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dissertation entitled

HREM EXAMINATION 0F CORE STRUCTURES
OF DISLOCATIONS IN BZ INTERMETALLIC

COMPOUND Co-Al

presented by
Yu Zhang

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HREM EXAMINATION OF CORE STRUCTURES
OF DISLOCATION S IN B2 INTERMETALLIC
COMPOUND Co-Al

By

Yu Zhang

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

Doctor of Philosophy

Department of Materials Science and Mechanics

1995

ABSTRACT

HREM EXAMINATION OF CORE STRUCTURES
OF DISLOCATIONS IN B2 INTERMETALLIC

COMPOUND Co-Al
By

Yu Zhang

Mechanical properties of single crystal BZ Co-Al intermetallic compounds were
measured at both room and elevated temperatures. Off-stoichiometric Co-48Al and Co-
52Al are stronger at high temperatures and more brittle at room temperatures than stoichi-
ometric Co-50Al. Dislocations in deformed Co-Al were investigated via diffraction TEM
analysis (g-b=0 criteria). Slip system activation was found to be temperature and orienta-
tion dependent. <010> type edge dislocations were found to always dominate the defor-
mation under the various conditions. <111> and <110> dislocations were observed
following defamation at 1300 K and are regarded as the reaction products of <010> dis-
locations. Stoichiometry deviations were found to have no effect on the selection of slip
systems. Core structures of the predominant <010> dislocations generated by 1300 K
deformation were examined via high resolution transmission electron microscopy
(HREM). No significant core dissociation is observed in Co-SOAl, while significant disso-
ciation is seen in Co—48Al and Co-52Al. Simulations of HREM images, based on theoret-
ical structures were compared with the experimental observations. The simulations match
well only with the experimental results in Co-50Al. The dislocation core structures in Co-
Al were compared with those observed in Ni-Al and Fe-Al. The <010> dislocations in

off-stoichiometric Co-Al have significantly more complicated core structures than in off-

off-stoichiometn'c Co-Al have significantly more complicated core structures than in off-
stoichiometric Ni-Al or Fe-Al. The core structures of <010> edge dislocations in B2

alloys are responsible for the high strength and low ductility and are highly sensitive to

deviations from Stoichiometry.

To my wife and daughter

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to Dr. M.A. Crimp, my major advi-
sor, for his guidence and support throughout my doctoral studies and for his many helpful
suggestions and paintaking reviews during the preparation of the dissertation.

I would like to thank the Office of Naval Research and Dr. G. Yoder (scientific
officer). This research would not have been fulfilled without the ONR’s support and fund-
in g (contract number: N00014-90-J-l910). A

I would like to acknowledge the committee members for their precious time on
reviewing my disseratation and attending the comprehensive and oral examinations.

A special thank you is to be extended to Mr. P. Madill, vice president and general
manager of Stevens International Corp/Berna] Division for his understanding and sup-
port.

I also wish to thank the following groups of people: Dr. D. Parks of Virginia Poly-
technic Institute and State University for providing EAM calculation results; Naval Air
Research Development Center and Dr. D. Pope of the University of Pennsylvania for pro-
viding single crystal Co-Al; Electron Microanalysis Laboratory and Dr. J. Mansfield of the
University of Michigan for the use of the JOEL-4000EX; Mr. Z. Cai, the Ph.D candidate
of Dr. D. Grumman’s Thin Film Laboratory for providing assistance in mechanical test-

ing; Mr. B. Holmes of the Case Center for his thoughtful assistance in computer program-

ming and EMS software package; Mr. S.C. Tonn and Mr. D. Scharrott, my research
partners and friends, for their invaluable assistance; Mr. A. Gibson and his wife Mrs. B.
Gibson for their proof reading my first manuscript.

