
Thirdly, there are the coherent phases which are normally
ordered superlattices of the disordered FCC matrix. The
major FCC ordered phase in such Ni-Al alloys is N3AI, an
Ll2 superlattice also known as gamma prime. This is
normally the strengthening phase in Ni-Al alloys. When
refractory metals are added to Ni-Al alloys, other
coherent phases can also be present as either the minor
precipitate or as the major strengthening precipitate,
e.g., DO22 phase in In 718 (Quist et al., 1971; Cozar and
Pineau, 1973).
Alloys under development at Pratt and Whitney
Government Products Division in West Palm Beach, Florida,
are also based on the Ni-Al system. They are similar to
the ternary alloy WAZ-20-Ds (Sims and Hagel, 1972), but
additionally contain small quaternary additions of Ta and
W. A host of unforeseen solid state reactions proceeds
during low temperature heat treating of the Pratt and
Whitney superalloys (Aigeltinger and Kersker, 1981;
Aigeltinger, Kersker, and Hren, 1979). These reactions
are very similar to those in the Ni-Mo binary system.
Much effort in studying Ni rich, Ni-Mo binary alloys has
been devoted to describing the transition from the
4
disordered state to the ordered state, typically a
transition through the short range ordered state. Very
elegant theories dealing with the nucleation of these
phases have been developed.
These metastable phases can be found in alloys of the
ternary Ni-Mo-Al system, and also in the Pratt and Whitney
quaternary alloys (Aigeltinger, Kersker, and Hren, 1979).
They are not present at the high temperatures normally
encountered in the turbine section of an engine, at
temperatures in the range of 1100 C, and therefore do not
contribute to high temperature strength in such Ni based
ternary and quaternary alloys. Nevertheless, certain
aspects of their microstructures suggest that they might
still contribute to alloy strength at lower than normal
turbine operating temperatures.
The metastable phases investigated here are of the
type NixMo, where x can be 2, 3 or 4. They are coherent
with the FCC matrix which is a Ni rich solution in the
above superalloys. They may be present at temperatures of
700 degrees C and lower for very long times (Martin,
1982), and may delay the precipitation of the equilibrium
phases that would be predicted from the equilibrium phase
diagram.
Though there are similarities in the precipitation of
these NixMo metastable phases among the binary, ternary,
and quaternary alloys described earlier, there are
5
differences, chemistries aside, between the Ni-Mo binaries
and Ni-Mo-Al-(x) alloys, most importantly the presence in
the ternaries and quaternaries of primary gamma prime
phase. Could this gamma prime phase affect the
precipitation behavior of the Nix(Mo,x) phases which
precipitate from gamma solution? Would the physical
constraints imposed by the gamma prime precipitate affect
the "equilibrium" structure of these precipitates after
coarsening? What would be the effect of the quaternary
additions on the metastable precipitation behavior of
these alloys? Would these quaternary additions have any
effect on the gamma prime phase?
In order to answer questions such as these, it was
necessary to characterize the Pratt and Whitney alloys in
a way that such information could be directed towards
answering these questions. The study was to focus on the
use of the electron microscope. The advantage offered by
this instrument in studying fine scale precipitation
phenomena are trivially obvious, copiously documented, and
relatively straightforward. Some microstructural
measurements, however, are not easily accomplished in the
microscope -- the measurement of local composition or the
measurement of local lattice parameters, for example.
These applications were in their infancy and had, for the
most part, not as yet been directed toward practical
problem solving in materials science.
6
This dissertation is about the various phases, both
stable and metastable, that form in the quaternary
Ni-Mo-Al-(Ta or W) alloys. It is about their
crystallography and about various aspects of the alloys'
microstructure that could affect this crystallography. It
is additionally an electron microscope study devoted in
part to exploring methods for studying these phases.
Chapter 2 introduces the reader to the various binary
metastable phases that occur in the alloys and
additionally to theories dealing with their formation. A
brief background in the Ni-Al system will also be
developed. Chapter 3 outlines the alloys, experiments,
and experimental methods chosen for this study. Chapter 4
develops the necessary background in certain special
methods that were employed to study critical features of
the superalloy microstructure. These methods include
convergent beam diffraction and energy dispersive x-ray
analysis. Chapter 5 reports on the results of the
experiments described in Chapter 3. The dissertation
concludes with Chapter 6, a discussion of the results with
the conclusions and inferences therefrom.
CHAPTER 2
BACKGROUND
This chapter will provide the background necessary to
understand the crystallography and precipitate types that
will be described in detail in Chapter 5. It additionally
provides some seminal ideas on nucleation mechanisms for
the ordered nonequilibrium coherent phases that will be
shown to precipitate in the otherwise disordered gamma
matrix. All the known equilibrium phases are also
described and the relevant phase diagrams presented.
Interpretation of the diffraction patterns of the NixMo
coherent phases is explained last.
2.1Phase Diagrams
2.1.1 Binary Phase Diagrams
2.1.1.1 Ni-Mo
The binary Ni-Mo equilibrium phase diagram is shown
in Figure 2.1 (Hansen, 1958). This diagram has been
recently confirmed by Heijnegen and Rieck (1973). Three
equilibrium intermetallic phases can occur: N4M0, a Dla
superlattice, N3M0, an orthorhombic phase, and NiMo, an
orthorhombic phase. Only NiMo is ever at equilibrium with
the liquid.
7
8
WEIGHT PERCENT NICKEL
10 20 30 40 50 60 70 80 90
Figure 2.1 Ni-Mo binary equilibrium phase diagram
(after Hansen, 1958).
9
The N4M0 and N3M0 phases are the result of solid-solid
transformations. There is no true order-disorder
transition temperature for either of them. The N4M0
phase is formed by a peritectoid reaction between gamma
and N3M0: gamma + N3M0 ^=)> N4M0, at 875 C. The N3M0
phase also forms by peritectoid reaction at 910 C; gamma +
NiMo <^=^> N3M0. Above 900 C an alloy of composition N4M0
will be wholly in the gamma disordered FCC region. An
alloy of N3M0 stoichiometry will be a solid solution
above 1135 C.
2.1.1.2 Ni-Al
Figure 2.2 is the equilibrium diagram for the Ni-Al
system (Hansen, 1958). This diagram has been more
recently confirmed by Taylor and Doyle (1972). Two phases
exist on the Ni rich side of the diagram. They are AINi,
a congruently melting compound, and N3AI, an ordered LI2
superlattice phase commonly referred to as gamma prime.
Gamma prime is formed eutectically with gamma (solid
solution Ni and Al) at 1385 C. No solid state reactions
occur in this system at lower temperatures.
2.1.1.3 Ni-W
The Ni-W binary diagram as modified by Walsh and
Donachie (1973) is shown in Figure 2.3 (Moffatt, 1977).
The modified diagram includes the intermetallics NiW and
NiW2
10
Al-N 103
WEIGHT PERCENT NICKEL
Figure 2.2 Ni-Al binary equilibrium phase diagram
(after Hansen, 1958).
temperature
11
WEIGHT % W
Nl 20 40 50 60 70 75 80 85 90 95 W
i''' i i i i _i i i 1 1
1800
1500
1200
900-
600-
300-
Ni 10 20 30 40 50 60 70 80 90 W
ATOM % \N
Figure 2.3
Ni-W binary equilibrium phase diagram
(after Moffatt, 1977).
12
The intermetallic N4W forms by the peritectoid reaction
Ni + NiW ^ = ^>Ni4W at 970 C. The crystal structure of N4W
is isostructural with N4M0 (Epremian and Harker, 1949).
Note the absence of any phase comparable to N3M0.
2.1.1.4 Ni-Ta
The Ni-Ta diagram as given by Shunk (1969) has been
modified to include the low temperature NigTa
intermetallic by Larson et al. (1970). It is shown in
Figure 2.4 (Moffatt, 1977). The NigTa intermetallic forms
sluggishly by peritectoid reaction with NigTa and Ni. It
is reported to be F.C.T. The NigTa phase has been found
to be monoclinic with a possible orthorhombic variant
(TiCog type), or as a tetragonal DO24 superlattice (TiAlg
type). The phase is thus not isostructural with either
NigMo DO22 or with orthorhombic equilibrium NigMo.
2.1.2 Ternary Diagrams
2.1.2.1 Ni-Al-Mo
High temperature Ni-Mo-Al isotherms show a
quasibinary eutectic between the NiAl and Mo phases
(Bagaryatski and Ivanovskaya, 1960). This allows the
diagram to be conveniently split in two at a line
connecting the NiAl and Mo phase fields. At the time this
investigation was originally begun, the Ni-rich low
temperature phase equilibria of this ternary system were
TEMPERATURE,
13
WEIGHT % Ta
Ni 20 4 0 60 70 75 6 0 8 5 9 0 95 Ta
Figure 2.4 Ni-Ta binary equilibrium phase diagram
(after Moffatt, 1977).
14
in question. Guard and Smith (1959-1960) reported the
presence of a ternary compound at 1000 C on the Ni-rich
side of the diagram. This phase was included in a
subsequently derived equilibrium diagram by Aigeltinger et
al. (1978). No other investigator has reported the
presence of a ternary Ni-Mo-Al compound (Bagaryatski and
Ivanovskaya, 1960; Virkar & Raman, 1969; Raman and
Schubert, 1965; Pryakhina et al., 1971; Miracle et al.,
1984).
Aigeltinger et al. (1978), Loomis et al. (1972), and
recently Miracle et al. (1984), extend the maximum
solubility of Mo in N3AI to 6.0 at. % Mo, a value much
higher than that previously reported by Guard and Smith
(1959-1960), Bagaryatski and Ivanovskaya (1960), Virkar
and Raman (1969), Raman and Schubert (1965), and Pryakhina
et al. (1971). Miracle et al. (1984) also report an
additional class II reaction at 1090 C involving gamma,
gamma prime, NiMo, and Mo. This reaction brings gamma
prime, gamma, and NiMo into equilibrium at lower
temperatures. This class II reaction was previously
unreported. A 1000 C isotherm from their work is compared
with the 600 C section from Pryakhina et al. (1971) in
Figure 2.5.
2.1.2.2 Ni-Al-Ta
The Ni-rich side of this diagram has recently been
reviewed by Nash and West (1979). They confirm the
15
b.
Figure 2.5 Ternary Ni-Al-Mo isotherms;
a.) 1038 C (after Miracle et al., 1984)
and b.) 600 C (after Pryakhina et al.
1971) .
>
16
presence of the ternary phase Ni^TaAl, and also NigTa.
The former phase is hexagonal and is not isostructural
with any Ni-Mo-Al phase. According to their 1000 C
section, Ta can substitute for A1 up to 8.0 at.% in gamma
prime (N3AI). It is soluble to approximately 10.0 at.%
at 1250 C.
2.1.2.3 Ni-Al-W
This diagram has been recently determined by Nash et
al. (1983). A 1250 C isotherm from their work is shown in
Figure 2.6. No ternary phase is shown in the isotherm,
nor is a ternary phase reported at temperatures as low as
1000 C. The diagram is qualitatively very similar to the
Ni-Mo-Al ternary diagram shown in Figure 2.5b.
2.2 Binary Phases
2.2.1 Ni-Mo
In addition to the equilibrium phases mentioned in
the previous section, there are intermediate metastable
phases that can precipitate from Ni rich solutions of
Ni-Mo binaries. The practical limit of Mo solubility in
Ni is about 27 atomic percent. Molybdenum in excess of
this amount cannot be put into solution. If a Ni-Mo
binary of 27.0 at.% or less Mo is quenched from a
temperature high enough for the alloy to have been a
17
Figure 2.6 Ternary Ni-Al-W 1250 C isotherm;
(after Nash et al., 1983).
18
single phase solid solution, and subsequently heat treated
below the solvus temperature for that particular
as-quenched composition, intermediate metastable phases
may precipitate instead of the equilibrium phases
predicted by the equilibrium phase diagram. These phases
are N2M0, a Pt2Mo superlattice; N3M0, as a DO22 phase
rather than the equilibrium orthorhombic phase; and/or
N4M0, the previously described binary equilibrium phase
which can exist as a metastable phase at certain NiMo
compositions.
2.2.1.1 N4M0
The N4M0 phase is a BCT structure derived from the
disordered FCC lattice. Its lattice parameters as a BCT
cell are a* = b' = 5.727 Angstroms, c' = 3.566 Angstroms.
The BCT unit cell can be derived from the FCC parent by
using the following transformation:
Al' = 1/2 (3A1+A2); A2' = 1/2 (-A1+32); A3' = 3,
where Al, A2, and S3 are the lattice vectors for FCC and
Al', A2', and A3' are the vectors from the BCT unit cell
(Mishra, 1979). The c axis of the Dla undergoes a
contraction of 1.2% during the transformation from
disordered FCC to ordered Dla. Hence, A3' is only
approximately equal to A3. A convenient way to visualize
the N4M0 structure is to consider the ordering of Mo on
19
a
\* o o, /,.#
o o *\ o d/cP^/o
T\ ? *
? \* r / o/ \ o
o/*yp/# o \*
\ o d'ji\d/o
-\*/ ei ,'jdj^r'm o
V O o
o
o Ni
Open circles: atoms in first and
third layers
Closed circles: atoms in second
layer
Figure 2.7 Two dimensional representation of Dla
stacking showing 1.) FCC unit cell ( ),
2.) Dla unit cell ( ), and 3.) 420 FCC
stacking sequence ( ).
20
every fifth 420 plane of the FCC parent lattice (Okamoto
and Thomas, 1971), as described in Figure 2.7. This
stacking sequence is pertinent. With slight variation it
can also describe the stacking sequences of both N2M0
Pt2Mo and N3M0 DO22 It also simplifies the
visualization of the diffraction patterns for these
phases, c.f., section 2.3.4.2.
2.2.1.2 N3M0
The N3M0 phase exists stoichiometrically as both an
orthorhombic equilibrium phase, where a = 5.064 Angstroms
b = 4.448 Angstroms, and c = 4.224 Angstroms, and as a
metastable DO22 superlattice phase where a* = b' = 3.560
Angstroms, and c' = 7.12 Angstroms. Note that
c(FCC)=c'/2=3.560 Angstroms. The orthorhombic structure
was determined by Saito and Beck (1959) and was shown to
be isostructural with CU3T. The DO22 phase is an
equilibrium phase in the Ni-V system (Tanner, 1968). In
the Ni-Mo system it is not. Figure 2.8a shows the DO22
tetragonal cell. The prominent 420 planes of Mo are now
separated by three 420 planes of Ni instead of four Ni
planes as in N4M0. Figure 2.8b describes this packing.
2.2.1.3 N ip Mo
The N2M0 phase was first discovered by Saburi et al
(1969). It is a Pt2Mo type superlattice, as shown in
21
to
Figure 2.8 The N3M0 DO22 phase;
a.) N3M0 DO22 unit cell and
b.) two dimensional representation
of Figure 2.8a. showing 1.) FCC unit'
cell ( ), 2.) DO22 unit cell
( and 3.) 420 FCC stacking
sequence ( ).
22
a'
Ni
a.
B
to^Of O 0,9 o
>c / Q/ft/jji s
0/\o
o/ o (o,iv0 yo
*"Q x* o Jp/f'/So/
oy^fMoy^
& o 0 'm'o W o O
O Mo
O Ni
B'
b.
Figure 2.9 The N2M0 DO22 phase;
a.) N2M0 Pt2Mo unit cell and b.) two
dimensional representation of Figure
2.9a showing 1.) FCC unit cell ( ) ,
2.) Pt2Mo unit cell ( ), and 3.) 420
FCC stacking sequence ( ) .
23
Figure 2.9a, with lattice constants a' = 2.588 Angstroms,
b* = 7.674 Angstroms, and c* = 3.618 Angstroms. It is
again best described in relation to the FCC lattice. Here
the stacking sequence is 420 planes of Mo separated by two
420 planes of Ni. This stacking is shown in Figure 2.9b.
The Pt2Mo phase is stable in the Ni-V system (Tanner,
1972) .
2.2.1.4 NiMo
The equilibrium delta NiMo phase is orthorhombic with
lattice constants a = 9.107 Angstroms, b = 9.107
Angstroms, and c = 8.852 Angstroms (Shoemaker and
Shoemaker, 1963; Shoemaker et al., 1960). This phase has
deleterious effects on the mechanical behavior of Ni-Mo-Al
superalloys (its crystal structure is very similar to
structures for the embrittling sigma phases) and the
conditions under which it will form in ternary and higher
order alloys should be more extensively studied now that
its deleterious effect on mechanical properties is better
understood.
2.2.2 Ni-W
According to the published phase diagram shown in
Figure 2.3, a NiW alloy of N4W stoichiometry cannot be
put into solid solution. However, a NiW alloy of 20 at.%
W or less quenched from above the peritectoid reaction
temperature and subsquently aged below this temperature
24
will decompose in a fashion similar to the decomposition
of the Ni-Mo alloys and will produce Ni-W phases similar
to those described in Section 2.2.1 (Mishra, 1979). For
example, N3W DO22 and N2W Pt2Mo phases are observed
during the decomposition of quenched and aged N4W
stoichiometric alloys (Mishra, 1979). These metastable
NixW phases are crystallographically identical to the
NixMo phases described in Section 2.2.1.
2.2.2.1 N14W
The N4W is a Dla superlattice with lattice parameters
a' = b' = 5.730 Angstroms and c* = 3.553 Angstroms. This
structure can be derived from the FCC alpha matrix with a
slight tetragonal distortion; here c'/c = .98. It is
isostructural and presumably isomorphous with N4M0.
2.2.2.2 N13W
This phase is crystallographically identical to N3M0
DO22 (see Section 2.2.1.2).
2.2.2.3 Ni?W
This phase is crystallographically identical to N2M0
Pt2Mo (see Section 2.2.1.3).
2.2.2.4 NiW
Equilibrium NiW is an orthorhombic phase (Walsh and
Donachie, 1973) with lattice constants a = 7.76, b =
25
12.48, and c = 7.10. All of these phases and the relevant
Ni-Ta phases are summarized in Table 2.1.
2.2.3 Domain Variants/Antiphase Boundaries
The phases just described exhibit wide variability in
both the crystallographic habits which they can take and
in the interfaces that result from domain impingement.
When these different variants come into contact out of
phase, domain boundaries are created. These interfaces
are known as antiphase boundaries. Common to all of the
ordered precipitates previously described are 1)
translational antiphase boundaries, 2) antiparallel twin
boundaries, 3) perpendicular twin boundaries, and 4)
dissociated antiphase boundaries. The permissible
variants and three of the four antiphase boundary types
are described in the following sections.
2.2.3.1 N4X (Dla)
Thirty different variants can form in this structure
(Harker, 1944). First, the tetrad (c) axis can be
parallel to any one of the three cube axes of the parent
lattice. Second, the a axis of the Ni^x lattice can be
rotated clockwise or counterclockwise relative to the FCC
cube axis. Third, the origin can be shifted, allowing
five independent variants (one x and 4 Ni) to exist.
There are thus 3x2x5 = 30 domain orientations. Ruedl et
al. (1968) have reviewed the three domain boundaries that
Table 2.1
Structural Data
Lattice
Crystal Structure
Lattice Parameter (A)
Ni-Mo
N4M0
BCT/10 atoms
Dla
a
5.727
b
5.727
c
3.566
N3M0
BCT/8 atoms
OO22
3.566
3.566
7.132
N3M0
N2M0
OR/8 atoms
CU3T
5.064
4.448
4.224
BCO/6 atoms
Pt2Mo
2.588
7.674
3.618
NiMo
OR/--
Orthorhombic
9.107
9.107
8.852
Ni-W
N4W
BCT/10 atoms
Dla
5.730
5.730
3.553
N3W
BCT/8 atoms
DO22
N2W
BCO/6 atoms
Pt2Mo
NiW
OR/--
Orthorhombic
7.76
12.48
7.10
NiTa
NigTa
Ni3Ta
Tetr./ --
Ortho/Tetr.
Orth./DO24
7.67
5.10
7.67
4.42
3.48
4.24
NiAl
Ni 3 Al
Cubic/4 atoms
Ll2
3.60
3.60
3.60
NiTaAl
NigTaAl
Hex./--
N3T
5.112
8.357
27
are possible in N4M0. They would be similar in all Dla
structures. They are 1) translational antiphase
boundaries (TAPB), 2) antiparallel twin boundaries (ATB),
and 3) perpendicular twin boundaries (PT).
A translation APB results when the domains have
parallel axes but the origins are shifted by a lattice
translation vector. Figure 2.10 shows one of four
possible TAPB in N4X. The lattice translation vector is
1/5 [130]. The other three vectors are 1/5 [210], 1/10
[135], and 1/10 [3l5].
The antiparallel twin boundary results when two
contiguous domains have their tetrad axes antiparallel.
The possible twinning planes are of the type 200, 020, and
220, relative to the parent lattice. An APT boundary with
200 twinning plane is shown in Figure 2.11.
A perpendicular twin results when the c axis of the
ordered domains aligns with two different axes of the FCC
cube. The lattices are not continuous across the
interface, unlike the other two boundaries. This occurs
in N4X because c/c' is not an integer (see Section
2.2.1.2). Combinations of all three interfaces are
possible.
2.2.3.2 Ni^x (DO22)
The DO22 phase can form twelve variants. The c axis
of the crystal may lie along any one of the FCC cube
axes .
28
Figure 2.10 A translation antiphase boundary in the
Dla structure.
) vector ( )
is in the plane
/
o
o
o
o
o
o
o
r o
o
o
o
o
o
0
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o J
0
o
o
o
G
o
o
o
o
o
o
o
Figure 2.11 An antiparallel
Dla structure.
FCC coordinates
The lattice translation
is 1/5 (130). This vector
of the figure.
o
\0
o
\
o
o\ o
o
o
\
o
o .
o \ o
o
""o
\
\
o
o
o \
o
o
o
\
"""o \
o
o \
. o
o
o
\ 0
o
\
\
o
o
, o
twin boundary in the
The twinning plane in
is the (200).
29
Four origins are possible for each orientation. Thus,
3x4 = 12 variants exist. TAPB and PT interfaces can
result (Ruedl et al., 1968).
2.2.3.3 Nipx (Pt?Mo)
Eighteen different variants can exist. The
orthorhombic cell can have six relationships with respect
to the FCC unit cell. Each domain may have three
different origins. There are thus 6x3 = 18 variants
possible. TAPB, ATB, and PT boundaries have been reported
for the Pt2Mo superlattice N2V (Tanner, 1972).
2.2.4 SRO in Ni-x Binaries
The Nix binary alloys can also exhibit short range
order (SRO). Briefly, SRO in binary alloys is a local
arrangement of atoms in which an A atom has a greater
preference for another unlike atom, say a B atom, than for
another A atom. The presence of diffuse (1, 1/2, 0)
maxima in both x-ray and electron diffraction patterns has
been offered as evidence for the existence of short range
order in Ni-Mo and Ni-W alloys.
Considerable controversy exists over the explanation
of this diffuse (1, 1/2, 0) scattering. These scattered
intensities can be calculated from a model of statistical
arrangements of atoms in which statistical short range
order is maintained, that is, a model in which there is a
30
higher probability of finding a B atom next to an A atom
than there is of finding a B atom next to another B atom.
This model is the statistical-mechanical model originally
proposed by Clapp and Moss (1966, 1968a, 1968b). It is
derived from classical descriptions of SRO.
The scattered intensities can also be derived from a
model in which very small long range ordered (LRO) regions
within the normally disordered matrix diffract to produce
the diffuse maxima. This is the microdomain model,
originally proposed by Spruiell and Stansbury (1965).
They used x-ray diffraction to study the phenomenon in
Ni-Mo alloys. Ruedl et al. (1968) used dark field
electron microscopy to image these small LRO domains.
They found, as did Das and Thomas (1974), Okamoto and
Thomas (1971), and Das et al. (1973), that the microdomain
model could explain the very fine precipitate that they
were able to image using the (1, 1/2, 0) diffuse
reflections. Similarly, deRidder et al. (1976) proposed a
cluster model which describes clusters of atoms with
simple polyhedral arrangements. The polyhedral clusters
so described are actually prototypes of long range order,
though they can also be considered as most probable
arrangements and hence statistical. In addition to
explaining diffuse maxima at the (1, 1/2, 0) positions,
these clusters can explain other diffuse maxima in
electron diffraction patterns of Ni-Mo binary alloys.
31
The former statistical model implies that the short
range ordered structure will probably not be the same as
the structure of the long range ordered phases that will
ultimately precipitate. In the microdomain model, the
short range ordered structure may be the same as the final
long range ordered structure since the model structure is
in fact merely a microcell of the final long range ordered
cell.
2.2.5 Ordering Reactions and Kinetics
2.2.5.1 Binary Alloys
Ni-20% Mo. This composition corresponds to
stoichiometric N4M0. Saburi et al. (1969) used electron
microscopy to study the ordering kinetics of a Ni-20% Mo
binary alloy quenched from solid solution and aged at 800
C. They conclude that the ordering process is
heterogeneous. Long range ordered domains of N4M0
nucleate in the matrix and grow with time. Domain
impingement is characterized by numerous perpendicular
twin plates. Chakravarti et al. (1970) used both TEM and
FIM (Field Ion Microscopy) to study the ordering of Ni-20%
Mo from solid solution. At 700 C they report that the
transformation is wholly homogeneous. A fine, mottled
"tweed" structure develops with aging times of up to and
less than three hours. After three hours, heterogeneous
precipitation of N4M0 is observed along grain
boundaries. Ling and Starke (1971) used x-ray line
32
broadening techniques to calculate LRO parameters, domain
size, and microstrains in similarly aged material. Their
conclusions support those of Chakravarti et al. (1970).
Das and Thomas (1974) used TEH to study ordering at
650 C. After eight hours at 650 C they found diffraction
evidence for the existence of N2M0 and N4M0. They
explain the presence of N2M0 as being due to
nonconservative antiphase boundaries on (420) planes of
N4M0. The regions of APB thus formed correspond to small
ordered regions of N2M0 within the N4M0 ordered layers.
Above 650 C, there was no evidence of N2M0
precipitation. Only N4M0 precipitated.
Ni-25% Mo. Yamamoto et al. (1970) were the first to
study the structural changes during aging of a
stoichiometric N3M0 binary alloy rapidly quenched from
1100 C. At 860 C, both N2M0 and N4M0 precipitate from
the disordered matrix. These phases are subsequently
consumed by the growth of the ordered orthorhombic N3M0
phase which nucleates at grain boundaries. Following this
work, Das and Thomas (1974) aged a quenched stoichiometric
N3M0 alloy at 650 C. They hoped, by aging at this lower
temperature, to reduce the nucleation kinetics so that the
earlier stages of decomposition (which were presumably
missed in the work of Yamamoto et al.) could be studied.
They confirm the results of Yamamoto et al. (1970), i.e.,
the presence of both N2M0 and N4M0 during the initial
33
stages of ordering. In this study the N2M0 existed as a
discreet phase, unlike the N2M0 in the N4M0 aging study,
which Das and Thomas (1974) presume occurred as the result
of the formation of a non-conservative AFB.
Van Tendeloo et al. (1975) have summarized their work
on Ni-2570 Mo alloys and the works of the others as
follows: at 800 C, the N3M0 ordering (decomposition)
follows the sequence FCC SRO DO22 N4M0/N2M0 HCP
- N3M0 orthorhombic. In their work, the DO22 phase forms
only when the quench from solid solution is especially
fast. From this observation they presume that the DO22
phase precedes the precipitation of both the N2M0 and
N4M0 phases, and further, that this DO22 precipitation
was not reported by any of the other previous
investigators because the alloys were not quenched fast
enough in the previous studies. Nevertheless, both the
work of Van Tendeloo et al. (1975) and the work of Das et
al. (1973) show that the stabilization of DO22 at the
N3M0 stoichiometry is especially difficult.
Ni-10% Mo. The first work in an off stoichiometric
alloy was that of Spruiell and Stansbury (1965) who
proposed to have found SRO in their x-ray study of
quenched Ni-10% Mo. The diffuse maxima they detected at
(1, 1/2, 0) positions were retained for aging times of up
to 100 hours at a temperature of 450 C, and though these
maxima sharpened with time, no superlattice ever
developed.
34
Ni-17% Mo. Nesbit and Laughlin (1978) studied off
stoichiometric Ni-16.7% Ho. Two mechanisms of ordering
are suggested from their study:
1. the ordered phase (N4M0) may form
heterogeneously from the disordered
supersaturated solid solution by heterogeneous
nucleation, or
2. the ordered N4M0 phase may form homogeneously
throughout the gamma matrix by one of the
following mechanisms:
a. spinodal clustering followed by ordering
within the solute region,
b. spinodal ordering, and
c. continuous ordering in which the final
equilibrium structure evolves continuously
from a low amplitude quasi-homogeneous
concentration wave.
Their results show that ordering at 750 C takes place
by the homogeneous nucleation of N4M0. At 700 C,
reasonable evidence exists for the mechanism to be
spinodal ordering. Continuous ordering is not plausible
since the SRO maxima do not correspond to maxima in the
long range ordered state. They did not age at a high
enough temperature to draw any conclusion about the
possibility of heterogeneous nucleation of N4M0.
35
2.2.5.2 Ternary Alloys
Yamamoto et al. (1970) studied the effects on the
precipitation behavior of the NixMo of small ternary
additions of Ta to stoichiometric N3M0. They found that
the DO22 phase was formed in the alloy containing 5 at.%
Ta. Van Tendeloo et al. (1975) and Das et al. (1973) were
not able to stabilize the DO22 phase in binary Ni-25%
alloys. In aged ternary alloys containing 2 at.% and less
Ta, no DO22 phase was detected. The diffuse scattering at
the (1, 1/2, 0) positions in electron diffraction patterns
was characteristically present, but no DO22 superlattice
spots developed during aging. They speculate that other
elements might stabilize DO22 phase, for example, Ti and
Nb. These are similar to Ta in that the atomic radius of
each is larger than the atomic radius of the Mo. Elements
which might not stabilize DO22 are presumed therefore to
be V, Fe, and Co, even though N3V as DO22 is the stable
precipitate in the Ni-V system (Section 2.2.1.2). These
atoms are of smaller atomic radius than Mo. No evidence
is offered to support these speculations.
Martin (1982) has recently studied the effects of
additions of Al, Ta, and W to N3M0 stoichiometric alloys
on the nucleation and growth of NixMo metastable phases.
His explanations for the precipitation of phases in these
alloys follow closely those of deFontaine (1975), deRidder
et al. (1976), Chevalier and Stobbs (1979), and
36
originally, Clapp and Moss (1966, 1968a, 1968b). His
findings show that the transformation from the SRO ordered
state to the long range ordered one is as follows.
Initially the Pt2Mo phase forms in all the ternary
alloys. In the A1 containing alloy, the Pt2Mo
precipitates concurrently with DC>22* In the W containing
alloy, DO22 is not stabilized. All three NixMo metastable
phases can co-exist in the A1 bearing ternary, but only
N2M0 and N4M0 in the Ta and W containing one. The final
ordered state in all three cases is the equilibrium
orthorhombic N3M0 phase, which heterogeneously nucleates
at grain boundaries and subsequently consumes the body of
the grain. The presence of Ta greatly accelerates the
kinetics of the formation of this final, equilibrium
phase.
2.2.6 Ni-Al N3AI
Nickel-Aluminum alloys that would be candidates for
superalloy applications are generally two phase alloys
consisting of gamma phase, the disordered FCC matrix, and
gamma prime phase, an LI2 superlattice of the FCC matrix
corresponding to the approximate stoichiometric
composition N3AI. The crystal structure of this compound
is shown in Figure 2.12.
When small volume fractions of gamma prime are
precipitated from gamma solid solution, that is, when the
alloy is relatively lean in A1, the gamma prime will first
37
A
c
b
Al
Ni
Figure 2.12 The N3AI unit cell.
38
appear as fine, spherical precipitate (Weatherly, 1973).
This spherical morphology will change as the lattice
mismatch between the gamma prime and gamma matrix
changes. The spherical precipitates occur for mismatches
of -0.3% above which cube morphologies predominate,
independent of size or volume fraction of gamma prime
(Merrick, 1978). When gamma prime precipitates as cubes,
the cube habit is (100) gamma//(100) gamma prime.
When the gamma prime precipitate size is small
(100-300 Angstroms), the coherency of the precipitate is
not lost and can be maintained by a tetragonal distortion
at the matrix/precipitate interface (Merrick, 1978). When
coherency is lost, the lattice mismatch between the two
phases can be accommodated by a dislocation network. This
network has been characterized for Ni based superalloys by
Lasalmonie and Strudel (1975). Since the morphology of
the gamma prime is a sensitive function of lattice
mismatch, it follows that this mismatch can be varied by
making alloy additions to the binary alloy which will
partition preferentially to one or the other of the two
predominant phases. In pure binary alloys, Phillips
reports this lattice mismatch at 0.53% (Phillips, 1966).
In ternary and higher order alloys, the mismatch is widely
variable due to elemental partitioning differences between
the two phases.
Gamma prime is a unique intermetallic phase. Its
major contributions to strength are the result of both
39
antiphase boundary formation and modulus strengthening
(Sims and Hagel, 1972). The strength of the gamma prime
increases with temperature, an anomaly not yet fully
explained. The phase also remains fully ordered to very
high temperatures (Pope and Garin, 1977).
In the early stages of gamma prime precipitation in
Ni-Al alloys, side band satellites in x-ray powder
diffraction patterns appear. These satellites were first
thought to correspond to periodic modulations in structure
(Kelly and Nicholson, 1963). These presumed modulations
lead to the speculation that the mechanism of Ni-Al
decomposition was spinodal. Cahn (1961) originally
suggested this possibility. The data of Corey et al.
(1973) and Gentry and Fine (1972) suggest that this
mechanism is possible at high supersaturations. Faulkner
and Ralph (1972) studied the early stages of precipitation
in a more dilute Ni-Al 6.5 wt.% alloy using FIM and
conclude that the spinodal ordering mechanism is
unlikely. They suggest that the sidebands are due to
particle morphology changes during the early stages of
decomposition.
The nucleation of the gamma prime could not likely
explain the "macro" order in the microstructure, the large
uniformly sized and distributed gamma prime precipitates
that are present in the alloys studied here. Ardell et
al. (1966) explain this ordered microstructure with a
40
model which explains the gamma prime alignment and uniform
size by considering the coarsening behavior of gamma prime
precipitates under the influences of mutual elastic
interactions between the coarsening gamma prime
precipitates. Ardell's model provides the most reasonable
explanation for the development of the microstructures in
alloys like those discussed in Chapter 5 of this
dissertation.
2.3 Diffraction Patterns: NiyMo Phases/Ni^Al
The reciprocal lattices of the various NixMo phases
can be constructed easily based on the crystallography of
each precipitate type. Since it is easiest to relate the
diffraction patterns of each to the parent FCC lattice,
(here the disordered gamma phase), this will be done for
the DO22 N3M0 phase. The other diffraction patterns were
similarly constructed.
2.3.1 DO?? Reciprocal Lattice
The DO22 is a tetragonal cell with atom positions at
Mo (000), (1/2, 1/2, 1/2);
Ni (1/2, 1/2, 0), (1/2, 0, 1/4), (1/2, 0, 3/4)
(0, 1/2, 1/4), (0, 0, 1/2), (0, 1/2, 3/4).
The structure factor can then be written as the summation:
F= Mof (1+exp ("IT i (h-f-k+1) ) + wif t (exP 71" i (h+k) ) +
exp(TTi(l)) + exp(tt(h+1 /2)) + exp(tr i(k+l/2)) +
exp(TTi(h+3l/2)) + exp(rr i(k+31/2)) L
41
h k 1
E 0 0
0 0 E
0 E 0
E E 0
E 0 E
0 E E
0 0 0
0 0 0
0 0 0
0 E 0
E 0 0
0 0 0
0 0 E
0 0 E
0 0 0
0 0 0
E 0 0
0 E 0
* A = 2fMo
+ B = 2fMo
Table 2.2 -- Structure Factor Values
F
A*
B+ if 1 = 2(n+1), n even OR
A if 1 = 2n
A
A
B if 1 = 2(n+1)
A if 1 2n
B if 1 = 2(n+1)
A if 1 = 2n
0
0
0
0
0
B
0
0
B
B
0
0
+
6fNi
2fNi
42
Substitution of values for h, k, and 1 yields the series
of values for F in Table 2.2
The DO22 reciprocal lattice constructed using those
values of F listed in Table 2.2 is shown in Figure 2.13a.
The lattice is constructed using DO22 coordinates and
compared to a corresponding FCC construction in the two
dimensional B = [100] and B = [001] sections shown in
Figure 2.13b. Note that both the (020) and (200) of the
DO22 correspond to the (020) and the (200) of the parent
FCC lattice since a/2 FCC = a/2D022* Also, the (004) DO22
= l/4(2a) (the "A" indices from Table 2.2) = a/2 FCC. The
fundamental reflections of the DO22 are then in the same
reciprocal lattice positions as the fundamental FCC
reflections. The (Oil), (022), etc. of the DO22 are 1/4
multiples of the FCC (042). This makes the Mo rich (Oil)
planes of the DO22 structure the (042) Mo rich planes of
the FCC parent lattice.
2.3.2 Dla/Pt2Mo/Ll2 Reciprocal Lattices
Similar constructions result in the reciprocal
lattices of N4M0 and N2M0, shown respectively in Figures
2.14 and 2.15, both lattices in FCC coordinates. The
reciprocal lattice of the FCC ordered gamma prime is shown
in Figure 2.16.
43
a.
004 0?4
002 042
000 020
.200 220
b.
Figure 2.13 The DO22 phase;
a.) the reciprocal lattice for the DO22
phase and b.) B= [010] left, [OOl] right,
DO22 left, FCC right.
44
02
022
Figure 2.14 The reciprocal lattice for Dla.
Figure 2.15 The reciprocal lattice for Pt2Mo.
45
Figure 2.16 The reciprocal lattice for the LI2
structure.
46
2.3.3 SRO (1, 1/2, 0) Scattering
In Ni-Mo binary alloys, SRO is characterized by
diffuse scattering at the (1, 1/2, 0) positions. (All g
vectors will subsequently be defined in FCC coordinates.)
Diffraction patterns of (1, 1/2, 0) SRO for B = [100] and
B = [112] are shown in Figure 2.19a. Characteristic of
this scattering is the absence of any true superlattice
reflection, for example, the (100) and (011) reflections
of either the DO22 or the LI2 superlattices. Because
gamma prime phase is always present in the alloys studied
here, any selected area diffraction pattern will always
contain LI2 superlattice reflections. Discriminating
between the DO22 superlattice reflections and scattering
at (1, 1/2, 0) SRO positions with superimposed LI2
superlattice reflections is difficult. There are two ways
to differentiate SRO from the LI2 and DO22 superlattices,
both of which are discussed in Chapter 5.
2.3.4 Variant Imaging
In section 2.2.3 of this chapter, a plethora of
possible variants for each precipitate were given. As
should be readily apparent from the reciprocal lattice
constructions of this section, only certain of these
variants are imagable with the electron microscope. Many
47
of the aforementioned antiphase boundaries are
indistinguishable.
2.3.4.1. P022: N3M0
There are three easily differentiated variants in the
DO22 structure, each corresponding to the c axis of the
DO22 being parallel to one of the cube axes of the parent
FCC lattice. This is shown in Figure 2.17a. All three
variants may be visible simultaneously. Indexed [001] and
[112] diffraction patterns are shown in Figure 2.19b.
2.3.4.2 Da: N4M0
Six distinguishable variants of Ni4Mo are possible.
These correspond to the tetrad axis of the Dla being
parallel to the parent FCC cube axes (three variants) and
further, the a axis of the N4M0 rotated cw or ccw about
the c axis relative to each FCC cube axis. Only two of
the six distinguishable variants will be visible along any
B = 100 imaging condition. These two are the single
axis clockwise and counterclockwise rotated variants shown
in Figure 2.18a. The B=[100] indexed diffraction pattern
corresponding to these two real space variants is shown in
Figure 2.18b. Indexed B = [001] and B = [112] N4M0
diffraction patterns are shown in Figure 2.19c.
a.
002
022
r¡
III
? A *
II
000
Alll 0
020
Fundamental
A
Superlattice
b.
Figure 2.17 The DO22 phase;
a.) DO22 variants along FCC axes
and b.) B = [lOO] SADP with variants
o
\ o o o .\ O
o \ o O *^o O \m
o o \ o # o ^ o J&r'
"o \ o #o\# o *-C5r o
o # o \* o -* o *\ o o'
o o .\o|o\. O^J^)-
Cr* o ' o § o'* o £r* o *\
A
o / o <£V / o / o
o^./o O/* o */o
^ / O # o / o '(A O
o / t. o # o 4 oi-
/ o / -f o o 0/
0^0 ./O# o/, o , O /
o*'* o O O / o ^
B
a.
b.
