Title Page
 Table of Contents
 Experimental procedure
 Special methods
 Discussion and conclusions
 Holz pattern calculation
 Interplanar angles
 Biographical sketch

Title: Precipitation in nickel-aluminum-molybdenum superalloys
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00085802/00001
 Material Information
Title: Precipitation in nickel-aluminum-molybdenum superalloys
Physical Description: viii, 202 leaves : ill. ; 28 cm.
Language: English
Creator: Kersker, Michael Miller, 1948-
Publication Date: 1986
Subject: Heat resistant alloys   ( lcsh )
Electron precipitation   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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.
 Record Information
Bibliographic ID: UF00085802
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000900946
oclc - 15539055
notis - AEK9766

Table of Contents
    Title Page
        Page i
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page v
        Page vi
        Page vii
        Page viii
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    Experimental procedure
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
    Special methods
        Page 61
        Page 62
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    Discussion and conclusions
        Page 170
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    Holz pattern calculation
        Page 191
        Page 192
        Page 193
        Page 194
        Page 195
        Page 196
        Page 197
        Page 198
    Interplanar angles
        Page 199
        Page 200
    Biographical sketch
        Page 201
        Page 202
        Page 203
        Page 204
Full Text








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.


ACKNOWLEDGEMENTS.................................... ii

ABSTRACT ....................................... .. vii


1 INTRODUCTION..................... ........1

2 BACKGROUND ............ ....... .. ... ... ... 7

2.1 Phase Diagrams ......................7

2.1.1 Binary Phase Diagrams......... 7 Ni-Mo................7 Ni-Al............ 9 Ni-W................. 9 Ni-Ta...............12

2.1.2 Ternary

Diagrams ............. 12

2.2 Binary Phases...................... 16

2.2.1 Ni-Mo...

2.2.2 Ni-W....

................... 16
Ni4Mo............... 18
Ni2Mo...... ........ 20
Ni-Mo. ..............23

..................... 23
Ni4W ...............24
Ni3W .................24
Ni2W ................24
NiW ................. 24

2.2.3 Domain Variants/Antiphase
Boundaries..................25 Ni4x(Dla)...........25 Ni3x(D022). .....27 Ni2x(Pt2Mo).........29

2.2.4 SRO in Ni-x Binaries.........29

2.2.5 Ordering Reactions and Kinetics....31 Binary Alloys.............31 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 DO22: Ni3Mo...............47 Dla: Ni4Mo.................47 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 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours.................... 111 Lattice imaging of D022
and Dla Phases ............ 127 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours ....... ........... .132 Solution Heat Treated,
Quenched and Aged at
870 C for up to 100
Hours ....... ......... ... 134 Aging Summary RSR 197...140

5.1.5 RSR 209 As Solution Heat
Treated and Quenched............... 142
5.1.6 RSR 209 Aging.....................142 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours...................... 142 Solution Heat Treated,
Quenched and Aged at
810 C for up to 100
Hours .............. ......145 Solution Heat Treated,
Quenched and Aged at
760 C for up to 100
Hours........... .. ...... 149 Aging Summary RSR 209...152
5.1.7 Special Aging/Special Alloys.......153 Alloy #17 Solution
Heat Treated, Quenched
and Aged at 760 C for
100 Hours................153 Alloy #17 Solution
Heat Treated, Quenched
and Aged at 870 C for
100 Hours................. 153 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 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


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



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.



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


Though there are similarities in the precipitation of

these NixMo metastable phases among the binary, ternary,

and quaternary alloys described earlier, there are


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.


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 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.


Mo 0.1 02 0.3 04 0.5 0 6 0.7 0.8 0.9 N.

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. 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. 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



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).


Ni 20 4050 60 70 75 80 85 90 95 W

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-
L (Ni)

(Ni4W) (NiW) (NiW,)
+ + +
300. (NiW) (NmW,) (W)


Ni. 10 20 30 40 50 60 70 80 90 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. 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 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

60 70 75 80 85

ouuU. N 2998

d d 2

2500. z z z ,

1 1 1 -
,' 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

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.,


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. Ni-Al-Ta

The Ni-rich side of this diagram has recently been

reviewed by Nash and West (1979). They confirm the



N( 4At If)
f/i -/ / A/

Nt()I / 80 I O M ,' tf Mo ZO Mo
c MONV4 Ay/i.3 N, ,am %"O


Figure 2.5 Ternary Ni-Al-Mo isotherms;
a.) 1038 C (after Miracle et al., 1984)
and b.) 600 C (after Pryakhina et al.,

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. 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


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. 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

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 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. Ni2Mo

The Ni2Mo phase was first discovered by Saburi et al.

(1969). It is a Pt2Mo type superlattice, as shown in



S Ni

Q c8~-

~~0 -~



Figure 2.8


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




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 (-- -).



-- k



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). 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


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. 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. Ni3W

This phase is crystallographically identical to Ni3Mo

D022 (see Section Ni2W

This phase is crystallographically identical to Ni2Mo

Pt2Mo (see Section 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. 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


Parameter (A)







BCT/10 atoms
BCT/8 atoms
OR/8 atoms
BCO/6 atoms

BCT/10 atoms
BCT/8 atoms
BCO/6 atoms

Tetr./ --

Cubic/4 atoms






Ni3Ti 5.112




















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 Combinations of all three interfaces are

possible. Ni3x (D022)

The D022 phase can form twelve variants. The c axis

of the crystal may lie along any one of the FCC cube


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). 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


2.2.5 Ordering Reactions and Kinetics 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


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. 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 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


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


Figure 2.12


O Ni

The Ni3Al unit cell.


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


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

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


B+ if 1 = 2(n+l), n even OR
A if 1 = 2n



B if
A if

B if
A if

1 = 2(n+l)
1 = 2n

1 = 2(n+l)
1 = 2n




















* 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



000 020

000 020

0 0:


.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.

%(2 /4(042)

*1/4(042) *

000 042

004 024
0I A&

200 220


E Superlattice

Figure 2.14 The reciprocal lattice for Dla.

^^^-^ 0


w Ii



o0 Fundamental


Figure 2.15 The reciprocal lattice for Pt2Mo.



ooo 200 W Fundamental

Figure 2.16 The reciprocal lattice for the L12

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. 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. 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.




Alll i

& Superlattice


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

.*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 .


*" *
000 200
000 200

020 420

0 E
000 [





(3 0 a 0

* *0

27 0

zZU 402
0 0 A

So 0, 0


,,m m B
-p i Et


* 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. 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.


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


m a

Figure 2.20

* O0\ 0 0o 0O o0 s
* oo o* oOoB* O
o'o* CO- o o oO* o


The Pt2Mo phase;
a.) Pt2Mo variants along FCC axes.
A and B can exist along each axis.
b.) B = [100] SADP with variants.


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


3.2 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


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.



Solution heat
treat 1315 C, 2 hr.

Air Quench


Air Quench

Solution Heat
treat 1315 C, 4 hr.

Cold Water
........ Quench


760 C, 100 hr.
870 C, 1 hr.

Cold Water

Figure 3.1 Processing Variables


Table 3.1 -- Alloy Compositions

RSR 197
at% wt%






RSR 209
at% wt%










RSR 185
at% wt%

73.8 72.6

15.0 6.7

9.0 14.4

2.0 6.0

.2 -





at% wt%





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

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,


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


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


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

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

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


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


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








Indices for B=[114]

751 571


860 680

913 193 931 391

1002 0102


















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



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

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,



E .58
ca .57


r .55


r .53





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


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

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


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


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


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

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