In addition, I owe gratitude to my Chinese friends and colleagues at the depart-
ment, including Mr. Y. Wu, Mr. Z. Yeh, Mr. L. Wang and Dr. P. Sheng, for their assis—
tance and friendship. I

Last but not least, a special thank you is to be extended to my wife, Yuqing
and daughter, Chloe for their patience, understanding and continual encoragement

during the many months of this research.

vi

TABLE OF CONTENTS

List of Tables

List of Figures

1. Introduction/Background

1.1 Barriers to industrial application of 82 intermetallic compounds
1.2 Mechanical properties of B2 structure CoAl, MA] and FeAl
1.3 Dislocations and slip modes

1.4 Dislocation cores

1.5 General characteristics of CoAl

1.6 Motivation of this research

1.7 Expected imact of the project

2. Experimental Method

2.] Materials

2.2 Specimen preparation

2.3 Mechanical testing

2.4 Slip trace analysis

2.5 Transmission electron microscopy

2.6 Dislocation analysis

2.7 High resolution electron microscopy

vii

xi

12

27

28

3O

52

52

52

53

53

54

55

56

2.8 HREM image simulation

3.0 Results and Discussion

3.1 Mechanical behavior of Co-Al alloys

3.1.1 Deformation of Co-Al under high temperature compression
3.1.2 Mechanical behavior of Co-Al and Ni-Al at room temperature
3.1.3 Slip trace analysis

3.2 Dislocation analysis

3.2.1 As-grown single crystal Co—50Al

3.2.2 [123] oriented Co-50Al deformed at high temperatures
3.2.3 [011] Co-Al deformed at elevated temperatures

3.2.3.1 [011] Co-Al deformed at 873 K

3.2.3.2 [011] Co-Al alloys deformed at 1300 K

3.2.4 [001] Co-Al deformed at high temperatures

3.3 Core structures of <010> edge dislocations

3.3.1 Co-SUA

3.3.2 Co-48Al

3.3.4 Co-52Al

3.4 HREM Image Simulation Of Core Strutures

3.4.1 Simulation of core structures for Co-Al system

3.4.1.] <010>{001} edge dislocation

3.4.1.2 <010>{011} edge dislocation

3.4.2 Simulation of core structures in the Ni—Al system

3.4.2.] <010>{001} edge dislocations

viii

59

75

75

75

77

78

79

79

80

86

86

88

92

96

96

98

100

104

104

104

107

108

108

3.4.2.2 Simulalted core structures of <111> screw dislocations
3.4.3 Simulation of core structures in Fe-Al system

3.4.3.1 <010>{001} edge dislocations

3.4.3.2 <010>{ 101} edge dislocations

4. Further Discussions

4.1 Mechanical properties

4.1.1 Mechanical properties of Co-Al at elevated temperatures
4.1.2 Mechanical properties of other B2 alloys

4.2 Dislocations in Co-Al, Ni-Al and Fe-Al

4.2.1 Dislocation density in Co-48Al, Co-SOA] and Co-52A
4.2.2 Dislocation density in Ni-Al and Fe-Al

4.3 Core structures

4.3.1 Core structures in stoichiometn’c B2 alloys

4.3.2. Core structures in off—stoichiometric B2 alloys

4.3.3. Simulations of core structures

5. Conclusions

5.1 Mechanical properties

5.2 Dislocations and slip systems

5.3 Core structures of <010> edge dislocations

5.4 Computer simulations

5.5 Mechanical behavior and core structures

References

Appendices

ix

110

113

114

114

207

207

207

209

210

210

211

212

213

214

216

223

223

223

224

224

224

226

233

Appendix I The parameters used in computer image simulation 231
Appendix 2 Conversion program 233

Appendix 3 Autorun in C-shell 235

LIST OF TABLES

1. Physical parameters of CON and MA]
2. CRSS of some B2 aluminides
3. Slip system in CoAl, MA] and FeAl

4. Summary of the simulation results for the various slip system
in the order of decreasing mobility [68]

5. Anisotropic parameters of Co-Al, Ni—Al and FeAl

6. Edge dislocations and the corresponding
line direction in B2 structure

7. Description of image features in figure 38

8. Description of image features in figure 39

9. Calculation of Dislocation Energy and Mobilities for CoAl
10. Debye-Waller factors

11. CRSS of [011] Co-Al and [001] Co-50A1

12. Parameters used for simulation of dislocation “b”

13. Parameters used for simulation of dislocation “3”

xi

48

49

50

51

73

74

153

154

155

206

222

233

234

LIST OF FIGURES

Figure

1 B2 structure is the ordered bcc lattice. Two kinds of atoms (A and B)
occupy the corner positions or body center postion respectively.

2 Hardness-composition isotherms in B2 interrnetallic compounds.

This figure shows the high-temperature hardness and sensitivity to
composition deviation of these compounds.

3 Ductile-to-brittle transition temperatue for binary Co-Al alloy [21]
The transition temperature is the lowest at stoichiometric Co—50Al.