Figure 2.18
The Dla phase;
a.) Dla variants along FCC axes and
b.) B = [lOO SADP with variants.
50
C20
420
0 0 0 Q
s'
iv2o
000 200
220
0
y
y
s
y 0
402
a.
220
402
/
020 420
0 jm
0
9"
y
0 ^
0 0 j¡y
0
/
0
y u
a
000
Ooo
in
b.
020
420
0 0^,0''
ja'
s ^ -ffT a
^er
000
2 20
3
4 02
X
e y
0 y£ a
Ja 0 a
r
000 ii
0
0
020
2 2 0 4J>2
420
/
0 0 0 0 j£ 0 El
s'
0 a j-y
G
/
0 0^00 00
0
\
m
0
/
000 111
d.
Fundamental
a Superlattice
Figure 2.19 Indexed B = [001] and B = [Tl2]
reciprocal lattice sections of
a.) (1, 1/2, 0) S.R.O., b.) DO02,
c.) Dla, and d.) Pt2Mo.
51
2.3.4.3 Pt?Mo: NipMo
In N2M0, the imaging conditions are identical to
those for N4M0. The c axis of the superlattice may be
parallel to one of the cube directions in the FCC parent.
As in Dla, there are two orientation possibilities per
cube axis, as shown in Figure 2.20a. The real space
lattice and the corresponding B=[001] indexed diffraction
pattern are shown in Figures 2.20a and 2.20b. Indexed B =
[001] and B = [112] diffraction patterns are shown in
Figure 2.19d.
All of the above phases may be present
simultaneously. When this happens, all of the diffraction
patterns overlap.
*o
52
t
0 S Os 0*0 S Os o
jfo*Os m xos
0*.Z*os'XSO
O o#o r O o % o
/o*oyo40i o>o
^ o'^o O o'#
V V v
O *sO # o ^0,o # O
VO soA\o\X0 *
v,*x VO v,^ *p
Vo,* vO vA* *p
#o*0*o#*0*o
B
002
B A
ffl
b.
Figure 2.20 The Pt2Mo phase;
a.) Pt2Mo variants along FCC axes.
A and B can exist along each axis.
b.) B = [100] SADP with variants.
CHAPTER 3
EXPERIMENTAL PROCEDURE
3.1 Composition
Two major alloy compositions were chosen for this
investigation. They both represent potentially attractive
alloys for gas turbine blade applications. These two
alloys are designated as RSR 197 and RSR 209. They are
prepared by a powder metallurgy process developed at Pratt
and Whitney Aircraft Government Products Division. They
are two of a multitude of experimental alloys under
development for future high temperature turbine blade
materials. The RSR in the alloy designation is an acronym
for a rapid solidification process to be described
subsequently. The numbers 197 and 209 are arbitrary
numbers representative of the sequence in which the alloys
were prepared. The composition of these two alloys is
given in Table 3.1.
In the RSR process, the desired alloy is melted under
inert conditions (under argon gas) and allowed to impinge
in the molten state onto a rapidly rotating disc (Holiday
et al., 1978). The resulting spherical liquid metal
droplets are quenched in a stream of cooled He gas. The
powder is collected and canned under inert conditions.
53
54
In addition to alloys 197 and 209, an additional
ternary alloy was prepared by arc melting rather than by
the RSR process. The composition of this ternary, alloy
//17, was chosen as being representative of a compromise
ternary composition between the composition of RSR 197 and
RSR 209 (Table 3.1). The Ta and W were, of course, not
present in the ternary alloy.
Alloy 185, an alloy similar to RSR 209, was used for
only one experiment. Its composition is given in Table
3.1.
3.2 Heat Treatments
The canned RSR 197 and RSR 209 alloys were soaked at
1315 degrees C for four hours and extruded as bar at an
extrusion ratio of 43/1 at 1200 C. The extruded bars were
subjected to the various heat treatments described in
Figure 3.1. The heat treatments were conducted in a
vacuum furnace accurate to + 5 C. The times and
temperatures for these thermal treatments were chosen
based on the times and temperatures for aging binary Ni-Mo
alloys described in Chapter 2. The processing variables
are summarized in Figure 3.1.
The arc melted sample and an RSR 185 sample were
encapsulated in evacuated and He backfilled quartz tubing
prior to thermal treatment. The arc melted samples were
wrapped in four nines pure Ni foil to prevent reaction
55
with the quartz tube during solution heat treating and
aging. The arc melted samples were solution treated at
1315 C for four hours in a tube furnace and water quenched
upon completion of the solution treatment. RSR 185 was
prepared for electron microscopy directly after quenching
(Martin, 1982). Alloy //17 was re-encapsulated, as above,
and subsequently aged in a second tube furnace. The aging
practice is described in Table 3.1. Samples were water
quenched upon completion of aging.
3.3 Characterization: Methods of Analysis
Longitudinal slices were taken from the bar centers
of the extruded RSR alloys and from the center of the
sliced button, alloy //17, mechanically thinned to 130
microns, and jet polished in a solution of 80% methanol,
20% perchloric acid until perforated. The foil for the
RSR 185 alloy was prepared by Martin as described by
Martin (1982). Foils thus prepared were examined in a
Philips 301 Scanning Transmission Electron Microscope
(STEM) and in a special Philips 400 STEM. This latter
microscope is equipped with a field emission gun which
allows small, high intensity beams to be used in the TEM
mode. Special operating features of this microscope are
described in Section 4.1.1 of Chapter 4.
Four different electron diffraction methods were used
to generate the diffraction patterns shown and discussed
56
in Chapters 4 and 5. They are 1) selected area
diffraction (SAD), 2) Riecke method C-2 aperture limited
microdiffraction, 3) convergent beam diffraction, and 4)
convergent beam microdiffraction.
If the sample area selected by the selected area
aperture was reasonably strain free, that is, free of
buckling and bending, then the selected area diffraction
mode was used to generate large area diffraction
patterns. The area defined by the aperture was minimally
3 square microns. If this method could not be used
because of buckling and bending, the Riecke method
(Warren, 1979) was used. The area defined by this method
is much smaller than that defined by the selected area
method, about 0.6 square microns. This area is too small
to be representative of the sample as a whole. The above
two methods produce diffraction patterns that are similar
in appearance and application. They both produce fine
diffraction spots in the diffraction patterns and are thus
amenable to the detection of subtle scattering effects.
Convergent beam diffraction is a spatially localized
diffraction method. Only hundreds of square Angstroms are
analyzed. The diffraction pattern consists of large discs
rather than diffraction spots. Subtle diffraction effects
are usually masked by the elastic intensity distributions
in these discs. The elastic information in the discs
57
makes the convergent beam method uniquely suitable for
other purposes, however. These are reviewed in the
following chapter.
Convergent beam microdiffraction is also a spatially
localized diffraction method. Again, only hundreds of
square Angstroms are analyzed. The diffraction pattern
consists of discs rather than spots. These discs are
quite small in comparison to normal CBED discs and may be
dimensionally comparable to the spots seen in selected
area and Riecke patterns. If subtle diffraction effects
are present, they will not be masked if this diffraction
method is used.
In addition to electron diffraction, the electron
microscopes were used to produce bright field, dark field,
and lattice images. The 400 FEG instrument was also used,
in conjunction with a KEVEX energy dispersive x-ray
detector and a DEC 1103 minicomputer, as an analytical
x-ray system for x-ray analysis of the RSR alloys. The
data reduction scheme for quantification was developed by
Zaluzec (1978) Details of these analyses are discussed
in the following chapter.
To test the accuracy and applicability of the
convergent beam diffraction method for the measurement of
local lattice parameters, the lattice parameters of the
RSR alloys were measured using x-ray diffraction. The
58
measurements were made with a General Electric horizonal
main protractor diffractometer using Ni filtered Cu
K-alpha radiation. Data thus generated were also used to
measure the lattice mismatch between the gamma and gamma
prime phase in the RSR alloys.
Rockwell C microhardness measurements were made on
most of the RSR aged alloys. Six hardness values from
each sample were recorded.
ARC MELTED
Figure 3.1 Processing Variables
60
Table 3.1 Alloy Compositions
RSR 197
RSR 209
RSR 185
//17
at% wt%
at% wt%
at% wt%
at7o wtT,
Ni
76.0 73.9
74.0 72.6
73.8 72.6
77.0
A1
13.0 5.8
15.0 6.8
15.0 6.7
14.0
Mo
9.0 14.3
9.0 14.4
9.0 14.4
9.0
Ta
2.0 6.0
W
2.0 6.1
2.0 6.0
Y
.015
LO
I1
o
C
.2
--
CHAPTER 4
SPECIAL METHODS
This chapter will explain the methods used to measure
the partitioning of elements to the gamma and gamma prime
phases. The convergent beam diffraction method is one
method described extensively in this chapter. Simple
equations are developed which aid in interpreting the
patterns and further allow simulated patterns of
experimental patterns to be generated. The results of the
lattice parameter measurements and strain measurements
made using the CBED method are given in Chapter Five.
Chapter Four also includes a brief section on energy
dispersive analysis, specifically as it relates to the
characterization of the alloys analyzed in this study.
4.1 Convergent Beam Electron Diffraction
(CBED)Methods
A convergent beam electron diffraction pattern is
similar to a selected area diffraction pattern with one
major and self-defining difference: a convergent beam
pattern uses a focussed beam with a large convergence
angle to define the area from which the diffraction
61
62
pattern will be taken. Beam convergence angles generally
range between 2 x 10"3 rads to 20 x 10"3 rads. The
resulting pattern consists of a number of diffracted
discs, each disc corresponding to a diffracted beam.
The selected area diffraction pattern is formed using
a large beam that is essentially parallel. The area from
which the diffraction pattern is taken is defined by an
aperture, the selected area aperture. Beam convergence is
usually on the order of 1 x 10"^ rads. The resulting
pattern consists of diffraction spots. Each spot
corresponds to a diffracted beam.
The convergent beam electron diffraction (CBED)
pattern is usually formed in the back focal plane of the
objective lens, just as is the diffraction pattern in the
selected area diffraction mode (Steeds, 1979). The CBED
pattern contains a wealth of information about the
crystallography of the diffracting crystal, in many cases
much more information than is contained in the selected
area diffraction pattern. This information appears in the
discs of the pattern and can be used in 1) identification
of the diffracting crystal's point and space groups
(Buxton et al., 1976), 2) identification of Burgers
vectors (Carpenter and Spence, 1982), 3) the measurement
of local lattice parameters (Jones et al., 1977), 4) the
measurement of foil thickness (Kelly et al., 1975),
63
and 5) the measurement of uniform lattice strain (Steeds,
1979) .
4.1.1 Experimental Technique
There are a number of methods for forming the
convergent probe. The most common method in modern STEM
instruments is to use the STEM "spot" mode to translate
the already convergent probe to the area from which the
pattern will be taken. In the STEM mode, the imaging and
projector lenses are already configured to form a
diffraction pattern. Convergence in the probe is
controlled by the selection of a suitable second condenser
aperture. Suitable is defined as the maximum aperture
size that will still give discreet, non-overlapping discs
in the diffraction patterns. The covergence angle alpha
is defined as the angle subtended by the radius of the
disc. Choice of the proper aperture size will obviously
depend on the lattice parameter and orientation of the
crystal from which the pattern will be taken.
Even more simply, the probe may be focussed directly
in the TEM mode, a situation which yields acceptable beam
convergence but usually with large probe sizes. Once the
probe has been focussed using the condenser controls, the
proper lens excitations to image the diffraction pattern
are selected, usually by selecting the diffraction mode of
the instrument, and a CBED pattern results.
65
crystal diffracting conditions will appear in the
diffracted discs. As focus is more closely approached,
the magnification of the images in the discs will increase
until, at focus, the magnification in the discs reaches
infinity. By watching the image "blow-up" in the disc,
the exact location of the beam on the sample can be
monitored. This technique is referred to as the shadow
technique (Steeds, 1979). The image in the transmitted
disc is the shadow image. This method is the only sure
way to eliminate diffraction error that is generally
present if the probe is focussed in the imaging mode
rather than in the diffraction mode, as just described.
(Diffraction error is the noncoincidence of the probe
position in the imaging and diffraction modes
respectively.) If the probe is formed by overexciting the
objective lens, the resulting out of focus image is the
shadow image. There is thus no diffraction error if this
latter technique is used to form the convergent probe.
Diffraction error is not a serious problem and can be
easily eliminated. In any event, it does not affect the
information that is present in the pattern, only the area
from which the information is taken. This information is
usually confined to the discs of the diffraction pattern.
There can be considerable detail in both the diffracted
and transmitted discs, depending on the diffracting
conditions under which the pattern is formed.
64
Alternatively, the objective lens may be overexcited
in the TEM mode (a situation that approximates a STEM
condition), and the probe then focussed with the second
condenser lens. The resulting probe will be smaller than
a conventional TEM probe, but generally, depending on the
amount of overexcitation, larger than the standard STEM
probe (Steeds, 1979). Under this condition, the
diffraction pattern appears in the imaging plane of the
objective lens rather than in the back focal plane. The
lens optics for this condition cannot be found in standard
texts. The reader is referred to Olsen and Goodman (1979)
for details.
The method chosen for this investigation uses the
focussed TEM probe. The beam convergence is controlled by
the size of the second condenser aperture. After
selection and centering of the proper C-2 aperture, the
diffraction mode of the instrument is selected and the
condenser lens is brought to crossover. The result is a
focussed convergent beam and the image will be a focussed
convergent beam diffraction pattern. The beam is not
imagable under this condition. As the beam is focussed
(as the condenser lense is brought to crossover), the
second condenser aperture will become visible as a disc in
the diffraction pattern and a bright field image of the
sample will appear in the central transmitted disc of the
pattern. Dark field images corresponding to the various
66
The applications of this information to materials
science were discussed earlier in this chapter. The
information in the discs includes 1) HOLZ (High Order Laue
Zone) lines, for lattice parameter measurements and for
pattern symmetry determinations, 2) Pendellosung Fringes,
used in making foil thickness determinations, 3) the
shadow image, used for tilting the sample and placing the
beam, and 4) dynamical features (absences and excesses)
that reveal detailed information about the crystal space
group for crystal symmetry and space group
determinations. Since HOLZ lines were used extensively in
this study, they are described in more detail below.
4.1.2 HOLZ Lines (High Order Laue Zone Lines)
A HOLZ line is a locus of diffracted beams. It is
the result of elastic scattering from Laue zones beyond
the zero order zone. HOLZ lines are analogous to Kikuchi
lines in two respects. First, they are a Bragg
diffraction phenomenon, and second, they result in lines
rather than diffraction spots. Like Kikuchi lines, the
spacing between the HOLZ lines in the diffracting disc and
the transmitted disc represents the spacing of the planes
that are responsible for Bragg diffraction in the HOLZ.
It is only necessary to index the discs that are
diffracting in the HOLZ to determine which lines in the
ZOLZ (Zero Order Laue Zone) correspond to these
diffracting discs. Any HOLZ line in the ZOLZ will
67
be parallel to its counterpart in the HOLZ, analogous to
excess and defect lines in Kikuchi patterns. It is the
HOLZ lines in the ZOLZ that are used for most HOLZ line
measurements.
An example of what one expects to see in a
transmitted disc containing HOLZ lines is shown in Figure
4.1. The lines in the disc (labelled a in the figure) are
the HOLZ lines. The lines outside the discs but seen as
continuations of the HOLZ lines (labelled b in the figure)
are the Kikuchi lines. The Kikuchi lines extend across
the transmitted disc, thus overlapping the HOLZ lines in
the disc.
The clarity and contrast of the HOLZ line patterns
and the accuracy of the HOLZ line positions are dependent
on at least five factors. First, there are limitations to
the thickness of the diffracting crystal (Jones et al.,
1977). This thickness should usually be on the order of
100-200 nm. If the crystal is much thicker, excessive
diffuse scattering in the ZOLZ will attenuate the HOLZ
lines entirely; if much thinner, no HOLZ lines will be
present at all.
Second, the energy loss as the beam is transmitted
through the sample added to the inherent energy spread of
electron sources (i.e., W filament, LaBg, or FEG) can
affect the accuracy of the line position. This energy
loss will affect the thickness of the HOLZ line, reducing
the accuracy to which it can be measured. Foil
69
thickness can also affect the HOLZ line thickness (Jones
et al., 1977).
Third, tilting the crystal away from normal
perpendicular incidence means a different thickness may be
encountered across the diameter of the beam with a
consequent change in intensity across the pattern.
(Recall that the beam is convergent.) This is not usually
a problem since only the intensity, not the actual line
position, is affected.
Fourth, the distortion in the pattern introduced by
the objective lens can affect the accuracy of direct
measurements in the Higher Order zone (Ecob et al.,
1981). Since one almost always uses zone axis patterns to
generate HOLZ information, the final tilt necessary to
obtain an exact zone axis pattern can be accomplished by
tilting the beam rather than tilting the sample. This
tilting can be done in two ways. The beam can be tilted
electronically using the deflector system of the
instrument, or the beam can be tilted by displacing the
second condenser aperture. Either of these procedures is
easier than tilting the sample using the goniometer
controls of the microscope stage. However, a beam
entering the objective lens off axis is subject to the
inherent spherical abberation effects of the lens. The
abberation increases with increasing off axis angle,
degrading the accuracy of the pattern. For this reason it
is best to tilt the sample as close to the exact zone
70
axis orientation as possible using the goniometer tilt
controls, rather than tilting the beam. This will not in
itself completely eliminate the spherical abberation
effect since diffracted beams from the higher order zones
must enter the lens at large angles anyway. It is thus
more accurate to use the HOLZ line in the transmitted disc
than its counterpart in the HOLZ ring. The subsequent
image forming lenses of the instrument will also impart
radial and spiral distortion to the diffraction pattern.
These distortions are minimized on the optical axis of the
instrument.
Fifth, the ubiquitous presence of carbonaceous matter
both in the microscope and on the sample surface can lead
to contamination spikes at the specimen/beam interface
with a consequent attenuation of the beam current, a loss
in spatial resolution due to scattering, and the
introduction of astigmatism into the beam due to
charging. All of these are undesirable. Methods for
reducing contamination have been reviewed elsewhere (Hren,
1979). Contamination and its effects were minimized in
this study by using the minimum practical time to focus
the diffraction pattern, to tilt to the proper
orientation, to determine the exposure time for each
pattern, and to record the image.
In consideration of the above effects, the following
procedure for obtaining HOLZ patterns is recommended:
71
1. The crystal should be tilted to the approximate
zone axis using the shadow technique. This greatly
simplifies tilting in polycrystalline samples.
2. An area in the crystal that is the proper
thickness for good HOLZ line formation should be found.
3. The sample should be in focus at the eucentric
position. These two conditions will insure that the
objective lens excitation is constant for every pattern
thus standardizing both the camera length and the
convergence angle for each pattern.
4. The condenser aperture should be centered.
5. The sample should be tilted to the exact zone
axis, again using the shadow image technique.
(By iterating between 5 and 3, a good zone axis
pattern can be obtained.)
6. The spot exposure meter should be used to
determine the proper exposure time for recording the
diffraction pattern.
Under the above conditions, only STEM and focussed
TEM probes should be used for generating the convergent
beam. If a convergent probe is formed using the
overexcited objective lens method, the sample must still
be at the eucentric position, but since the image will not
be focussed, the objective lens current must be recorded
so that it may be reproduced for each subsequent pattern.
72
4.1.3 Indexing HOLZ Lines
There area a number of ways to index HOLZ lines
(Steeds, 1979; Ecob et al., 1981). The approach taken in
this study is somewhat different from the approach
described in the above references in that the actual HOLZ
diffracting conditions are calculated. This method gives
a more intuitive feel for HOLZ detail and permits a more
rapid indexing of the patterns. The subsequent use of the
HOLZ lines for lattice parameter measurements is similar
to that developed by Jones et al. (1977).
To calculate the HOLZ line positions, one need only
determine the intersections of the Ewald sphere with the
reciprocal lattice beyond the zero order zone of the
reciprocal lattice. The equations necessary to do this
for a cubic crystal are presented below.
Let h, k, 1 be the Miller indices of
planes in the diffracting crystal.
These will also define the g vector for
the diffraction pattern.
Let a be the lattice parameter of the
material.
Let U, V, W be the idices of the beam
direction, B, in the crystal. These
indices are, by convention, given in
crystal coordinates. They are also
taken as antiparallel to the actual beam
direction in the instrument.
In reciprocal space, the center of the Ewald sphere for
the cubic crystal will be at
UR/|B|, VR/|B|, and WR/|B|, where R = 1/ .
73
Values of h, k, 1 which satisfy the following equation are
simultaneous solutions to the intersection of the Ewald
sphere with the reciprocal lattice:
(h/a UR/|B|)2 + (k/a VR/|B|)2 + (1/a WR/|B|)2 = R2.
Expansion and rearrangement of this equation yield
h2+k2+12 + R2.1U2+V2+W2) 2 (hU+kV+lW) R = R2.
a (U2+V2+W2) 3 T5T
This can be simplified to
h2+k2+l2
(1)
This equation says that the sum of the squares of the
planar indices of a diffracting plane is equal to a
constant for a given electron accelerating potential,
lattice parameter, beam direction and cubic Bravais
lattice type.
To solve the equation, one must know the microscope
accelerating potential, the approximate lattice parameter
of the examined crystal, and the beam direction in the
crystal. The accelerating potential is never known to
great accuracy. When only relative and comparative
lattice parameter measurements are to be made, this
uncertainty cancels. The lattice parameter can be
approximately derived from either a calibrated selected
area diffraction pattern, or from a calibrated CBED
pattern. The beam direction must be known.
74
To solve equation (1), only the value of g*B needs to
be derived (we assume here that the other information is
at hand). The values of gB will depend on the specific
cubic Bravais lattice.
For an FCC crystal, as for both the matrix and the
gamma prime phase in the RSR alloys, diffraction pattern
planar indices cannot be mixed. The three values of g in
g*B will thus be all odd or all even. Indices for the
beam direction can be reduced to three combinations of
terms: B is odd, odd, odd; B is odd, even, even; and B is
odd, odd, even. The following cases are constructed to
show values for the dot products of unmixed g indices and
the three combinations of B terras given above.
Case 1) B h,k,l Case 2) B h,k,l Case 3) B h,k,l
0
E
0
E
lQ
E
0
0
E
0
0
E
0
0
E
0
0
E
E
E
E
0
0
E
0
0
E
E
E
E
E
E
E
The first case will be used as an example. If B is all
odd, for example, B = (111), the individual terms in the
dot product of this B and an odd set of g indices will
contain all odd terms. The algebraic sum of all odd terms
is odd. For this case, g*B can equal one, since one is an
odd term. The results in Case 2 are the same. For
Case 3, the algebraic sum will always be even. For this
case, g*B will equal two. These results can be
generalized as follows: if U+V+W = even, g*B will
75
equal two. If U+V+W = odd, g*B will equal one. This
calculation applies only to the first order zone.
Most of the CBED patterns in this study were taken
from the gamma prime phase, an LI2 superlattice. In such
a superlattice, the superlattice reflections appear in the
forbidden positions for FCC. The true first order Laue
zone for U+V+W = even will consist only of superlattice
reflections. The first zone can be clearly seen in Figure
4.2, a B = CBED pattern of the gamma prime phase in
alloy RSR 197. These superlattice reflections are usually
too weak to give HOLZ lines in the central disc. Only the
HOLZ lines from the B = <114)>- "second" order zone were
used in this study. This "second" zone will hereafter be
referred to as the first order zone (FOLZ) since it in
fact corresponds to the first order zone for a typical FCC
crystal.
An alternate way of deriving the preceding result is
through construction of the Ewald sphere and geometrical
solution of the intersection with the reciprocal lattice.
With reference to Figure 4.3^
the angle 0 equals 9' by similar triangles.
Then Sin 9' = H/|g|/2R and Sin 9' = H/|g|.
Combining these two equations gives g2 = 2RH.
By definition, g2 = l/d^ = (h2+k^+l2)/aQ2.
Substituting for |g|2 gives h2+k2+l2 = 2a2 RH.
H can be shown to equal (g*B/a ) (u2+v2+v/2) 1/2.
Therefore, h^+k2+l2 = (2aR/|B|)(g*B).
78
At this point, both the graphical and calculated
methods yield a solution that is valid for a single beam
direction only. Neither method has included the effect of
the beam convergence. There are numerical methods for
including this convergence (Warren, 1979). An alternate
way is to calculate an upper and lower limit of h2+k2+l2
values for a given beam convergence angle. This approach
provides a useful and intuitive estimate of the
convergence effect. It has the shortcoming of slightly
overestimating this effect. A more rigorous method is
described in a following section.
For a given |B|, gB = |g||B|*cos.
Let K2 = Ki (gB) where Ki = 2aR/|B|.
Terms aQ, R, and B are as previously defined.
Then K2 = |g|2 = [g-B/( | B | cos) ]2
and = cos'1 (g.B/(|B|)(K2)1/2).
Two limiting values of h2+k2+l2 (limiting values of
k£), can now be calculated:
K2
1
(B_Lg)2
TfB | cos ( +<*) J 2
>
k22 = (B_ig)2
L |B|cos-<) J2 ,
where < is the convergence angle.
79
Values of h2+k2+l2 between these limiting K£ values will
define a plane (h,k,l) that will diffract in the FOLZ. As
an example, consider the solution to a CBED pattern from
the gamma prime phase of RSR 197. The approximate
constants for substitution into the equations are
aQ 3.36,
R = 27.07 (100 keV electrons),
B = <114>,
and alpha = 2.5 x 103 rads.
The calculated values of and are 101 and 82,
respectively. Any plane h, k, 1 with values of h2+k2+l2
between 82 and 101 which also satisfies the g*b = 2
criterion will diffract under Bragg conditions and will
thus yield a FOLZ line in the transmitted disc. Possible
values are given in Table 4.1.
The value of K2 for the zero convergence case is the
exact Bragg solution. It is seldom an integer. If its
value were an integer, a set of conditions could be
achieved that would yield some set of FOLZ lines directly
through the center of the pattern. For example, for the
case just calculated, h2+k2+l2 = 90.713. This value is
very close to the exact solution for h2+k2+l2 (h=9, k=3,
1=1) = 91.0. The (931) lines should pass almost directly
through the center of the transmitted disc. They could be
made to pass directly through the center by either
increasing the alloy lattice parameter from 3.560 to 3.571
Angstroms, or by changing the accelerating potential
80
of the microscope to adjust the wavelength. This latter
can now be done to great accuracy in most modern STEM
equipment.
The advantage of having all of one type of line
passing directly through the center of the pattern is
explained below. If it were possible to have all of one
line type (the £931^ 1 ines for a B =(ll4^pattern) in the
center of the pattern, a reference microscope operating
potential could then be defined for that particular
lattice parameter. For a material of different lattice
parameter, the difference in accelerating potential
required to bring the lines to the center of the pattern
compared to the reference would be proportional to the
difference in lattice parameter between the two materials
(Steeds, 1979). To measure a change in lattice parameter
in this way, one would merely note the change in
accelerating potential required to achieve identical
patterns in the central disc.
To more rigorously solve the effect of beam
convergence on HOLZ line formation, the Bragg angle and
the actual angle the beam makes with each specific HOLZ
diffracting plane must be determined. For example, for B
= ^114^, a = 3.56, and R = 27.07 (100 kV electrons), the
calculated value for h2+k2+l2 using equation (1) is
90.713. Because this number is not an integer, the Bragg
condition in the first order zone is not satisfied for B =
^114^. Consider a second beam direction B'.
If B1 were
81
Table 4.1 HOLZ Planes
hkl
h^^fl2
g*'
Yes
7 5 1
75
X
7 5 3
83
7 5 5
99
7 7 1
99
7 7 3
107
X
8 4 0
80
8 4 2
84
8 4 4
96
8 6 0
100
X
8 6 2
104
9 11
83
9 13
71
X
9 15
107
9 3 3
99
10 0 0
100
10 2 0
104
X
10 2 2
108
2 Indices for B=[114]
No
X
X
X
X
X
X
X
X
X
X
X
751 571
773
860 680
913 193 931 391
1002 0102
X
82
inclined slighty to B (Fig. 4.4), it might be possible for
B* to satisfy the Bragg condition for the above value of
h2+k2+l2. Fortnuately, it is not necessary to calculate
the indices of B1. One first calculates the Bragg angles
for the planes that can diffract in the FOLZ (those planes
listed in Table 4.1) and then calculates the actual angle
these planes make with the given beam direction, in this
case, the ^114^. If the difference between theta a, the
angle the low index beam makes with the plane, and theta
b, the calculated Bragg angle for that plane, is less than
alpha, the angle of convergence, then that diffracting
plane will produce a FOLZ line. This situation is
described in Figure 4.5. If theta a and theta b are both
plotted against h2+k2-fi2} the two intersecting curves in
Figure 4.5 result. Note that the two curves intersect at
the value of h2+k2+l2 calculated from the equation. Any
convergence angle up to 4.8 mrad can be superimposed onto
this figure and the resulting range of h2+k2+l2 values
determined. For an alpha of 2.5 x 10~3 rads, this range
of values is 100 to 83, a slightly smaller range than
determined by the first method.
Once the range of h2+k2+l2 values has been determined
and the actual indices assigned as in Table 4.1, it is a
simple matter to index any pattern for the FCC crystal.
One first indexes the zero order Laue zone (ZOLZ) in the
normal way (Edington, 1976). This zero order indexed
pattern is shown in Figure 4.6 for a [114] CBED pattern
83
A= Alpha, the convergence angle
0,= Bragg angle
0 = Calculated angle between B and
diffracting plane
Figure 4.4 Method for determining HOLZ line formation
limits for a given convergence angle.
r
Figure 4.5 Plot of data for 100 KV, a=3.56
Angstroms, B=(114^, from Figure 4.4.
86
from the FCC gamma prime phase. One then calculates the
angles between the planes represented by any zero order
indexed spot and the FOLZ reflections listed in Table
4.1. The indexed spots in the FOLZ using the calculated
angles are shown in Figure 4.6. The indexing in the FOLZ
must be consistent with the indexing in the ZOLZ. Once
the FOLZ reflections have been indexed, the HOLZ lines in
the central spot can be indexed. The lines in the pattern
center are parallel to the lines through the FOLZ discs,
as illustrated in Figure 4.7.
One advantage to indexing patterns from the
calculations is that the line pattern in the central spot
can be indexed directly without first indexing the
reflections in the HOLZ. An indexing of a B = [114] line
pattern is shown in Figure 4.8. To index in this way, one
first identifies the line types using Table 4.1. Next,
one finds the lowest symmetry line, if it exists, and
indexes it. This is easily done in this pattern for the
773 line. One then finds the next lowest symmetry lines
and indexes them, and so on. The sign of the vector cross
product between these lines must be consistent with the
choice of beam direction. The direction of g can be
determined from Table 1. The remaining lines are then
indexed using the calculated interplanar angles (Figure
4.6). The angles measured between HOLZ lines are slightly
different from the calculated values. In addition to
normal measurement error, these measured angles are
89
projected from the higher order zone onto the zero order
zone and are different from the calculated ones. The
difference is explained in Appendix B.
Once the FOLZ has been indexed, FOLZ line positions
in the transmitted disc can be used to determine relative
lattice parameter differences and can be used to measure
small symmetry differences due to crystallographic changes
as a result of alloying, strain, or transformation.
4.1.4 Lattice Parameter Changes
The easiest way to visualize the changes in the FOLZ
line position in the central spot that accompany changes
in lattice parameter is to look at a few examples of
patterns to see what happens when the lattice parameter is
varied. Figure 4.9a illustrates a case where the lattice
parameter of a diffracting crystal is such that at 100 kV,
the four 931 lines in a B = ^114^ pattern pass exactly
through the center of the transmitted disc. This is
equivalent to saying that the Bragg condition is satisfied
for g = (93l) when B = ^114^. For this to be true, the
lattice parameter of the crystal must be exactly 3.5712
Angstroms. If the lattice parameter is greater than this,
a pattern like that shown in Figure 4.9b will result. If
the lattice parameter is less than 3.5712 Angstroms, the
pattern will look like Figure 4.8c. The shaded area in
the figure outlines the symmetry changes. This change is
91
exagerated compared to the micrographs. The calculations
required to determine the line positions of the patterns
are summarized in Appendix A.
Since only a relative change in lattice parameter can
be realistically measured, measuring this relative change
involves measuring and quantifying changes in the HOLZ
line positions from one pattern to the next. This is
easily and most accurately accomplished by using HOLZ
lines that both intersect at shallow angles, and most
desirably, that move in opposite directions to one another
when the lattice parameter is varied. Distances between
intersections are then measured and these distances
ratioed for different values of absolute lattice
parameter. Figure 4.10 is a plot of the ratio a/b versus
relative change in lattice parameter. Parameters a and b
are defined in Figure 4.9. The calculation of the values
for Figure 4.10 is given in Appendix A.
4.1.5 The Effect of Strain and Non-Cubicity on
Pattern Symmetry
If a previously cubic crystal is nonisotropically
strained or has become noncubic due to transformation or
change in order, the CBED pattern will reflect this change
by a reduction in the symmetry of the HOLZ line pattern.
The CBED technique is especially sensitive, theoretically
capable of detecting changes in lattice parameter on the
order of two parts in ten thousand at 100 kV (Steeds,
3.60
.59
o
S-
58
^ r* -7
en 57
c:
.56
(V
4->
O)
| .55
rd
Q_
S -54
.53
.52
.51
3.50
.7 .8
.9 1.0 1.1
RATIO a/b
Figure 4.10 Plot of lattice parameter verses the
ratio of a to b (a and b defined in
Figure 4.9).
93
1979). This would of course apply to nonsymmetrical
changes in lattice parameter as well. The magnitude of
these nonsymmetrical changes can be deduced by measuring
the change in HOLZ line positions as the lattice parameter
changes, described in the preceding section.
Again, the easiest way to visualize the effects of
crystal asymmetry is to look at a few examples of CBED
HOLZ patterns to see how this asymmetry affects HOLZ line
position. The direction of shift of the lines will depend
on the orientation of the now noncubic crystal with
respect to the beam direction. For example, if the
expansion or contraction is along the c axis, the c
direction defined as being parallel to the beam, the
symmetry of the pattern changes very little. If the beam
is a parallel to either of the a or b cube axes, the
change in symmetry is very marked, as shown in Figures
4.11a, 4.11b, and 4.11c. The method for calculating these
HOLZ line patterns is explained in Appendix A.
It is not straightforward to differentiate symmetry
changes from lattice parameter changes to arrive at a
measure of both lattice parameter and loss of cubicity.
Ecob et al. (1981) simulated CBED HOLZ line patterns to
measure the lattice parameter differences in gamma/gamma
prime alloys, and to measure the changes in symmetry of
the gamma prime phase after recrystallization. The
simulations were then compared to actual patterns.
Numerous trial and error iterations would usually
b.
a.
c.
Figure 4.11 The effect of non-symmetrial changes in
the lattice parameter on the symmetry of the
transmitted HOLZ pattern; a.) a, b, and c
3.5713 Angstroms, b.) a, b, and c 3.5713
Angstroms, and c.) a = 3.5713, b and c a.
The mirror symmetry in the pattern has been
lost. The mirror is perpendicular to this
caption.
95
provide an adequate match. They used the B = (111)
pattern to make these measurements. This pattern is a
simple one to analyze because of the threefold symmetry in
the ZOLZ transmitted disc. This pattern could not be used
in the study of the Pratt and Whitney alloys, however,
because of the microstructural scale in these alloys.
When the sample is in a B = (111) orientation, the gamma
prime precipitates usually overlap either the gamma phase
or the gamma phase and another gamma prime precipitate.
The result is either a highly distorted HOLZ pattern or no
pattern at all. If B = (114), the beam is more closely
parallel to the 100 direction; 19 degrees from the B =
(100) direction. Eades (1977) used this orientation to
study the gamma/gamma prime mismatch in In-100, a Ni-based
superalloy. The B = (114) CBED pattern can be used to
measure both lattice parameter and noncubicity. The
method is outlined in Appendix A.
The B = pattern has been used recently by
Braski (1982) and by Lin (1984) to measure lattice
parameter change in ordered alloys. In both cases, the
microscope accelerating voltage was continuously variable,
meaning that the HOLZ line positions in these patterns
could be varied. Because the B =(111) pattern in a cubic
material always exhibits either sixfold or threefold
symmetry, it is always possible to find three FOLZ lines
that can be made to pass directly through the center of a
CBED pattern, and hence intersect at a point in the
96
center of the pattern. If a lattice parameter measurement
is to be made using the relative voltage differences
required to go from one three line point intersection to
another three line point intersection, this measurement
cannot be accurate if any noncubicity is present. Braski
alluded to the nonacceptability of using the B = (^11*0
patterns for his measurements because of the sensitivity
of this pattern for noncubic effects. All patterns are
sensitive to strain effects.
There should be other CBED zone axis patterns that
could be used to make the measurements for which the B =
<.114> pattern was used in this study. The B = <.100>
pattern would be the most crystallographically sensible.
There is no gamma/gamma prime overlap along this
direction.
Using equation (1), it is simple to calculate the
expected HOLZ for B = ^001^.
At 100 kV:
R = 27.07,
aG = 3.56 Angstroms,
B = <001>,
gB = 1, and
h2+k2+l2 = 193.
The Bragg angle for this F0LZ ring is about 4.2 degrees at
100 kV. This means the F0LZ will be 8.4 degrees from the
center of the pattern, far from the transmitted spot and
97
hence possibly too weak to give strong FOLZ lines in the
central spot.
If the accelerating potential of the microscope is
lowered, the FOLZ ring will move in toward the center of
the pattern. The scattering amplitude increases as the
ring moves in and the diffracted intensity consequently
increases (Steeds, 1979).
4.2 Energy Dispersive Methods
The use of energy dispersive x-ray analysis is a well
established means of characterizing the compositions of
materials on a microscale (Goldstein, 1979). The effects
of various experimental variables on the accuracy and
precision of the final EDS results are of paramount
importance. These effects have been reviewed extensively
elsewhere (Zaluzec, 1979). They are summarized here as 1)
instrument related, 2) specimen related, and 3) data
reduction related. Care must be taken in defining the
effects of all three if an accurate result is to be
obtained.
Consider first the instrument and its effects.
Microscopes of the late 1970's vintage are generally less
than perfect experimental benches for x-ray
microanalysis. In unmodified instruments, many
uncollimated electrons and x-rays make their way to the
specimen environment where they then contribute to the
x-ray signals that are supposed to be generated only by
98
the local interaction of the specimen and the beam. These
stray electrons and x-rays can be mostly eliminated by
proper specimen shielding and by proper design of the
column. The 400T STEM at Oak Ridge National Lab is
properly modified to minimize spurious x-ray fluorescence
through the use of top hat condenser apertures, and to
reduce sprayed, uncollimated electrons through the use of
spray apertures below the condenser lenses. Hole counts
are consequently low, in the neighborhood of 1 to 2
percent of the total elemental counts when the beam is on
the sample. A hole count spectrum was always accummulated
for each specimen and subtracted from each specimen
generated spectrum before any subsequent curve fitting and
peak deconvolution (Zaluzec, 1979).
The specimen related effects are more difficult to
assess. These effects are primarily due to absorption of
specimen generated x-rays by the specimen itself. The
most common method for quantitative analysis in the
analytical TEM follows the Cliff-Lorimer equation (Cliff
and Lorimer, 1972). This equation relates the ratio of
the concentrations of unknowns in the sample to the ratios
of the beam generated x-ray itensities:
CA/CB = (K) IA/lB,
The major assumption in the equation is that the k term,
the proportionality constant, is independent of the
specimen thickness. This assumption is not valid
99
in the alloys that were characterized in this study.
The proportionality constant can either be measured,
in which case the standard from which it is measured must
satisfy a criterion called the "thin film criterion," a
criterion that defines the maximum thickness of the
standard, or the constant can be calculated. Both of
these methods are outlined by Goldstein (1979) and Zalusec
(1979) It is primarily the effect of thickness on the k
term in the Cliff-Lorimer equation that defines the
specimen related effects. This thickness effect is a very
serious problem in Ni-Al alloys. The aluminum x-rays are
preferentially absorbed by the Ni, to the extent that the
thin film criterion in Ni-Mo-Al of RSR composition is not
satisfied for thicknesses in excess of about 600
Angstroms.
The ternary alloy //17 will be used as an example of
how thickness affects quantitation. A large beam was used
in an attempt to measure a "bulk" composition of the
alloy. The results are summarized below:
Nominal Composition
Ni
Mo
A1
wt.%
78.5
15.0
6.5
at .X
77.0
9.0
14.0
X-Ray Results
No thickness correction
wt.%
79.2
15.6
5.22
No thickness correction
at.%
79.1
9.5
11.3
1000 Angstrom correction
wt.%
78.8
15.5
5.6
100
1000 Angstrom
correction
at.%
78.4
9.4
12.2
1500 Angstrom
correction
wt.%
78.7
15.4
5.9
1500 Angstrom
correction
at.%
78.0
9.4
12.7
1800 Angstrom
correction
wt.%
78.6
15.4
6.0
1800 Angstrom
correction
at.%
77.7
9.3
13.0
The value corrected for a thickness of 1800 Angstroms
is quite close to the actual composition of the alloy.