Deviation from stoichiometry results in increase of the transition
temperatures.

4 Temperature-dependent of the yield stress of stoichiometric NiAl
single crystal] of soft orientation [23]. Brittle-to-ductile transition
temperature is around 150 K.

5. Creep resistance of CON and MA] at temperature 1300 K [25].
CoAl has significantly slower strain rates than NiAl.

. Creep stress of polycrystalline Co-Al and Ni-Al [27]. CoAl has

higher creep strength than NiAl. On the other hand, the creep strength
is more sensitive to composition deviation in CoAl than in NiAl.

. Diffusivities of Co60 in CON and in NiAl [29]. Around 1000 K -1400 K,
CoAl has the comparable diffusion coefficients with NiAl

. Core strucuture of 1/2<111> screw dislocation in bcc structure

. Diagram of computer modelling. Introduction of displacement field and

application of boundary conditions and relaxation method are key steps in
core modelling.

10. Diagram of relaxation calculation. When the displaced lattice reaches its
equalibrium condition, the force upon an atom should be balanced.

xii

32

33

34

35

36

37

38

39

40

lLDNO CORD gurations of dissociated screw dislocation 1/2[111]. The arrow
directions indicate that the l/2[l 11] screw dislocation spreads on three
intersected planes. The Burgers vectors of fractional dislocations are still

12. Changes in core structure under influence of strss. The non-planar
spreading of 1/2<111> dislocation on (110) and (011) are contracted
under the applied stress. The process is shown from (a) to (c).

13. Two configurations of simulated core structure of <100> edge
dislocation in BZ structure

14. Phase diagram for binary B2system. (a) Co-Al diagram, (b) Ni-Al
diagram, (c) Fe-Al diagram

15. Schematic of an edge dislocation width.

16. The size of compression specimen is 3x3x9 and a notch
was made at upper right comer

l7. Slip trace analysis. The angles or and [3 were measured on the surface
and the normal of slip plane was determined using Wuff net.

18. Coordinate system for [011] oriented single crystal Co-Al.
The angles between slip traces depend on the coordinate system.
Slip traces in [100][011][011] system can be easily identified.
Slip traces in the other system can be determined using eqs. 18 and 19.

19. HRTEM foil section and end-on dislocations. The TEM foils were
sectioned in the direction parallel to slip plane while the HREM foils were
sectioned in the direction perpendicular to the dislocation line.

20. Projected lattice for dislocation lines correspond to various zones.
For some zones, the projected atom spacings of the lattices are

below the resolution the high resolution transmission electron microscope.
(a) <100>, (b) <110>, (c) <11 l>, (d) <112>.

21. (a) Regular lattice: schematic core structure of [010] dislocation.
(b) Superlattice: schematic core structure of [010] dislocation.

22. Schematic representation of the multislice principal. The incident
wavefield interacts with crystal potentials, resulting in
a modified output wavefield.

23. Simulation path for multislice calculations. Phase objective function,
wave function and image calculation are key steps in HREM simulation.

xiii

41

43

47

62

63

65

66

67

68

69

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

Representation of a Supercell used for image simulations.

The supercell was made with a and b borders much longer than its thickness.

Slice program map. The number of slice should be large
enough in order to pass the unitary test.

Iteration diagram illustrating interation procedure. The exit wavefunction
of the previous subslice was regarded as the incident wavefunction of
the current subslice.

Mechanical behavior of [011] oriented Co-Al deformed at 1300 K.
Co-52Al has the highest resistance to and Co-50Al has the
lowest resistance to deformation at this temperature.

Effect of orientation on mechanical behavior of Co-SOA] at T=1300 K.
[001] oriented Co—SOAl displayed kinging during deformation.

Mechanical behavior of Co-Al and N i50Al in compression at room
temperature. Co-Al appear to be more brittle than N i-SOAl.

Slip traces on two perpendicular surfaces of Co-50Al. The specimen was
oriented in the [011] direction and deformed at 873 K.

Slip traces on two perpendicular surfaces of Co-48Al. The specimen
was oriented in the [011] direction and deformed at 873 K.

Slip traces on two perpendicular surfaces of Co-52Al. The specimen
was oriented in the [011] direction and deformed at 873 K.

Slip traces on two perpendicular surfaces of Co-50Al. The specimen
was oriented in the [011] direction and deformed at 1300 K.

Analysis of dislocations in as—grown single crystal Co-50A1. .
There exist two types of dislocations, labeled a and b.

(a) (ll—1) zone, (b) (TOT) zone, (C) (III) zone,

((1) (001) zone, (e) (01]) zone, (f) (001) zone.

Dislocation line direction determination for dislocations by tracein analysis
in fig. 34. Both the beam direction (bi) and the projected line direction (Pi)

are lying on the same great circle. The intersection of two or three great
circles give the true line direction of the dislocation.

Dislocation analysis in [123] oriented Co-50Al that was deformed at
1300 K. Three types of dislocations labeled a, b and c were characterized.

xiv

70

71

117

118

119

120

122

123

127

128

37. Dislocation reaction in the [123] oriented Co-50Al deformed at 1300 K. 131
Two <100> dislocations form one <110> dislocation.

38. Computer simulation of dislocation labeled “b” in fig. 36 . 133
The micrographes were taken at the reflection conditionsg=(0T1).
g=( 1T0) and g=(l21). The simulations were performed by varrying the
conditions of g-vectors and the Burgers vectors, while the other
parameters were kept constant

39. Computer simulation of dislocation labeled “c” in fig. 37. 134
The micrographes were taken at the reflection condition g=(1TO),
g=(OIl) and g=(l21). The simulations wer performed on the conditions
of g-vectors and Burgers vectors, while the other parameters are kept constant.

40. Dislocations observed in [123] Co-SOAl deformed at 1000 K. 135
(a) Arrangement of dislocations in single crystal compression sample,
and (b) schematic illustration of dislocation distribution in a (001) foil.

41. Dislocation analysis for [011] oriented Co-50Al deformed at 873 K. 136
Inclined dislocations, end-on dislocations and dislocation loops
were all observed.

42. Three dimensional schematic illustration of the distribution of dislocations 138
observed in [011] oriented Co-50Al deformed at 873 K.

43. Dislocation analysis for [011] Co-52Al deformed at 873 K. Inclined 139
dislocations, end-on dislocations and dislocation loops were observed.

44. Analysis of dislocations in [011] Co-SOAl deformed at 1300 K. 141
Dislocations labeled “a”, “b” and “c” were identified. Dislocation
reactions were also observed in the foil.

45. Dislocation analysis for [011] Co-48Al deformed at 1300 K. 143
Dislocation labeled “a” and “b” were identified.

46. Dislocation analysis for [011] Co—52Al deformed at 1300 K. 145
Dislocations labeled “a”and “b” were characterized.

47. Dislocation analysis for [001] oriented Co-SOAl deformed 148
at 1300 K. <100> dislocations were observed.

48. Analysis of dislocations in [001] oriented Co-50Al deformed at 1300 K. 150
<110> dislocations were found.

XV

49. Core structure of an [010] edge dislocation in Co-50Al deformed
at 1300 K:
(a) HREM micrograph and Burgers circuit,
(b) perspective view (front view) along [001] direction,
(c) perspective view (side view) along [010] direction,

((1) perspective view (45° view) along [011] direction,
(e) perspective view (450 view) along [01 1] direction.

50. Core structure of an [010] edge dislocation in Co-SOAl deformed at 1300 K:

(a) HREM micrograph and Burgers circuit,
(b) perspective view (front view) along [001] direction,

(c) perspective view (45° view) along [0T1] direction,
((1) perspective view (45° view) along [011] direction.

51. Core structure of an [010] edge dislocation in Co-SOAl deformed at 1300 K:

(a) HREM micrograph and Burgers circuit,
(b) perspective view along [011] direction,
(c) perspective view along [0T1] direction,
((1) perspective view along [011] direction.

52. Core structure of an [010] edge dislocation in Co-48A1 deformed at 1300 K:

(a) HREM micrograph and Burgers circuit,

(b) perspective view (front) along [001] direction,
(c) perspective view (side) along [010] direction,
(d) perspective view along [011] direction,

(e) perspective view along [011]direction,

(1“) Burgers circuit on partial dislocations.

53. Core structure of an [010] edge dislocation in Co-52Al deformed at 1300 K.

(a) HREM micrograph and Burgers circuit
(b) Perspective view along [010] direction
(c) Perspective view along [011] direction
((1) Perspective view along [0T1] direction.