The actual thickness of the sample is unknown. The data
show, however, a 20% difference in total aluminum as a
result of absorption. In all subsequent spectra, a
specimen thickness of 1000 Angstroms was presumed.
In this research, every effort was made to reduce
specimen related artifacts by orienting the specimen such
that the absorption path length was minimized between the
flourescing area of the sample and the detector, and by
orienting the crystal so that only the desired phase was
analyzed. Because the detector was a horizontal detector,
this was a significant limitation. It was necessary to
orient the crystal as close as possible to a B =C.100^
direction in order to minimize gamma/gamma prime phase
overlap.
A further complication was contamination. The
effects on spatial resolution are well documented (Hren,
1979). In order to generate sufficient signal for
adequate statistics, it was necessary to count for very
long times, usually in excess of 100 seconds. No data
101
was ever accumulated for more than 20 seconds without
interrupting the analysis, checking the probe position,
and if contamination were noted, repositioning the probe
to an area that was not contaminated.
The data related variables are variables over which
there was little or no experimental control. These
effects are primarily related to various data reduction
schemes, i.e., background subtraction, peak deconvolution,
peak modeling, etc. These effects on quantitative
analysis are documented by Zalusec (1979) The background
fitting routine was the source of most difficulty in the
data reduction. In this routine, developed by Zalusec
(1978), the background is modeled to fit a 4th order
polynominal with three operator selectable regions of the
background to provide input data for the fitting routine.
Figure 4.12b is a spectrum of the gamma phase of RSR 209
solution heat treated, quenched and aged at 870 C for one
hour. A background fit in the low energy region of this
spectrum is very difficult due to overlapping Ni-L, Al-K,
W-M, and Mo-L (in order of increasing energy) peaks in
this region. The consequence of this overlap is that no
isolated background region exists in this part of the
spectrum for entry into the modeling routine.
It was generally not possible to fit the whole
spectrum successfully. A good fit in the low energy
region did not necessarily mean a good fit at higher
102
energies. For this reason, the Mo-L rather than the Mo-K
was used for the quantification, and the W-L or Ta-L
lines were not used at all. An example of a comparison
between results calculated from both the Mo-K<=
Mo-If
The sample is the ternary alloy #17. As in the
previous example, a large probe size was used.
a)
Using the Mo-L line:
No absorption
correction
Calculated
with 1000 .
absorption
correction
wt.%
at .%
wt.%
at.%
Ni
78.2
78.3
77.5
77.3
Mo
16.45
10.1
16.7
10.2
A1
5.36
11.7
5.8
12.5
b)
Using the Mo-K
line:
No absorption
correction
Calculated
with 1000 .
absorption
correction
wt.%
at .7o
wt .X
at.%
Ni
78.1
78.2
77.5
77.4
Mo
16.6
10.1
16.5
10.0
A1
5.35
11.7
5.8
12.5
Note
: The ratio Lp/L0^3 .2265 was
used to reduce the
measured intensity of the Mo-L<< + Mo-LP peak. The Lp/L0*-
ratio was calculated from the MAGIC program.
The EDS results in Table 5.3 do not include values for
either the W or Ta quaternary additions. The analyses will
103
obviously be in error because of this, not only because
they exclude the quaternary elements, but also because
this exclusion will affect the quantitative total and the
relative amounts of the other elements also. Fortunately,
the concentrations of the quaternary elements in the bulk
alloys are low, 2.0 atomic X for both RSR 197 and 209.
Representative spectra from RSR 209 and RSR 197 gamma and
gamma prime phases are shown in Figures 4.12 a, b, c, and
d. The partitioning of the Ta and W to the gamma and
gamma prime phases is different. Ta partitions almost
exclusively to the gamma prime phase. W appears to be
about equally partitioned between the gamma and gamma
prime phases.
Interestingly, the nickel content of the gamma and
gamma prime phases was very similar (Table 5.3). This
allowed the Ni-K^peak to be used as an internal standard
for ratioing against the Mo, Ta, and W lines in order to
measure the partitioning of the Ta or W between the gamma
prime and gamma phases.
The Ta in the gamma prime cannot exceed about 4
atomic percent. This figure is based on the assumption
that the gamma prime volume fraction is not less than 50X,
a safe underestimate judging from the microstructural
features described in Chapter 5.
For the same reason, the amount of Ta in the gamma
phase must be less than one percent based on the ratio of
Ta to Ta in the gamma prime and gamma, respectively.
4N10-2S 8.06 KEU O C-'S
2k 1A + 8 M H$*= 20 E 0 1AB
4NJ0-2S 8 06 KEO o C t
"$ = 2K 1A + B H HS= 20E" lwB
Figure 4. ] 2
Spectra from the gamma and gamma prime phases of RSR 209 and
RSR 197; a.) RSR 197 Gamma, b.) RSR 197 gamma prime, c.) RSR 209
gamma, and d.) RSR 209, gamma prime.
105
The amount of W in both gamma and gamma prime phases
is approximately the same, that is, "homogeneously"
distributed, and consequently about 2.0 atomic % in the
gamma and 2.0% in the gamma prime phase.
Kriege and Baris (1969) measured the partitioning of
Ta and W between the gamma and gamma prime phases of a
number of Ni base alloys, all of which contained
considerable Cr. The Ta ratio between gamma prime and
gamma in numerous Ta containing alloys is approximately
1:4,*05. The ratio between gamma prime and gamma in a
number of W containing alloys (Mar-M200, TRW/900,
Microtung, etc.) is approximately one to one. This is in
close agreement with the present study. The ternary
Ni-Mo-Al compositions of the quaternary alloy gamma and
gamma prime phases are given in Table 5.3.
CHAPTER 5
RESULTS
5.1Microstructural Characterization
5.1.1 As Extruded RSR 197 and RSR 209 Alloys
Figure 5.1 is a low magnification TEM micrograph of a
typical as extruded microstructure. The alloy is RSR
209. The large grains are gamma prime grains that have
precipitated during the extrusion process. The other
areas of the microstructure consist of small cubes of
gamma prime that have precipitated from the gamma solid
solution during the cool down after extrusion. Details of
the optical microstructure can be found in the relevant
Pratt and Whitney quarterly reports (Cox and et al.,
1978). Other phases were present but were not analyzed.
It is probable that they are Mo.
5.1.2 RSR 197 --As Solution Heat Treated and Quenched
Figure 5.2a shows the general microstructural
features of this as quenched alloy. This is basically the
starting structure and starting phase distribution for all
subsequent aging practices of RSR 197. There are no
remnants of the primary gamma prime phase that had
106
109
developed during the extrusion process. This phase was
taken into solution during the solution heat treatment.
The larger gamma prime precipitates along the grain
boundaries result from accelerated coarsening of gamma
prime at the high angle grain boundaries (Funkenbusch,
1983). This coarsening presumably takes place during the
air quench from the solution heat treatment temperature.
The major features of the microstructure include the
gamma prime cuboids and the surrounding gamma matrix.
Many of the gamma prime cuboids are impinging, as shown in
Figure 5.2b. Some precipitation of DO22 phase has
occurred within the gamma matrix. The selected area
diffraction pattern shown in Figure 5.3a clearly shows the
presence of the DO22 superlattice reflections (cf. Figure
2.20b). There is very strong streaking associated with
each DO22 reflection. The streaks are not visible on the
fluorescent screen of the microscope and can be seen only
after long photographic exposure. Figure 5.3b is a g =
1/4 (420) dark field image of the DO22 phase. The beam
direction is approximately along a B = 001 direction.
The fine DO22 phase is distributed uniformly throughout
the gamma matrix. A high magnification g=l/4(420),
B=<001> image of this DO22 phase is shown in Figure 5.3c.
Note the angularity of the precipitate and the presence of
what appear to be many unidirectional faults in the DO22
precipitates.
Ill
5.1.3 General Microstructural Features
Alloy RSR 197, as solution heat treated and quenched,
will be used as an example to illustrate some general
microstructural features of all or most of the alloys
described in the chapter.
The distribution of the gamma prime and its geometry
within each foil is the same for all the alloys to be
described subsequently. Though each gamma prime cuboid
appears to completely penetrate the foil (see, for
example, Figure 5.2b), many in fact do not. The actual
distribution is as described schematically in Figure 5.4.
In all of the alloys the scale of the microstructure
is very similar. The gamma prime precipitate is
approximately 200 to 300 nm along any edge, and the gamma
generally extends some 20 to 30 nm between the gamma prime
cuboids.
When the DO22 phase is present, the DO22 reflections
appear to be shifted with respect to the LI2 N3AI. There
are two possible explanations for this displacement. Both
are discussed in Section 5.1.4.5.
5.1.4 RSR 197 Aging
5.1.4.1 Solution Heat Treated, Quenched and Aged at
760 C for up to 100 Hours
One hour aging at 760 C has produced discreet N4M0
Dla reflections. Figure 5.5a, a B = <^100^ SAD pattern,
112
e
' >
Figure 5.4 Schematic showing the distribution of
gamma prime phase in a thin foil. All the
conditions except E are commonly encountered.
113
shows both DO22 and Dla superlattice reflections. There
is still streaking present through the DO22 reflections,
as in Figure 5.3a. Figures 5.5b and 5.5c are g = 1/5
(420) and g = 1/4 (420) dark field images. The beam
direction was approximately parallel to a B=[121]
direction. The figures show that both phases are randomly
distributed throughout the gamma phase. The DO22 phase
has coarsened.
After 10 hours, all three NixMo phases are present.
The DO22 and Dla phases continue to grow, and the N2M0
that is present is very sparsely distributed, even to the
extent that it may not appear in selected area and Riecke
method diffraction patterns.
Aging for 100 hours results in almost complete
ordering throughout the gamma phase by the NixMo
precipitates. All three metastable NixMo phases are
present as evidenced by the B = \100)> diffraction pattern
shown in Figure 5.6a. As after ten hours aging, the two
dominant phases are N3M0 DO22 and N4M0 Dla. Figures
5.6b and 5.6c are B = [001], g = 1/4 (420) and g = 1/5
(420) dark field images of the DO22 and Dla phases,
respectively. The Pt2Mo phasse is shown in Figure 5.6d, a
B = [001], g = 1/3 (420) dark field image.
In addition to the three metastable NixMo phases, the
disordered gamma phase, and the cuboidal gamma prime
117
phase, there is a sixth phase present in this alloy;
NiMo. An image of this precipitate and its diffraction
pattern are shown in Figures 5.7a and 5.7b. The
diffraction pattern is indexed in Figure 5.7c. The phase
was found almost exclusively along grain boundaries.
In order to characterize the Dla and DO22 phases
adequately, a number of variants for each precipitate type
were imaged. This required that images be taken from at
least two different FCC crystal orientations. The two
orientations are the B = [001] and the B = [112]. Figure
5.8 shows these two diffraction patterns and additionally
delineates which diffraction variants were imaged.
As explained in Section 2.3.4.1, there are three
imagable of 12 possible variants in N3M0 D022* All three
of these variants may be imaged along any B =
direction since all three can be present simultaneously in
a B = <^100)> diffraction pattern (Section 2.3.4.1). Figure
5.6b is the dark field image of the 1/4 (420) variant.
This variant does not fill the intercuboidal regions. It
appears along only two faces of the gamma prime. Figure
5.6c is a dark field image of the 1/4 (240) variant. It
appears along the other two gamma prime faces, but not on
the same faces as does the 1/4 (420) variant.
The interpretation of these two dark field images is
straightforward. Figure 5.9 describes the relationship of
the variant orientation with the matrix and interpretation
119
420
Figure 5.8 Imaging conditions for the various dark field
images for RSR 197 SHTQ and aged 100 hours at
760 C.
120
o O
[o o # o o
i o o o 9 o
|oo0*oo
o o o
_ N4M0 Variant
C B, Figure 2.18
420
|0 o O
^ O
'o O
o #0 o
O o o Ni Mo Variant
o # O O Hit Figure 2.17
O O*
o o # o o o o o o
O O %/o 00*0#0# (Jt-Q
NiMo Variant #000#000*0
Ganma Prime
Cube
1 0 0 Face
O
:o
O
II?, Fig. 2.17
o o/m o o o O o o o
o#oioiO*o*o|ooO
o m/o mO*omo%omomO*om
o*oOo*oO*oo0o
o/% lo#o#o0o#ooo#
o|#o#0oo#oo0o
2 40
Ni Mo Variant A,
Figure 2.18
Common 240 plane between Ni^Mo and Ni^Mo
Figure 5.9 Arrangement of DO22 and Dla on the cube
faces of N3AI. The C axis of the DO22 is
perpendicular to the cube faces. Two
variants of Dla are shown. The Dla phase
can grow around the corner of the N3AI cube.
121
of the diffraction pattern. The figure shows clearly that
the c axis of the DO22 phase is perpendicular to a 100
face of the gamma prime. The third variant will thus
appear only in regions of overlapping gamma and gamma
prime, regions where the DO22 axis is parallel to the
beam, regions B, C, D, and E in Figure 5.4. The
diffraction spot from which a dark field image of variant
A (Figure 2.18b) would be formed corresponds to the same
spot from which an LI2 dark field image would be formed.
Both the DO22 and LI2 crystals have a superlattice
reflection at g = (110). Imaging the third variant, then,
is rendered impossible by the presence of the gamma prime.
A comparison of the images in Figures 5.6b and 5.6f
with the schematic in Figure 5.9 also shows that the (420)
habit of the DO22 phase can easily be reconciled with the
(420) Ho planes of the DO22 The crystallography of the
DO22 would seem to determine the morphology of the DO22
precipitate. The DO22 precipitates can be seen to be
comprised exclusively of either combinations of the {420}
planes or combinations of {420} planes and the limiting
(lOo) planes of the LI2 interfaces. For example, many of
the DO22 precipitates are triangular in projection. This
is consistent with four {420} planes truncated by a {l00},
e.g., an (024), (024), (420), and (420) plane truncated by
an (010) plane. This pyramid would appear as a triangle
in either an [001] or an [010] projection. Two such
122
pyramids could share a common {100} face. The resulting
TEM image would be a diamond. A third possibility would
be two parallel sets of {420} planes truncated by two
parallel {lOO} planes, perhaps two facing {100} gamma
prime faces. The resulting image would be a rhombus. All
of these features can be readily seen in the dark field
images, Figures 5.6f and 5.6b, of the DO22 N3M0.
Only two Dla variants are imagable along any B =
<100> direction. Both of these variants are associated
closely with the DO22 morphologies just described. The
two visible Dla variants (reference the indexing in Figure
5.8) contain the following four 420 planes: the clockwise
variant contains a 420 and a 240. From the previously
described DO22 4-20 stacking sequence, Figure 5.9, a
clockwise Dla variant could share a DO22 420 plane between
010 faces of the gamma prime, or, could share the DO22 240
on the 100 faces. Similarly, the counterclockwise variant
could share a DO22 4-20 on the 010 face, or a DO22 4-20 on
the 100 face. This stacking is schematically represented
in Figure 5.9. Dark field images of the Dla corresponding
to the schematic are shown in Figures 5.6c and 5.6e.
Because one Dla variant can grow on both the 010 and
the 100 faces of the gamma prime, the N4M0 Dla can
readily grow around the edge of the gamma prime cuboids
without introducing a stacking fault. (The DO22 would
always form a perpendicular twin boundary when it impinged
123
at the cuboid edge.) This is shown clearly in Figure 5.9
and in a lattice image, section 5.1.4.2. Note the
concentrations of the Dla phase at the corners of the
gamma prime cuboids in Figures 5.6c and 5.6e.
The Pt2Mo phase is also present in the alloy. It can
be present as discreet N2M0 precipitates, or it can be
present layered with the DO22 and Dla, as it appears to be
in Figure 5.6d.
In order to describe the actual three dimensional
arrangement of these NixMo phases, it is necessary to look
along the third 100 direction in the crystal. This can be
done by tilting from B = [001] to a B = [112] direction, a
tilt of 35.3 degrees. When tilted to this orientation,
multiples of the (042) and (402) reflections can be used
to image the DO22 and Dla precipitates (Figure 5.8).
Imaging with a 1/4 multiple of either of these reflections
will yield an image of the DO22 phase on the previously
unimageable 001 face of the gamma prime. Using the 1/5
multiples will image two additional Dla variants.
Figure 5.10 shows the three faces of the gamma prime
cube with the four possible DO22 planes on each face. The
1/4 (402) and the 1/4 (042) variants are on the same 001
face. Since they are from the same DO22 variant, imaging
with either of them will give the same image.
The 1/5 (042) variant will appear on two faces of the
gamma prime. First, it will appear on the (001) face. It
124
Figure 5.10
A gamma prime cube showing the 420 phases
that will appear on each face of the cube.
125
must also appear on the (010) face since this face
contains an 024 plane which is also a plane in the 1/5
(042) variant. In a similar way, the 1/5 (402) variant
will appear on the 001 face, but since it is a different
variant of the Dla, its morphology will not be the same as
the Dla morphology of the 1/5 (042). The 1/5 (402)
variant will also appear on the 100 face, since this
variant also contains a 204 plane. To differentiate the
Dla precipitate on the 001 face from the same variants on
the other 100 faces, it is necessary to compare the DO22
images with the Dla images. The DO22 images appear only
on the (001) faces of the gamma prime.
The DO22 precipitates form in discreet lines along
<100> directions, analogous to the alignment of the gamma
prime described by Ardell et al. (1966). Figure 5.11a
shows this morphology. The individual morphologies of the
DO22 are consistent with the morphologies explained
earlier. The morphology of the Dla phase is also as
predicted from the B = <(001^> images. The variants of
N4M0 Dla, shown in Figures 5.12b and 5.12c, form along
the DO22 precipitates, just as they did in the B = <(00l)>
images. These third axis dark field images show that the
interlacing of the Dla and DO22 phases results in almost
complete order of the gamma phase.
127
5.1.4.2 Lattice Imaging of DO?? and Dla Phases
The lattice imaging technique is well established and
will not be reviewed here. An excellent review has been
prepared by Sinclair (1979). Briefly, all the information
contained in a lattice image is in the diffraction pattern
from which the lattice image is produced. The advantage
of the lattice image over the diffraction pattern is the
significantly better spatial resolution in a lattice image
compared to a diffraction pattern. There are exceptions
to this, of course. If a focused electron probe is used
to form a diffraction pattern, the diffracting volume will
be on the order of the probe size which can sometimes
approach lattice dimensions.
The DO22 and Dla phases do not present major
difficulties for lattice imaging. From Figures 2.20b and
2.20c, it should be clear that the simplest image can be
formed with the 1/4(420) and 1/5(420) reflections. These
represent real lattice spacings of 3.18 Angstroms and 3.98
Angstroms, respectively. Figure 5.12 is a lattice image
of both the Dla and DO22 phases using the 1/4(420) and
1/5(420) reflections from a B = [001] zone axis under
axial illumination conditions. The inset describes this
imaging condition. The large lattice spacings are about
3.9 Angstroms. Next to these are lattice planes of 3.2
Angstroms spacing. The former corresponds to N4M0
129
lattice fringes, the latter to N3M0 lattice fringes. At
the interfaces of these phases there is no discontinuity.
This is completely consistent with the type of stacking
that is possible with 420 phases where the two phases
share a common 420 plane. Only the stacking sequence
changes across the interface.
Figure 5.13 is an image of the Dla phase in which
there is a small faulted region (Region A), most probably
of N3M0. The crosshatched region is N4M0. The lattice
fringes in the fault are from {l00} planes of an ordered
phase, either the LI2 {OOl} plane or the DO22 {002}
plane. The fringes are more likely from DO22 since there
are no equivalent fringes in the gamma prime cube, the
areas at the top and bottom of the image.
Figure 5.14 is a lattice image of the Dla precipitate
on the edge of four gamma prime cubes. This precipitate
covers the edge of all four cubes and grows into the
intergamma prime cuboid region along the cube faces of all
four cubes. This it can do readily without the
introduction of a stacking fault. The DO22 phase, as
discussed in Section 5.4.1, would introduce high energy
perpendicular twin boundaries if it were to impinge at the
cube edges.
132
5.1.4.3 Solution Heat Treated, Quenched and Aged at
810 C for up to 1UU hours
The aging behavior of this alloy at this temperature
is considerably less complex than that previously
described for the 760 C aging practice. The only NixMo
phase that forms during aging is the DO22 N3M0 phase.
After one hour at 810 C, the DO22 phase is well
established, as shown in Figure 5.15a, a 1/4 (420), B =
[001] dark field image. After ten hours, the DO22 has
coarsened considerably, as in Figure 5.15b. A B =
diffraction pattern showing only DO22 is shown in Figure
5.15c. Though the dark field image should be sufficient
to establish the presence of this NixMo phase, the
diffraction pattern is shown to serve as an example of one
method used to differentiate among the LI2 superlattice
reflections, overlapping DO22 superlattice reflections,
and diffuse (1, 1/2, 0) SRO reflections, all three of
which, as previously discussed in Section 2.3.3, are
difficult to differentiate from the diffraction pattern.
The DO22 and LI2 (100) and (010) reflections which
would normally occupy the same reciprocal lattice
positions are split into two discreet and distinct
reflections that are easily differentiable when the g
vector is large. One of the two reflections is the LI2
superlattice reflection. The other is the DO22
134
superlattice reflection. When the (1, 1/2, 0) reflections
are the result of the SRO, there will be no splitting of
the LI2 spots, since there is no overlapping spot (there
is no SRO superlattice spot at LI2 superlattice positions)
and no shifts in the positions of the (1, 1/2, 0)
reflections, as discussed in Section 5.3, for DO22
reflections. These shifts are discussed in Kersker et al.
(1980) .
After 100 hours, the DO22 phase is still present and
seems to fill most of the intercuboidal gamma prime
regions. The morphology of the DO22 after 100 hours at
this temperature is not similar to that after 100 hours at
760 C. Figure 5.15d is a B = [001], g = 1/4 (420) dark
field of the DO22 after 100 hours at 810 C.
In addition to the D022> the gamma prime, and
presumably the gamma phase, there is an additional phase
present at the interface between the grain boundaries and
the coarsened gamma prime that decorates these
boundaries. Its diffraction pattern was not recorded. It
is probably NiMo.
5.1.4.4 Solution Heat Treated, Quenched and Aged at
870 C for up to 100 Hours
One of the more noticeable features of the high
temperature aged RSR 197 is the development, after one
hours heat treatment, of an ordered dislocation array at
135
the gamma-gamma prime interfaces. Figure 5.16 shows these
interfacial dislocations. The beam direction is along the
B = . The dislocation images are consequently from
the overlapping regions of gamma and gamma prime, regions
B, C, D, and E in Figure 5.4. The fact that this network
forms as a result of the mismatch between the gamma-gamma
prime phases means that the dislocation spacing will be
representative of this mismatch (Lasalmonie and Strudel,
1976). The measurement of the mismatch using this method
was not attempted here.
The dislocations are imagable at the gamma-gamma
prime interface, for example, with B = [001]. The network
is comprised primarily of dislocations of the following
Burger's vectors: b = + [110] and + 1/2[110]. The nodes
at the intersections of these two orthogonal dislocation
types may be relaxed, resulting in fourfold nodes of
dislocations corresponding to Burger's vectors of +
1/2[10T], + 1/2[Oil], + 1/2[Oil], and + 1/2[101]. Any low
index two beam imaging condition near B = [001] will
always yield some visible set of these dislocations. As
an example, Figures 5.16a, a g = (220), B = [001[ image,
and 5.16b, a g = (220), B = [001] image, show opposite
sets of primary dislocations, as expected from the g*BxU=0
criterion for edge dislocation invisibility (Edington,
1976). These figures do not show the fourfold nodes
plainly.
137
Figure 5.17a is a microdiffraction pattern from the
gamma phase. The DO22 reflections are present in this
convergent beam microdiffraction pattern. A dark field
image can be formed if one of these DO22 reflections is
used to form the image. Figure 5.17b is an image taken
using a 1/4(420) reflection. There are two features of
special interest in this image. First, the fine
precipitate is imaged throughout the gamma phase. Second,
as was the case when DO22 was responsible for the (1, 1/2,
0) reflections, one variant of the DO22 predominates along
any single gamma prime cube face, though the other variant
is present as well. Both variants can be plainly seen in
the diffraction pattern. The fine scale of this
precipitate shows that it precipitated during the cool
down from the aging temperature and that it was not
present in the alloy at the aging temperature.
After 100 hours aging, large platelets of equilibrium
delta NiMo have formed throughout the grains. An example
is shown in Figure 5.18a, a low magnification image
showing numerous rod-like and plate-like precipitates.
The diffraction pattern of the needle or edge on plate
shown in Figure 5.18b is shown in Figure 5.18c. The
diffraction pattern is not a low index one, but is close
to a B = NiMo pattern and close to a B = <^100^ gamma
matrix diffraction pattern.
140
It is possible to form an image using a (1, 1/2, 0)
reflection, as shown in Figure 5.19b. Figure 5.19a is a B
= <^100^> microdiffraction pattern showing only gamma prime
and short range order (1, 1/2, 0) reflections. As after
one hour aging, an interfacial dislocation network is
present, as shown in Figure 5.18b.
5.1.4.5 Aging Summary -- RSR 197
At 760 C, all three NixMo metastable phases form and
coarsen with time. The N3M0 DO22 and N4M0 Dla phases
predominate. After one hundred hours, the matrix has
become highly ordered, the DO22 and Dla phase essentially
filling the intercuboidal regions. These two phases are
crystallographically related. Aging at 810 C produces
only DO22 precipitate. This precipitate coarsens and
eventually fills the intercuboidal regions. At 870 C, no
metastable phase forms during aging. An interfacial
dislocation network forms, apparently very rapidly since
it is present after only one hour at temperature.
The equilibrium NiMo phase may be present at all
aging temperatures. At the two lower aging temperatures,
it is usually found decorating the grain boundaries,
usually in regions contiguous to the cellular
intergranular gamma prime. At the highest aging
temperature, the NiMo forms throughout the grains.
142
5.1.5 RSR 209 -- As Solution Heat Treated
and Quenched
Figure 5.20a shows the general microstructural
features of the as-quenched alloy. As in alloy 197, there
are no remnants of the primary gamma prime phase that was
present in the as-extruded microstructure. There is also
cellular gamma prime at the grain boundaries.
Figure 5.20b is a B = \100^ diffraction pattern
showing Pt2Mo reflections and short range order or DO22
reflections. When imaged, the Pt2Mo is very fine. The
Pt2Mo reflections are elongated in 110 directions. This
streaking is consistent with their morphology, a topic to
be dealt with in more detail in Section 5.1.6.2.
5.1.6 RSR 209 Aging
5.1.6.1 Solution Heat Treated. Quenched and Aged
at 760 C for up to 100 Hours
After 10 hours at 760, fine Pt2Mo and fine DO22 phase
have precipitated, as shown in the B = <^100^ diffraction
pattern, Figure 5.21a, and in the dark field images shown
in Figures 5.21b and 5.21c. The diffraction pattern,
Figure 5.21d, taken after 100 hours aging, shows that
N4M0 has formed. The pattern suggests that the N2M0 is
still the dominant phase.
145
5.1.6.2 Solution Heat Treated, Quenched and Aged
at 810 C for up to 100 Hours
The predominant phase at this aging temperature is
the Pt2Mo phase. After one hour at 810 C, Pt2Mo is
densely distributed throughout the gamma matrix. Figures
5.22a and 5.22b are dark field images taken using two of
the six visible Pt2Mo variants. These two variants are
described in Figure 2.21.
The morphologies of the Pt2Mo precipitates are very
much dependent on their crystallography. The two visible
variants and their relationship to the gamma prime cube
axes are described schematically in Figure 2.21. These
lenticular shaped Pt2Mo precipitates are actually
platelets with (lioj habits (Saburi et al., 1969). Figure
5.23a is a B = [001'], g = 1/3(220) image. If the sample
is rotated 54.7 degrees from this orientation about the
axis described in the figure to the B = [111] orientation
and the 1/3 (220) again used to form the image, an image
like that shown in Figure 5.23b results. The plate-like
nature of the precipitate is very apparent by comparing
these two figures. It is likely that all six Pt2Mo
variants can co-exist simultaneously in any given gamma
region.
The Pt2Mo N2M0 precipitates grow with time, as shown
in Figure 5.24a, a B = [001], g = 1/3(420) dark field
image of the Pt2Mo phase after 100 hours at 810 C. There
149
are also some elongated dark rods here that do not index
as N2M0. They are identified in Section 5.1.6.3.
NiMo can be found on the grain boundaries. Figure
5.24b is an example of the NiMo on the boundary between
the cellular gamma prime and the grain boundary itself.
A NiMo B = \100X> diffraction pattern is indexed in Figure
5.24c. An interfacial dislocation network has developed,
as shown in Figure 5.24b.
5.1.6.3 Solution Heat Treated, Quenched, and Aged
at 870 C for up to 100 Hours
The processes observed to be taking place after 100
hours at 810 C are already advanced after 1 hours aging
at 870 C. Numerous inter-gamma prime platelets have
precipitated, as shown in Figure 5.25a. This figure also
shows a well developed dislocation structure. The N2M0
Pt2Mo is still present, as shown in the convergent beam
microdiffraction pattern, Figure 5.25b. The consequence
of increasing the aging time to 100 hours at this
temperature is to coarsen the precipitate that was
observed at the shorter aging time. Figure 5.25c shows
that the rod-like recipitate occupies most of the
intercuboidal region. X-ray diffraction patterns identify
this precipitate as Mo. Two convergent beam
microdiffraction patterns from one of these precipitates
indexed as Mo are shown in Figures 5.26a and 5.26b.
152
Figure 5.26c, a B = <^111^> selected area diffraction
pattern, shows no Pt2Mo 1/3 220 reflections.
5.1.6.4 Aging Summary -- RSR 209
Aging at the lowest temperature produces a mixture of
N2M0 Pt2Mo, DO22 N3M0, and after 100 hours, Da N4M0
phase. These first two phases coarsen during aging, as
would be expected. At 810 C, platelets of Pt2Mo N2M0 and
presumably DO22 phase as well, are present. The Pt2Mo
coarsens considerably during aging. An intercuboidal
phase precipitates prior to the 100 hour treatment. A
morphologically similar phase, identified by electron and
x-ray diffraction pattern analysis of the 870 C aged
sample, is shown to be alpha Mo. An interfacial
dislocation network has developed after 1 hour at 810 C.
Aging at 870 C merely accelerates the coarsening of
those phases that precipitate at 810 C. Pt2Mo is
initially present after one hours aging but has
disappeared after 100 hours. An intercuboidal phase,
identified as Mo from both x-ray and electron diffraction
patterns is predominant in the intercuboidal regions. An
interfacial dislocation structure is present after only
one hours aging. Whenever a grain boundary could be
imaged, this grain boundary invariably contained cellular
gamma prime, sometimes decorated with a phase identified
as NiMo.
153
5.1.7 Special Aging/Special Alloys
5.1.7.1 Alloy //17 -- Solution Heat Treated, Quenched
and Aged at 760 C for 100 Hours
An image of this ternary alloy along a B = <(ll2^>
direction is shown in Figure 5.27c. The microstructure of
this alloy is essentially identical to the RSR alloys.
This would be expected since both the RSR alloys and the
cast alloys were solution heat treated prior to aging.
After the 100 hour heat treatment, the phase
distribution is similar to the phase distribution in RSR
197 after a similar thermal treatment (see section
5.1.4.1). Figure 5.27a is a B = <100^ selected area
diffraction pattern. This pattern should be compared with
Figure 5.6a. Figure 5.27b is a combined g=l/4(420),
g=l/5(420) dark field image showing the similarity in the
precipitate morphology between the DO22 and Dla phases in
this ternary alloy and RSR 197, aged for the same time.
5.1.7.2 Alloy //17 -- Solution Heat Treated, Quenched
and Aged at 870 C for 100 Hours
Figure 5.28a is a B = [001] two beam image showing a
well developed interfacial dislocation structure. Figure
5.28b, a B = <(100^ selected area diffraction pattern shows
that no metastable phases are present at the aging
temperature. This sample was water quenched after aging.
The RSR alloys were all air quenched after aging.
156
5.1.7.3 RSR 197 -- Solution Heat Treated, Quenched,
and aged at 870 C for 1 Hour, Furnace
Cooled to 760 C and Aged for 100 Hours
at 760 C.
Even after aging at 870 C for one hour, the D022 and
Dla phases readily form when aged at a lower temperature.
The dark field images shown in Figures 5.29a and 5.29b are
B = [001] dark field images taken using both 1/4(420)
(Figure 5.29a) and 1/5(420) (Figure 5.29b) reflections.
5.1.7.4 RSR 185 -- Solution Heat Treated at 1315 C
and Water Quenched
The sample was only used to measure the gamma matrix
lattice parameter using the CBED technique. The sample
was chosen because it was water quenched from the solution
heat treatment temperature and consequently showed only
very weak (1, 1/2, 0) SRO reflections. A B = CBED
pattern from the RSR 185 gamma phase is shown in Figures
5.30a and 5.30b. There is no asymmetry in the central
spot of the pattern shown in Figue 5.30a. Note the
absence of 110 superlattice reflections in Figure 5.30b.
5.2 X-Ray Diffraction Measurements
The gamma prime and gamma lattice parameters, as
measured by x-ray diffraction, are listed in Table 5.1.
The gamma prime lattice parameter is consistently larger
in the Ta containing alloy, the RSR 197 alloy, than
Table 5.1 -- Lattice Parameters From X-Ray Measurements
Alloy
Heat Treatment
Line
Ill
331
v'
v v-
-v'/v
v'
V
V-V1/v
RSR 209
As Solution and
Quench
3.5791
3.5775
1 hr @ 760 C
3.5803
3.63
1.3
3.581
- .
...
3.5764
3.63
1.43
3.580
3.5819
3.63
1.3
3.579
100 hr @ 760 C
3.5842
3.636
1.4
3.582
100 hr @ 810 C
3.5810
1 hr @ 870 C
3.576
3.608
.87
3.583
3.573
3.599
.76
3.5764
3.6244
1.3
100 hr @ 870 C
3.5826
3.6196
1.0
3.5798
3.5710
3.619
1.3
RSR 197
As Solution and
Quench
3.5862
3.5869
1 hr @ 760 C
3.5842
3.6038
.55
3.5904
3.614
.66
3.5897
3.6054
.43
100 hr @ 760 C
3.5881
3.65(18)*
1.77
100 hr @ 810 C
3.5898
3.5892
100 hr @ 870 C
3.592
3.604
.33
3.592
3.616
.68
3.5880
3.61
.64
3.588
3.609
.58
JL
Value is affected by presence of NixMo precipitates.
159
Table 5.1 continued
RSR 209
3.585
RSR 197
3.595
3.593
220
v
3.619
Line
v-v'/v v'
311
V v-v'/v
.69 3.584
3.586
3.589 3.613 .65
160
161
in the W containing alloy, RSR 209. The mismatch between
the gamma prime and gamma lattice parameters in the two
alloys is also different: larger in the RSR 209 than in
the RSR 197. Mismatch is defined as aD gamma prime minus
aG gamma divided by a0 gamma (Sims and Hagel, 1972).
In many cases, Table 5.1 does not list the lattice
parameter of the gamma phase. The measurement of the
exact gamma peak position was not always possible, due to
either insufficient signal, a texture effect, or to the
presence of the metastable Ni-Mo phases. As an example,
the gamma lattice parameter could not be unambiguously
measured for the RSR 197 sample that was aged for 100
hours at 760 C. The diffraction peak in the gamma region
was smeared to such an extent in this spectrum that
locating the exact maximum in the gamma peak intensity was
not possible. Without the TEM result showing significant
NixMo precipitation, interpretation of this x-ray
diffractogram would be difficult.
5.3 Convergent Beam Measurements
Numerous measurements of the gamma prime lattice
parameter were made using the B = <(ll4)> convergent beam
electron diffraction and HOLZ line patterns described
extensively in Chapter 4. The results of these
measurements are listed in Table 5.2. Measurements were
made directly from the negatives using a 10X loupe
Table 5.2 -- Lattice Parameters From CBED Measurements
Alloy
Aging Temp./Time
Phase*
Measured Ratio
a/b
RSR 197
As Solution Heat
Treated and Quenched
GP
1.0
ASQ, Aged 760 C
1 hr
GP
1.06
100 hr
GP
1.08
ASQ, Aged 870 C
1 hr
GP
1.0
100 hr
GP
1.06
RSR 209
As Solution Heat
Treated and Quenched
ASQ, Aged 760 C
10 hr
GP
.90
100 hr
GP
.92
.94
ASQ, Aged 870 C
100 hr
GP
.90
.90
RSR 185
ASQ
GP
.91
.98
G
1.23
*Gp gamma prime
G gamma
Lattice Parameter
3.573
3.577
3.578
3.573
3.577
3.566
3.567
3.569
3.566
3.566
3.567
3.572
3.584
162
Table 5.2
continued
Alloy
Aging Temp./Time
Phase*
#17
As Solution Heat
Treated and Quenched
Aged @ 760 C
100 hr
GP
ASQ, Aged @ 870 C
GP
* GP gamma prime
G gamma
Measured Ratio
a/b Lattice Parameter
.90 3.565
.90 3.565
.90 3.565
163
164
and are reproducible to .1 mm. The accuracy in absolute
lattice parameter measurement is very poor, as previously
explained in Chapter 4. No absolute measurement was
attempted. The relative differences in lattice parameter
as measured with CBED between the RSR 197 and RSR 209 is
on the order of .3%. This number compares very favorably
with the x-ray diffraction results of the previous
section.
Not all the CBED patterns from the gamma prime phase
were as symmetrical as those shown in Figure 4.9. Figure
4.1, for example, shows an asymmetrical pattern from the
gamma prime. The origin of the assymetry is unclear.
Measurements from the gamma phase were extremely
difficult to make. Figure 5.30b is a low camera length
B=\114^> CBED pattern from the gamma phase of RSR 185.
Figure 5.30a shows the detail in the central spot.
Figure 5.30b shows both a lack of any {llO} superlattice
reflections in the zero order zone, and no superlattice
FOLZ lines. The pattern is thus clearly from the gamma
phase only. The fine structure in 5.30a shows that the
lattice parameter of the gamma is greater than the lattice
parameter of the gamma prime. There is no perceptible
distortion or loss of symmetry in this gamma B = ,\114/>
CBED pattern. This implies that there is no measurable
strain unless that strain is parallel to the beam.
165
Figure 5.31a is a B = <.14)> CBED pattern from the
gamma phase in the RSR 197 as solution heat treated and
quenched sample. The gamma phase contains a very fine
distribution of the DO22 precipitate, as described in
Section 5.1.2. The pattern represents either diffraction
from the gamma phase strained due to the influence of the
DC>22j or from the DO22 itself. There would be no
superlattice from the DO22 in the zero order zone, and
hence no {lio} reflections. None were observed.
The pattern in Figure 5.31a was taken from an
intercuboidal area such that the gamma lattice can be
shown to be expanded in the direction of the c axis of the
DO22 phase. This direction is perpendicular to a (100)
face of the gamma prime.
The a/b ratio used to measure the lattice parameters
in the gamma prime phase can still be used to measure the
lattice parameters from this assymetric pattern. The
values of a/b will be negative (see Appendix A) because of
the line shift algorithm used for the calculation. The
ratio is negative when the intersection of the 193 and 391
lines crosses the 10 0 2 line. This pattern has an Rp
value of -5.3 and an R2 value of 0.5. The lattice
parameters corresponding to these R values are a = 3.575
Angstroms and b = 3.645 Angstroms, assuming that c = 3.575
Angstroms. The FCC c axis here is parallel to the beam.
167
Thus there is about 1.9% "strain" in the lattice in the c
axis direction of the DO22
5.4 Energy Dispersive X-ray Measurements
The energy dispersive x-ray methodology was explained
in detail in Section 4.2. The results of the
measurements are given in Table 5.3.
5.5 Microhardness Measurements
Microhardness measurements were made on most of the
aged samples. Rockwell C was the test method. The values
represent the average values of six measurements. The
data is shown in Figure 5.32.
Rockwel1
As Quenched
i h r
lOhrs
lOOhrs
A
Aged at
760C
Solid figures:
RSR 197
Aged at
81OC
Open figures:
RSR 209
O
Aged at
870C
Figure 5.32
Microhardness measurements of SHTQ and aged
RSR alloys.
Table 5.3 -- EDX Measurements
Alloy
Heat Treatment
Ni
Gamma Prime
Mo
A1
Ni
Gamma
Mo
A1
197
Solution Heat Treated
and Quenched (SHTQ)
77.2
3.8
19.0
78.0
16.7
5.0
SHTQ,
760
C
for
100 hrs
85.0
2.1
12.9
88.0
9.9
1.5
SHTQ,
810
C
for
100 hrs
76.0
5.0
19.0
76.0
17.0
7.0
SHTQ,
870
C
for
1 hr
77.0
4.8
18.2
78.1
15.6
6.3
SHTQ,
870
C
for
100 hrs
78.0
5.4
16.6
80.5
16.3
3.2
209
SHTQ
Not Analyzed
77.0
16.2
7.1
SHTQ,
760
C
for
100 hrs
77.1
4.6
18.3
75.0
18.1
6.9
SHTQ,
810
C
for
100 hrs
77.0
5.0
18.0
77.7
16.5
5.8
SHTQ,
870
C
for
1 hr
76.3
5.7
18.0
77.0
19.0
4.0
SHTQ,
870
C
for
100 hrs
77.2
3.6
19.2
80.5
16.2
3.4
//17
SHTQ,
870
C
for
1 hr
76.2
6.3
17.5
76.1
17.9
6.0
168
CHAPTER 6
DISCUSSION AND CONCLUSIONS
6.1 Metastable NiyMo Phase Formation:
Effects of Chemistry and
Microstructure
There are clearly differences at all aging
temperatures between the precipitation sequences of the
metastable NixMo phases in the RSR alloys. From the EDS
measurements it is probable that Ta in RSR 197 cannot have
a direct effect on the precipitation of these NixMo phases
in the gamma phase of RSR 197 alloy. This is confirmed by
ternary alloy //17 according to the results discussed in
Section 5.1.7.1. The precipitate and the precipitate
morphologies in alloy //17 are essentially identical to
those in the Ta containing RSR 197. One can conclude that
if it is the presence of an element that allows all three
NixMo precipitates to co-exist, this element must be A1,
not Ta.
The presence of W in the RSR 209 must be a
controlling factor in establishing the precipitation
sequence in this alloy, since this sequence differs from
the ternary alloy //17. The Pt2Mo phase is the predominant
phase, not DO22 and Dla. This is very similar behavior to
170
171
what would be expected from a binary N3M0 alloy, as
described in Section 2.2.5.1.
A major question in this research was, what are the
compositions of the major phases, of the gamma prime and
gamma phases in the RSR alloys? This information is
needed in order to define the precipitation behavior of
the NixMo precipitates in the RSR alloys since in the
binary alloys, the precipitate types vary as a function of
composition, as described in Section 2.2.5. This was the
purpose for the EDS measurements described in Section
4.2. The experimental values for the gamma and gamma
prime compositions given in Table 5.3 vary enough from
alloy to alloy that only the approximate composition can
be determined. For the gamma prime phase in RSR 197,
excluding the 760 for 100 hour aging data, this average
composition is 77 + 1.4 % Ni, 4.75 + 1.18 % Mo, and 18.2 +
2 7o Al, all in atomic percent. For gamma, again excluding
the data for the 760 C for 100 hour aging data, the
average values for the composition of this phase are 78.15
+3.2 1 Ni, 16.4 + 1.0 1 Mo, and 5.4 + 2.0 % Al, all in
atomic percent. It is reasonable, based on the binary
phase diagram solubility information shown in Figures 2.1
and 2.2, to take an average of the compositions even
though the solubility changes slightly with temperature
over the range of aging temperatures.
172
For RSR 209, the values for the gamma prime phase are
76.8 + .8 at. % Ni, 5.04 + 1.8 at.% Mo, and 18.2 + 1.2 at.%
A1. For the gamma phase, these values are 77.2 + 3.39
at.% Ni, 17.3 + 2.1 at.% Mo, and 5.5 + 2.4 at.% A1. These
averages are similar to those measured by Miracle et al.
(1984) for the equilibrium gamma and gamma prime phase
compositions that were determined in their study of
Ni-Mo-Al ternary alloys.
The EDX data defines the ternary composition of the
gamma phase in which the nonequilibrium precipitation is
observed. This ternary composition is similar in both
alloys and somewhere between the N3M0 stoichiometry and
N4M0 stoichiometry, assuming that the Al enters into the
ordering reactions.
The partitioning of Al to the gamma matrix lends
further credence to the fact that Al influences the
precipitation behavior in RSR. 197, RSR 209, and alloy //17
since DO22 phase was almost never observed in aged Ni-Mo
binaries of any stoichiometry (see Section 2.2.5). The
exception was in the work of Van Tendeloo et al. (1975) in
which DO22 phase precipitated when the alloy was very
rapidly quenched. Under these circumstances, the DO22
phase was only transient, described as a transition phase
between short range order and the more stable N4M0/N2M0
phases. In both RSR alloys and in the ternary alloy //17,
the DO22 is obviously not transient.
173
The DC>22 phase, as Ni^Nb, has been observed in
preferential orientation with gamma prime phase in other
alloy systems (Cozar and Pineau, 1973). In the Inconel
(In) 718 type alloys that they characterized, the DO22
nucleated on the gamma prime cuboids with c axis of the
DO22 perpendicular to the 100 faces of the gamma prime.
The situation is similar in the R.SR 197 and RSR 209 except
that the DO22 does not nucleate on the gamma prime. It
nucleates throughout the intercuboidal gamma matrix, as
shown in Section 5.4.
Oblak et al. (1974) studied the aging, under tensile
and compressive stresses, of single 100 crystals of In
718. The primary strengthening phase in this alloy is
DO22 Ni3Nb in which small smounts of Al substitute for the
Nb (Paulonis et al., 1969). Oblak et al. (1974) found
that certain DO22 variants could be suppressed by
application of tensile and compressive loads. When a
tensile load of 69 Mn/m^ was applied parallel to the [100]
axis, the DO22 variant with c axis parallel to the stress
axis was observed. The morphology of the DO22 in this
alloy is an ellipsoidal plate with the c axis
perpendicular to the plate axis, clearly different from
the DO22 in the RSR 197 samples aged at 760 C. A
compressive stress along the [100] lead to precipitation
of the other two variants.
174
Martin (1982) has studied the nucleation of the DO22
phase. (Mishra (1979), Chevalier and Stobbs (1979), and
Nesbit and Laughlin (1978) studied nucleation in NiMo
binaries using electron microscopy, but were only able to
study the nucleation of N4M0 Dla and N2M0 Pt2Mo. The
DO22 is not stable in the binary alloy.) In Martin's
N4M0 A1 containing ternary (this ternary does not contain
gamma prime) the DO22 and Pt2Mo were shown to form more
or less simultaneously when aged at 600 C. The Dla formed
sluggishly and was present after 2000 hours. The DO22 and
Pt2Mo were still present after this long aging time.
Pt2Mo was the predominant phase, very similar to alloy RSR
209.
In the RSR 197 alloy, the DO22 phase nucleates during
the slow quench from solution heat treatment temperature.
The streaks that appear to emanate from the DO22
reflections towards the Dla reciprocal lattice positions
shown in Figure 5.3a could be better described as
emanating from N4M0 nodes. This would imply that the
N4M0 Dla has formed as very thin platelets, possibly as
faults in the N3M0 crystal structure. This could be
determined by lattice imaging. Figure 5.3c shows both the
DO22 phase and the bright faults that would correspond to
the N4M0.
In the RSR. 197 alloy quenched and aged at 870 C, two
(1, 1/2, 0) microstructures have formed. In the sample
175
aged for one hour there appears to be DO22 and possibly
(1, 1/2, 0) short range order. After aging at the highest
temperature for 100 hours, only SRO spots are present
after the quench. These SRO spots are also imageable.
Since the as-quenched microstructure contained D022>
the presence of DO22 in the material aged for one hour at
870 C might mean that the DO22 that had precipitated
during the quench was not fully in solution after one hour
at 870 C. The solvus for DO22 has been reported at about
800 C for an A1 containing ternary (Martin, 1982). It is
stable to at least 810 C in the RSR 197 alloy. In the
ternary alloy aged for one hour at 870 C and water
quenched, no reflections corresponding to SRO or DO22
phase were seen. Thus, the presence of SRO and DO22
phases in RSR 197 alloy air quenched from the aging
temperature is probably the result of precipitation from
solution during the air quench. The fact that in one
case, the one hour aging case, both SRO and DO22 form and
in the other, only SRO, implies that the gamma phase could
be depleting in Mo during high temperature aging which
would show that the Mo in the as-quenched and lower
temperature aged samples is supersaturated in the gamma
phase with respect to the equilibrium concentration. This
would be expected since no equilibrium Mo rich phases are
present in the alloys aged at lower temperature.
176
6.2 Precipitation in RSR 197
The precipitation of the phases in RSR 197 can be
summarized as follows. Upon quenching, the DO22 phase
precipitates from the Mo supersaturated matrix. The DO22
phase is stabilized by Al. (DO22 has also been shown to be
stabilized by Ta additions to in Ni-Mo binaries. There is
not enough Ta in the matrix phase of RSR 197, however, to
account for the DO22 precipitation in RSR 197). The DO22
phase may nucleate preferentially in at least one of two
ways: 1) under the influence of a strain gradient between
the gamma prime cuboids, or 2) because the distribution of
gamma prime cubes is such that this distribution prohibits
the nucleation of the other two variants between the cubes
in preference for the variant whose c axis is perpendicular
to a gamma prime cube face. Either could explain the
preference of the DO22 to form as a single variant on these
unique 100 faces of the gamma prime cubes. After the DO22
has nucleated, this strain is shown to be about +1.9% in the
direction of the DO22 c axis. Convergent beam electron
diffraction was used to make this measurement.
The N4M0 phase seems to precipitate after the DO22 has
precipitated. The two coarsen and grow in a mutual
relationship along the 100 direction of the cube face,
presumably under the influence of self stress, analogous to
the coarsening behavior of N3AI in Ni-Al binary alloys
(Ardell et al., 1966).
177
Both phases can grow from cuboid to cuboid with
mutual 420 habit planes, as demonstrated by the lattice
image in Figure 5.12. These phases merely represent a
change in the stacking sequence across a common 420 plane.
It is entirely likely that there is no gamma phase
present in RSR 197 aged at 760 C for 100 hours. The dark
field images in Section 5.4.1 show no volume of
intercuboidal gamma phase not occuped by DO22 or Dla.
When aged at 810 C, above the solvus for the N4M0,
only the DO22 phase forms. This is never observed in
Ni-Mo binary alloys. The DO22 still has a slight 420
character but the alloy does not seem as well ordered as
at lower temperatures. The DO22 at this temperature also
precipitates with its c axis perpendicular to a specific
100 face of the gamma prime.
In samples air quenched from 870 after aging, short
range order can exist. This short range order gives rise
to dark field diffraction contrast. This means that it
can be imaged as discreet domains. This very strongly
indicates that the type of (1, 1/2, 0) short range order
diffraction effect observed in RSR 197 is due to
microdomains.
At this highest aging temperature, interfacial
dislocations are formed. If the dislocations are first
allowed to form by aging the alloy at 870 C for one hour
and then the aging is continued at 760 C for 100 hours
without an intermediate quench, the DO22 and Dla phases
178
precipitate and grow just as in the RSR 197 alloy aged
only at 760 C, as discussed in Section 5.1.4.1. The high
temperature aging should reduce any interfacial strain and
thus presumably any intercuboidal strain. The DO22 and
Dla phases still form as previously in the sample aged
only at 760 C for 100 hours. This very strongly indicates
that it is not a strain gradient between the gamma prime
precipitates that leads to preferential nucleation, but
rather the strain induced by the nucleus that will prevent
the nucleation of the variants of DO22 whose c axis is not
perpendicular to the 100 faces of the gamma prime.
The N4M0 Dla phase is not observed as having the
same crystallographic constraints as the DC>22* Along
either cube face, either or both visible variants are
imageable. Based on the observations made in Section
5.4.1, only four N4M0 variants should ever exist between
any two gamma prime faces. If the other two variants were
present, perpendicular twin boundaries would result
between these impinging Dla precipitates. This is the
highest energy antiphase boundary in Dla (Ling and Starke,
1971). These other two variants would also not exhibit
the same crystallographic relationships with the DO22
phase that were described earlier in Section 5.1.4.1.
179
6.3 Precipitation in RSR 209
The N2M0 and N3M0 DO22 phases precipitate during
the air quench from the solution heat treatment
temperature. The presence of aluminum in the gamma phase
stabilizes the DO22 phase. At the lowest aging
temperature, these phases coarsen and eventually the Dla
phase forms. The N2M0 remains the dominant phase for
aging times up to 100 hours.
The N2M0 is also the dominant phase when the RSR 209
is aged at 810 C. It coarsens quickly and is consumed by
equilibrium Mo when aged at the highest temperature.
The formation of the Pt2Mo phase is not a function of
the gamma prime cube distribution, as was the DO22 phase.
It is reasonable to assume that all six Pt2Mo variants can
exist simultaneously in any one region of the gamma
matrix.
6.4 Mechanical Response to Aging
The microhardness data shown in Figure 5.32 are now
mostly explicable by considering the aging processes that
take place in these two alloys. In RSR 197 aged at 760 C,
the alloy begins to order immediately following the
quench. The DO22 and Dla phases continue to order during
aging, and the gamma matrix becomes essentially fully
ordered after 100 hours at the aging temperature. The
increase in hardness correlates with this ordering trend.
180
The alloy aged at 810 C shows almost no change in
strength when aged at this temperature. The DO22 phase
was shown to be present in the gamma matrix. Further
characterization of this heat treatment would be necessary
in order to characterize the DO22 phase more clearly.
This result is not consistent with order strengthening.
Aging at 870 C has little or no effect on the
strength. As no strengthening phase precipitates at this
temperature, this is not a surprising result.
The as-quenched RSR 209 alloy is stronger than the
as-quenched RSR 197 alloy. Apart from the obvious
chemical differences between the two alloys, no other
explanation for this strength difference can be inferred
from any of the observations made in this study. During
the subsequent aging, the alloy, within the time
resolution of testing, loses strength monotonically,
typical of an alloy that is overaging.
The implications of these observations for alloy
design are significant. The mechanical response of the
RSR 209 to aging is what would be expected of an alloy
that undergoes overaging, a common observation in metals
that are strengthened by fine percipitate. The mechanical
response to aging in RSR 197 aged at 760 C would
presumably represent the effect of ordering. Since it is
possible that the Dla phase is the equilibrium phase for
this aging temperature, it may be possible to fully order
181
the matrix with Dla. This would impart high strength to
the alloy, and probably great stability as well.
6.5 Convergent Beam/X-ray Diffraction
The use of the convergent beam technique for lattice
parameter measurements must seem redundant in light of the
x-ray diffraction measurements that were made. The
convergent beam method is a powerful tool with which to
make these measurements since it can be used to make local
lattice parameter measurements, local strain measurements,
and perhaps measurements that would reflect subtle changes
in ordering, ternary ordering, for example. Ternary
ordering might change the symmetry of the convergent beam
FOLZ structure (Ecob et al., 1982).
Only lattice parameter measurements in the gamma
prime phase were practical. The gamma phase was in
general too fine with respect to the beam size to form a
pattern unique to the gamma phase. There was significant
interference between the gamma and gamma prime phases,
invariably resulting in unusuable diffraction patterns.
The same effect was observed in the gamma prime phase when
the beam was placed too close to the gamma phase, yet
still in the gamma prime phase.
It is not possible to quantitatively differentiate
alloying effects using lattice parameter measurements
unless numerous standards exist, and then generally, only
182
in binary alloys can these differences be accurately and
unambiguously determined. Nevertheless, there are some
generalizations that can be stated regarding the lattice
parameter measurements and the partitioning effects in the
RSR alloys. First, the lattice mismatch as measured by
x-ray diffraction between the gamma and gamma prime phases
is greater in the RSR 209 alloy than in the RSR 197
alloy. In both alloys, the gamma phase lattice parameter
is greater than the gamma prime lattice parameter. The
high Mo content in both alloys is responsible for this
effect. In the Ta containing alloy, RSR 197, the gamma
prime phase has a larger lattice parameter than the gamma
prime phase in RSR 209. One interpretation of these
observations is that the Ta, which substitutes readily for
A1 in the gamma prime phase, is the factor that increases
the lattice parameter of the gamma prime in RSR 197. Nash
and West (1979) report that about 8% Ta will increase the
lattice parameter of gamma prime to about 3.59 Angstroms.
The comparable unalloyed N3AI lattice parameter is about
3.57 Angstroms. The EDS data supports this Ta
partitioning hypothesis since it was clearly shown that
the Ta partitions predominantly to the gamma prime phase
in RSR 197 under all the aging conditions in which it was
measured. Thus, the local measurement of the gamma prime
lattice parameter using the convergent beam technique can
show the elemental partitioning differences in a
183
qualitative way that were measured in a semiquantitative
way using the energy dispersive method.
6.6 Conclusions
a) Aluminum stabilizes the DO22 phase in both RSR
197 and RSR 209.
b) Tungsten offsets the effect in a) in RSR 209.
c) Tantalum exerts no effect on the aging behavior
of RSR 197.
d) The partitioning of the quaternary elements can
be determined by quantitative EDS measurements.
These elements are shown to partition as
follows:
1) Ta partitions almost entirely to the gamma
prime phase and
2) W partitions equally between the gamma and
gamma prime phases.
e) The DO22 and Dla phases in RSR 197 aged at 760
are closely related crystallographically and are
shown to share a common 420 plane at their
interfaces.
f) This study has shown that convergent beam
electron diffraction, convergent beam
microdiffraction, and energy dispersive x-ray
analysis provide unique and relevant information
about the microstructures of these superalloys.
184
The multitude of complex reactions described in
this dissertation are mostly explicable based on
the results from the application of these
methods. Convergent beam diffraction is shown
to have sufficient sensitivity to measure the
relative lattice parameter differences between
the gamma prime phases of the two RSR alloys.
These meaurements compare favorably with x-ray
diffraction measurements. Convergent beam
diffraction is also shown to be a powerful but
limited method for measuring strains in
micro-volumes of material.
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APPENDIX A
HOLZ PATTERN CALCULATION
Central to the calculations described in this
appendix is the assumption that the microscope
accelerating voltage can be arbitrarily defined. This
will in turn define a relative crystal standard for the
material that will be characterized. The standard
operating voltage of the microscope is defined to be
100.00 KeV, for which the wavelength will be .037
Angstroms. For B=<(ll4>and 9,3,1 diffracting planes, the
resultant lattice parameter that exactly satisfies the
equation in Section 4.1.3, is 3.5712 Angstroms. For the
standard values just given, the four 9,3,1 HOLZ lines will
intersect at a point in the center of the transmitted
disc. The ratio of A to B (see Figure A) is referenced at
this point to the values of A1 and B1 given in the
attached program listing. A larger or smaller lattice
parameter will cause this ratio to vary. The ratio is
listed as R1 in the table following the program.
To account for noncubic effects, values of A3 and B3
are also calculated in the program. They are ratioed in
the program and appear in the Table as the ratio R2. The
values TI, T2, etc. which appear in the program and in
Figure A are delta theta-Bragg values, where delta
191
192
theta-Bragg equals the value of theta Bragg for aQ =
3.5712minus a0 = x. The standard value for theta-Bragg
is calculated first for each affected line. For example,
theta-Bragg for the 931 lines using a lattice parameter of
3.5712Angstroms, is 2.83255 degrees. A lattice parameter
value larger than 3.5712 Angstroms will result in a
smaller theta-Bragg and hence a positive value of delta
theta-Bragg. Likewise, a lattice parameter smaller than
3.5712Angstroms will result in a negative value for delta
theta-Bragg.
193
Angle PO=angle between
Angle Pl=angle between
Angle S0=angle between
Angle Sl=angle between
10
10
I
I
0 2 and 153
0 2 and 3 9 I
5 3 and 5 I 3
5 3 and 3 9 I
Figure A CBED calculation.
1 o o
1 1 o
1 2 O
1 30
1 4 0
ISO
1 6 O
1 70
1 3 O
1 9 O
200
2 1 O
22 0
23 0
2 4 0
25 0
2 6 0
270
2 8 0
2 9 0
3 0 0
3 1 O
3 2 0
3 3 0
3 4 0
35 0
3 6 0
3 7 0
3 8 0
3 9 0
4 0 0
4 1 O
420
43 0
4 4 0
4 5 0
46 0
470
4 8 0
4 90
5 0 0
5 1 O
52 0
5 3 0
5 4 0
550
56 0
570
5 8 0
5 9 0
6 0 0
6 1 O
6 2 0
6 30
6 4 0
6 5 0
6 6 0
6 7 0
6 8 0
6 9 0
7 0 0
7 1 O
720
7 3 0
7 40
75 0
7 60
770
7 8 0
194
P r t r = 4 O
RESTORE
c r'r nrrnrpc:
DATA 0. 189,G. 1943, 80. 54, 72. 74, 73. 3,27. 113
|
j
REM DEFINE STANDARD CONDITIONS AND INTERFLANAR ANCLES
READ Al,B1,P0,SO,P1,SI
I
i
REM DEFINE LATTICE PARAMETERS
I nd = 0
PRINT 8Pr t r : L_"
PRINT SPrtr: USING 460:
REM
! ***********************
***** DEFINITIONS *****
i *******************'.***
!DlaDspacing:
{
< i
9 3 )
!02sDspac:ng:
j
< 1 0
0 2 >
! D3--spacing :
1
( 9
1 3 )
!D4 sDspacing:
j
( 3
9 1 )
!D5 sDspacing:
i
( 0
10 2)
!DsDspacing:
i
C 9
3 1 >
FOR A* 3.56 TO 3
62
STEP 0
Ind=Ind +1
IF Inda S THEN
PRINT SPrtr:"L"
PRINT SPrtr: USING 460:
IMAGE 5 X "A" 14 X "B" 12X "Rl" 12X"R2"
I nd = 0
END IF
C-A
I nd 2 >1
FOR B*3.56 TO 3.62 STEP 0.005
Dl-l/(l/A*2+81/B*2+9/C2>*0.5
D2-1/ ( 100/A* 2 + 4 /C 2) 0 5
D3l/ <81/A*2+l/B*2+9/C2) 0 5
D 4 1/ <9/A*2+81/B*2+l/C42) *0 .5
D5-1/(100/B* 2 + 4/C 2) 0 5
D 6 a 1/ (81/A*2 + 9/ B2 + l/ C'2) *0 5
TI a2 8 3 2 5 5 -ASN( 0.037/C2*Dl)>
T2a3 0 2 8 3-ASNC 0.037/C2*D2>>
T3a2. 83255 -ASN< 0.037/<2*D4>>
T4-2.83255-ASN(0.037/(2*D3)>
T63 0 2 8 3 -ASN( 0.037/(2*D5>>
T7-2 8 3 2 5 5 -ASN( 0 037/ < 2*D6) >
A 2
AND
B 2
DEFINED
IN
FI CURE
A
A3
AND
B 3
DEFINED
IN
FIGURE
A
A2*A1-TI /TAN(P0)-T2/SIN(P0)+T1 /TAN(SO >-T4/SINCSG)
B2 = B1-T3/TAN(P1 )-T2/SIN(Pl >-T3/TAN(Sl )-Tl /SINiSl >
R1 A 2/B 2
A3 a A 1-T 4/TAN-TI /SIN(SO >
B 3 a B1-T7/T AN(P1>-T6/SIN(P1)-T7/TAN(S1 )-T4/SIN(51 )
R2 =A3/B3
IF Ind2 a 1 THEN
PRINT SPrtr: USING 780:A,B,R1,R2
IMAGE 4(4D.4D,5X)
79 0
8 0 0
8 1 0
820
83 0
8 40
8 5 0
8 6 0
870
8 8 0
195
ELSE
PRINT gPrtr: USING 810:B,R1,R2
IMAGE 14X, 3 < 4D 4D, 5X)
END I F
Ind 2 = 0
NEXT B
Ind 2 = 1
PRINT ?Pr t r :
NEXT A
END
\
196
A
3.5600
3.5650
3.5700
3.5750
B
R1
R 2
3.5 6 0 0
0.8475
0.8475
3.5 6 5 0
0.9082
0.8332
3.5700
0.9777
0.8183
3.5750
1 .0 5 8 0
0.8028
3.5800
1.1520
0.7866
3.5 8 5 0
1 .2 6 3 4
0.7697
3 .5 9 0 0
1.3976
0.7520
3.5 95 0
1 .5 6 23
0.7335
3.6000
1 .76 9 3
0.7140
3.6050
2.0373
0.6936
3.6100
2.3978
0.6722
3.6150
2.9089
0.6497
3 .62 0 0
3.6898
0.6259
3.5600
0.8350
0.9104
3 .56 5 0
0.8966
0.8966
3.5700
0.9673
0.8821
3 .5 75 0
1.0495
0.8669
3.5800
1.1462
0.8510
3.5850
1.2616
0.8343
3.5900
1.4016
0.8168
3.5950
1 .57 5 1
0.7983
3.6000
1 .7 9 5 7
0.7789
3.6050
2.0856
0.7585
3.6100
2.4837
0.7369
3.6150
3.0642
0.7140
3.6200
3.9899
0.6899
3.5600
0.8218
0.9833
3.5650
0.8843
0.9701
3.5700
0.9563
0.9563
3.5750
1.0405
0.9419
3.5800
1 .14 00
0.9266
3.5850
1 .2 5 9 6
0.9105
3.5900
1.4059
0.8936
3.5950
1 .5 8 9 1
0.8756
3.6000
1.8251
0.8567
3.6050
2.1406
0.8365
3.6100 .
2.5838
0.8152
3.6150
3.2520
0.7924
3.6200
4.3750
0.7682
3.56 0 0
0.8080
1.0686
3.5 6 5 0
0.8713
1 .0 5 6 7
3.5700
0.9447
1.0441
3 .5 7 5 0
1 .0 3 0 8
1 .0 3 0 8
3.5800
1.1334
1.0168
3.5850
1 .25 7 4
1 .0019
3.5900
1 .4107
0.9861
3.5950
1 .6 0 4 7
0.9693
3.6000
1 .8 5 8 2
0.9514
3.6050
2.2036
0.9323
3.6100
2.7021
0.9119
3.6150
3.4839
0.8899
3.6 2 0 0
4.8871
0.8664
197
A
3.5800
3.5850
3.5900
3.59 5 0
3.6000
E
R 1
R 2
3.5600
0.7933
1.1698
3.5650
0.8575
1.1599
3.5700
0.9322
1.1493
3.5750
1.0204
1 1 3 e 1
3.5800
1.1261
1.1261
3.5850
1.2551
1.113 4
3.5900
1.4158
1 .0 9 9 7
3.5950
1 .6219
1 .0 8 5 1
3.6000
1 .8 9 5 6
1.0694
3.6050
2.2767
1 .0 5 2 6
3.6100
2.8439
1.0343
3.6150
3.7774
1 .0146
3.6200
5.6014
0.9931
3.5600
0.7778
1 .2 9 2 0
3.5650
0.8428
1 .28 5 1
3.5700
0.9189
1 .2 77 8
3.5750
1.0093
1.2699
3.5800
1.1183
1.2615
3.5850
1 .25 2 4
1 .2 5 2 4
3.5900
1 .4215
1 .2 4 2 7
3.5950
1.6412
1.2321
3.6000
1.9384
1 .2 2 0 6
3.6050
2.3625
1.2081
3.6100
3.0172
1.1944
3.6150
4.1609
1.1794
3.6200
6.6674
1.1629
3.5600
0.7615
1 .4 4 2 2
3.5650
0.8272
1 .4 4 0 2
3.5700
0.9047
1 4 3 8 2
3.5750
0.9972
1 .4 3 5 9
3.5800
1.1098
1,4334.
3.5850
1.2495
1.4307
3.5900
1 .4 2 78
1.4278
3.5950
1 .6 6 3 0
1.4246
3.6000
1 .9 876
1 .4210
3.6050
2.4645
1 .4170
3.6100
3.2338
1.4127
3.6150
4.6833
1 .4 0 7 7
3.6200
8.4299
1 .40 2 2
3.5600
0.7441
1 .6314
3.5650
0.8106
1 .6 3 75
3.5700
0.8894
1 .6 4 4 0
3.5750
0.9842
1.6512
3.5800
1.1004
1 .6 5 9 0
3.5850
1 .2 4 6 3
1 .6 6 7 6
3.5900
1.4348
1.6771
3.5950
1 .6 8 7 7
1 .6 8 7 7
3 6 000
2.0449
1 .6 9 95
3.6050
2.5879
1.7127
3.6100
3.5122
1 .7 2 7 7
3.6150
5.4370
1.7449
3.6200
11.9025
1 .7 6 4 7
3.5600
0.7256
1.8772
3.5650
0.7928
1 .8 9 6 6
3.5700
0.8730
1.9180
3.5750
0.9701
1 .9417
3.5800
1 .0 9 02
1.9681
3.5850
1 .2 4 2 7
1 .9 9 77
3.5900
1.4426
2.0311
3.5950
1.7160
2.0690
3.6000
2.1126
2.1126
3.6050
2.7402
2.1632
3.6100
3.8833
2.2225
3.6150
6.6189
2.2931
198
A
3.6050
3.6100
3.6150
3.6 2 00
B
HI
R 2
3.5600
0.7059
2.2092
3.5650
0.7738
2.2522
3.5700
0.8553
2.3004
3.5750
0.9547
2.3551
3.5800
1.0790
2.4174
3.5850
1 2 38 7
2.4893
3.5900
1.4514
2.5728
3.5950
1.7487
2.6714
3.6000
2.1937
2.7894
3.6050
2.9330
2.9330
3.6100
4.4026
3.1119
3.6150
8.7398
3.3408
3.6200
361.6017
3.6439
3.5600
0.6850
2.6825
3.5650
0.7534
2.7703
3.5700
0.8361
2.8718
3.5750
0 93 BO
2.9903
3.5800
1.0666
3.1306
3.5850
1 .2 3 42
3.2993
3.5900
1.4614
3.5060
3.5950
1.7870
3.7653
3.6000
2.2927
4 0 99 9
3.6050
3.1849
4.5485
3.6100
5.1813
5.1813
3.6150
1 3 6 5 5 9
6.1409
3.6200
-22.0450 .
7.7691
3.5600
0.6626
3.4116
3.5650
0.7315
3.5955
3.5700
0.8153
3.8176
3.5750
0.9196
4.0912
3.5800
1.0529
4.4364
3.5850
1.2290
4.8857
3.5900
1.4728
5.4946
3.5950
1.8324
6.3666
3.6000
2.4161
7.7190
3.6050
3.5281
10.1003
3.6100
6.4786
15.4049
3.6150
37.5772
37.5772
3.6200
-10.0193
-59.7642
3.5600
0.6386
4.6810
3.5650
0.7078
5.1160
3.5700
0.7927
5.6861
3.5750
0.8994
6.4663
3.5800
1.0375
7.5986
3.5850
1.2232
9.3911
3.5900
1.4861
1 2 6 5 e 8
3.5950
1 .8 8 7 3
20.4968
3.6000
2.5744
64.7951
3.6050
4.0231
-46.3215
3.6100
9.0716
-15.8939
3.6150
-37.6188
-9.1446
3.6200
-6.1763
-6 1763
APPENDIX B
INTERPLANAR ANGLES
If the interplanar angles for the 931 lines are
calculated and summed, the sum will not total 180
degrees. For example, for the interplanar angles a (see
Figure 4.8) (angle between 193 and 391), b (angle between
391 and 931), c (angle between 931 and 913), and d (angle
between 913 and 193), the calculated interplanar angles
are a = 27.113 degrees, b = 54.38 degrees, c = 27.113
degrees, and d = 72.74 degrees. The sum of these angles
is 181.35 degrees. Figure 4.8 clearly shows that this
value should be 180 degrees. The discrepancy of 1.35
degrees arises because the calculated values of the
interplanar angles are not the interplanar angles in the
114 plane, the plane in which the diffracted information
appears. The calculated angles are calculated in a plane
perpendicular to the zone axis of the two intersecting
planes. This zone axis, for high order Laue zone lines,
is not perpendicular to the 114 plane. As an example,
consider the angle formed by the intersection of the 111
plane and the 111 plane. The calculated angle between
these two planes is 70.53 degrees. The angle of
intersection projected onto the 001 plane is clearly 90
degrees. A vector common to both the 001 plane and either
111 plane is the cross product of these two vectors. For
199
200
the 001 plane and the 111, the common vector is 110. For
the 001 and the 111, the vector is 110. The angle between
these two <(110]> vectors is 90 degrees, and hence the angle
of intersection of the two ^lll} planes projected onto the
[001] plane. For the 931 planes in the first order zone
of a B = [114] CBED pattern, the interplanar angles in the
[114] plane are a = 26.526, b = 54.11, 3 = 26.526, and d =
72.84. These angles are very close to those calculated
from the standard formula, as above. The sum of the
latter angles is 180.000 degrees, as it must be.
BIOGRAPHICAL SKETCH
Michael Miller Kersker was born on December 30, 1948,
to Peter B. and Marjorie W. Kersker. His birthplace, St.
Petersburg, Florida, was also his home during his
pre-collegiate experiences. He is a graduate of Northeast
High School, St. Petersburg, Florida, and holds a Bachelor
of Arts degree in chemistry from the University of South
Florida, Tampa, Florida.
After graduation, he attended Air Force Officers
Training School at Lackland Air Force Base, San Antonio,
Texas, and subsequently graduated from the Air Force Jet
Pilot Training Program at Webb Air Force Base, Big Spring,
Texas. After graduation, he accumulated thousands of
flying hours while serving in Germany, Thailand, and
finally with the 89th Military Airlift Wing at Andrews Air
Force Base, Maryland. He holds a civilian airline
transport pilot rating, the Ph.D. of flying.
In 1976, after the expiration of his military
obligation, he returned to Florida and was admitted for
graduate study at the University of Florida under
Professor John J. Hren. From 1981 to 1983 he was a senior
scientist at the Alcoa Technical Center, Alcoa Center,
Pennsylvania. From 1983 to the end of 1985, he was
201
202
employed by JEOL USA, Inc., Peabody, Massachusetts, as
product manager for transmission electron microscopes. He
is presently the General Manager and co-founder of a
venture funded company, Electro-Scan Corporation. The
company is engaged in the development, manufacturing, and
sales of a state-of-the-art multi-environmental scanning
electron microscope.
He is a member of EMSA, Tau Beta Pi, Alpha Sigma Mu,
AIME, and MAS. His interests outside of his profession
include reading, music, and racquetball. At the time of
this writing he is the father of four outstanding boys and
the husband of the finest woman south of Fairbanks,
Alaska.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
, Ms)i L
Johh J. Hren, Chairman
Ppfessor of Materials
Science and Engineering
I certify that 1 have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
R. T. DeHoFI
Professor of'Materials
Science and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
, /' L
G.J. Abbaschian
Professor of Materials
Science and Engineering
I certify that 1 have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
-i
E.D. Ver ink, Jr.
Department Chairman and
Distinguished Service
Professor of Materials
Science and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
R. Pepinsk}
Professor of PhyVics
This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
August, 1986 lldLyt Cl-jS
Dean, College of Engineering
Dean, Graduate School
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TITLE: Precipitation in nickel-aluminum-molybdenum superalloys / (record
number: 900946)
PUBLICATION DATE: 1986
fiVr'tA
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Personal information blurred
PRECIPITATION IN
NICKEL-ALUMINUM-MOLYBDENUM SUPERALLOYS
By
MICHAEL MILLER KERSKER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1986
ACKNOWLEDGEMENTS
Special thanks are given to John J. Hren, my mentor
and advisor. I am especially grateful that he is as
stubborn as I. The assistance of Scott Walck, my
colleague and friend, in handling the logistics and
mechanics of my dissertation, is especially appreciated.
The continued support of Dr. E. Aigeltinger is sincerely
acknowledged. I am also grateful to Drs. Kenik, Bentley,
Lehman, and Carpenter for their generous assistance during
my visits to the Oak Ridge National Laboratory. For the
perserverance and persistance of my wife, Janice, I am
most endebted.
I am also indebted to Pratt and Whitney Government
Products Division, West Palm Beach, for providing the
necessary funding to see this project through to
completion, to the SHARE programs at ORNL for the generous
use of their instruments and expertise, and to the
Department of Materials Science and Engineering at the
University of Florida for providing the education,
training, and constant devotion to excellence in research
that have directed my career and scientific character.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii
ABSTRACT vii
CHAPTER
1 INTRODUCTION 1
2 BACKGROUND 7
2.1 Phase Diagrams 7
2.1.1 Binary Phase Diagrams 7
2.1.1.1 Ni-Mo 7
2.1.1.2 Ni-Al 9
2.1.1.3 Ni-W 9
2.1.1.4 Ni-Ta 12
2.1.2 Ternary Diagrams 12
2.1.2.1 Ni-Al-Mo 12
2.1.2.2 Ni-Al-Ta 14
2.1.2.3 Ni-Al-W 16
2.2 Binary Phases 16
2.2.1 Ni-Mo 16
2.2.1.1 N4M0 18
2.2.1.2 N3M0 20
2.2.1.3 N2M0 20
2.2.1.4 Ni-Mo... 23
2.2.2 Ni-W 23
2.2.2.1 N4W 24
2.2.2.2 Ni3W 24
2.2.2.3 Ni£W 24
2.2.2.4 NiW 24
2.2.3 Domain Variants/Antiphase
Boundaries 25
2.2.3.1 N4X (Dla) 25
2.2.3.2 Ni3x(D022> 27
2.2.3.3 Ni2x(Pt2Mo) 29
2.2.4 SRO in Ni-x Binaries 29
111
2.2.5 Ordering Reactions and Kinetics .... 31
2.2.5.1 Binary Alloys 31
2.2.5.2 Ternary Alloys 35
2.2.6 Ni-Al N3AI 36
2.3 Diffraction Patterns: NixMo Phases/
N3AI 40
2.3.1 DO22 Reciprocal Lattice 40
2.3.2 Dla/Pt2Mo/Ll2 Reciprocal Lattices..42
2.3.3 SRO (1, 1/2, 0) Scattering 46
2.3.4 Variant Imaging 46
2.3.4.1 DO22: N3M0 47
2.3.4.2 Da: N4M0 47
2.3.4.3 Pt2Mo: N2M0 51
3 EXPERIMENTAL PROCEDURE 53
3.1 Composition 53
3.2 Heat Treatments 54
3.3 Characterization: Methods of Analysis ....55
4 SPECIAL METHODS 61
4.1 Convergent Beam Electron Diffraction
(CBED) Methods 61
4.1.1 Experimental Technique 63
4.1.2 HOLZ Lines (High Order Laue
Zone Lines) 66
4.1.3 Indexing HOLZ Lines 72
4.1.4 Lattice Parameter Changes 89
4.1.5 The Effect of Strain and
Non-Cubicity on Pattern Symmetry... 91
4.2 Energy Dispersive Methods 97
5 RESULTS 106
5.1Microstructural Characterization 106
5.1.1 As Extruded RSR 197 and RSR 209
Alloys 106
5.1.2 RSR 197-As Solution Heat Treated
and Quenched 106
5.1.3 General Microstructural Features..Ill
5.1.4 RSR 197 Aging Ill
5.1.4.1Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours Ill
IV
5.1.4.2 Lattice imaging of D022
and Dla Phases 127
5.1.4.3 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours 132
5.1.4.4 Solution Heat Treated,
Quenched and Aged at
870 C for up to 100
Hours 134
5.1.4.5 Aging Summary RSR 197...140
5.1.5 RSR 209 As Solution Heat
Treated and Quenched 142
5.1.6 RSR 209 Aging 142
5.1.6.1 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours 142
5.1.6.2 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours 145
5.1.6.3 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours 149
5.1.6.4 Aging Summary RSR 209...152
5.1.7 Special Aging/Special Alloys 153
5.1.7.1 Alloy ?/17 Solution
Heat Treated, Quenched
and Aged at 760 C for
100 Hours 153
5.1.7.2 Alloy //17 Solution
Heat Treated, Quenched
and Aged at 870 C for
100 Hours 153
5.1.7.3 RSR 197 Solution Heat
Treated, Quenched and
Aged at 870 C for 1 Hour,
Furnace Cooled to 760 C
and Aged for 100 Hours at
760 C 156
5.1.7.4 RSR 185 Solution Heat
Treated at 1315 C and
Water Quenched 156
5.2 X-Ray Diffraction Measurements 156
5.3 Convergent Beam Measurements 161
V
5.4 Energy Dispersive X-Ray Measurements ....167
5.5 Microhardness Measurements 167
6 DISCUSSION AND CONCLUSIONS 170
6.1 Metastable NixMo Phase
Formation: Effects of Chemistry
and Microstructure 170
6.2 Precipitation in RSR 197 176
6.3 Precipitation in RSR 209 179
6.4 Mechanical Response to Aging 179
6.5 Convergent Beam/X-Ray Diffraction 181
6.6 Conclusions 183
REFERENCES 185
APPENDICES
A HOLZ PATTERN CALCULATION 191
B INTERPLANAR ANGLES 199
BIOGRAPHICAL SKETCH 201
vi
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
PRECIPITATION IN
NICKEL-ALUMINUM-MOLYBDENUM SUPERALLOYS
By
Michael Miller Kersker
August, 1986
Chairman: John J. Hren
Major Department: Materials Science and Engineering
The precipitation of 420 phases, common in the NiMo
binary system, is also observed in Ni-Al-Mo-(x)
superalloys. Two such superalloys, where x is Ta or W,
were characterized, after aging, using a variety of
electron microscopy methods.
The 420 type NixMo phases that precipitate during
aging depend strongly on the partitioning of the
quaternary elements. The DO22 and Dla phases predominate
in the Ta containing quaternary. The strain between the
gamma prime precipitates is sufficient to suppress the
nucleation of specific DO22 (N3M0) variants, in turn
affecting the subsequent coarsening behavior of the Dla
phase. The crystallographic similarity of these two
VI1
phases is demonstrated by simultaneously imaging the
lattices of the two phases at common interfaces. The
predominant NixMo precipitate in the W bearing quaternary
is Pt2Mo (N2M0), though DO22 and Dla can be present
concurrent with the Pt2Mo.
When aged at temperatures above the solvi for the
NixMo phases, equilibrium NiMo and equilibrium Mo phases
precipitate, the former in the Ta containing alloy, the
latter in the W containing alloy. The presence of these
phases is in general agreement with the expected phase
equilibria predicted by the phase diagram.
Convergent beam electron diffraction, one of the
methods used in the characterization of the alloys, is
shown to have sufficient sensitivity for lattice parameter
variations to qualitatively measure the difference in
partitioning of the quaternary additions to the gamma
prime and gamma phases of both quaternary alloys. The
method is compared to x-ray diffraction results and
confirmed by energy dispersive x-ray analysis. In
addition to the measurement of partitioning, the fine
spatial resolution of the convergent beam method makes it
ideal for the measurement of other factors that are
reflected in lattice parameter changes -- strain, for
example. Simple equations are developed for the indexing
of HOLZ line patterns and for the measurement of lattice
parameters and uniform strain. Examples are given using
the superalloys characterized in this study.
Vlll
CHAPTER 1
INTRODUCTION
No single factor in jet engine design has been as
important as the development of high strength, high
temperature alloys for the hot turbine section of the
engine. This development has proceeded over the
relatively short period from the early 1930's, the early
development days of the jet engine, to the present. These
high strength, high temperature alloys had to maintain
their strength at very high temperatures under very high
load conditions yet still maintain close dimensional
tolerances so that thrust levels would not deteriorate
significantly with time. They had to be capable of
withstanding extremes in thermal cycling and had to resist
degradation under the most severe of hot corrosion
environments. It is no wonder these materials were and
are referred to as superalloys.
Alloy development has proceeded in superalloy systems
as it has historically proceeded in other metallurgical
systems -- empirical trial and test. In this approach
numerous alloys are prepared, fabricated, heat treated,
and tested. The winners are selected based on their
property responses. Compositional tolerances are
determined based again on desirable property limits.
1
2
It is especially fortunate that considerable
microstructural analysis of successful (and unsuccessful)
alloys has accompanied this standard approach to alloy
design. The property-microstructure relationships
developed as a result of correlations made following this
approach have been instrumental in elucidating many of the
known strengthening mechanisms that are now known to
contribute to both high and low temperature strength in
metals. These mechanisms include, among others,
1) precipitation strengthening, 2) solid solution
strengthening, 3) order strengthening, and 4) dispersion
strengthening. An alphabet of elements may be required to
activate these mechanisms and alloys such as TRWNASAVIA
(composition, at.%: Ni-61.0, Cr-6.1, Co-7.5, Mo-2.0,
W-5.8, Ta-9.0, Cb-.5, Al-0.4, Ti-1.0, C-0.13, B-0.02,
Zr-0.13, Re-0.5, and Hf-0.4) were developed seemingly as
confirmation of the old superalloy adage, "The more stuff
we put in, the better it is."
Though TRWNASAVIA is an extreme example of maximizing
desirable properties based on intentional additions (the
alloy contains 1/7 of all known naturally occurring
elements), many other superalloys also contain a large
number of intentionally added elements. These superalloy
compositions are often based on the Ni-Al system. The
microstructure of this "average" Ni based superalloy
consists of essentially three distinct microstructural
features. The first is the matrix, which is usually
3
disordered FCC nickel and can contain numerous elements in
solution. Secondly, there are incoherent precipitates
which can include the carbides, nitrides, and Ni bearing
phases, phases like sigma phase (Sims and Hagel, 1972).
Thirdly, there are the coherent phases which are normally
ordered superlattices of the disordered FCC matrix. The
major FCC ordered phase in such Ni-Al alloys is N3AI, an
Ll2 superlattice also known as gamma prime. This is
normally the strengthening phase in Ni-Al alloys. When
refractory metals are added to Ni-Al alloys, other
coherent phases can also be present as either the minor
precipitate or as the major strengthening precipitate,
e.g., DO22 phase in In 718 (Quist et al., 1971; Cozar and
Pineau, 1973).
Alloys under development at Pratt and Whitney
Government Products Division in West Palm Beach, Florida,
are also based on the Ni-Al system. They are similar to
the ternary alloy WAZ-20-Ds (Sims and Hagel, 1972), but
additionally contain small quaternary additions of Ta and
W. A host of unforeseen solid state reactions proceeds
during low temperature heat treating of the Pratt and
Whitney superalloys (Aigeltinger and Kersker, 1981;
Aigeltinger, Kersker, and Hren, 1979). These reactions
are very similar to those in the Ni-Mo binary system.
Much effort in studying Ni rich, Ni-Mo binary alloys has
been devoted to describing the transition from the
4
disordered state to the ordered state, typically a
transition through the short range ordered state. Very
elegant theories dealing with the nucleation of these
phases have been developed.
These metastable phases can be found in alloys of the
ternary Ni-Mo-Al system, and also in the Pratt and Whitney
quaternary alloys (Aigeltinger, Kersker, and Hren, 1979).
They are not present at the high temperatures normally
encountered in the turbine section of an engine, at
temperatures in the range of 1100 C, and therefore do not
contribute to high temperature strength in such Ni based
ternary and quaternary alloys. Nevertheless, certain
aspects of their microstructures suggest that they might
still contribute to alloy strength at lower than normal
turbine operating temperatures.
The metastable phases investigated here are of the
type NixMo, where x can be 2, 3 or 4. They are coherent
with the FCC matrix which is a Ni rich solution in the
above superalloys. They may be present at temperatures of
700 degrees C and lower for very long times (Martin,
1982), and may delay the precipitation of the equilibrium
phases that would be predicted from the equilibrium phase
diagram.
Though there are similarities in the precipitation of
these NixMo metastable phases among the binary, ternary,
and quaternary alloys described earlier, there are
5
differences, chemistries aside, between the Ni-Mo binaries
and Ni-Mo-Al-(x) alloys, most importantly the presence in
the ternaries and quaternaries of primary gamma prime
phase. Could this gamma prime phase affect the
precipitation behavior of the Nix(Mo,x) phases which
precipitate from gamma solution? Would the physical
constraints imposed by the gamma prime precipitate affect
the "equilibrium" structure of these precipitates after
coarsening? What would be the effect of the quaternary
additions on the metastable precipitation behavior of
these alloys? Would these quaternary additions have any
effect on the gamma prime phase?
In order to answer questions such as these, it was
necessary to characterize the Pratt and Whitney alloys in
a way that such information could be directed towards
answering these questions. The study was to focus on the
use of the electron microscope. The advantage offered by
this instrument in studying fine scale precipitation
phenomena are trivially obvious, copiously documented, and
relatively straightforward. Some microstructural
measurements, however, are not easily accomplished in the
microscope -- the measurement of local composition or the
measurement of local lattice parameters, for example.
These applications were in their infancy and had, for the
most part, not as yet been directed toward practical
problem solving in materials science.
6
This dissertation is about the various phases, both
stable and metastable, that form in the quaternary
Ni-Mo-Al-(Ta or W) alloys. It is about their
crystallography and about various aspects of the alloys'
microstructure that could affect this crystallography. It
is additionally an electron microscope study devoted in
part to exploring methods for studying these phases.
Chapter 2 introduces the reader to the various binary
metastable phases that occur in the alloys and
additionally to theories dealing with their formation. A
brief background in the Ni-Al system will also be
developed. Chapter 3 outlines the alloys, experiments,
and experimental methods chosen for this study. Chapter 4
develops the necessary background in certain special
methods that were employed to study critical features of
the superalloy microstructure. These methods include
convergent beam diffraction and energy dispersive x-ray
analysis. Chapter 5 reports on the results of the
experiments described in Chapter 3. The dissertation
concludes with Chapter 6, a discussion of the results with
the conclusions and inferences therefrom.
CHAPTER 2
BACKGROUND
This chapter will provide the background necessary to
understand the crystallography and precipitate types that
will be described in detail in Chapter 5. It additionally
provides some seminal ideas on nucleation mechanisms for
the ordered nonequilibrium coherent phases that will be
shown to precipitate in the otherwise disordered gamma
matrix. All the known equilibrium phases are also
described and the relevant phase diagrams presented.
Interpretation of the diffraction patterns of the NixMo
coherent phases is explained last.
2.1Phase Diagrams
2.1.1 Binary Phase Diagrams
2.1.1.1 Ni-Mo
The binary Ni-Mo equilibrium phase diagram is shown
in Figure 2.1 (Hansen, 1958). This diagram has been
recently confirmed by Heijnegen and Rieck (1973). Three
equilibrium intermetallic phases can occur: N4M0, a Dla
superlattice, N3M0, an orthorhombic phase, and NiMo, an
orthorhombic phase. Only NiMo is ever at equilibrium with
the liquid.
7
8
WEIGHT PERCENT NICKEL
10 20 30 40 50 60 70 80 90
Figure 2.1 Ni-Mo binary equilibrium phase diagram
(after Hansen, 1958).
9
The N4M0 and N3M0 phases are the result of solid-solid
transformations. There is no true order-disorder
transition temperature for either of them. The N4M0
phase is formed by a peritectoid reaction between gamma
and N3M0: gamma + N3M0 ^=)> N4M0, at 875 C. The N3M0
phase also forms by peritectoid reaction at 910 C; gamma +
NiMo <^=^> N3M0. Above 900 C an alloy of composition N4M0
will be wholly in the gamma disordered FCC region. An
alloy of N3M0 stoichiometry will be a solid solution
above 1135 C.
2.1.1.2 Ni-Al
Figure 2.2 is the equilibrium diagram for the Ni-Al
system (Hansen, 1958). This diagram has been more
recently confirmed by Taylor and Doyle (1972). Two phases
exist on the Ni rich side of the diagram. They are AINi,
a congruently melting compound, and N3AI, an ordered LI2
superlattice phase commonly referred to as gamma prime.
Gamma prime is formed eutectically with gamma (solid
solution Ni and Al) at 1385 C. No solid state reactions
occur in this system at lower temperatures.
2.1.1.3 Ni-W
The Ni-W binary diagram as modified by Walsh and
Donachie (1973) is shown in Figure 2.3 (Moffatt, 1977).
The modified diagram includes the intermetallics NiW and
NiW2
10
Al-N 103
WEIGHT PERCENT NICKEL
Figure 2.2 Ni-Al binary equilibrium phase diagram
(after Hansen, 1958).
temperature
11
WEIGHT % W
Nl 20 40 50 60 70 75 80 85 90 95 W
i''' i i i i _i i i 1 1
1800
1500
1200
900-
600-
300-
Ni 10 20 30 40 50 60 70 80 90 W
ATOM % \N
Figure 2.3
Ni-W binary equilibrium phase diagram
(after Moffatt, 1977).
12
The intermetallic N4W forms by the peritectoid reaction
Ni + NiW ^ = ^>Ni4W at 970 C. The crystal structure of N4W
is isostructural with N4M0 (Epremian and Harker, 1949).
Note the absence of any phase comparable to N3M0.
2.1.1.4 Ni-Ta
The Ni-Ta diagram as given by Shunk (1969) has been
modified to include the low temperature NigTa
intermetallic by Larson et al. (1970). It is shown in
Figure 2.4 (Moffatt, 1977). The NigTa intermetallic forms
sluggishly by peritectoid reaction with NigTa and Ni. It
is reported to be F.C.T. The NigTa phase has been found
to be monoclinic with a possible orthorhombic variant
(TiCog type), or as a tetragonal DO24 superlattice (TiAlg
type). The phase is thus not isostructural with either
NigMo DO22 or with orthorhombic equilibrium NigMo.
2.1.2 Ternary Diagrams
2.1.2.1 Ni-Al-Mo
High temperature Ni-Mo-Al isotherms show a
quasibinary eutectic between the NiAl and Mo phases
(Bagaryatski and Ivanovskaya, 1960). This allows the
diagram to be conveniently split in two at a line
connecting the NiAl and Mo phase fields. At the time this
investigation was originally begun, the Ni-rich low
temperature phase equilibria of this ternary system were
TEMPERATURE,
13
WEIGHT % Ta
Ni 20 4 0 60 70 75 6 0 8 5 9 0 95 Ta
Figure 2.4 Ni-Ta binary equilibrium phase diagram
(after Moffatt, 1977).
14
in question. Guard and Smith (1959-1960) reported the
presence of a ternary compound at 1000 C on the Ni-rich
side of the diagram. This phase was included in a
subsequently derived equilibrium diagram by Aigeltinger et
al. (1978). No other investigator has reported the
presence of a ternary Ni-Mo-Al compound (Bagaryatski and
Ivanovskaya, 1960; Virkar & Raman, 1969; Raman and
Schubert, 1965; Pryakhina et al., 1971; Miracle et al.,
1984).
Aigeltinger et al. (1978), Loomis et al. (1972), and
recently Miracle et al. (1984), extend the maximum
solubility of Mo in N3AI to 6.0 at. % Mo, a value much
higher than that previously reported by Guard and Smith
(1959-1960), Bagaryatski and Ivanovskaya (1960), Virkar
and Raman (1969), Raman and Schubert (1965), and Pryakhina
et al. (1971). Miracle et al. (1984) also report an
additional class II reaction at 1090 C involving gamma,
gamma prime, NiMo, and Mo. This reaction brings gamma
prime, gamma, and NiMo into equilibrium at lower
temperatures. This class II reaction was previously
unreported. A 1000 C isotherm from their work is compared
with the 600 C section from Pryakhina et al. (1971) in
Figure 2.5.
2.1.2.2 Ni-Al-Ta
The Ni-rich side of this diagram has recently been
reviewed by Nash and West (1979). They confirm the
15
b.
Figure 2.5 Ternary Ni-Al-Mo isotherms;
a.) 1038 C (after Miracle et al., 1984)
and b.) 600 C (after Pryakhina et al.
1971) .
>
16
presence of the ternary phase Ni^TaAl, and also NigTa.
The former phase is hexagonal and is not isostructural
with any Ni-Mo-Al phase. According to their 1000 C
section, Ta can substitute for A1 up to 8.0 at.% in gamma
prime (N3AI). It is soluble to approximately 10.0 at.%
at 1250 C.
2.1.2.3 Ni-Al-W
This diagram has been recently determined by Nash et
al. (1983). A 1250 C isotherm from their work is shown in
Figure 2.6. No ternary phase is shown in the isotherm,
nor is a ternary phase reported at temperatures as low as
1000 C. The diagram is qualitatively very similar to the
Ni-Mo-Al ternary diagram shown in Figure 2.5b.
2.2 Binary Phases
2.2.1 Ni-Mo
In addition to the equilibrium phases mentioned in
the previous section, there are intermediate metastable
phases that can precipitate from Ni rich solutions of
Ni-Mo binaries. The practical limit of Mo solubility in
Ni is about 27 atomic percent. Molybdenum in excess of
this amount cannot be put into solution. If a Ni-Mo
binary of 27.0 at.% or less Mo is quenched from a
temperature high enough for the alloy to have been a
17
Figure 2.6 Ternary Ni-Al-W 1250 C isotherm;
(after Nash et al., 1983).
18
single phase solid solution, and subsequently heat treated
below the solvus temperature for that particular
as-quenched composition, intermediate metastable phases
may precipitate instead of the equilibrium phases
predicted by the equilibrium phase diagram. These phases
are N2M0, a Pt2Mo superlattice; N3M0, as a DO22 phase
rather than the equilibrium orthorhombic phase; and/or
N4M0, the previously described binary equilibrium phase
which can exist as a metastable phase at certain NiMo
compositions.
2.2.1.1 N4M0
The N4M0 phase is a BCT structure derived from the
disordered FCC lattice. Its lattice parameters as a BCT
cell are a* = b' = 5.727 Angstroms, c' = 3.566 Angstroms.
The BCT unit cell can be derived from the FCC parent by
using the following transformation:
Al' = 1/2 (3A1+A2); A2' = 1/2 (-A1+32); A3' = 3,
where Al, A2, and S3 are the lattice vectors for FCC and
Al', A2', and A3' are the vectors from the BCT unit cell
(Mishra, 1979). The c axis of the Dla undergoes a
contraction of 1.2% during the transformation from
disordered FCC to ordered Dla. Hence, A3' is only
approximately equal to A3. A convenient way to visualize
the N4M0 structure is to consider the ordering of Mo on
19
a
\* o o, /,.#
o o *\ o d/cP^/o
T\ ? *
? \* r / o/ \ o
o/*yp/# o \*
\ o d'ji\d/o
-\*/ ei ,'jdj^r'm o
V O o
o
o Ni
Open circles: atoms in first and
third layers
Closed circles: atoms in second
layer
Figure 2.7 Two dimensional representation of Dla
stacking showing 1.) FCC unit cell ( ),
2.) Dla unit cell ( ), and 3.) 420 FCC
stacking sequence ( ).
20
every fifth 420 plane of the FCC parent lattice (Okamoto
and Thomas, 1971), as described in Figure 2.7. This
stacking sequence is pertinent. With slight variation it
can also describe the stacking sequences of both N2M0
Pt2Mo and N3M0 DO22 It also simplifies the
visualization of the diffraction patterns for these
phases, c.f., section 2.3.4.2.
2.2.1.2 N3M0
The N3M0 phase exists stoichiometrically as both an
orthorhombic equilibrium phase, where a = 5.064 Angstroms
b = 4.448 Angstroms, and c = 4.224 Angstroms, and as a
metastable DO22 superlattice phase where a* = b' = 3.560
Angstroms, and c' = 7.12 Angstroms. Note that
c(FCC)=c'/2=3.560 Angstroms. The orthorhombic structure
was determined by Saito and Beck (1959) and was shown to
be isostructural with CU3T. The DO22 phase is an
equilibrium phase in the Ni-V system (Tanner, 1968). In
the Ni-Mo system it is not. Figure 2.8a shows the DO22
tetragonal cell. The prominent 420 planes of Mo are now
separated by three 420 planes of Ni instead of four Ni
planes as in N4M0. Figure 2.8b describes this packing.
2.2.1.3 N ip Mo
The N2M0 phase was first discovered by Saburi et al
(1969). It is a Pt2Mo type superlattice, as shown in
21
to
Figure 2.8 The N3M0 DO22 phase;
a.) N3M0 DO22 unit cell and
b.) two dimensional representation
of Figure 2.8a. showing 1.) FCC unit'
cell ( ), 2.) DO22 unit cell
( and 3.) 420 FCC stacking
sequence ( ).
22
a'
Ni
a.
B
to^Of O 0,9 o
>c / Q/ft/jji s
0/\o
o/ o (o,iv0 yo
*"Q x* o Jp/f'/So/
oy^fMoy^
& o 0 'm'o W o O
O Mo
O Ni
B'
b.
Figure 2.9 The N2M0 DO22 phase;
a.) N2M0 Pt2Mo unit cell and b.) two
dimensional representation of Figure
2.9a showing 1.) FCC unit cell ( ) ,
2.) Pt2Mo unit cell ( ), and 3.) 420
FCC stacking sequence ( ) .
23
Figure 2.9a, with lattice constants a' = 2.588 Angstroms,
b* = 7.674 Angstroms, and c* = 3.618 Angstroms. It is
again best described in relation to the FCC lattice. Here
the stacking sequence is 420 planes of Mo separated by two
420 planes of Ni. This stacking is shown in Figure 2.9b.
The Pt2Mo phase is stable in the Ni-V system (Tanner,
1972) .
2.2.1.4 NiMo
The equilibrium delta NiMo phase is orthorhombic with
lattice constants a = 9.107 Angstroms, b = 9.107
Angstroms, and c = 8.852 Angstroms (Shoemaker and
Shoemaker, 1963; Shoemaker et al., 1960). This phase has
deleterious effects on the mechanical behavior of Ni-Mo-Al
superalloys (its crystal structure is very similar to
structures for the embrittling sigma phases) and the
conditions under which it will form in ternary and higher
order alloys should be more extensively studied now that
its deleterious effect on mechanical properties is better
understood.
2.2.2 Ni-W
According to the published phase diagram shown in
Figure 2.3, a NiW alloy of N4W stoichiometry cannot be
put into solid solution. However, a NiW alloy of 20 at.%
W or less quenched from above the peritectoid reaction
temperature and subsquently aged below this temperature
24
will decompose in a fashion similar to the decomposition
of the Ni-Mo alloys and will produce Ni-W phases similar
to those described in Section 2.2.1 (Mishra, 1979). For
example, N3W DO22 and N2W Pt2Mo phases are observed
during the decomposition of quenched and aged N4W
stoichiometric alloys (Mishra, 1979). These metastable
NixW phases are crystallographically identical to the
NixMo phases described in Section 2.2.1.
2.2.2.1 N14W
The N4W is a Dla superlattice with lattice parameters
a' = b' = 5.730 Angstroms and c* = 3.553 Angstroms. This
structure can be derived from the FCC alpha matrix with a
slight tetragonal distortion; here c'/c = .98. It is
isostructural and presumably isomorphous with N4M0.
2.2.2.2 N13W
This phase is crystallographically identical to N3M0
DO22 (see Section 2.2.1.2).
2.2.2.3 Ni?W
This phase is crystallographically identical to N2M0
Pt2Mo (see Section 2.2.1.3).
2.2.2.4 NiW
Equilibrium NiW is an orthorhombic phase (Walsh and
Donachie, 1973) with lattice constants a = 7.76, b =
25
12.48, and c = 7.10. All of these phases and the relevant
Ni-Ta phases are summarized in Table 2.1.
2.2.3 Domain Variants/Antiphase Boundaries
The phases just described exhibit wide variability in
both the crystallographic habits which they can take and
in the interfaces that result from domain impingement.
When these different variants come into contact out of
phase, domain boundaries are created. These interfaces
are known as antiphase boundaries. Common to all of the
ordered precipitates previously described are 1)
translational antiphase boundaries, 2) antiparallel twin
boundaries, 3) perpendicular twin boundaries, and 4)
dissociated antiphase boundaries. The permissible
variants and three of the four antiphase boundary types
are described in the following sections.
2.2.3.1 N4X (Dla)
Thirty different variants can form in this structure
(Harker, 1944). First, the tetrad (c) axis can be
parallel to any one of the three cube axes of the parent
lattice. Second, the a axis of the Ni^x lattice can be
rotated clockwise or counterclockwise relative to the FCC
cube axis. Third, the origin can be shifted, allowing
five independent variants (one x and 4 Ni) to exist.
There are thus 3x2x5 = 30 domain orientations. Ruedl et
al. (1968) have reviewed the three domain boundaries that
Table 2.1
Structural Data
Lattice
Crystal Structure
Lattice Parameter (A)
Ni-Mo
N4M0
BCT/10 atoms
Dla
a
5.727
b
5.727
c
3.566
N3M0
BCT/8 atoms
OO22
3.566
3.566
7.132
N3M0
N2M0
OR/8 atoms
CU3T
5.064
4.448
4.224
BCO/6 atoms
Pt2Mo
2.588
7.674
3.618
NiMo
OR/--
Orthorhombic
9.107
9.107
8.852
Ni-W
N4W
BCT/10 atoms
Dla
5.730
5.730
3.553
N3W
BCT/8 atoms
DO22
N2W
BCO/6 atoms
Pt2Mo
NiW
OR/--
Orthorhombic
7.76
12.48
7.10
NiTa
NigTa
Ni3Ta
Tetr./ --
Ortho/Tetr.
Orth./DO24
7.67
5.10
7.67
4.42
3.48
4.24
NiAl
Ni 3 Al
Cubic/4 atoms
Ll2
3.60
3.60
3.60
NiTaAl
NigTaAl
Hex./--
N3T
5.112
8.357
27
are possible in N4M0. They would be similar in all Dla
structures. They are 1) translational antiphase
boundaries (TAPB), 2) antiparallel twin boundaries (ATB),
and 3) perpendicular twin boundaries (PT).
A translation APB results when the domains have
parallel axes but the origins are shifted by a lattice
translation vector. Figure 2.10 shows one of four
possible TAPB in N4X. The lattice translation vector is
1/5 [130]. The other three vectors are 1/5 [210], 1/10
[135], and 1/10 [3l5].
The antiparallel twin boundary results when two
contiguous domains have their tetrad axes antiparallel.
The possible twinning planes are of the type 200, 020, and
220, relative to the parent lattice. An APT boundary with
200 twinning plane is shown in Figure 2.11.
A perpendicular twin results when the c axis of the
ordered domains aligns with two different axes of the FCC
cube. The lattices are not continuous across the
interface, unlike the other two boundaries. This occurs
in N4X because c/c' is not an integer (see Section
2.2.1.2). Combinations of all three interfaces are
possible.
2.2.3.2 Ni^x (DO22)
The DO22 phase can form twelve variants. The c axis
of the crystal may lie along any one of the FCC cube
axes .
28
Figure 2.10 A translation antiphase boundary in the
Dla structure.
) vector ( )
is in the plane
/
o
o
o
o
o
o
o
r o
o
o
o
o
o
0
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o J
0
o
o
o
G
o
o
o
o
o
o
o
Figure 2.11 An antiparallel
Dla structure.
FCC coordinates
The lattice translation
is 1/5 (130). This vector
of the figure.
o
\0
o
\
o
o\ o
o
o
\
o
o .
o \ o
o
""o
\
\
o
o
o \
o
o
o
\
"""o \
o
o \
. o
o
o
\ 0
o
\
\
o
o
, o
twin boundary in the
The twinning plane in
is the (200).
29
Four origins are possible for each orientation. Thus,
3x4 = 12 variants exist. TAPB and PT interfaces can
result (Ruedl et al., 1968).
2.2.3.3 Nipx (Pt?Mo)
Eighteen different variants can exist. The
orthorhombic cell can have six relationships with respect
to the FCC unit cell. Each domain may have three
different origins. There are thus 6x3 = 18 variants
possible. TAPB, ATB, and PT boundaries have been reported
for the Pt2Mo superlattice N2V (Tanner, 1972).
2.2.4 SRO in Ni-x Binaries
The Nix binary alloys can also exhibit short range
order (SRO). Briefly, SRO in binary alloys is a local
arrangement of atoms in which an A atom has a greater
preference for another unlike atom, say a B atom, than for
another A atom. The presence of diffuse (1, 1/2, 0)
maxima in both x-ray and electron diffraction patterns has
been offered as evidence for the existence of short range
order in Ni-Mo and Ni-W alloys.
Considerable controversy exists over the explanation
of this diffuse (1, 1/2, 0) scattering. These scattered
intensities can be calculated from a model of statistical
arrangements of atoms in which statistical short range
order is maintained, that is, a model in which there is a
30
higher probability of finding a B atom next to an A atom
than there is of finding a B atom next to another B atom.
This model is the statistical-mechanical model originally
proposed by Clapp and Moss (1966, 1968a, 1968b). It is
derived from classical descriptions of SRO.
The scattered intensities can also be derived from a
model in which very small long range ordered (LRO) regions
within the normally disordered matrix diffract to produce
the diffuse maxima. This is the microdomain model,
originally proposed by Spruiell and Stansbury (1965).
They used x-ray diffraction to study the phenomenon in
Ni-Mo alloys. Ruedl et al. (1968) used dark field
electron microscopy to image these small LRO domains.
They found, as did Das and Thomas (1974), Okamoto and
Thomas (1971), and Das et al. (1973), that the microdomain
model could explain the very fine precipitate that they
were able to image using the (1, 1/2, 0) diffuse
reflections. Similarly, deRidder et al. (1976) proposed a
cluster model which describes clusters of atoms with
simple polyhedral arrangements. The polyhedral clusters
so described are actually prototypes of long range order,
though they can also be considered as most probable
arrangements and hence statistical. In addition to
explaining diffuse maxima at the (1, 1/2, 0) positions,
these clusters can explain other diffuse maxima in
electron diffraction patterns of Ni-Mo binary alloys.
31
The former statistical model implies that the short
range ordered structure will probably not be the same as
the structure of the long range ordered phases that will
ultimately precipitate. In the microdomain model, the
short range ordered structure may be the same as the final
long range ordered structure since the model structure is
in fact merely a microcell of the final long range ordered
cell.
2.2.5 Ordering Reactions and Kinetics
2.2.5.1 Binary Alloys
Ni-20% Mo. This composition corresponds to
stoichiometric N4M0. Saburi et al. (1969) used electron
microscopy to study the ordering kinetics of a Ni-20% Mo
binary alloy quenched from solid solution and aged at 800
C. They conclude that the ordering process is
heterogeneous. Long range ordered domains of N4M0
nucleate in the matrix and grow with time. Domain
impingement is characterized by numerous perpendicular
twin plates. Chakravarti et al. (1970) used both TEM and
FIM (Field Ion Microscopy) to study the ordering of Ni-20%
Mo from solid solution. At 700 C they report that the
transformation is wholly homogeneous. A fine, mottled
"tweed" structure develops with aging times of up to and
less than three hours. After three hours, heterogeneous
precipitation of N4M0 is observed along grain
boundaries. Ling and Starke (1971) used x-ray line
32
broadening techniques to calculate LRO parameters, domain
size, and microstrains in similarly aged material. Their
conclusions support those of Chakravarti et al. (1970).
Das and Thomas (1974) used TEH to study ordering at
650 C. After eight hours at 650 C they found diffraction
evidence for the existence of N2M0 and N4M0. They
explain the presence of N2M0 as being due to
nonconservative antiphase boundaries on (420) planes of
N4M0. The regions of APB thus formed correspond to small
ordered regions of N2M0 within the N4M0 ordered layers.
Above 650 C, there was no evidence of N2M0
precipitation. Only N4M0 precipitated.
Ni-25% Mo. Yamamoto et al. (1970) were the first to
study the structural changes during aging of a
stoichiometric N3M0 binary alloy rapidly quenched from
1100 C. At 860 C, both N2M0 and N4M0 precipitate from
the disordered matrix. These phases are subsequently
consumed by the growth of the ordered orthorhombic N3M0
phase which nucleates at grain boundaries. Following this
work, Das and Thomas (1974) aged a quenched stoichiometric
N3M0 alloy at 650 C. They hoped, by aging at this lower
temperature, to reduce the nucleation kinetics so that the
earlier stages of decomposition (which were presumably
missed in the work of Yamamoto et al.) could be studied.
They confirm the results of Yamamoto et al. (1970), i.e.,
the presence of both N2M0 and N4M0 during the initial
33
stages of ordering. In this study the N2M0 existed as a
discreet phase, unlike the N2M0 in the N4M0 aging study,
which Das and Thomas (1974) presume occurred as the result
of the formation of a non-conservative AFB.
Van Tendeloo et al. (1975) have summarized their work
on Ni-2570 Mo alloys and the works of the others as
follows: at 800 C, the N3M0 ordering (decomposition)
follows the sequence FCC SRO DO22 N4M0/N2M0 HCP
- N3M0 orthorhombic. In their work, the DO22 phase forms
only when the quench from solid solution is especially
fast. From this observation they presume that the DO22
phase precedes the precipitation of both the N2M0 and
N4M0 phases, and further, that this DO22 precipitation
was not reported by any of the other previous
investigators because the alloys were not quenched fast
enough in the previous studies. Nevertheless, both the
work of Van Tendeloo et al. (1975) and the work of Das et
al. (1973) show that the stabilization of DO22 at the
N3M0 stoichiometry is especially difficult.
Ni-10% Mo. The first work in an off stoichiometric
alloy was that of Spruiell and Stansbury (1965) who
proposed to have found SRO in their x-ray study of
quenched Ni-10% Mo. The diffuse maxima they detected at
(1, 1/2, 0) positions were retained for aging times of up
to 100 hours at a temperature of 450 C, and though these
maxima sharpened with time, no superlattice ever
developed.
34
Ni-17% Mo. Nesbit and Laughlin (1978) studied off
stoichiometric Ni-16.7% Ho. Two mechanisms of ordering
are suggested from their study:
1. the ordered phase (N4M0) may form
heterogeneously from the disordered
supersaturated solid solution by heterogeneous
nucleation, or
2. the ordered N4M0 phase may form homogeneously
throughout the gamma matrix by one of the
following mechanisms:
a. spinodal clustering followed by ordering
within the solute region,
b. spinodal ordering, and
c. continuous ordering in which the final
equilibrium structure evolves continuously
from a low amplitude quasi-homogeneous
concentration wave.
Their results show that ordering at 750 C takes place
by the homogeneous nucleation of N4M0. At 700 C,
reasonable evidence exists for the mechanism to be
spinodal ordering. Continuous ordering is not plausible
since the SRO maxima do not correspond to maxima in the
long range ordered state. They did not age at a high
enough temperature to draw any conclusion about the
possibility of heterogeneous nucleation of N4M0.
35
2.2.5.2 Ternary Alloys
Yamamoto et al. (1970) studied the effects on the
precipitation behavior of the NixMo of small ternary
additions of Ta to stoichiometric N3M0. They found that
the DO22 phase was formed in the alloy containing 5 at.%
Ta. Van Tendeloo et al. (1975) and Das et al. (1973) were
not able to stabilize the DO22 phase in binary Ni-25%
alloys. In aged ternary alloys containing 2 at.% and less
Ta, no DO22 phase was detected. The diffuse scattering at
the (1, 1/2, 0) positions in electron diffraction patterns
was characteristically present, but no DO22 superlattice
spots developed during aging. They speculate that other
elements might stabilize DO22 phase, for example, Ti and
Nb. These are similar to Ta in that the atomic radius of
each is larger than the atomic radius of the Mo. Elements
which might not stabilize DO22 are presumed therefore to
be V, Fe, and Co, even though N3V as DO22 is the stable
precipitate in the Ni-V system (Section 2.2.1.2). These
atoms are of smaller atomic radius than Mo. No evidence
is offered to support these speculations.
Martin (1982) has recently studied the effects of
additions of Al, Ta, and W to N3M0 stoichiometric alloys
on the nucleation and growth of NixMo metastable phases.
His explanations for the precipitation of phases in these
alloys follow closely those of deFontaine (1975), deRidder
et al. (1976), Chevalier and Stobbs (1979), and
36
originally, Clapp and Moss (1966, 1968a, 1968b). His
findings show that the transformation from the SRO ordered
state to the long range ordered one is as follows.
Initially the Pt2Mo phase forms in all the ternary
alloys. In the A1 containing alloy, the Pt2Mo
precipitates concurrently with DC>22* In the W containing
alloy, DO22 is not stabilized. All three NixMo metastable
phases can co-exist in the A1 bearing ternary, but only
N2M0 and N4M0 in the Ta and W containing one. The final
ordered state in all three cases is the equilibrium
orthorhombic N3M0 phase, which heterogeneously nucleates
at grain boundaries and subsequently consumes the body of
the grain. The presence of Ta greatly accelerates the
kinetics of the formation of this final, equilibrium
phase.
2.2.6 Ni-Al N3AI
Nickel-Aluminum alloys that would be candidates for
superalloy applications are generally two phase alloys
consisting of gamma phase, the disordered FCC matrix, and
gamma prime phase, an LI2 superlattice of the FCC matrix
corresponding to the approximate stoichiometric
composition N3AI. The crystal structure of this compound
is shown in Figure 2.12.
When small volume fractions of gamma prime are
precipitated from gamma solid solution, that is, when the
alloy is relatively lean in A1, the gamma prime will first
37
A
c
b
Al
Ni
Figure 2.12 The N3AI unit cell.
38
appear as fine, spherical precipitate (Weatherly, 1973).
This spherical morphology will change as the lattice
mismatch between the gamma prime and gamma matrix
changes. The spherical precipitates occur for mismatches
of -0.3% above which cube morphologies predominate,
independent of size or volume fraction of gamma prime
(Merrick, 1978). When gamma prime precipitates as cubes,
the cube habit is (100) gamma//(100) gamma prime.
When the gamma prime precipitate size is small
(100-300 Angstroms), the coherency of the precipitate is
not lost and can be maintained by a tetragonal distortion
at the matrix/precipitate interface (Merrick, 1978). When
coherency is lost, the lattice mismatch between the two
phases can be accommodated by a dislocation network. This
network has been characterized for Ni based superalloys by
Lasalmonie and Strudel (1975). Since the morphology of
the gamma prime is a sensitive function of lattice
mismatch, it follows that this mismatch can be varied by
making alloy additions to the binary alloy which will
partition preferentially to one or the other of the two
predominant phases. In pure binary alloys, Phillips
reports this lattice mismatch at 0.53% (Phillips, 1966).
In ternary and higher order alloys, the mismatch is widely
variable due to elemental partitioning differences between
the two phases.
Gamma prime is a unique intermetallic phase. Its
major contributions to strength are the result of both
39
antiphase boundary formation and modulus strengthening
(Sims and Hagel, 1972). The strength of the gamma prime
increases with temperature, an anomaly not yet fully
explained. The phase also remains fully ordered to very
high temperatures (Pope and Garin, 1977).
In the early stages of gamma prime precipitation in
Ni-Al alloys, side band satellites in x-ray powder
diffraction patterns appear. These satellites were first
thought to correspond to periodic modulations in structure
(Kelly and Nicholson, 1963). These presumed modulations
lead to the speculation that the mechanism of Ni-Al
decomposition was spinodal. Cahn (1961) originally
suggested this possibility. The data of Corey et al.
(1973) and Gentry and Fine (1972) suggest that this
mechanism is possible at high supersaturations. Faulkner
and Ralph (1972) studied the early stages of precipitation
in a more dilute Ni-Al 6.5 wt.% alloy using FIM and
conclude that the spinodal ordering mechanism is
unlikely. They suggest that the sidebands are due to
particle morphology changes during the early stages of
decomposition.
The nucleation of the gamma prime could not likely
explain the "macro" order in the microstructure, the large
uniformly sized and distributed gamma prime precipitates
that are present in the alloys studied here. Ardell et
al. (1966) explain this ordered microstructure with a
40
model which explains the gamma prime alignment and uniform
size by considering the coarsening behavior of gamma prime
precipitates under the influences of mutual elastic
interactions between the coarsening gamma prime
precipitates. Ardell's model provides the most reasonable
explanation for the development of the microstructures in
alloys like those discussed in Chapter 5 of this
dissertation.
2.3 Diffraction Patterns: NiyMo Phases/Ni^Al
The reciprocal lattices of the various NixMo phases
can be constructed easily based on the crystallography of
each precipitate type. Since it is easiest to relate the
diffraction patterns of each to the parent FCC lattice,
(here the disordered gamma phase), this will be done for
the DO22 N3M0 phase. The other diffraction patterns were
similarly constructed.
2.3.1 DO?? Reciprocal Lattice
The DO22 is a tetragonal cell with atom positions at
Mo (000), (1/2, 1/2, 1/2);
Ni (1/2, 1/2, 0), (1/2, 0, 1/4), (1/2, 0, 3/4)
(0, 1/2, 1/4), (0, 0, 1/2), (0, 1/2, 3/4).
The structure factor can then be written as the summation:
F= Mof (1+exp ("IT i (h-f-k+1) ) + wif t (exP 71" i (h+k) ) +
exp(TTi(l)) + exp(tt(h+1 /2)) + exp(tr i(k+l/2)) +
exp(TTi(h+3l/2)) + exp(rr i(k+31/2)) L
41
h k 1
E 0 0
0 0 E
0 E 0
E E 0
E 0 E
0 E E
0 0 0
0 0 0
0 0 0
0 E 0
E 0 0
0 0 0
0 0 E
0 0 E
0 0 0
0 0 0
E 0 0
0 E 0
* A = 2fMo
+ B = 2fMo
Table 2.2 -- Structure Factor Values
F
A*
B+ if 1 = 2(n+1), n even OR
A if 1 = 2n
A
A
B if 1 = 2(n+1)
A if 1 2n
B if 1 = 2(n+1)
A if 1 = 2n
0
0
0
0
0
B
0
0
B
B
0
0
+
6fNi
2fNi
42
Substitution of values for h, k, and 1 yields the series
of values for F in Table 2.2
The DO22 reciprocal lattice constructed using those
values of F listed in Table 2.2 is shown in Figure 2.13a.
The lattice is constructed using DO22 coordinates and
compared to a corresponding FCC construction in the two
dimensional B = [100] and B = [001] sections shown in
Figure 2.13b. Note that both the (020) and (200) of the
DO22 correspond to the (020) and the (200) of the parent
FCC lattice since a/2 FCC = a/2D022* Also, the (004) DO22
= l/4(2a) (the "A" indices from Table 2.2) = a/2 FCC. The
fundamental reflections of the DO22 are then in the same
reciprocal lattice positions as the fundamental FCC
reflections. The (Oil), (022), etc. of the DO22 are 1/4
multiples of the FCC (042). This makes the Mo rich (Oil)
planes of the DO22 structure the (042) Mo rich planes of
the FCC parent lattice.
2.3.2 Dla/Pt2Mo/Ll2 Reciprocal Lattices
Similar constructions result in the reciprocal
lattices of N4M0 and N2M0, shown respectively in Figures
2.14 and 2.15, both lattices in FCC coordinates. The
reciprocal lattice of the FCC ordered gamma prime is shown
in Figure 2.16.
43
a.
004 0?4
002 042
000 020
.200 220
b.
Figure 2.13 The DO22 phase;
a.) the reciprocal lattice for the DO22
phase and b.) B= [010] left, [OOl] right,
DO22 left, FCC right.
44
02
022
Figure 2.14 The reciprocal lattice for Dla.
Figure 2.15 The reciprocal lattice for Pt2Mo.
45
Figure 2.16 The reciprocal lattice for the LI2
structure.
46
2.3.3 SRO (1, 1/2, 0) Scattering
In Ni-Mo binary alloys, SRO is characterized by
diffuse scattering at the (1, 1/2, 0) positions. (All g
vectors will subsequently be defined in FCC coordinates.)
Diffraction patterns of (1, 1/2, 0) SRO for B = [100] and
B = [112] are shown in Figure 2.19a. Characteristic of
this scattering is the absence of any true superlattice
reflection, for example, the (100) and (011) reflections
of either the DO22 or the LI2 superlattices. Because
gamma prime phase is always present in the alloys studied
here, any selected area diffraction pattern will always
contain LI2 superlattice reflections. Discriminating
between the DO22 superlattice reflections and scattering
at (1, 1/2, 0) SRO positions with superimposed LI2
superlattice reflections is difficult. There are two ways
to differentiate SRO from the LI2 and DO22 superlattices,
both of which are discussed in Chapter 5.
2.3.4 Variant Imaging
In section 2.2.3 of this chapter, a plethora of
possible variants for each precipitate were given. As
should be readily apparent from the reciprocal lattice
constructions of this section, only certain of these
variants are imagable with the electron microscope. Many
47
of the aforementioned antiphase boundaries are
indistinguishable.
2.3.4.1. P022: N3M0
There are three easily differentiated variants in the
DO22 structure, each corresponding to the c axis of the
DO22 being parallel to one of the cube axes of the parent
FCC lattice. This is shown in Figure 2.17a. All three
variants may be visible simultaneously. Indexed [001] and
[112] diffraction patterns are shown in Figure 2.19b.
2.3.4.2 Da: N4M0
Six distinguishable variants of Ni4Mo are possible.
These correspond to the tetrad axis of the Dla being
parallel to the parent FCC cube axes (three variants) and
further, the a axis of the N4M0 rotated cw or ccw about
the c axis relative to each FCC cube axis. Only two of
the six distinguishable variants will be visible along any
B = 100 imaging condition. These two are the single
axis clockwise and counterclockwise rotated variants shown
in Figure 2.18a. The B=[100] indexed diffraction pattern
corresponding to these two real space variants is shown in
Figure 2.18b. Indexed B = [001] and B = [112] N4M0
diffraction patterns are shown in Figure 2.19c.
a.
002
022
r¡
III
? A *
II
000
Alll 0
020
Fundamental
A
Superlattice
b.
Figure 2.17 The DO22 phase;
a.) DO22 variants along FCC axes
and b.) B = [lOO] SADP with variants
o
\ o o o .\ O
o \ o O *^o O \m
o o \ o # o ^ o J&r'
"o \ o #o\# o *-C5r o
o # o \* o -* o *\ o o'
o o .\o|o\. O^J^)-
Cr* o ' o § o'* o £r* o *\
A
o / o <£V / o / o
o^./o O/* o */o
^ / O # o / o '(A O
o / t. o # o 4 oi-
/ o / -f o o 0/
0^0 ./O# o/, o , O /
o*'* o O O / o ^
B
a.
b.
Figure 2.18
The Dla phase;
a.) Dla variants along FCC axes and
b.) B = [lOO SADP with variants.
50
C20
420
0 0 0 Q
s'
iv2o
000 200
220
0
y
y
s
y 0
402
a.
220
402
/
020 420
0 jm
0
9"
y
0 ^
0 0 j¡y
0
/
0
y u
a
000
Ooo
in
b.
020
420
0 0^,0''
ja'
s ^ -ffT a
^er
000
2 20
3
4 02
X
e y
0 y£ a
Ja 0 a
r
000 ii
0
0
020
2 2 0 4J>2
420
/
0 0 0 0 j£ 0 El
s'
0 a j-y
G
/
0 0^00 00
0
\
m
0
/
000 111
d.
Fundamental
a Superlattice
Figure 2.19 Indexed B = [001] and B = [Tl2]
reciprocal lattice sections of
a.) (1, 1/2, 0) S.R.O., b.) DO02,
c.) Dla, and d.) Pt2Mo.
51
2.3.4.3 Pt?Mo: NipMo
In N2M0, the imaging conditions are identical to
those for N4M0. The c axis of the superlattice may be
parallel to one of the cube directions in the FCC parent.
As in Dla, there are two orientation possibilities per
cube axis, as shown in Figure 2.20a. The real space
lattice and the corresponding B=[001] indexed diffraction
pattern are shown in Figures 2.20a and 2.20b. Indexed B =
[001] and B = [112] diffraction patterns are shown in
Figure 2.19d.
All of the above phases may be present
simultaneously. When this happens, all of the diffraction
patterns overlap.
*o
52
t
0 S Os 0*0 S Os o
jfo*Os m xos
0*.Z*os'XSO
O o#o r O o % o
/o*oyo40i o>o
^ o'^o O o'#
V V v
O *sO # o ^0,o # O
VO soA\o\X0 *
v,*x VO v,^ *p
Vo,* vO vA* *p
#o*0*o#*0*o
B
002
B A
ffl
b.
Figure 2.20 The Pt2Mo phase;
a.) Pt2Mo variants along FCC axes.
A and B can exist along each axis.
b.) B = [100] SADP with variants.
CHAPTER 3
EXPERIMENTAL PROCEDURE
3.1 Composition
Two major alloy compositions were chosen for this
investigation. They both represent potentially attractive
alloys for gas turbine blade applications. These two
alloys are designated as RSR 197 and RSR 209. They are
prepared by a powder metallurgy process developed at Pratt
and Whitney Aircraft Government Products Division. They
are two of a multitude of experimental alloys under
development for future high temperature turbine blade
materials. The RSR in the alloy designation is an acronym
for a rapid solidification process to be described
subsequently. The numbers 197 and 209 are arbitrary
numbers representative of the sequence in which the alloys
were prepared. The composition of these two alloys is
given in Table 3.1.
In the RSR process, the desired alloy is melted under
inert conditions (under argon gas) and allowed to impinge
in the molten state onto a rapidly rotating disc (Holiday
et al., 1978). The resulting spherical liquid metal
droplets are quenched in a stream of cooled He gas. The
powder is collected and canned under inert conditions.
53
54
In addition to alloys 197 and 209, an additional
ternary alloy was prepared by arc melting rather than by
the RSR process. The composition of this ternary, alloy
//17, was chosen as being representative of a compromise
ternary composition between the composition of RSR 197 and
RSR 209 (Table 3.1). The Ta and W were, of course, not
present in the ternary alloy.
Alloy 185, an alloy similar to RSR 209, was used for
only one experiment. Its composition is given in Table
3.1.
3.2 Heat Treatments
The canned RSR 197 and RSR 209 alloys were soaked at
1315 degrees C for four hours and extruded as bar at an
extrusion ratio of 43/1 at 1200 C. The extruded bars were
subjected to the various heat treatments described in
Figure 3.1. The heat treatments were conducted in a
vacuum furnace accurate to + 5 C. The times and
temperatures for these thermal treatments were chosen
based on the times and temperatures for aging binary Ni-Mo
alloys described in Chapter 2. The processing variables
are summarized in Figure 3.1.
The arc melted sample and an RSR 185 sample were
encapsulated in evacuated and He backfilled quartz tubing
prior to thermal treatment. The arc melted samples were
wrapped in four nines pure Ni foil to prevent reaction
55
with the quartz tube during solution heat treating and
aging. The arc melted samples were solution treated at
1315 C for four hours in a tube furnace and water quenched
upon completion of the solution treatment. RSR 185 was
prepared for electron microscopy directly after quenching
(Martin, 1982). Alloy //17 was re-encapsulated, as above,
and subsequently aged in a second tube furnace. The aging
practice is described in Table 3.1. Samples were water
quenched upon completion of aging.
3.3 Characterization: Methods of Analysis
Longitudinal slices were taken from the bar centers
of the extruded RSR alloys and from the center of the
sliced button, alloy //17, mechanically thinned to 130
microns, and jet polished in a solution of 80% methanol,
20% perchloric acid until perforated. The foil for the
RSR 185 alloy was prepared by Martin as described by
Martin (1982). Foils thus prepared were examined in a
Philips 301 Scanning Transmission Electron Microscope
(STEM) and in a special Philips 400 STEM. This latter
microscope is equipped with a field emission gun which
allows small, high intensity beams to be used in the TEM
mode. Special operating features of this microscope are
described in Section 4.1.1 of Chapter 4.
Four different electron diffraction methods were used
to generate the diffraction patterns shown and discussed
56
in Chapters 4 and 5. They are 1) selected area
diffraction (SAD), 2) Riecke method C-2 aperture limited
microdiffraction, 3) convergent beam diffraction, and 4)
convergent beam microdiffraction.
If the sample area selected by the selected area
aperture was reasonably strain free, that is, free of
buckling and bending, then the selected area diffraction
mode was used to generate large area diffraction
patterns. The area defined by the aperture was minimally
3 square microns. If this method could not be used
because of buckling and bending, the Riecke method
(Warren, 1979) was used. The area defined by this method
is much smaller than that defined by the selected area
method, about 0.6 square microns. This area is too small
to be representative of the sample as a whole. The above
two methods produce diffraction patterns that are similar
in appearance and application. They both produce fine
diffraction spots in the diffraction patterns and are thus
amenable to the detection of subtle scattering effects.
Convergent beam diffraction is a spatially localized
diffraction method. Only hundreds of square Angstroms are
analyzed. The diffraction pattern consists of large discs
rather than diffraction spots. Subtle diffraction effects
are usually masked by the elastic intensity distributions
in these discs. The elastic information in the discs
57
makes the convergent beam method uniquely suitable for
other purposes, however. These are reviewed in the
following chapter.
Convergent beam microdiffraction is also a spatially
localized diffraction method. Again, only hundreds of
square Angstroms are analyzed. The diffraction pattern
consists of discs rather than spots. These discs are
quite small in comparison to normal CBED discs and may be
dimensionally comparable to the spots seen in selected
area and Riecke patterns. If subtle diffraction effects
are present, they will not be masked if this diffraction
method is used.
In addition to electron diffraction, the electron
microscopes were used to produce bright field, dark field,
and lattice images. The 400 FEG instrument was also used,
in conjunction with a KEVEX energy dispersive x-ray
detector and a DEC 1103 minicomputer, as an analytical
x-ray system for x-ray analysis of the RSR alloys. The
data reduction scheme for quantification was developed by
Zaluzec (1978) Details of these analyses are discussed
in the following chapter.
To test the accuracy and applicability of the
convergent beam diffraction method for the measurement of
local lattice parameters, the lattice parameters of the
RSR alloys were measured using x-ray diffraction. The
58
measurements were made with a General Electric horizonal
main protractor diffractometer using Ni filtered Cu
K-alpha radiation. Data thus generated were also used to
measure the lattice mismatch between the gamma and gamma
prime phase in the RSR alloys.
Rockwell C microhardness measurements were made on
most of the RSR aged alloys. Six hardness values from
each sample were recorded.
ARC MELTED
Figure 3.1 Processing Variables
60
Table 3.1 Alloy Compositions
RSR 197
RSR 209
RSR 185
//17
at% wt%
at% wt%
at% wt%
at7o wtT,
Ni
76.0 73.9
74.0 72.6
73.8 72.6
77.0
A1
13.0 5.8
15.0 6.8
15.0 6.7
14.0
Mo
9.0 14.3
9.0 14.4
9.0 14.4
9.0
Ta
2.0 6.0
W
2.0 6.1
2.0 6.0
Y
.015
LO
I1
o
C
.2
--
CHAPTER 4
SPECIAL METHODS
This chapter will explain the methods used to measure
the partitioning of elements to the gamma and gamma prime
phases. The convergent beam diffraction method is one
method described extensively in this chapter. Simple
equations are developed which aid in interpreting the
patterns and further allow simulated patterns of
experimental patterns to be generated. The results of the
lattice parameter measurements and strain measurements
made using the CBED method are given in Chapter Five.
Chapter Four also includes a brief section on energy
dispersive analysis, specifically as it relates to the
characterization of the alloys analyzed in this study.
4.1 Convergent Beam Electron Diffraction
(CBED)Methods
A convergent beam electron diffraction pattern is
similar to a selected area diffraction pattern with one
major and self-defining difference: a convergent beam
pattern uses a focussed beam with a large convergence
angle to define the area from which the diffraction
61
62
pattern will be taken. Beam convergence angles generally
range between 2 x 10"3 rads to 20 x 10"3 rads. The
resulting pattern consists of a number of diffracted
discs, each disc corresponding to a diffracted beam.
The selected area diffraction pattern is formed using
a large beam that is essentially parallel. The area from
which the diffraction pattern is taken is defined by an
aperture, the selected area aperture. Beam convergence is
usually on the order of 1 x 10"^ rads. The resulting
pattern consists of diffraction spots. Each spot
corresponds to a diffracted beam.
The convergent beam electron diffraction (CBED)
pattern is usually formed in the back focal plane of the
objective lens, just as is the diffraction pattern in the
selected area diffraction mode (Steeds, 1979). The CBED
pattern contains a wealth of information about the
crystallography of the diffracting crystal, in many cases
much more information than is contained in the selected
area diffraction pattern. This information appears in the
discs of the pattern and can be used in 1) identification
of the diffracting crystal's point and space groups
(Buxton et al., 1976), 2) identification of Burgers
vectors (Carpenter and Spence, 1982), 3) the measurement
of local lattice parameters (Jones et al., 1977), 4) the
measurement of foil thickness (Kelly et al., 1975),
63
and 5) the measurement of uniform lattice strain (Steeds,
1979) .
4.1.1 Experimental Technique
There are a number of methods for forming the
convergent probe. The most common method in modern STEM
instruments is to use the STEM "spot" mode to translate
the already convergent probe to the area from which the
pattern will be taken. In the STEM mode, the imaging and
projector lenses are already configured to form a
diffraction pattern. Convergence in the probe is
controlled by the selection of a suitable second condenser
aperture. Suitable is defined as the maximum aperture
size that will still give discreet, non-overlapping discs
in the diffraction patterns. The covergence angle alpha
is defined as the angle subtended by the radius of the
disc. Choice of the proper aperture size will obviously
depend on the lattice parameter and orientation of the
crystal from which the pattern will be taken.
Even more simply, the probe may be focussed directly
in the TEM mode, a situation which yields acceptable beam
convergence but usually with large probe sizes. Once the
probe has been focussed using the condenser controls, the
proper lens excitations to image the diffraction pattern
are selected, usually by selecting the diffraction mode of
the instrument, and a CBED pattern results.
64
Alternatively, the objective lens may be overexcited
in the TEM mode (a situation that approximates a STEM
condition), and the probe then focussed with the second
condenser lens. The resulting probe will be smaller than
a conventional TEM probe, but generally, depending on the
amount of overexcitation, larger than the standard STEM
probe (Steeds, 1979). Under this condition, the
diffraction pattern appears in the imaging plane of the
objective lens rather than in the back focal plane. The
lens optics for this condition cannot be found in standard
texts. The reader is referred to Olsen and Goodman (1979)
for details.
The method chosen for this investigation uses the
focussed TEM probe. The beam convergence is controlled by
the size of the second condenser aperture. After
selection and centering of the proper C-2 aperture, the
diffraction mode of the instrument is selected and the
condenser lens is brought to crossover. The result is a
focussed convergent beam and the image will be a focussed
convergent beam diffraction pattern. The beam is not
imagable under this condition. As the beam is focussed
(as the condenser lense is brought to crossover), the
second condenser aperture will become visible as a disc in
the diffraction pattern and a bright field image of the
sample will appear in the central transmitted disc of the
pattern. Dark field images corresponding to the various
65
crystal diffracting conditions will appear in the
diffracted discs. As focus is more closely approached,
the magnification of the images in the discs will increase
until, at focus, the magnification in the discs reaches
infinity. By watching the image "blow-up" in the disc,
the exact location of the beam on the sample can be
monitored. This technique is referred to as the shadow
technique (Steeds, 1979). The image in the transmitted
disc is the shadow image. This method is the only sure
way to eliminate diffraction error that is generally
present if the probe is focussed in the imaging mode
rather than in the diffraction mode, as just described.
(Diffraction error is the noncoincidence of the probe
position in the imaging and diffraction modes
respectively.) If the probe is formed by overexciting the
objective lens, the resulting out of focus image is the
shadow image. There is thus no diffraction error if this
latter technique is used to form the convergent probe.
Diffraction error is not a serious problem and can be
easily eliminated. In any event, it does not affect the
information that is present in the pattern, only the area
from which the information is taken. This information is
usually confined to the discs of the diffraction pattern.
There can be considerable detail in both the diffracted
and transmitted discs, depending on the diffracting
conditions under which the pattern is formed.
66
The applications of this information to materials
science were discussed earlier in this chapter. The
information in the discs includes 1) HOLZ (High Order Laue
Zone) lines, for lattice parameter measurements and for
pattern symmetry determinations, 2) Pendellosung Fringes,
used in making foil thickness determinations, 3) the
shadow image, used for tilting the sample and placing the
beam, and 4) dynamical features (absences and excesses)
that reveal detailed information about the crystal space
group for crystal symmetry and space group
determinations. Since HOLZ lines were used extensively in
this study, they are described in more detail below.
4.1.2 HOLZ Lines (High Order Laue Zone Lines)
A HOLZ line is a locus of diffracted beams. It is
the result of elastic scattering from Laue zones beyond
the zero order zone. HOLZ lines are analogous to Kikuchi
lines in two respects. First, they are a Bragg
diffraction phenomenon, and second, they result in lines
rather than diffraction spots. Like Kikuchi lines, the
spacing between the HOLZ lines in the diffracting disc and
the transmitted disc represents the spacing of the planes
that are responsible for Bragg diffraction in the HOLZ.
It is only necessary to index the discs that are
diffracting in the HOLZ to determine which lines in the
ZOLZ (Zero Order Laue Zone) correspond to these
diffracting discs. Any HOLZ line in the ZOLZ will
67
be parallel to its counterpart in the HOLZ, analogous to
excess and defect lines in Kikuchi patterns. It is the
HOLZ lines in the ZOLZ that are used for most HOLZ line
measurements.
An example of what one expects to see in a
transmitted disc containing HOLZ lines is shown in Figure
4.1. The lines in the disc (labelled a in the figure) are
the HOLZ lines. The lines outside the discs but seen as
continuations of the HOLZ lines (labelled b in the figure)
are the Kikuchi lines. The Kikuchi lines extend across
the transmitted disc, thus overlapping the HOLZ lines in
the disc.
The clarity and contrast of the HOLZ line patterns
and the accuracy of the HOLZ line positions are dependent
on at least five factors. First, there are limitations to
the thickness of the diffracting crystal (Jones et al.,
1977). This thickness should usually be on the order of
100-200 nm. If the crystal is much thicker, excessive
diffuse scattering in the ZOLZ will attenuate the HOLZ
lines entirely; if much thinner, no HOLZ lines will be
present at all.
Second, the energy loss as the beam is transmitted
through the sample added to the inherent energy spread of
electron sources (i.e., W filament, LaBg, or FEG) can
affect the accuracy of the line position. This energy
loss will affect the thickness of the HOLZ line, reducing
the accuracy to which it can be measured. Foil
69
thickness can also affect the HOLZ line thickness (Jones
et al., 1977).
Third, tilting the crystal away from normal
perpendicular incidence means a different thickness may be
encountered across the diameter of the beam with a
consequent change in intensity across the pattern.
(Recall that the beam is convergent.) This is not usually
a problem since only the intensity, not the actual line
position, is affected.
Fourth, the distortion in the pattern introduced by
the objective lens can affect the accuracy of direct
measurements in the Higher Order zone (Ecob et al.,
1981). Since one almost always uses zone axis patterns to
generate HOLZ information, the final tilt necessary to
obtain an exact zone axis pattern can be accomplished by
tilting the beam rather than tilting the sample. This
tilting can be done in two ways. The beam can be tilted
electronically using the deflector system of the
instrument, or the beam can be tilted by displacing the
second condenser aperture. Either of these procedures is
easier than tilting the sample using the goniometer
controls of the microscope stage. However, a beam
entering the objective lens off axis is subject to the
inherent spherical abberation effects of the lens. The
abberation increases with increasing off axis angle,
degrading the accuracy of the pattern. For this reason it
is best to tilt the sample as close to the exact zone
70
axis orientation as possible using the goniometer tilt
controls, rather than tilting the beam. This will not in
itself completely eliminate the spherical abberation
effect since diffracted beams from the higher order zones
must enter the lens at large angles anyway. It is thus
more accurate to use the HOLZ line in the transmitted disc
than its counterpart in the HOLZ ring. The subsequent
image forming lenses of the instrument will also impart
radial and spiral distortion to the diffraction pattern.
These distortions are minimized on the optical axis of the
instrument.
Fifth, the ubiquitous presence of carbonaceous matter
both in the microscope and on the sample surface can lead
to contamination spikes at the specimen/beam interface
with a consequent attenuation of the beam current, a loss
in spatial resolution due to scattering, and the
introduction of astigmatism into the beam due to
charging. All of these are undesirable. Methods for
reducing contamination have been reviewed elsewhere (Hren,
1979). Contamination and its effects were minimized in
this study by using the minimum practical time to focus
the diffraction pattern, to tilt to the proper
orientation, to determine the exposure time for each
pattern, and to record the image.
In consideration of the above effects, the following
procedure for obtaining HOLZ patterns is recommended:
71
1. The crystal should be tilted to the approximate
zone axis using the shadow technique. This greatly
simplifies tilting in polycrystalline samples.
2. An area in the crystal that is the proper
thickness for good HOLZ line formation should be found.
3. The sample should be in focus at the eucentric
position. These two conditions will insure that the
objective lens excitation is constant for every pattern
thus standardizing both the camera length and the
convergence angle for each pattern.
4. The condenser aperture should be centered.
5. The sample should be tilted to the exact zone
axis, again using the shadow image technique.
(By iterating between 5 and 3, a good zone axis
pattern can be obtained.)
6. The spot exposure meter should be used to
determine the proper exposure time for recording the
diffraction pattern.
Under the above conditions, only STEM and focussed
TEM probes should be used for generating the convergent
beam. If a convergent probe is formed using the
overexcited objective lens method, the sample must still
be at the eucentric position, but since the image will not
be focussed, the objective lens current must be recorded
so that it may be reproduced for each subsequent pattern.
72
4.1.3 Indexing HOLZ Lines
There area a number of ways to index HOLZ lines
(Steeds, 1979; Ecob et al., 1981). The approach taken in
this study is somewhat different from the approach
described in the above references in that the actual HOLZ
diffracting conditions are calculated. This method gives
a more intuitive feel for HOLZ detail and permits a more
rapid indexing of the patterns. The subsequent use of the
HOLZ lines for lattice parameter measurements is similar
to that developed by Jones et al. (1977).
To calculate the HOLZ line positions, one need only
determine the intersections of the Ewald sphere with the
reciprocal lattice beyond the zero order zone of the
reciprocal lattice. The equations necessary to do this
for a cubic crystal are presented below.
Let h, k, 1 be the Miller indices of
planes in the diffracting crystal.
These will also define the g vector for
the diffraction pattern.
Let a be the lattice parameter of the
material.
Let U, V, W be the idices of the beam
direction, B, in the crystal. These
indices are, by convention, given in
crystal coordinates. They are also
taken as antiparallel to the actual beam
direction in the instrument.
In reciprocal space, the center of the Ewald sphere for
the cubic crystal will be at
UR/|B|, VR/|B|, and WR/|B|, where R = 1/ .
73
Values of h, k, 1 which satisfy the following equation are
simultaneous solutions to the intersection of the Ewald
sphere with the reciprocal lattice:
(h/a UR/|B|)2 + (k/a VR/|B|)2 + (1/a WR/|B|)2 = R2.
Expansion and rearrangement of this equation yield
h2+k2+12 + R2.1U2+V2+W2) 2 (hU+kV+lW) R = R2.
a (U2+V2+W2) 3 T5T
This can be simplified to
h2+k2+l2
(1)
This equation says that the sum of the squares of the
planar indices of a diffracting plane is equal to a
constant for a given electron accelerating potential,
lattice parameter, beam direction and cubic Bravais
lattice type.
To solve the equation, one must know the microscope
accelerating potential, the approximate lattice parameter
of the examined crystal, and the beam direction in the
crystal. The accelerating potential is never known to
great accuracy. When only relative and comparative
lattice parameter measurements are to be made, this
uncertainty cancels. The lattice parameter can be
approximately derived from either a calibrated selected
area diffraction pattern, or from a calibrated CBED
pattern. The beam direction must be known.
74
To solve equation (1), only the value of g*B needs to
be derived (we assume here that the other information is
at hand). The values of gB will depend on the specific
cubic Bravais lattice.
For an FCC crystal, as for both the matrix and the
gamma prime phase in the RSR alloys, diffraction pattern
planar indices cannot be mixed. The three values of g in
g*B will thus be all odd or all even. Indices for the
beam direction can be reduced to three combinations of
terms: B is odd, odd, odd; B is odd, even, even; and B is
odd, odd, even. The following cases are constructed to
show values for the dot products of unmixed g indices and
the three combinations of B terras given above.
Case 1) B h,k,l Case 2) B h,k,l Case 3) B h,k,l
0
E
0
E
lQ
E
0
0
E
0
0
E
0
0
E
0
0
E
E
E
E
0
0
E
0
0
E
E
E
E
E
E
E
The first case will be used as an example. If B is all
odd, for example, B = (111), the individual terms in the
dot product of this B and an odd set of g indices will
contain all odd terms. The algebraic sum of all odd terms
is odd. For this case, g*B can equal one, since one is an
odd term. The results in Case 2 are the same. For
Case 3, the algebraic sum will always be even. For this
case, g*B will equal two. These results can be
generalized as follows: if U+V+W = even, g*B will
75
equal two. If U+V+W = odd, g*B will equal one. This
calculation applies only to the first order zone.
Most of the CBED patterns in this study were taken
from the gamma prime phase, an LI2 superlattice. In such
a superlattice, the superlattice reflections appear in the
forbidden positions for FCC. The true first order Laue
zone for U+V+W = even will consist only of superlattice
reflections. The first zone can be clearly seen in Figure
4.2, a B = CBED pattern of the gamma prime phase in
alloy RSR 197. These superlattice reflections are usually
too weak to give HOLZ lines in the central disc. Only the
HOLZ lines from the B = <114)>- "second" order zone were
used in this study. This "second" zone will hereafter be
referred to as the first order zone (FOLZ) since it in
fact corresponds to the first order zone for a typical FCC
crystal.
An alternate way of deriving the preceding result is
through construction of the Ewald sphere and geometrical
solution of the intersection with the reciprocal lattice.
With reference to Figure 4.3^
the angle 0 equals 9' by similar triangles.
Then Sin 9' = H/|g|/2R and Sin 9' = H/|g|.
Combining these two equations gives g2 = 2RH.
By definition, g2 = l/d^ = (h2+k^+l2)/aQ2.
Substituting for |g|2 gives h2+k2+l2 = 2a2 RH.
H can be shown to equal (g*B/a ) (u2+v2+v/2) 1/2.
Therefore, h^+k2+l2 = (2aR/|B|)(g*B).
78
At this point, both the graphical and calculated
methods yield a solution that is valid for a single beam
direction only. Neither method has included the effect of
the beam convergence. There are numerical methods for
including this convergence (Warren, 1979). An alternate
way is to calculate an upper and lower limit of h2+k2+l2
values for a given beam convergence angle. This approach
provides a useful and intuitive estimate of the
convergence effect. It has the shortcoming of slightly
overestimating this effect. A more rigorous method is
described in a following section.
For a given |B|, gB = |g||B|*cos.
Let K2 = Ki (gB) where Ki = 2aR/|B|.
Terms aQ, R, and B are as previously defined.
Then K2 = |g|2 = [g-B/( | B | cos) ]2
and = cos'1 (g.B/(|B|)(K2)1/2).
Two limiting values of h2+k2+l2 (limiting values of
k£), can now be calculated:
K2
1
(B_Lg)2
TfB | cos ( +<*) J 2
>
k22 = (B_ig)2
L |B|cos-<) J2 ,
where < is the convergence angle.
79
Values of h2+k2+l2 between these limiting K£ values will
define a plane (h,k,l) that will diffract in the FOLZ. As
an example, consider the solution to a CBED pattern from
the gamma prime phase of RSR 197. The approximate
constants for substitution into the equations are
aQ 3.36,
R = 27.07 (100 keV electrons),
B = <114>,
and alpha = 2.5 x 103 rads.
The calculated values of and are 101 and 82,
respectively. Any plane h, k, 1 with values of h2+k2+l2
between 82 and 101 which also satisfies the g*b = 2
criterion will diffract under Bragg conditions and will
thus yield a FOLZ line in the transmitted disc. Possible
values are given in Table 4.1.
The value of K2 for the zero convergence case is the
exact Bragg solution. It is seldom an integer. If its
value were an integer, a set of conditions could be
achieved that would yield some set of FOLZ lines directly
through the center of the pattern. For example, for the
case just calculated, h2+k2+l2 = 90.713. This value is
very close to the exact solution for h2+k2+l2 (h=9, k=3,
1=1) = 91.0. The (931) lines should pass almost directly
through the center of the transmitted disc. They could be
made to pass directly through the center by either
increasing the alloy lattice parameter from 3.560 to 3.571
Angstroms, or by changing the accelerating potential
80
of the microscope to adjust the wavelength. This latter
can now be done to great accuracy in most modern STEM
equipment.
The advantage of having all of one type of line
passing directly through the center of the pattern is
explained below. If it were possible to have all of one
line type (the £931^ 1 ines for a B =(ll4^pattern) in the
center of the pattern, a reference microscope operating
potential could then be defined for that particular
lattice parameter. For a material of different lattice
parameter, the difference in accelerating potential
required to bring the lines to the center of the pattern
compared to the reference would be proportional to the
difference in lattice parameter between the two materials
(Steeds, 1979). To measure a change in lattice parameter
in this way, one would merely note the change in
accelerating potential required to achieve identical
patterns in the central disc.
To more rigorously solve the effect of beam
convergence on HOLZ line formation, the Bragg angle and
the actual angle the beam makes with each specific HOLZ
diffracting plane must be determined. For example, for B
= ^114^, a = 3.56, and R = 27.07 (100 kV electrons), the
calculated value for h2+k2+l2 using equation (1) is
90.713. Because this number is not an integer, the Bragg
condition in the first order zone is not satisfied for B =
^114^. Consider a second beam direction B'.
If B1 were
81
Table 4.1 HOLZ Planes
hkl
h^^fl2
g*'
Yes
7 5 1
75
X
7 5 3
83
7 5 5
99
7 7 1
99
7 7 3
107
X
8 4 0
80
8 4 2
84
8 4 4
96
8 6 0
100
X
8 6 2
104
9 11
83
9 13
71
X
9 15
107
9 3 3
99
10 0 0
100
10 2 0
104
X
10 2 2
108
2 Indices for B=[114]
No
X
X
X
X
X
X
X
X
X
X
X
751 571
773
860 680
913 193 931 391
1002 0102
X
82
inclined slighty to B (Fig. 4.4), it might be possible for
B* to satisfy the Bragg condition for the above value of
h2+k2+l2. Fortnuately, it is not necessary to calculate
the indices of B1. One first calculates the Bragg angles
for the planes that can diffract in the FOLZ (those planes
listed in Table 4.1) and then calculates the actual angle
these planes make with the given beam direction, in this
case, the ^114^. If the difference between theta a, the
angle the low index beam makes with the plane, and theta
b, the calculated Bragg angle for that plane, is less than
alpha, the angle of convergence, then that diffracting
plane will produce a FOLZ line. This situation is
described in Figure 4.5. If theta a and theta b are both
plotted against h2+k2-fi2} the two intersecting curves in
Figure 4.5 result. Note that the two curves intersect at
the value of h2+k2+l2 calculated from the equation. Any
convergence angle up to 4.8 mrad can be superimposed onto
this figure and the resulting range of h2+k2+l2 values
determined. For an alpha of 2.5 x 10~3 rads, this range
of values is 100 to 83, a slightly smaller range than
determined by the first method.
Once the range of h2+k2+l2 values has been determined
and the actual indices assigned as in Table 4.1, it is a
simple matter to index any pattern for the FCC crystal.
One first indexes the zero order Laue zone (ZOLZ) in the
normal way (Edington, 1976). This zero order indexed
pattern is shown in Figure 4.6 for a [114] CBED pattern
83
A= Alpha, the convergence angle
0,= Bragg angle
0 = Calculated angle between B and
diffracting plane
Figure 4.4 Method for determining HOLZ line formation
limits for a given convergence angle.
r
Figure 4.5 Plot of data for 100 KV, a=3.56
Angstroms, B=(114^, from Figure 4.4.
86
from the FCC gamma prime phase. One then calculates the
angles between the planes represented by any zero order
indexed spot and the FOLZ reflections listed in Table
4.1. The indexed spots in the FOLZ using the calculated
angles are shown in Figure 4.6. The indexing in the FOLZ
must be consistent with the indexing in the ZOLZ. Once
the FOLZ reflections have been indexed, the HOLZ lines in
the central spot can be indexed. The lines in the pattern
center are parallel to the lines through the FOLZ discs,
as illustrated in Figure 4.7.
One advantage to indexing patterns from the
calculations is that the line pattern in the central spot
can be indexed directly without first indexing the
reflections in the HOLZ. An indexing of a B = [114] line
pattern is shown in Figure 4.8. To index in this way, one
first identifies the line types using Table 4.1. Next,
one finds the lowest symmetry line, if it exists, and
indexes it. This is easily done in this pattern for the
773 line. One then finds the next lowest symmetry lines
and indexes them, and so on. The sign of the vector cross
product between these lines must be consistent with the
choice of beam direction. The direction of g can be
determined from Table 1. The remaining lines are then
indexed using the calculated interplanar angles (Figure
4.6). The angles measured between HOLZ lines are slightly
different from the calculated values. In addition to
normal measurement error, these measured angles are
89
projected from the higher order zone onto the zero order
zone and are different from the calculated ones. The
difference is explained in Appendix B.
Once the FOLZ has been indexed, FOLZ line positions
in the transmitted disc can be used to determine relative
lattice parameter differences and can be used to measure
small symmetry differences due to crystallographic changes
as a result of alloying, strain, or transformation.
4.1.4 Lattice Parameter Changes
The easiest way to visualize the changes in the FOLZ
line position in the central spot that accompany changes
in lattice parameter is to look at a few examples of
patterns to see what happens when the lattice parameter is
varied. Figure 4.9a illustrates a case where the lattice
parameter of a diffracting crystal is such that at 100 kV,
the four 931 lines in a B = ^114^ pattern pass exactly
through the center of the transmitted disc. This is
equivalent to saying that the Bragg condition is satisfied
for g = (93l) when B = ^114^. For this to be true, the
lattice parameter of the crystal must be exactly 3.5712
Angstroms. If the lattice parameter is greater than this,
a pattern like that shown in Figure 4.9b will result. If
the lattice parameter is less than 3.5712 Angstroms, the
pattern will look like Figure 4.8c. The shaded area in
the figure outlines the symmetry changes. This change is
91
exagerated compared to the micrographs. The calculations
required to determine the line positions of the patterns
are summarized in Appendix A.
Since only a relative change in lattice parameter can
be realistically measured, measuring this relative change
involves measuring and quantifying changes in the HOLZ
line positions from one pattern to the next. This is
easily and most accurately accomplished by using HOLZ
lines that both intersect at shallow angles, and most
desirably, that move in opposite directions to one another
when the lattice parameter is varied. Distances between
intersections are then measured and these distances
ratioed for different values of absolute lattice
parameter. Figure 4.10 is a plot of the ratio a/b versus
relative change in lattice parameter. Parameters a and b
are defined in Figure 4.9. The calculation of the values
for Figure 4.10 is given in Appendix A.
4.1.5 The Effect of Strain and Non-Cubicity on
Pattern Symmetry
If a previously cubic crystal is nonisotropically
strained or has become noncubic due to transformation or
change in order, the CBED pattern will reflect this change
by a reduction in the symmetry of the HOLZ line pattern.
The CBED technique is especially sensitive, theoretically
capable of detecting changes in lattice parameter on the
order of two parts in ten thousand at 100 kV (Steeds,
3.60
.59
o
S-
58
^ r* -7
en 57
c:
.56
(V
4->
O)
| .55
rd
Q_
S -54
.53
.52
.51
3.50
.7 .8
.9 1.0 1.1
RATIO a/b
Figure 4.10 Plot of lattice parameter verses the
ratio of a to b (a and b defined in
Figure 4.9).
93
1979). This would of course apply to nonsymmetrical
changes in lattice parameter as well. The magnitude of
these nonsymmetrical changes can be deduced by measuring
the change in HOLZ line positions as the lattice parameter
changes, described in the preceding section.
Again, the easiest way to visualize the effects of
crystal asymmetry is to look at a few examples of CBED
HOLZ patterns to see how this asymmetry affects HOLZ line
position. The direction of shift of the lines will depend
on the orientation of the now noncubic crystal with
respect to the beam direction. For example, if the
expansion or contraction is along the c axis, the c
direction defined as being parallel to the beam, the
symmetry of the pattern changes very little. If the beam
is a parallel to either of the a or b cube axes, the
change in symmetry is very marked, as shown in Figures
4.11a, 4.11b, and 4.11c. The method for calculating these
HOLZ line patterns is explained in Appendix A.
It is not straightforward to differentiate symmetry
changes from lattice parameter changes to arrive at a
measure of both lattice parameter and loss of cubicity.
Ecob et al. (1981) simulated CBED HOLZ line patterns to
measure the lattice parameter differences in gamma/gamma
prime alloys, and to measure the changes in symmetry of
the gamma prime phase after recrystallization. The
simulations were then compared to actual patterns.
Numerous trial and error iterations would usually
b.
a.
c.
Figure 4.11 The effect of non-symmetrial changes in
the lattice parameter on the symmetry of the
transmitted HOLZ pattern; a.) a, b, and c
3.5713 Angstroms, b.) a, b, and c 3.5713
Angstroms, and c.) a = 3.5713, b and c a.
The mirror symmetry in the pattern has been
lost. The mirror is perpendicular to this
caption.
95
provide an adequate match. They used the B = (111)
pattern to make these measurements. This pattern is a
simple one to analyze because of the threefold symmetry in
the ZOLZ transmitted disc. This pattern could not be used
in the study of the Pratt and Whitney alloys, however,
because of the microstructural scale in these alloys.
When the sample is in a B = (111) orientation, the gamma
prime precipitates usually overlap either the gamma phase
or the gamma phase and another gamma prime precipitate.
The result is either a highly distorted HOLZ pattern or no
pattern at all. If B = (114), the beam is more closely
parallel to the 100 direction; 19 degrees from the B =
(100) direction. Eades (1977) used this orientation to
study the gamma/gamma prime mismatch in In-100, a Ni-based
superalloy. The B = (114) CBED pattern can be used to
measure both lattice parameter and noncubicity. The
method is outlined in Appendix A.
The B = pattern has been used recently by
Braski (1982) and by Lin (1984) to measure lattice
parameter change in ordered alloys. In both cases, the
microscope accelerating voltage was continuously variable,
meaning that the HOLZ line positions in these patterns
could be varied. Because the B =(111) pattern in a cubic
material always exhibits either sixfold or threefold
symmetry, it is always possible to find three FOLZ lines
that can be made to pass directly through the center of a
CBED pattern, and hence intersect at a point in the
96
center of the pattern. If a lattice parameter measurement
is to be made using the relative voltage differences
required to go from one three line point intersection to
another three line point intersection, this measurement
cannot be accurate if any noncubicity is present. Braski
alluded to the nonacceptability of using the B = (^11*0
patterns for his measurements because of the sensitivity
of this pattern for noncubic effects. All patterns are
sensitive to strain effects.
There should be other CBED zone axis patterns that
could be used to make the measurements for which the B =
<.114> pattern was used in this study. The B = <.100>
pattern would be the most crystallographically sensible.
There is no gamma/gamma prime overlap along this
direction.
Using equation (1), it is simple to calculate the
expected HOLZ for B = ^001^.
At 100 kV:
R = 27.07,
aG = 3.56 Angstroms,
B = <001>,
gB = 1, and
h2+k2+l2 = 193.
The Bragg angle for this F0LZ ring is about 4.2 degrees at
100 kV. This means the F0LZ will be 8.4 degrees from the
center of the pattern, far from the transmitted spot and
97
hence possibly too weak to give strong FOLZ lines in the
central spot.
If the accelerating potential of the microscope is
lowered, the FOLZ ring will move in toward the center of
the pattern. The scattering amplitude increases as the
ring moves in and the diffracted intensity consequently
increases (Steeds, 1979).
4.2 Energy Dispersive Methods
The use of energy dispersive x-ray analysis is a well
established means of characterizing the compositions of
materials on a microscale (Goldstein, 1979). The effects
of various experimental variables on the accuracy and
precision of the final EDS results are of paramount
importance. These effects have been reviewed extensively
elsewhere (Zaluzec, 1979). They are summarized here as 1)
instrument related, 2) specimen related, and 3) data
reduction related. Care must be taken in defining the
effects of all three if an accurate result is to be
obtained.
Consider first the instrument and its effects.
Microscopes of the late 1970's vintage are generally less
than perfect experimental benches for x-ray
microanalysis. In unmodified instruments, many
uncollimated electrons and x-rays make their way to the
specimen environment where they then contribute to the
x-ray signals that are supposed to be generated only by
98
the local interaction of the specimen and the beam. These
stray electrons and x-rays can be mostly eliminated by
proper specimen shielding and by proper design of the
column. The 400T STEM at Oak Ridge National Lab is
properly modified to minimize spurious x-ray fluorescence
through the use of top hat condenser apertures, and to
reduce sprayed, uncollimated electrons through the use of
spray apertures below the condenser lenses. Hole counts
are consequently low, in the neighborhood of 1 to 2
percent of the total elemental counts when the beam is on
the sample. A hole count spectrum was always accummulated
for each specimen and subtracted from each specimen
generated spectrum before any subsequent curve fitting and
peak deconvolution (Zaluzec, 1979).
The specimen related effects are more difficult to
assess. These effects are primarily due to absorption of
specimen generated x-rays by the specimen itself. The
most common method for quantitative analysis in the
analytical TEM follows the Cliff-Lorimer equation (Cliff
and Lorimer, 1972). This equation relates the ratio of
the concentrations of unknowns in the sample to the ratios
of the beam generated x-ray itensities:
CA/CB = (K) IA/lB,
The major assumption in the equation is that the k term,
the proportionality constant, is independent of the
specimen thickness. This assumption is not valid
99
in the alloys that were characterized in this study.
The proportionality constant can either be measured,
in which case the standard from which it is measured must
satisfy a criterion called the "thin film criterion," a
criterion that defines the maximum thickness of the
standard, or the constant can be calculated. Both of
these methods are outlined by Goldstein (1979) and Zalusec
(1979) It is primarily the effect of thickness on the k
term in the Cliff-Lorimer equation that defines the
specimen related effects. This thickness effect is a very
serious problem in Ni-Al alloys. The aluminum x-rays are
preferentially absorbed by the Ni, to the extent that the
thin film criterion in Ni-Mo-Al of RSR composition is not
satisfied for thicknesses in excess of about 600
Angstroms.
The ternary alloy //17 will be used as an example of
how thickness affects quantitation. A large beam was used
in an attempt to measure a "bulk" composition of the
alloy. The results are summarized below:
Nominal Composition
Ni
Mo
A1
wt.%
78.5
15.0
6.5
at .X
77.0
9.0
14.0
X-Ray Results
No thickness correction
wt.%
79.2
15.6
5.22
No thickness correction
at.%
79.1
9.5
11.3
1000 Angstrom correction
wt.%
78.8
15.5
5.6
100
1000 Angstrom
correction
at.%
78.4
9.4
12.2
1500 Angstrom
correction
wt.%
78.7
15.4
5.9
1500 Angstrom
correction
at.%
78.0
9.4
12.7
1800 Angstrom
correction
wt.%
78.6
15.4
6.0
1800 Angstrom
correction
at.%
77.7
9.3
13.0
The value corrected for a thickness of 1800 Angstroms
is quite close to the actual composition of the alloy.
The actual thickness of the sample is unknown. The data
show, however, a 20% difference in total aluminum as a
result of absorption. In all subsequent spectra, a
specimen thickness of 1000 Angstroms was presumed.
In this research, every effort was made to reduce
specimen related artifacts by orienting the specimen such
that the absorption path length was minimized between the
flourescing area of the sample and the detector, and by
orienting the crystal so that only the desired phase was
analyzed. Because the detector was a horizontal detector,
this was a significant limitation. It was necessary to
orient the crystal as close as possible to a B =C.100^
direction in order to minimize gamma/gamma prime phase
overlap.
A further complication was contamination. The
effects on spatial resolution are well documented (Hren,
1979). In order to generate sufficient signal for
adequate statistics, it was necessary to count for very
long times, usually in excess of 100 seconds. No data
101
was ever accumulated for more than 20 seconds without
interrupting the analysis, checking the probe position,
and if contamination were noted, repositioning the probe
to an area that was not contaminated.
The data related variables are variables over which
there was little or no experimental control. These
effects are primarily related to various data reduction
schemes, i.e., background subtraction, peak deconvolution,
peak modeling, etc. These effects on quantitative
analysis are documented by Zalusec (1979) The background
fitting routine was the source of most difficulty in the
data reduction. In this routine, developed by Zalusec
(1978), the background is modeled to fit a 4th order
polynominal with three operator selectable regions of the
background to provide input data for the fitting routine.
Figure 4.12b is a spectrum of the gamma phase of RSR 209
solution heat treated, quenched and aged at 870 C for one
hour. A background fit in the low energy region of this
spectrum is very difficult due to overlapping Ni-L, Al-K,
W-M, and Mo-L (in order of increasing energy) peaks in
this region. The consequence of this overlap is that no
isolated background region exists in this part of the
spectrum for entry into the modeling routine.
It was generally not possible to fit the whole
spectrum successfully. A good fit in the low energy
region did not necessarily mean a good fit at higher
102
energies. For this reason, the Mo-L rather than the Mo-K
was used for the quantification, and the W-L or Ta-L
lines were not used at all. An example of a comparison
between results calculated from both the Mo-K<=
Mo-If
The sample is the ternary alloy #17. As in the
previous example, a large probe size was used.
a)
Using the Mo-L line:
No absorption
correction
Calculated
with 1000 .
absorption
correction
wt.%
at .%
wt.%
at.%
Ni
78.2
78.3
77.5
77.3
Mo
16.45
10.1
16.7
10.2
A1
5.36
11.7
5.8
12.5
b)
Using the Mo-K
line:
No absorption
correction
Calculated
with 1000 .
absorption
correction
wt.%
at .7o
wt .X
at.%
Ni
78.1
78.2
77.5
77.4
Mo
16.6
10.1
16.5
10.0
A1
5.35
11.7
5.8
12.5
Note
: The ratio Lp/L0^3 .2265 was
used to reduce the
measured intensity of the Mo-L<< + Mo-LP peak. The Lp/L0*-
ratio was calculated from the MAGIC program.
The EDS results in Table 5.3 do not include values for
either the W or Ta quaternary additions. The analyses will
103
obviously be in error because of this, not only because
they exclude the quaternary elements, but also because
this exclusion will affect the quantitative total and the
relative amounts of the other elements also. Fortunately,
the concentrations of the quaternary elements in the bulk
alloys are low, 2.0 atomic X for both RSR 197 and 209.
Representative spectra from RSR 209 and RSR 197 gamma and
gamma prime phases are shown in Figures 4.12 a, b, c, and
d. The partitioning of the Ta and W to the gamma and
gamma prime phases is different. Ta partitions almost
exclusively to the gamma prime phase. W appears to be
about equally partitioned between the gamma and gamma
prime phases.
Interestingly, the nickel content of the gamma and
gamma prime phases was very similar (Table 5.3). This
allowed the Ni-K^peak to be used as an internal standard
for ratioing against the Mo, Ta, and W lines in order to
measure the partitioning of the Ta or W between the gamma
prime and gamma phases.
The Ta in the gamma prime cannot exceed about 4
atomic percent. This figure is based on the assumption
that the gamma prime volume fraction is not less than 50X,
a safe underestimate judging from the microstructural
features described in Chapter 5.
For the same reason, the amount of Ta in the gamma
phase must be less than one percent based on the ratio of
Ta to Ta in the gamma prime and gamma, respectively.
4N10-2S 8.06 KEU O C-'S
2k 1A + 8 M H$*= 20 E 0 1AB
4NJ0-2S 8 06 KEO o C t
"$ = 2K 1A + B H HS= 20E" lwB
Figure 4. ] 2
Spectra from the gamma and gamma prime phases of RSR 209 and
RSR 197; a.) RSR 197 Gamma, b.) RSR 197 gamma prime, c.) RSR 209
gamma, and d.) RSR 209, gamma prime.
105
The amount of W in both gamma and gamma prime phases
is approximately the same, that is, "homogeneously"
distributed, and consequently about 2.0 atomic % in the
gamma and 2.0% in the gamma prime phase.
Kriege and Baris (1969) measured the partitioning of
Ta and W between the gamma and gamma prime phases of a
number of Ni base alloys, all of which contained
considerable Cr. The Ta ratio between gamma prime and
gamma in numerous Ta containing alloys is approximately
1:4,*05. The ratio between gamma prime and gamma in a
number of W containing alloys (Mar-M200, TRW/900,
Microtung, etc.) is approximately one to one. This is in
close agreement with the present study. The ternary
Ni-Mo-Al compositions of the quaternary alloy gamma and
gamma prime phases are given in Table 5.3.
CHAPTER 5
RESULTS
5.1Microstructural Characterization
5.1.1 As Extruded RSR 197 and RSR 209 Alloys
Figure 5.1 is a low magnification TEM micrograph of a
typical as extruded microstructure. The alloy is RSR
209. The large grains are gamma prime grains that have
precipitated during the extrusion process. The other
areas of the microstructure consist of small cubes of
gamma prime that have precipitated from the gamma solid
solution during the cool down after extrusion. Details of
the optical microstructure can be found in the relevant
Pratt and Whitney quarterly reports (Cox and et al.,
1978). Other phases were present but were not analyzed.
It is probable that they are Mo.
5.1.2 RSR 197 --As Solution Heat Treated and Quenched
Figure 5.2a shows the general microstructural
features of this as quenched alloy. This is basically the
starting structure and starting phase distribution for all
subsequent aging practices of RSR 197. There are no
remnants of the primary gamma prime phase that had
106
109
developed during the extrusion process. This phase was
taken into solution during the solution heat treatment.
The larger gamma prime precipitates along the grain
boundaries result from accelerated coarsening of gamma
prime at the high angle grain boundaries (Funkenbusch,
1983). This coarsening presumably takes place during the
air quench from the solution heat treatment temperature.
The major features of the microstructure include the
gamma prime cuboids and the surrounding gamma matrix.
Many of the gamma prime cuboids are impinging, as shown in
Figure 5.2b. Some precipitation of DO22 phase has
occurred within the gamma matrix. The selected area
diffraction pattern shown in Figure 5.3a clearly shows the
presence of the DO22 superlattice reflections (cf. Figure
2.20b). There is very strong streaking associated with
each DO22 reflection. The streaks are not visible on the
fluorescent screen of the microscope and can be seen only
after long photographic exposure. Figure 5.3b is a g =
1/4 (420) dark field image of the DO22 phase. The beam
direction is approximately along a B = 001 direction.
The fine DO22 phase is distributed uniformly throughout
the gamma matrix. A high magnification g=l/4(420),
B=<001> image of this DO22 phase is shown in Figure 5.3c.
Note the angularity of the precipitate and the presence of
what appear to be many unidirectional faults in the DO22
precipitates.
Ill
5.1.3 General Microstructural Features
Alloy RSR 197, as solution heat treated and quenched,
will be used as an example to illustrate some general
microstructural features of all or most of the alloys
described in the chapter.
The distribution of the gamma prime and its geometry
within each foil is the same for all the alloys to be
described subsequently. Though each gamma prime cuboid
appears to completely penetrate the foil (see, for
example, Figure 5.2b), many in fact do not. The actual
distribution is as described schematically in Figure 5.4.
In all of the alloys the scale of the microstructure
is very similar. The gamma prime precipitate is
approximately 200 to 300 nm along any edge, and the gamma
generally extends some 20 to 30 nm between the gamma prime
cuboids.
When the DO22 phase is present, the DO22 reflections
appear to be shifted with respect to the LI2 N3AI. There
are two possible explanations for this displacement. Both
are discussed in Section 5.1.4.5.
5.1.4 RSR 197 Aging
5.1.4.1 Solution Heat Treated, Quenched and Aged at
760 C for up to 100 Hours
One hour aging at 760 C has produced discreet N4M0
Dla reflections. Figure 5.5a, a B = <^100^ SAD pattern,
112
e
' >
Figure 5.4 Schematic showing the distribution of
gamma prime phase in a thin foil. All the
conditions except E are commonly encountered.
113
shows both DO22 and Dla superlattice reflections. There
is still streaking present through the DO22 reflections,
as in Figure 5.3a. Figures 5.5b and 5.5c are g = 1/5
(420) and g = 1/4 (420) dark field images. The beam
direction was approximately parallel to a B=[121]
direction. The figures show that both phases are randomly
distributed throughout the gamma phase. The DO22 phase
has coarsened.
After 10 hours, all three NixMo phases are present.
The DO22 and Dla phases continue to grow, and the N2M0
that is present is very sparsely distributed, even to the
extent that it may not appear in selected area and Riecke
method diffraction patterns.
Aging for 100 hours results in almost complete
ordering throughout the gamma phase by the NixMo
precipitates. All three metastable NixMo phases are
present as evidenced by the B = \100)> diffraction pattern
shown in Figure 5.6a. As after ten hours aging, the two
dominant phases are N3M0 DO22 and N4M0 Dla. Figures
5.6b and 5.6c are B = [001], g = 1/4 (420) and g = 1/5
(420) dark field images of the DO22 and Dla phases,
respectively. The Pt2Mo phasse is shown in Figure 5.6d, a
B = [001], g = 1/3 (420) dark field image.
In addition to the three metastable NixMo phases, the
disordered gamma phase, and the cuboidal gamma prime
117
phase, there is a sixth phase present in this alloy;
NiMo. An image of this precipitate and its diffraction
pattern are shown in Figures 5.7a and 5.7b. The
diffraction pattern is indexed in Figure 5.7c. The phase
was found almost exclusively along grain boundaries.
In order to characterize the Dla and DO22 phases
adequately, a number of variants for each precipitate type
were imaged. This required that images be taken from at
least two different FCC crystal orientations. The two
orientations are the B = [001] and the B = [112]. Figure
5.8 shows these two diffraction patterns and additionally
delineates which diffraction variants were imaged.
As explained in Section 2.3.4.1, there are three
imagable of 12 possible variants in N3M0 D022* All three
of these variants may be imaged along any B =
direction since all three can be present simultaneously in
a B = <^100)> diffraction pattern (Section 2.3.4.1). Figure
5.6b is the dark field image of the 1/4 (420) variant.
This variant does not fill the intercuboidal regions. It
appears along only two faces of the gamma prime. Figure
5.6c is a dark field image of the 1/4 (240) variant. It
appears along the other two gamma prime faces, but not on
the same faces as does the 1/4 (420) variant.
The interpretation of these two dark field images is
straightforward. Figure 5.9 describes the relationship of
the variant orientation with the matrix and interpretation
119
420
Figure 5.8 Imaging conditions for the various dark field
images for RSR 197 SHTQ and aged 100 hours at
760 C.
120
o O
[o o # o o
i o o o 9 o
|oo0*oo
o o o
_ N4M0 Variant
C B, Figure 2.18
420
|0 o O
^ O
'o O
o #0 o
O o o Ni Mo Variant
o # O O Hit Figure 2.17
O O*
o o # o o o o o o
O O %/o 00*0#0# (Jt-Q
NiMo Variant #000#000*0
Ganma Prime
Cube
1 0 0 Face
O
:o
O
II?, Fig. 2.17
o o/m o o o O o o o
o#oioiO*o*o|ooO
o m/o mO*omo%omomO*om
o*oOo*oO*oo0o
o/% lo#o#o0o#ooo#
o|#o#0oo#oo0o
2 40
Ni Mo Variant A,
Figure 2.18
Common 240 plane between Ni^Mo and Ni^Mo
Figure 5.9 Arrangement of DO22 and Dla on the cube
faces of N3AI. The C axis of the DO22 is
perpendicular to the cube faces. Two
variants of Dla are shown. The Dla phase
can grow around the corner of the N3AI cube.
121
of the diffraction pattern. The figure shows clearly that
the c axis of the DO22 phase is perpendicular to a 100
face of the gamma prime. The third variant will thus
appear only in regions of overlapping gamma and gamma
prime, regions where the DO22 axis is parallel to the
beam, regions B, C, D, and E in Figure 5.4. The
diffraction spot from which a dark field image of variant
A (Figure 2.18b) would be formed corresponds to the same
spot from which an LI2 dark field image would be formed.
Both the DO22 and LI2 crystals have a superlattice
reflection at g = (110). Imaging the third variant, then,
is rendered impossible by the presence of the gamma prime.
A comparison of the images in Figures 5.6b and 5.6f
with the schematic in Figure 5.9 also shows that the (420)
habit of the DO22 phase can easily be reconciled with the
(420) Ho planes of the DO22 The crystallography of the
DO22 would seem to determine the morphology of the DO22
precipitate. The DO22 precipitates can be seen to be
comprised exclusively of either combinations of the {420}
planes or combinations of {420} planes and the limiting
(lOo) planes of the LI2 interfaces. For example, many of
the DO22 precipitates are triangular in projection. This
is consistent with four {420} planes truncated by a {l00},
e.g., an (024), (024), (420), and (420) plane truncated by
an (010) plane. This pyramid would appear as a triangle
in either an [001] or an [010] projection. Two such
122
pyramids could share a common {100} face. The resulting
TEM image would be a diamond. A third possibility would
be two parallel sets of {420} planes truncated by two
parallel {lOO} planes, perhaps two facing {100} gamma
prime faces. The resulting image would be a rhombus. All
of these features can be readily seen in the dark field
images, Figures 5.6f and 5.6b, of the DO22 N3M0.
Only two Dla variants are imagable along any B =
<100> direction. Both of these variants are associated
closely with the DO22 morphologies just described. The
two visible Dla variants (reference the indexing in Figure
5.8) contain the following four 420 planes: the clockwise
variant contains a 420 and a 240. From the previously
described DO22 4-20 stacking sequence, Figure 5.9, a
clockwise Dla variant could share a DO22 420 plane between
010 faces of the gamma prime, or, could share the DO22 240
on the 100 faces. Similarly, the counterclockwise variant
could share a DO22 4-20 on the 010 face, or a DO22 4-20 on
the 100 face. This stacking is schematically represented
in Figure 5.9. Dark field images of the Dla corresponding
to the schematic are shown in Figures 5.6c and 5.6e.
Because one Dla variant can grow on both the 010 and
the 100 faces of the gamma prime, the N4M0 Dla can
readily grow around the edge of the gamma prime cuboids
without introducing a stacking fault. (The DO22 would
always form a perpendicular twin boundary when it impinged
123
at the cuboid edge.) This is shown clearly in Figure 5.9
and in a lattice image, section 5.1.4.2. Note the
concentrations of the Dla phase at the corners of the
gamma prime cuboids in Figures 5.6c and 5.6e.
The Pt2Mo phase is also present in the alloy. It can
be present as discreet N2M0 precipitates, or it can be
present layered with the DO22 and Dla, as it appears to be
in Figure 5.6d.
In order to describe the actual three dimensional
arrangement of these NixMo phases, it is necessary to look
along the third 100 direction in the crystal. This can be
done by tilting from B = [001] to a B = [112] direction, a
tilt of 35.3 degrees. When tilted to this orientation,
multiples of the (042) and (402) reflections can be used
to image the DO22 and Dla precipitates (Figure 5.8).
Imaging with a 1/4 multiple of either of these reflections
will yield an image of the DO22 phase on the previously
unimageable 001 face of the gamma prime. Using the 1/5
multiples will image two additional Dla variants.
Figure 5.10 shows the three faces of the gamma prime
cube with the four possible DO22 planes on each face. The
1/4 (402) and the 1/4 (042) variants are on the same 001
face. Since they are from the same DO22 variant, imaging
with either of them will give the same image.
The 1/5 (042) variant will appear on two faces of the
gamma prime. First, it will appear on the (001) face. It
124
Figure 5.10
A gamma prime cube showing the 420 phases
that will appear on each face of the cube.
125
must also appear on the (010) face since this face
contains an 024 plane which is also a plane in the 1/5
(042) variant. In a similar way, the 1/5 (402) variant
will appear on the 001 face, but since it is a different
variant of the Dla, its morphology will not be the same as
the Dla morphology of the 1/5 (042). The 1/5 (402)
variant will also appear on the 100 face, since this
variant also contains a 204 plane. To differentiate the
Dla precipitate on the 001 face from the same variants on
the other 100 faces, it is necessary to compare the DO22
images with the Dla images. The DO22 images appear only
on the (001) faces of the gamma prime.
The DO22 precipitates form in discreet lines along
<100> directions, analogous to the alignment of the gamma
prime described by Ardell et al. (1966). Figure 5.11a
shows this morphology. The individual morphologies of the
DO22 are consistent with the morphologies explained
earlier. The morphology of the Dla phase is also as
predicted from the B = <(001^> images. The variants of
N4M0 Dla, shown in Figures 5.12b and 5.12c, form along
the DO22 precipitates, just as they did in the B = <(00l)>
images. These third axis dark field images show that the
interlacing of the Dla and DO22 phases results in almost
complete order of the gamma phase.
127
5.1.4.2 Lattice Imaging of DO?? and Dla Phases
The lattice imaging technique is well established and
will not be reviewed here. An excellent review has been
prepared by Sinclair (1979). Briefly, all the information
contained in a lattice image is in the diffraction pattern
from which the lattice image is produced. The advantage
of the lattice image over the diffraction pattern is the
significantly better spatial resolution in a lattice image
compared to a diffraction pattern. There are exceptions
to this, of course. If a focused electron probe is used
to form a diffraction pattern, the diffracting volume will
be on the order of the probe size which can sometimes
approach lattice dimensions.
The DO22 and Dla phases do not present major
difficulties for lattice imaging. From Figures 2.20b and
2.20c, it should be clear that the simplest image can be
formed with the 1/4(420) and 1/5(420) reflections. These
represent real lattice spacings of 3.18 Angstroms and 3.98
Angstroms, respectively. Figure 5.12 is a lattice image
of both the Dla and DO22 phases using the 1/4(420) and
1/5(420) reflections from a B = [001] zone axis under
axial illumination conditions. The inset describes this
imaging condition. The large lattice spacings are about
3.9 Angstroms. Next to these are lattice planes of 3.2
Angstroms spacing. The former corresponds to N4M0
129
lattice fringes, the latter to N3M0 lattice fringes. At
the interfaces of these phases there is no discontinuity.
This is completely consistent with the type of stacking
that is possible with 420 phases where the two phases
share a common 420 plane. Only the stacking sequence
changes across the interface.
Figure 5.13 is an image of the Dla phase in which
there is a small faulted region (Region A), most probably
of N3M0. The crosshatched region is N4M0. The lattice
fringes in the fault are from {l00} planes of an ordered
phase, either the LI2 {OOl} plane or the DO22 {002}
plane. The fringes are more likely from DO22 since there
are no equivalent fringes in the gamma prime cube, the
areas at the top and bottom of the image.
Figure 5.14 is a lattice image of the Dla precipitate
on the edge of four gamma prime cubes. This precipitate
covers the edge of all four cubes and grows into the
intergamma prime cuboid region along the cube faces of all
four cubes. This it can do readily without the
introduction of a stacking fault. The DO22 phase, as
discussed in Section 5.4.1, would introduce high energy
perpendicular twin boundaries if it were to impinge at the
cube edges.
132
5.1.4.3 Solution Heat Treated, Quenched and Aged at
810 C for up to 1UU hours
The aging behavior of this alloy at this temperature
is considerably less complex than that previously
described for the 760 C aging practice. The only NixMo
phase that forms during aging is the DO22 N3M0 phase.
After one hour at 810 C, the DO22 phase is well
established, as shown in Figure 5.15a, a 1/4 (420), B =
[001] dark field image. After ten hours, the DO22 has
coarsened considerably, as in Figure 5.15b. A B =
diffraction pattern showing only DO22 is shown in Figure
5.15c. Though the dark field image should be sufficient
to establish the presence of this NixMo phase, the
diffraction pattern is shown to serve as an example of one
method used to differentiate among the LI2 superlattice
reflections, overlapping DO22 superlattice reflections,
and diffuse (1, 1/2, 0) SRO reflections, all three of
which, as previously discussed in Section 2.3.3, are
difficult to differentiate from the diffraction pattern.
The DO22 and LI2 (100) and (010) reflections which
would normally occupy the same reciprocal lattice
positions are split into two discreet and distinct
reflections that are easily differentiable when the g
vector is large. One of the two reflections is the LI2
superlattice reflection. The other is the DO22
134
superlattice reflection. When the (1, 1/2, 0) reflections
are the result of the SRO, there will be no splitting of
the LI2 spots, since there is no overlapping spot (there
is no SRO superlattice spot at LI2 superlattice positions)
and no shifts in the positions of the (1, 1/2, 0)
reflections, as discussed in Section 5.3, for DO22
reflections. These shifts are discussed in Kersker et al.
(1980) .
After 100 hours, the DO22 phase is still present and
seems to fill most of the intercuboidal gamma prime
regions. The morphology of the DO22 after 100 hours at
this temperature is not similar to that after 100 hours at
760 C. Figure 5.15d is a B = [001], g = 1/4 (420) dark
field of the DO22 after 100 hours at 810 C.
In addition to the D022> the gamma prime, and
presumably the gamma phase, there is an additional phase
present at the interface between the grain boundaries and
the coarsened gamma prime that decorates these
boundaries. Its diffraction pattern was not recorded. It
is probably NiMo.
5.1.4.4 Solution Heat Treated, Quenched and Aged at
870 C for up to 100 Hours
One of the more noticeable features of the high
temperature aged RSR 197 is the development, after one
hours heat treatment, of an ordered dislocation array at
135
the gamma-gamma prime interfaces. Figure 5.16 shows these
interfacial dislocations. The beam direction is along the
B = . The dislocation images are consequently from
the overlapping regions of gamma and gamma prime, regions
B, C, D, and E in Figure 5.4. The fact that this network
forms as a result of the mismatch between the gamma-gamma
prime phases means that the dislocation spacing will be
representative of this mismatch (Lasalmonie and Strudel,
1976). The measurement of the mismatch using this method
was not attempted here.
The dislocations are imagable at the gamma-gamma
prime interface, for example, with B = [001]. The network
is comprised primarily of dislocations of the following
Burger's vectors: b = + [110] and + 1/2[110]. The nodes
at the intersections of these two orthogonal dislocation
types may be relaxed, resulting in fourfold nodes of
dislocations corresponding to Burger's vectors of +
1/2[10T], + 1/2[Oil], + 1/2[Oil], and + 1/2[101]. Any low
index two beam imaging condition near B = [001] will
always yield some visible set of these dislocations. As
an example, Figures 5.16a, a g = (220), B = [001[ image,
and 5.16b, a g = (220), B = [001] image, show opposite
sets of primary dislocations, as expected from the g*BxU=0
criterion for edge dislocation invisibility (Edington,
1976). These figures do not show the fourfold nodes
plainly.
137
Figure 5.17a is a microdiffraction pattern from the
gamma phase. The DO22 reflections are present in this
convergent beam microdiffraction pattern. A dark field
image can be formed if one of these DO22 reflections is
used to form the image. Figure 5.17b is an image taken
using a 1/4(420) reflection. There are two features of
special interest in this image. First, the fine
precipitate is imaged throughout the gamma phase. Second,
as was the case when DO22 was responsible for the (1, 1/2,
0) reflections, one variant of the DO22 predominates along
any single gamma prime cube face, though the other variant
is present as well. Both variants can be plainly seen in
the diffraction pattern. The fine scale of this
precipitate shows that it precipitated during the cool
down from the aging temperature and that it was not
present in the alloy at the aging temperature.
After 100 hours aging, large platelets of equilibrium
delta NiMo have formed throughout the grains. An example
is shown in Figure 5.18a, a low magnification image
showing numerous rod-like and plate-like precipitates.
The diffraction pattern of the needle or edge on plate
shown in Figure 5.18b is shown in Figure 5.18c. The
diffraction pattern is not a low index one, but is close
to a B = NiMo pattern and close to a B = <^100^ gamma
matrix diffraction pattern.
140
It is possible to form an image using a (1, 1/2, 0)
reflection, as shown in Figure 5.19b. Figure 5.19a is a B
= <^100^> microdiffraction pattern showing only gamma prime
and short range order (1, 1/2, 0) reflections. As after
one hour aging, an interfacial dislocation network is
present, as shown in Figure 5.18b.
5.1.4.5 Aging Summary -- RSR 197
At 760 C, all three NixMo metastable phases form and
coarsen with time. The N3M0 DO22 and N4M0 Dla phases
predominate. After one hundred hours, the matrix has
become highly ordered, the DO22 and Dla phase essentially
filling the intercuboidal regions. These two phases are
crystallographically related. Aging at 810 C produces
only DO22 precipitate. This precipitate coarsens and
eventually fills the intercuboidal regions. At 870 C, no
metastable phase forms during aging. An interfacial
dislocation network forms, apparently very rapidly since
it is present after only one hour at temperature.
The equilibrium NiMo phase may be present at all
aging temperatures. At the two lower aging temperatures,
it is usually found decorating the grain boundaries,
usually in regions contiguous to the cellular
intergranular gamma prime. At the highest aging
temperature, the NiMo forms throughout the grains.
142
5.1.5 RSR 209 -- As Solution Heat Treated
and Quenched
Figure 5.20a shows the general microstructural
features of the as-quenched alloy. As in alloy 197, there
are no remnants of the primary gamma prime phase that was
present in the as-extruded microstructure. There is also
cellular gamma prime at the grain boundaries.
Figure 5.20b is a B = \100^ diffraction pattern
showing Pt2Mo reflections and short range order or DO22
reflections. When imaged, the Pt2Mo is very fine. The
Pt2Mo reflections are elongated in 110 directions. This
streaking is consistent with their morphology, a topic to
be dealt with in more detail in Section 5.1.6.2.
5.1.6 RSR 209 Aging
5.1.6.1 Solution Heat Treated. Quenched and Aged
at 760 C for up to 100 Hours
After 10 hours at 760, fine Pt2Mo and fine DO22 phase
have precipitated, as shown in the B = <^100^ diffraction
pattern, Figure 5.21a, and in the dark field images shown
in Figures 5.21b and 5.21c. The diffraction pattern,
Figure 5.21d, taken after 100 hours aging, shows that
N4M0 has formed. The pattern suggests that the N2M0 is
still the dominant phase.
145
5.1.6.2 Solution Heat Treated, Quenched and Aged
at 810 C for up to 100 Hours
The predominant phase at this aging temperature is
the Pt2Mo phase. After one hour at 810 C, Pt2Mo is
densely distributed throughout the gamma matrix. Figures
5.22a and 5.22b are dark field images taken using two of
the six visible Pt2Mo variants. These two variants are
described in Figure 2.21.
The morphologies of the Pt2Mo precipitates are very
much dependent on their crystallography. The two visible
variants and their relationship to the gamma prime cube
axes are described schematically in Figure 2.21. These
lenticular shaped Pt2Mo precipitates are actually
platelets with (lioj habits (Saburi et al., 1969). Figure
5.23a is a B = [001'], g = 1/3(220) image. If the sample
is rotated 54.7 degrees from this orientation about the
axis described in the figure to the B = [111] orientation
and the 1/3 (220) again used to form the image, an image
like that shown in Figure 5.23b results. The plate-like
nature of the precipitate is very apparent by comparing
these two figures. It is likely that all six Pt2Mo
variants can co-exist simultaneously in any given gamma
region.
The Pt2Mo N2M0 precipitates grow with time, as shown
in Figure 5.24a, a B = [001], g = 1/3(420) dark field
image of the Pt2Mo phase after 100 hours at 810 C. There
149
are also some elongated dark rods here that do not index
as N2M0. They are identified in Section 5.1.6.3.
NiMo can be found on the grain boundaries. Figure
5.24b is an example of the NiMo on the boundary between
the cellular gamma prime and the grain boundary itself.
A NiMo B = \100X> diffraction pattern is indexed in Figure
5.24c. An interfacial dislocation network has developed,
as shown in Figure 5.24b.
5.1.6.3 Solution Heat Treated, Quenched, and Aged
at 870 C for up to 100 Hours
The processes observed to be taking place after 100
hours at 810 C are already advanced after 1 hours aging
at 870 C. Numerous inter-gamma prime platelets have
precipitated, as shown in Figure 5.25a. This figure also
shows a well developed dislocation structure. The N2M0
Pt2Mo is still present, as shown in the convergent beam
microdiffraction pattern, Figure 5.25b. The consequence
of increasing the aging time to 100 hours at this
temperature is to coarsen the precipitate that was
observed at the shorter aging time. Figure 5.25c shows
that the rod-like recipitate occupies most of the
intercuboidal region. X-ray diffraction patterns identify
this precipitate as Mo. Two convergent beam
microdiffraction patterns from one of these precipitates
indexed as Mo are shown in Figures 5.26a and 5.26b.
152
Figure 5.26c, a B = <^111^> selected area diffraction
pattern, shows no Pt2Mo 1/3 220 reflections.
5.1.6.4 Aging Summary -- RSR 209
Aging at the lowest temperature produces a mixture of
N2M0 Pt2Mo, DO22 N3M0, and after 100 hours, Da N4M0
phase. These first two phases coarsen during aging, as
would be expected. At 810 C, platelets of Pt2Mo N2M0 and
presumably DO22 phase as well, are present. The Pt2Mo
coarsens considerably during aging. An intercuboidal
phase precipitates prior to the 100 hour treatment. A
morphologically similar phase, identified by electron and
x-ray diffraction pattern analysis of the 870 C aged
sample, is shown to be alpha Mo. An interfacial
dislocation network has developed after 1 hour at 810 C.
Aging at 870 C merely accelerates the coarsening of
those phases that precipitate at 810 C. Pt2Mo is
initially present after one hours aging but has
disappeared after 100 hours. An intercuboidal phase,
identified as Mo from both x-ray and electron diffraction
patterns is predominant in the intercuboidal regions. An
interfacial dislocation structure is present after only
one hours aging. Whenever a grain boundary could be
imaged, this grain boundary invariably contained cellular
gamma prime, sometimes decorated with a phase identified
as NiMo.
153
5.1.7 Special Aging/Special Alloys
5.1.7.1 Alloy //17 -- Solution Heat Treated, Quenched
and Aged at 760 C for 100 Hours
An image of this ternary alloy along a B = <(ll2^>
direction is shown in Figure 5.27c. The microstructure of
this alloy is essentially identical to the RSR alloys.
This would be expected since both the RSR alloys and the
cast alloys were solution heat treated prior to aging.
After the 100 hour heat treatment, the phase
distribution is similar to the phase distribution in RSR
197 after a similar thermal treatment (see section
5.1.4.1). Figure 5.27a is a B = <100^ selected area
diffraction pattern. This pattern should be compared with
Figure 5.6a. Figure 5.27b is a combined g=l/4(420),
g=l/5(420) dark field image showing the similarity in the
precipitate morphology between the DO22 and Dla phases in
this ternary alloy and RSR 197, aged for the same time.
5.1.7.2 Alloy //17 -- Solution Heat Treated, Quenched
and Aged at 870 C for 100 Hours
Figure 5.28a is a B = [001] two beam image showing a
well developed interfacial dislocation structure. Figure
5.28b, a B = <(100^ selected area diffraction pattern shows
that no metastable phases are present at the aging
temperature. This sample was water quenched after aging.
The RSR alloys were all air quenched after aging.
156
5.1.7.3 RSR 197 -- Solution Heat Treated, Quenched,
and aged at 870 C for 1 Hour, Furnace
Cooled to 760 C and Aged for 100 Hours
at 760 C.
Even after aging at 870 C for one hour, the D022 and
Dla phases readily form when aged at a lower temperature.
The dark field images shown in Figures 5.29a and 5.29b are
B = [001] dark field images taken using both 1/4(420)
(Figure 5.29a) and 1/5(420) (Figure 5.29b) reflections.
5.1.7.4 RSR 185 -- Solution Heat Treated at 1315 C
and Water Quenched
The sample was only used to measure the gamma matrix
lattice parameter using the CBED technique. The sample
was chosen because it was water quenched from the solution
heat treatment temperature and consequently showed only
very weak (1, 1/2, 0) SRO reflections. A B = CBED
pattern from the RSR 185 gamma phase is shown in Figures
5.30a and 5.30b. There is no asymmetry in the central
spot of the pattern shown in Figue 5.30a. Note the
absence of 110 superlattice reflections in Figure 5.30b.
5.2 X-Ray Diffraction Measurements
The gamma prime and gamma lattice parameters, as
measured by x-ray diffraction, are listed in Table 5.1.
The gamma prime lattice parameter is consistently larger
in the Ta containing alloy, the RSR 197 alloy, than
Table 5.1 -- Lattice Parameters From X-Ray Measurements
Alloy
Heat Treatment
Line
Ill
331
v'
v v-
-v'/v
v'
V
V-V1/v
RSR 209
As Solution and
Quench
3.5791
3.5775
1 hr @ 760 C
3.5803
3.63
1.3
3.581
- .
...
3.5764
3.63
1.43
3.580
3.5819
3.63
1.3
3.579
100 hr @ 760 C
3.5842
3.636
1.4
3.582
100 hr @ 810 C
3.5810
1 hr @ 870 C
3.576
3.608
.87
3.583
3.573
3.599
.76
3.5764
3.6244
1.3
100 hr @ 870 C
3.5826
3.6196
1.0
3.5798
3.5710
3.619
1.3
RSR 197
As Solution and
Quench
3.5862
3.5869
1 hr @ 760 C
3.5842
3.6038
.55
3.5904
3.614
.66
3.5897
3.6054
.43
100 hr @ 760 C
3.5881
3.65(18)*
1.77
100 hr @ 810 C
3.5898
3.5892
100 hr @ 870 C
3.592
3.604
.33
3.592
3.616
.68
3.5880
3.61
.64
3.588
3.609
.58
JL
Value is affected by presence of NixMo precipitates.
159
Table 5.1 continued
RSR 209
3.585
RSR 197
3.595
3.593
220
v
3.619
Line
v-v'/v v'
311
V v-v'/v
.69 3.584
3.586
3.589 3.613 .65
160
161
in the W containing alloy, RSR 209. The mismatch between
the gamma prime and gamma lattice parameters in the two
alloys is also different: larger in the RSR 209 than in
the RSR 197. Mismatch is defined as aD gamma prime minus
aG gamma divided by a0 gamma (Sims and Hagel, 1972).
In many cases, Table 5.1 does not list the lattice
parameter of the gamma phase. The measurement of the
exact gamma peak position was not always possible, due to
either insufficient signal, a texture effect, or to the
presence of the metastable Ni-Mo phases. As an example,
the gamma lattice parameter could not be unambiguously
measured for the RSR 197 sample that was aged for 100
hours at 760 C. The diffraction peak in the gamma region
was smeared to such an extent in this spectrum that
locating the exact maximum in the gamma peak intensity was
not possible. Without the TEM result showing significant
NixMo precipitation, interpretation of this x-ray
diffractogram would be difficult.
5.3 Convergent Beam Measurements
Numerous measurements of the gamma prime lattice
parameter were made using the B = <(ll4)> convergent beam
electron diffraction and HOLZ line patterns described
extensively in Chapter 4. The results of these
measurements are listed in Table 5.2. Measurements were
made directly from the negatives using a 10X loupe
Table 5.2 -- Lattice Parameters From CBED Measurements
Alloy
Aging Temp./Time
Phase*
Measured Ratio
a/b
RSR 197
As Solution Heat
Treated and Quenched
GP
1.0
ASQ, Aged 760 C
1 hr
GP
1.06
100 hr
GP
1.08
ASQ, Aged 870 C
1 hr
GP
1.0
100 hr
GP
1.06
RSR 209
As Solution Heat
Treated and Quenched
ASQ, Aged 760 C
10 hr
GP
.90
100 hr
GP
.92
.94
ASQ, Aged 870 C
100 hr
GP
.90
.90
RSR 185
ASQ
GP
.91
.98
G
1.23
*Gp gamma prime
G gamma
Lattice Parameter
3.573
3.577
3.578
3.573
3.577
3.566
3.567
3.569
3.566
3.566
3.567
3.572
3.584
162
Table 5.2
continued
Alloy
Aging Temp./Time
Phase*
#17
As Solution Heat
Treated and Quenched
Aged @ 760 C
100 hr
GP
ASQ, Aged @ 870 C
GP
* GP gamma prime
G gamma
Measured Ratio
a/b Lattice Parameter
.90 3.565
.90 3.565
.90 3.565
163
164
and are reproducible to .1 mm. The accuracy in absolute
lattice parameter measurement is very poor, as previously
explained in Chapter 4. No absolute measurement was
attempted. The relative differences in lattice parameter
as measured with CBED between the RSR 197 and RSR 209 is
on the order of .3%. This number compares very favorably
with the x-ray diffraction results of the previous
section.
Not all the CBED patterns from the gamma prime phase
were as symmetrical as those shown in Figure 4.9. Figure
4.1, for example, shows an asymmetrical pattern from the
gamma prime. The origin of the assymetry is unclear.
Measurements from the gamma phase were extremely
difficult to make. Figure 5.30b is a low camera length
B=\114^> CBED pattern from the gamma phase of RSR 185.
Figure 5.30a shows the detail in the central spot.
Figure 5.30b shows both a lack of any {llO} superlattice
reflections in the zero order zone, and no superlattice
FOLZ lines. The pattern is thus clearly from the gamma
phase only. The fine structure in 5.30a shows that the
lattice parameter of the gamma is greater than the lattice
parameter of the gamma prime. There is no perceptible
distortion or loss of symmetry in this gamma B = ,\114/>
CBED pattern. This implies that there is no measurable
strain unless that strain is parallel to the beam.
165
Figure 5.31a is a B = <.14)> CBED pattern from the
gamma phase in the RSR 197 as solution heat treated and
quenched sample. The gamma phase contains a very fine
distribution of the DO22 precipitate, as described in
Section 5.1.2. The pattern represents either diffraction
from the gamma phase strained due to the influence of the
DC>22j or from the DO22 itself. There would be no
superlattice from the DO22 in the zero order zone, and
hence no {lio} reflections. None were observed.
The pattern in Figure 5.31a was taken from an
intercuboidal area such that the gamma lattice can be
shown to be expanded in the direction of the c axis of the
DO22 phase. This direction is perpendicular to a (100)
face of the gamma prime.
The a/b ratio used to measure the lattice parameters
in the gamma prime phase can still be used to measure the
lattice parameters from this assymetric pattern. The
values of a/b will be negative (see Appendix A) because of
the line shift algorithm used for the calculation. The
ratio is negative when the intersection of the 193 and 391
lines crosses the 10 0 2 line. This pattern has an Rp
value of -5.3 and an R2 value of 0.5. The lattice
parameters corresponding to these R values are a = 3.575
Angstroms and b = 3.645 Angstroms, assuming that c = 3.575
Angstroms. The FCC c axis here is parallel to the beam.
167
Thus there is about 1.9% "strain" in the lattice in the c
axis direction of the DO22
5.4 Energy Dispersive X-ray Measurements
The energy dispersive x-ray methodology was explained
in detail in Section 4.2. The results of the
measurements are given in Table 5.3.
5.5 Microhardness Measurements
Microhardness measurements were made on most of the
aged samples. Rockwell C was the test method. The values
represent the average values of six measurements. The
data is shown in Figure 5.32.
Table 5.3 -- EDX Measurements
Alloy
Heat Treatment
Ni
Gamma Prime
Mo
A1
Ni
Gamma
Mo
A1
197
Solution Heat Treated
and Quenched (SHTQ)
77.2
3.8
19.0
78.0
16.7
5.0
SHTQ,
760
C
for
100 hrs
85.0
2.1
12.9
88.0
9.9
1.5
SHTQ,
810
C
for
100 hrs
76.0
5.0
19.0
76.0
17.0
7.0
SHTQ,
870
C
for
1 hr
77.0
4.8
18.2
78.1
15.6
6.3
SHTQ,
870
C
for
100 hrs
78.0
5.4
16.6
80.5
16.3
3.2
209
SHTQ
Not Analyzed
77.0
16.2
7.1
SHTQ,
760
C
for
100 hrs
77.1
4.6
18.3
75.0
18.1
6.9
SHTQ,
810
C
for
100 hrs
77.0
5.0
18.0
77.7
16.5
5.8
SHTQ,
870
C
for
1 hr
76.3
5.7
18.0
77.0
19.0
4.0
SHTQ,
870
C
for
100 hrs
77.2
3.6
19.2
80.5
16.2
3.4
//17
SHTQ,
870
C
for
1 hr
76.2
6.3
17.5
76.1
17.9
6.0
168
Rockwel1
As Quenched
i h r
lOhrs
lOOhrs
A
Aged at
760C
Solid figures:
RSR 197
Aged at
81OC
Open figures:
RSR 209
O
Aged at
870C
Figure 5.32
Microhardness measurements of SHTQ and aged
RSR alloys.
CHAPTER 6
DISCUSSION AND CONCLUSIONS
6.1 Metastable NiyMo Phase Formation:
Effects of Chemistry and
Microstructure
There are clearly differences at all aging
temperatures between the precipitation sequences of the
metastable NixMo phases in the RSR alloys. From the EDS
measurements it is probable that Ta in RSR 197 cannot have
a direct effect on the precipitation of these NixMo phases
in the gamma phase of RSR 197 alloy. This is confirmed by
ternary alloy //17 according to the results discussed in
Section 5.1.7.1. The precipitate and the precipitate
morphologies in alloy //17 are essentially identical to
those in the Ta containing RSR 197. One can conclude that
if it is the presence of an element that allows all three
NixMo precipitates to co-exist, this element must be A1,
not Ta.
The presence of W in the RSR 209 must be a
controlling factor in establishing the precipitation
sequence in this alloy, since this sequence differs from
the ternary alloy //17. The Pt2Mo phase is the predominant
phase, not DO22 and Dla. This is very similar behavior to
170
171
what would be expected from a binary N3M0 alloy, as
described in Section 2.2.5.1.
A major question in this research was, what are the
compositions of the major phases, of the gamma prime and
gamma phases in the RSR alloys? This information is
needed in order to define the precipitation behavior of
the NixMo precipitates in the RSR alloys since in the
binary alloys, the precipitate types vary as a function of
composition, as described in Section 2.2.5. This was the
purpose for the EDS measurements described in Section
4.2. The experimental values for the gamma and gamma
prime compositions given in Table 5.3 vary enough from
alloy to alloy that only the approximate composition can
be determined. For the gamma prime phase in RSR 197,
excluding the 760 for 100 hour aging data, this average
composition is 77 + 1.4 % Ni, 4.75 + 1.18 % Mo, and 18.2 +
2 7o Al, all in atomic percent. For gamma, again excluding
the data for the 760 C for 100 hour aging data, the
average values for the composition of this phase are 78.15
+3.2 1 Ni, 16.4 + 1.0 1 Mo, and 5.4 + 2.0 % Al, all in
atomic percent. It is reasonable, based on the binary
phase diagram solubility information shown in Figures 2.1
and 2.2, to take an average of the compositions even
though the solubility changes slightly with temperature
over the range of aging temperatures.
172
For RSR 209, the values for the gamma prime phase are
76.8 + .8 at. % Ni, 5.04 + 1.8 at.% Mo, and 18.2 + 1.2 at.%
A1. For the gamma phase, these values are 77.2 + 3.39
at.% Ni, 17.3 + 2.1 at.% Mo, and 5.5 + 2.4 at.% A1. These
averages are similar to those measured by Miracle et al.
(1984) for the equilibrium gamma and gamma prime phase
compositions that were determined in their study of
Ni-Mo-Al ternary alloys.
The EDX data defines the ternary composition of the
gamma phase in which the nonequilibrium precipitation is
observed. This ternary composition is similar in both
alloys and somewhere between the N3M0 stoichiometry and
N4M0 stoichiometry, assuming that the Al enters into the
ordering reactions.
The partitioning of Al to the gamma matrix lends
further credence to the fact that Al influences the
precipitation behavior in RSR. 197, RSR 209, and alloy //17
since DO22 phase was almost never observed in aged Ni-Mo
binaries of any stoichiometry (see Section 2.2.5). The
exception was in the work of Van Tendeloo et al. (1975) in
which DO22 phase precipitated when the alloy was very
rapidly quenched. Under these circumstances, the DO22
phase was only transient, described as a transition phase
between short range order and the more stable N4M0/N2M0
phases. In both RSR alloys and in the ternary alloy //17,
the DO22 is obviously not transient.
173
The DC>22 phase, as Ni^Nb, has been observed in
preferential orientation with gamma prime phase in other
alloy systems (Cozar and Pineau, 1973). In the Inconel
(In) 718 type alloys that they characterized, the DO22
nucleated on the gamma prime cuboids with c axis of the
DO22 perpendicular to the 100 faces of the gamma prime.
The situation is similar in the R.SR 197 and RSR 209 except
that the DO22 does not nucleate on the gamma prime. It
nucleates throughout the intercuboidal gamma matrix, as
shown in Section 5.4.
Oblak et al. (1974) studied the aging, under tensile
and compressive stresses, of single 100 crystals of In
718. The primary strengthening phase in this alloy is
DO22 Ni3Nb in which small smounts of Al substitute for the
Nb (Paulonis et al., 1969). Oblak et al. (1974) found
that certain DO22 variants could be suppressed by
application of tensile and compressive loads. When a
tensile load of 69 Mn/m^ was applied parallel to the [100]
axis, the DO22 variant with c axis parallel to the stress
axis was observed. The morphology of the DO22 in this
alloy is an ellipsoidal plate with the c axis
perpendicular to the plate axis, clearly different from
the DO22 in the RSR 197 samples aged at 760 C. A
compressive stress along the [100] lead to precipitation
of the other two variants.
174
Martin (1982) has studied the nucleation of the DO22
phase. (Mishra (1979), Chevalier and Stobbs (1979), and
Nesbit and Laughlin (1978) studied nucleation in NiMo
binaries using electron microscopy, but were only able to
study the nucleation of N4M0 Dla and N2M0 Pt2Mo. The
DO22 is not stable in the binary alloy.) In Martin's
N4M0 A1 containing ternary (this ternary does not contain
gamma prime) the DO22 and Pt2Mo were shown to form more
or less simultaneously when aged at 600 C. The Dla formed
sluggishly and was present after 2000 hours. The DO22 and
Pt2Mo were still present after this long aging time.
Pt2Mo was the predominant phase, very similar to alloy RSR
209.
In the RSR 197 alloy, the DO22 phase nucleates during
the slow quench from solution heat treatment temperature.
The streaks that appear to emanate from the DO22
reflections towards the Dla reciprocal lattice positions
shown in Figure 5.3a could be better described as
emanating from N4M0 nodes. This would imply that the
N4M0 Dla has formed as very thin platelets, possibly as
faults in the N3M0 crystal structure. This could be
determined by lattice imaging. Figure 5.3c shows both the
DO22 phase and the bright faults that would correspond to
the N4M0.
In the RSR. 197 alloy quenched and aged at 870 C, two
(1, 1/2, 0) microstructures have formed. In the sample
175
aged for one hour there appears to be DO22 and possibly
(1, 1/2, 0) short range order. After aging at the highest
temperature for 100 hours, only SRO spots are present
after the quench. These SRO spots are also imageable.
Since the as-quenched microstructure contained D022>
the presence of DO22 in the material aged for one hour at
870 C might mean that the DO22 that had precipitated
during the quench was not fully in solution after one hour
at 870 C. The solvus for DO22 has been reported at about
800 C for an A1 containing ternary (Martin, 1982). It is
stable to at least 810 C in the RSR 197 alloy. In the
ternary alloy aged for one hour at 870 C and water
quenched, no reflections corresponding to SRO or DO22
phase were seen. Thus, the presence of SRO and DO22
phases in RSR 197 alloy air quenched from the aging
temperature is probably the result of precipitation from
solution during the air quench. The fact that in one
case, the one hour aging case, both SRO and DO22 form and
in the other, only SRO, implies that the gamma phase could
be depleting in Mo during high temperature aging which
would show that the Mo in the as-quenched and lower
temperature aged samples is supersaturated in the gamma
phase with respect to the equilibrium concentration. This
would be expected since no equilibrium Mo rich phases are
present in the alloys aged at lower temperature.
176
6.2 Precipitation in RSR 197
The precipitation of the phases in RSR 197 can be
summarized as follows. Upon quenching, the DO22 phase
precipitates from the Mo supersaturated matrix. The DO22
phase is stabilized by Al. (DO22 has also been shown to be
stabilized by Ta additions to in Ni-Mo binaries. There is
not enough Ta in the matrix phase of RSR 197, however, to
account for the DO22 precipitation in RSR 197). The DO22
phase may nucleate preferentially in at least one of two
ways: 1) under the influence of a strain gradient between
the gamma prime cuboids, or 2) because the distribution of
gamma prime cubes is such that this distribution prohibits
the nucleation of the other two variants between the cubes
in preference for the variant whose c axis is perpendicular
to a gamma prime cube face. Either could explain the
preference of the DO22 to form as a single variant on these
unique 100 faces of the gamma prime cubes. After the DO22
has nucleated, this strain is shown to be about +1.9% in the
direction of the DO22 c axis. Convergent beam electron
diffraction was used to make this measurement.
The N4M0 phase seems to precipitate after the DO22 has
precipitated. The two coarsen and grow in a mutual
relationship along the 100 direction of the cube face,
presumably under the influence of self stress, analogous to
the coarsening behavior of N3AI in Ni-Al binary alloys
(Ardell et al., 1966).
177
Both phases can grow from cuboid to cuboid with
mutual 420 habit planes, as demonstrated by the lattice
image in Figure 5.12. These phases merely represent a
change in the stacking sequence across a common 420 plane.
It is entirely likely that there is no gamma phase
present in RSR 197 aged at 760 C for 100 hours. The dark
field images in Section 5.4.1 show no volume of
intercuboidal gamma phase not occuped by DO22 or Dla.
When aged at 810 C, above the solvus for the N4M0,
only the DO22 phase forms. This is never observed in
Ni-Mo binary alloys. The DO22 still has a slight 420
character but the alloy does not seem as well ordered as
at lower temperatures. The DO22 at this temperature also
precipitates with its c axis perpendicular to a specific
100 face of the gamma prime.
In samples air quenched from 870 after aging, short
range order can exist. This short range order gives rise
to dark field diffraction contrast. This means that it
can be imaged as discreet domains. This very strongly
indicates that the type of (1, 1/2, 0) short range order
diffraction effect observed in RSR 197 is due to
microdomains.
At this highest aging temperature, interfacial
dislocations are formed. If the dislocations are first
allowed to form by aging the alloy at 870 C for one hour
and then the aging is continued at 760 C for 100 hours
without an intermediate quench, the DO22 and Dla phases
178
precipitate and grow just as in the RSR 197 alloy aged
only at 760 C, as discussed in Section 5.1.4.1. The high
temperature aging should reduce any interfacial strain and
thus presumably any intercuboidal strain. The DO22 and
Dla phases still form as previously in the sample aged
only at 760 C for 100 hours. This very strongly indicates
that it is not a strain gradient between the gamma prime
precipitates that leads to preferential nucleation, but
rather the strain induced by the nucleus that will prevent
the nucleation of the variants of DO22 whose c axis is not
perpendicular to the 100 faces of the gamma prime.
The N4M0 Dla phase is not observed as having the
same crystallographic constraints as the DC>22* Along
either cube face, either or both visible variants are
imageable. Based on the observations made in Section
5.4.1, only four N4M0 variants should ever exist between
any two gamma prime faces. If the other two variants were
present, perpendicular twin boundaries would result
between these impinging Dla precipitates. This is the
highest energy antiphase boundary in Dla (Ling and Starke,
1971). These other two variants would also not exhibit
the same crystallographic relationships with the DO22
phase that were described earlier in Section 5.1.4.1.
179
6.3 Precipitation in RSR 209
The N2M0 and N3M0 DO22 phases precipitate during
the air quench from the solution heat treatment
temperature. The presence of aluminum in the gamma phase
stabilizes the DO22 phase. At the lowest aging
temperature, these phases coarsen and eventually the Dla
phase forms. The N2M0 remains the dominant phase for
aging times up to 100 hours.
The N2M0 is also the dominant phase when the RSR 209
is aged at 810 C. It coarsens quickly and is consumed by
equilibrium Mo when aged at the highest temperature.
The formation of the Pt2Mo phase is not a function of
the gamma prime cube distribution, as was the DO22 phase.
It is reasonable to assume that all six Pt2Mo variants can
exist simultaneously in any one region of the gamma
matrix.
6.4 Mechanical Response to Aging
The microhardness data shown in Figure 5.32 are now
mostly explicable by considering the aging processes that
take place in these two alloys. In RSR 197 aged at 760 C,
the alloy begins to order immediately following the
quench. The DO22 and Dla phases continue to order during
aging, and the gamma matrix becomes essentially fully
ordered after 100 hours at the aging temperature. The
increase in hardness correlates with this ordering trend.
180
The alloy aged at 810 C shows almost no change in
strength when aged at this temperature. The DO22 phase
was shown to be present in the gamma matrix. Further
characterization of this heat treatment would be necessary
in order to characterize the DO22 phase more clearly.
This result is not consistent with order strengthening.
Aging at 870 C has little or no effect on the
strength. As no strengthening phase precipitates at this
temperature, this is not a surprising result.
The as-quenched RSR 209 alloy is stronger than the
as-quenched RSR 197 alloy. Apart from the obvious
chemical differences between the two alloys, no other
explanation for this strength difference can be inferred
from any of the observations made in this study. During
the subsequent aging, the alloy, within the time
resolution of testing, loses strength monotonically,
typical of an alloy that is overaging.
The implications of these observations for alloy
design are significant. The mechanical response of the
RSR 209 to aging is what would be expected of an alloy
that undergoes overaging, a common observation in metals
that are strengthened by fine percipitate. The mechanical
response to aging in RSR 197 aged at 760 C would
presumably represent the effect of ordering. Since it is
possible that the Dla phase is the equilibrium phase for
this aging temperature, it may be possible to fully order
181
the matrix with Dla. This would impart high strength to
the alloy, and probably great stability as well.
6.5 Convergent Beam/X-ray Diffraction
The use of the convergent beam technique for lattice
parameter measurements must seem redundant in light of the
x-ray diffraction measurements that were made. The
convergent beam method is a powerful tool with which to
make these measurements since it can be used to make local
lattice parameter measurements, local strain measurements,
and perhaps measurements that would reflect subtle changes
in ordering, ternary ordering, for example. Ternary
ordering might change the symmetry of the convergent beam
FOLZ structure (Ecob et al., 1982).
Only lattice parameter measurements in the gamma
prime phase were practical. The gamma phase was in
general too fine with respect to the beam size to form a
pattern unique to the gamma phase. There was significant
interference between the gamma and gamma prime phases,
invariably resulting in unusuable diffraction patterns.
The same effect was observed in the gamma prime phase when
the beam was placed too close to the gamma phase, yet
still in the gamma prime phase.
It is not possible to quantitatively differentiate
alloying effects using lattice parameter measurements
unless numerous standards exist, and then generally, only
182
in binary alloys can these differences be accurately and
unambiguously determined. Nevertheless, there are some
generalizations that can be stated regarding the lattice
parameter measurements and the partitioning effects in the
RSR alloys. First, the lattice mismatch as measured by
x-ray diffraction between the gamma and gamma prime phases
is greater in the RSR 209 alloy than in the RSR 197
alloy. In both alloys, the gamma phase lattice parameter
is greater than the gamma prime lattice parameter. The
high Mo content in both alloys is responsible for this
effect. In the Ta containing alloy, RSR 197, the gamma
prime phase has a larger lattice parameter than the gamma
prime phase in RSR 209. One interpretation of these
observations is that the Ta, which substitutes readily for
A1 in the gamma prime phase, is the factor that increases
the lattice parameter of the gamma prime in RSR 197. Nash
and West (1979) report that about 8% Ta will increase the
lattice parameter of gamma prime to about 3.59 Angstroms.
The comparable unalloyed N3AI lattice parameter is about
3.57 Angstroms. The EDS data supports this Ta
partitioning hypothesis since it was clearly shown that
the Ta partitions predominantly to the gamma prime phase
in RSR 197 under all the aging conditions in which it was
measured. Thus, the local measurement of the gamma prime
lattice parameter using the convergent beam technique can
show the elemental partitioning differences in a
183
qualitative way that were measured in a semiquantitative
way using the energy dispersive method.
6.6 Conclusions
a) Aluminum stabilizes the DO22 phase in both RSR
197 and RSR 209.
b) Tungsten offsets the effect in a) in RSR 209.
c) Tantalum exerts no effect on the aging behavior
of RSR 197.
d) The partitioning of the quaternary elements can
be determined by quantitative EDS measurements.
These elements are shown to partition as
follows:
1) Ta partitions almost entirely to the gamma
prime phase and
2) W partitions equally between the gamma and
gamma prime phases.
e) The DO22 and Dla phases in RSR 197 aged at 760
are closely related crystallographically and are
shown to share a common 420 plane at their
interfaces.
f) This study has shown that convergent beam
electron diffraction, convergent beam
microdiffraction, and energy dispersive x-ray
analysis provide unique and relevant information
about the microstructures of these superalloys.
184
The multitude of complex reactions described in
this dissertation are mostly explicable based on
the results from the application of these
methods. Convergent beam diffraction is shown
to have sufficient sensitivity to measure the
relative lattice parameter differences between
the gamma prime phases of the two RSR alloys.
These meaurements compare favorably with x-ray
diffraction measurements. Convergent beam
diffraction is also shown to be a powerful but
limited method for measuring strains in
micro-volumes of material.
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APPENDIX A
HOLZ PATTERN CALCULATION
Central to the calculations described in this
appendix is the assumption that the microscope
accelerating voltage can be arbitrarily defined. This
will in turn define a relative crystal standard for the
material that will be characterized. The standard
operating voltage of the microscope is defined to be
100.00 KeV, for which the wavelength will be .037
Angstroms. For B=<(ll4>and 9,3,1 diffracting planes, the
resultant lattice parameter that exactly satisfies the
equation in Section 4.1.3, is 3.5712 Angstroms. For the
standard values just given, the four 9,3,1 HOLZ lines will
intersect at a point in the center of the transmitted
disc. The ratio of A to B (see Figure A) is referenced at
this point to the values of A1 and B1 given in the
attached program listing. A larger or smaller lattice
parameter will cause this ratio to vary. The ratio is
listed as R1 in the table following the program.
To account for noncubic effects, values of A3 and B3
are also calculated in the program. They are ratioed in
the program and appear in the Table as the ratio R2. The
values TI, T2, etc. which appear in the program and in
Figure A are delta theta-Bragg values, where delta
191
192
theta-Bragg equals the value of theta Bragg for aQ =
3.5712minus a0 = x. The standard value for theta-Bragg
is calculated first for each affected line. For example,
theta-Bragg for the 931 lines using a lattice parameter of
3.5712Angstroms, is 2.83255 degrees. A lattice parameter
value larger than 3.5712 Angstroms will result in a
smaller theta-Bragg and hence a positive value of delta
theta-Bragg. Likewise, a lattice parameter smaller than
3.5712Angstroms will result in a negative value for delta
theta-Bragg.
193
Angle PO=angle between
Angle Pl=angle between
Angle S0=angle between
Angle Sl=angle between
10
10
I
I
0 2 and 153
0 2 and 3 9 I
5 3 and 5 I 3
5 3 and 3 9 I
Figure A CBED calculation.
1 o o
1 1 o
1 2 O
1 30
1 4 0
ISO
1 6 O
1 70
1 3 O
1 9 O
200
2 1 O
22 0
23 0
2 4 0
25 0
2 6 0
270
2 8 0
2 9 0
3 0 0
3 1 O
3 2 0
3 3 0
3 4 0
35 0
3 6 0
3 7 0
3 8 0
3 9 0
4 0 0
4 1 O
420
43 0
4 4 0
4 5 0
46 0
470
4 8 0
4 90
5 0 0
5 1 O
52 0
5 3 0
5 4 0
550
56 0
570
5 8 0
5 9 0
6 0 0
6 1 O
6 2 0
6 30
6 4 0
6 5 0
6 6 0
6 7 0
6 8 0
6 9 0
7 0 0
7 1 O
720
7 3 0
7 40
75 0
7 60
770
7 8 0
194
P r t r = 4 O
RESTORE
c r'r nrrnrpc:
DATA 0. 189,G. 1943, 80. 54, 72. 74, 73. 3,27. 113
|
j
REM DEFINE STANDARD CONDITIONS AND INTERFLANAR ANCLES
READ Al,B1,P0,SO,P1,SI
I
i
REM DEFINE LATTICE PARAMETERS
I nd = 0
PRINT 8Pr t r : L_"
PRINT SPrtr: USING 460:
REM
! ***********************
***** DEFINITIONS *****
i *******************'.***
!DlaDspacing:
{
< i
9 3 )
!02sDspac:ng:
j
< 1 0
0 2 >
! D3--spacing :
1
( 9
1 3 )
!D4 sDspacing:
j
( 3
9 1 )
!D5 sDspacing:
i
( 0
10 2)
!DsDspacing:
i
C 9
3 1 >
FOR A* 3.56 TO 3
62
STEP 0
Ind=Ind +1
IF Inda S THEN
PRINT SPrtr:"L"
PRINT SPrtr: USING 460:
IMAGE 5 X "A" 14 X "B" 12X "Rl" 12X"R2"
I nd = 0
END IF
C-A
I nd 2 >1
FOR B*3.56 TO 3.62 STEP 0.005
Dl-l/(l/A*2+81/B*2+9/C2>*0.5
D2-1/ ( 100/A* 2 + 4 /C 2) 0 5
D3l/ <81/A*2+l/B*2+9/C2) 0 5
D 4 1/ <9/A*2+81/B*2+l/C42) *0 .5
D5-1/(100/B* 2 + 4/C 2) 0 5
D 6 a 1/ (81/A*2 + 9/ B2 + l/ C'2) *0 5
TI a2 8 3 2 5 5 -ASN( 0.037/C2*Dl)>
T2a3 0 2 8 3-ASNC 0.037/C2*D2>>
T3a2. 83255 -ASN< 0.037/<2*D4>>
T4-2.83255-ASN(0.037/(2*D3)>
T63 0 2 8 3 -ASN( 0.037/(2*D5>>
T7-2 8 3 2 5 5 -ASN( 0 037/ < 2*D6) >
A 2
AND
B 2
DEFINED
IN
FI CURE
A
A3
AND
B 3
DEFINED
IN
FIGURE
A
A2*A1-TI /TAN(P0)-T2/SIN(P0)+T1 /TAN(SO >-T4/SINCSG)
B2 = B1-T3/TAN(P1 )-T2/SIN(Pl >-T3/TAN(Sl )-Tl /SINiSl >
R1 A 2/B 2
A3 a A 1-T 4/TAN-TI /SIN(SO >
B 3 a B1-T7/T AN(P1>-T6/SIN(P1)-T7/TAN(S1 )-T4/SIN(51 )
R2 =A3/B3
IF Ind2 a 1 THEN
PRINT SPrtr: USING 780:A,B,R1,R2
IMAGE 4(4D.4D,5X)
79 0
8 0 0
8 1 0
820
83 0
8 40
8 5 0
8 6 0
870
8 8 0
195
ELSE
PRINT gPrtr: USING 810:B,R1,R2
IMAGE 14X, 3 < 4D 4D, 5X)
END I F
Ind 2 = 0
NEXT B
Ind 2 = 1
PRINT ?Pr t r :
NEXT A
END
\
196
A
3.5600
3.5650
3.5700
3.5750
B
R1
R 2
3.5 6 0 0
0.8475
0.8475
3.5 6 5 0
0.9082
0.8332
3.5700
0.9777
0.8183
3.5750
1 .0 5 8 0
0.8028
3.5800
1.1520
0.7866
3.5 8 5 0
1 .2 6 3 4
0.7697
3 .5 9 0 0
1.3976
0.7520
3.5 95 0
1 .5 6 23
0.7335
3.6000
1 .76 9 3
0.7140
3.6050
2.0373
0.6936
3.6100
2.3978
0.6722
3.6150
2.9089
0.6497
3 .62 0 0
3.6898
0.6259
3.5600
0.8350
0.9104
3 .56 5 0
0.8966
0.8966
3.5700
0.9673
0.8821
3 .5 75 0
1.0495
0.8669
3.5800
1.1462
0.8510
3.5850
1.2616
0.8343
3.5900
1.4016
0.8168
3.5950
1 .57 5 1
0.7983
3.6000
1 .7 9 5 7
0.7789
3.6050
2.0856
0.7585
3.6100
2.4837
0.7369
3.6150
3.0642
0.7140
3.6200
3.9899
0.6899
3.5600
0.8218
0.9833
3.5650
0.8843
0.9701
3.5700
0.9563
0.9563
3.5750
1.0405
0.9419
3.5800
1 .14 00
0.9266
3.5850
1 .2 5 9 6
0.9105
3.5900
1.4059
0.8936
3.5950
1 .5 8 9 1
0.8756
3.6000
1.8251
0.8567
3.6050
2.1406
0.8365
3.6100 .
2.5838
0.8152
3.6150
3.2520
0.7924
3.6200
4.3750
0.7682
3.56 0 0
0.8080
1.0686
3.5 6 5 0
0.8713
1 .0 5 6 7
3.5700
0.9447
1.0441
3 .5 7 5 0
1 .0 3 0 8
1 .0 3 0 8
3.5800
1.1334
1.0168
3.5850
1 .25 7 4
1 .0019
3.5900
1 .4107
0.9861
3.5950
1 .6 0 4 7
0.9693
3.6000
1 .8 5 8 2
0.9514
3.6050
2.2036
0.9323
3.6100
2.7021
0.9119
3.6150
3.4839
0.8899
3.6 2 0 0
4.8871
0.8664
197
A
3.5800
3.5850
3.5900
3.59 5 0
3.6000
E
R 1
R 2
3.5600
0.7933
1.1698
3.5650
0.8575
1.1599
3.5700
0.9322
1.1493
3.5750
1.0204
1 1 3 e 1
3.5800
1.1261
1.1261
3.5850
1.2551
1.113 4
3.5900
1.4158
1 .0 9 9 7
3.5950
1 .6219
1 .0 8 5 1
3.6000
1 .8 9 5 6
1.0694
3.6050
2.2767
1 .0 5 2 6
3.6100
2.8439
1.0343
3.6150
3.7774
1 .0146
3.6200
5.6014
0.9931
3.5600
0.7778
1 .2 9 2 0
3.5650
0.8428
1 .28 5 1
3.5700
0.9189
1 .2 77 8
3.5750
1.0093
1.2699
3.5800
1.1183
1.2615
3.5850
1 .25 2 4
1 .2 5 2 4
3.5900
1 .4215
1 .2 4 2 7
3.5950
1.6412
1.2321
3.6000
1.9384
1 .2 2 0 6
3.6050
2.3625
1.2081
3.6100
3.0172
1.1944
3.6150
4.1609
1.1794
3.6200
6.6674
1.1629
3.5600
0.7615
1 .4 4 2 2
3.5650
0.8272
1 .4 4 0 2
3.5700
0.9047
1 4 3 8 2
3.5750
0.9972
1 .4 3 5 9
3.5800
1.1098
1,4334.
3.5850
1.2495
1.4307
3.5900
1 .4 2 78
1.4278
3.5950
1 .6 6 3 0
1.4246
3.6000
1 .9 876
1 .4210
3.6050
2.4645
1 .4170
3.6100
3.2338
1.4127
3.6150
4.6833
1 .4 0 7 7
3.6200
8.4299
1 .40 2 2
3.5600
0.7441
1 .6314
3.5650
0.8106
1 .6 3 75
3.5700
0.8894
1 .6 4 4 0
3.5750
0.9842
1.6512
3.5800
1.1004
1 .6 5 9 0
3.5850
1 .2 4 6 3
1 .6 6 7 6
3.5900
1.4348
1.6771
3.5950
1 .6 8 7 7
1 .6 8 7 7
3 6 000
2.0449
1 .6 9 95
3.6050
2.5879
1.7127
3.6100
3.5122
1 .7 2 7 7
3.6150
5.4370
1.7449
3.6200
11.9025
1 .7 6 4 7
3.5600
0.7256
1.8772
3.5650
0.7928
1 .8 9 6 6
3.5700
0.8730
1.9180
3.5750
0.9701
1 .9417
3.5800
1 .0 9 02
1.9681
3.5850
1 .2 4 2 7
1 .9 9 77
3.5900
1.4426
2.0311
3.5950
1.7160
2.0690
3.6000
2.1126
2.1126
3.6050
2.7402
2.1632
3.6100
3.8833
2.2225
3.6150
6.6189
2.2931
198
A
3.6050
3.6100
3.6150
3.6 2 00
B
HI
R 2
3.5600
0.7059
2.2092
3.5650
0.7738
2.2522
3.5700
0.8553
2.3004
3.5750
0.9547
2.3551
3.5800
1.0790
2.4174
3.5850
1 2 38 7
2.4893
3.5900
1.4514
2.5728
3.5950
1.7487
2.6714
3.6000
2.1937
2.7894
3.6050
2.9330
2.9330
3.6100
4.4026
3.1119
3.6150
8.7398
3.3408
3.6200
361.6017
3.6439
3.5600
0.6850
2.6825
3.5650
0.7534
2.7703
3.5700
0.8361
2.8718
3.5750
0 93 BO
2.9903
3.5800
1.0666
3.1306
3.5850
1 .2 3 42
3.2993
3.5900
1.4614
3.5060
3.5950
1.7870
3.7653
3.6000
2.2927
4 0 99 9
3.6050
3.1849
4.5485
3.6100
5.1813
5.1813
3.6150
1 3 6 5 5 9
6.1409
3.6200
-22.0450 .
7.7691
3.5600
0.6626
3.4116
3.5650
0.7315
3.5955
3.5700
0.8153
3.8176
3.5750
0.9196
4.0912
3.5800
1.0529
4.4364
3.5850
1.2290
4.8857
3.5900
1.4728
5.4946
3.5950
1.8324
6.3666
3.6000
2.4161
7.7190
3.6050
3.5281
10.1003
3.6100
6.4786
15.4049
3.6150
37.5772
37.5772
3.6200
-10.0193
-59.7642
3.5600
0.6386
4.6810
3.5650
0.7078
5.1160
3.5700
0.7927
5.6861
3.5750
0.8994
6.4663
3.5800
1.0375
7.5986
3.5850
1.2232
9.3911
3.5900
1.4861
1 2 6 5 e 8
3.5950
1 .8 8 7 3
20.4968
3.6000
2.5744
64.7951
3.6050
4.0231
-46.3215
3.6100
9.0716
-15.8939
3.6150
-37.6188
-9.1446
3.6200
-6.1763
-6 1763
APPENDIX B
INTERPLANAR ANGLES
If the interplanar angles for the 931 lines are
calculated and summed, the sum will not total 180
degrees. For example, for the interplanar angles a (see
Figure 4.8) (angle between 193 and 391), b (angle between
391 and 931), c (angle between 931 and 913), and d (angle
between 913 and 193), the calculated interplanar angles
are a = 27.113 degrees, b = 54.38 degrees, c = 27.113
degrees, and d = 72.74 degrees. The sum of these angles
is 181.35 degrees. Figure 4.8 clearly shows that this
value should be 180 degrees. The discrepancy of 1.35
degrees arises because the calculated values of the
interplanar angles are not the interplanar angles in the
114 plane, the plane in which the diffracted information
appears. The calculated angles are calculated in a plane
perpendicular to the zone axis of the two intersecting
planes. This zone axis, for high order Laue zone lines,
is not perpendicular to the 114 plane. As an example,
consider the angle formed by the intersection of the 111
plane and the 111 plane. The calculated angle between
these two planes is 70.53 degrees. The angle of
intersection projected onto the 001 plane is clearly 90
degrees. A vector common to both the 001 plane and either
111 plane is the cross product of these two vectors. For
199
200
the 001 plane and the 111, the common vector is 110. For
the 001 and the 111, the vector is 110. The angle between
these two <(110]> vectors is 90 degrees, and hence the angle
of intersection of the two ^lll} planes projected onto the
[001] plane. For the 931 planes in the first order zone
of a B = [114] CBED pattern, the interplanar angles in the
[114] plane are a = 26.526, b = 54.11, 3 = 26.526, and d =
72.84. These angles are very close to those calculated
from the standard formula, as above. The sum of the
latter angles is 180.000 degrees, as it must be.
BIOGRAPHICAL SKETCH
Michael Miller Kersker was born on December 30, 1948,
to Peter B. and Marjorie W. Kersker. His birthplace, St.
Petersburg, Florida, was also his home during his
pre-collegiate experiences. He is a graduate of Northeast
High School, St. Petersburg, Florida, and holds a Bachelor
of Arts degree in chemistry from the University of South
Florida, Tampa, Florida.
After graduation, he attended Air Force Officers
Training School at Lackland Air Force Base, San Antonio,
Texas, and subsequently graduated from the Air Force Jet
Pilot Training Program at Webb Air Force Base, Big Spring,
Texas. After graduation, he accumulated thousands of
flying hours while serving in Germany, Thailand, and
finally with the 89th Military Airlift Wing at Andrews Air
Force Base, Maryland. He holds a civilian airline
transport pilot rating, the Ph.D. of flying.
In 1976, after the expiration of his military
obligation, he returned to Florida and was admitted for
graduate study at the University of Florida under
Professor John J. Hren. From 1981 to 1983 he was a senior
scientist at the Alcoa Technical Center, Alcoa Center,
Pennsylvania. From 1983 to the end of 1985, he was
201
202
employed by JEOL USA, Inc., Peabody, Massachusetts, as
product manager for transmission electron microscopes. He
is presently the General Manager and co-founder of a
venture funded company, Electro-Scan Corporation. The
company is engaged in the development, manufacturing, and
sales of a state-of-the-art multi-environmental scanning
electron microscope.
He is a member of EMSA, Tau Beta Pi, Alpha Sigma Mu,
AIME, and MAS. His interests outside of his profession
include reading, music, and racquetball. At the time of
this writing he is the father of four outstanding boys and
the husband of the finest woman south of Fairbanks,
Alaska.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
, Ms)i L
Johh J. Hren, Chairman
Ppfessor of Materials
Science and Engineering
I certify that 1 have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
R. T. DeHoFI
Professor of'Materials
Science and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
, /' L
G.J. Abbaschian
Professor of Materials
Science and Engineering
I certify that 1 have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
-i
E.D. Ver ink, Jr.
Department Chairman and
Distinguished Service
Professor of Materials
Science and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
R. Pepinsk}
Professor of PhyVics
This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
August, 1986 lldLyt Cl-jS
Dean, College of Engineering
Dean, Graduate School
Internet Distribution Consent Agreement
In reference to the following dissertation:
AUTHOR: Kersker, Michael
TITLE: Precipitation in nickel-aluminum-molybdenum superalloys / (record
number: 900946)
PUBLICATION DATE: 1986
fiVr'tA
I, ^ f f ^ c v s*£~'r ^ 6v- ; as copyright holder for the aforementioned
dissertation, hereby grant specific and limited archive and distribution rights to the Board of Trustees of
the University of Florida and its agents. I authorize the University of Florida to digitize and distribute
the dissertation described above for nonprofit, educational purposes via the Internet or successive
technologies.
This is a non-exclusive grant of permissions for specific off-line and on-line uses for an indefinite term.
Off-line uses shall be limited to those specifically allowed by "Fair Use" as prescribed by the terms of
United States copyright legislation (cf, Title 17, U.S. Code) as well as to the maintenance and
preservation of a digital archive copy. Digitization allows the University of Florida to generate mage-
and text-based versions as appropriate and to provide and enhance access using search software.
This grant of permissions prohibits use of the digitized versions for commercial use or profit.
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