54. Core structure of an [010] edge dislocation in Co-52Al deformed at 1300 K:

(a) HREM micrograph and Burgers circuit,

(b) perspective view along [011] direction,

(c) perspective view along [0T1]direction,

((1) Schematic drawing of core structure of [010] edge dislocation
in Co-52Al.

55. Another example of the core structure of an [010] edge dislocation
in [011] Co—52Al deformed at 1300 K:
(a) HREM micrograph and Burgers circuit,
(b) perspective view (front) along [001] direction,

xvi

156

159

162

165

169

172

175

(c) perspective view (side) along [010] direction,
((1) perspective view along [0T1] dorection,
(e) perspective view along [011] direction.

56. Another example of the core structure of an [010] edge dislocation
in Co-52Al deformed at 1300 K:
(a) HREM micrograph and Burgers circuit,
(b) view along [010] direction.

57. Simulated HREM image of the core structure of a [010] edge dislocation
in Co-50Al at the conditions of decocus ~70 nm and flil thickness 2.3 nm
(a) White spots represents atom columns. The core center consists of Al
column triangle,
(b) Atom positions superimposed onto the HREM image simulation.
Large dots represent Co and small dots represent Al.

58. A through focal series for core structures simulations of an <100>
edge dislocation. Defocus values are marked on the individual images.
The foil thickness is 2.32 nm.

59. HREM simulation of [010] dislocation. Thickness increases form
1.1 nm to 9.9 nm. The defocus value is -80 nm.

60. HREM simulations of [010] dislocation. Thickness condition
is same as figure 59. Defocus value is -60 nm.

61. Effect of temperature on HREM simulations is shown at the conditions of
df=-70 nm and thickness of 2.3 nm: (a) 20 K, (b) 93 K, and (c) 293 K.

62. a) Unit cell configuration used for <100>{001 } dislocation image
simulations. b) Alternate unit cell used for <100>{011 } dislocation image.

63. Unit cell sliced used in [100](011) core simulation. The different atom
shades indicate which slice the atoms are included in,

64. A [100](011) core in Co-50Al simulated at the conditions
df=-70 nm and thickness of 4 nm.

65. Core structure simulation of [010](001) dislocation in N i-50Al
simulated at conditions of defocus value -70 nm and thickness 2.3 nm
(a) Ni—50Al core, (b) same simulation with superimposed atom positions.

66. Effect of off-stoichiometric composition change on core structure
in Ni-SOAl. (a) Supercell of [010](001) edge dislocation core in

Ni-rich N i-Al. Large spheres represent Ni while small spheres represent A].

(b) Simulated HREM image of core structure of [010](001)

xvii

178

180

181

182

183

184

185

186

187

188

189

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

dislocation in N i—rich N i-Al.

Effect of stoichiometry deviation (Al rich) on core structure.

(a) Supercell of [010](001) edge dislocation core in Al-rich Ni-Al. Large
spheres represent Ni while small spheres representAl. Extra A1 atom
is indicated by the arrow.

(b) Simulated HREM image of core structure of [010](001) dislocation
in Al-rich Ni-Al.

Anti-site defect in core structure (a Ni atom exchanges position

with a Al atom) (a) Supercell of [010](001) edge dislocation core in
N i-Al. Large spheres are Ni while small spheres are Al.

The anti-sites are pointed by arrows. (b) Simulated HREM image of
core structure of [010](001) dislocation in Ni-Al.

Effect of right-in-core vacancies in core structure in Ni-Al.
(a) Two vacanies exist in dislocation core (pointed by arrows)
(b) HREM image simulated at df=-70 nm and thickness=2.2 nm.

Atom arrangement in N i48Al model structure. The supercell
contains five 1ayers(a) to (c) with Ni substitution. (f) HREM image

simulated at df=-70 nm and thickness=2.2 nm.

Simulated HREM images of core structures with random Ni
substitution in Ni-48Al. (a) seed 1 (b) seed 2.

Simulated HREM images of core structures using
random Al substitution in Ni-52Al. (a) seed 1, (b) seed 2.

Image simulation of core structure of [010](001) edge dislocation
in Ni-SOAl with random anti-sites.

HREM micrograph of a <111> screw dislocation in Ni-SOAl.
Schematic drawing of a twisted screw dislocation in single crystal.
Figure 76 Atom positions in data file used for core structure
simulations of <11 1> screw dislocation. (a) without Eshelby twist
(b) with Eshelby twist.

Core structures of <111> screw dislocation in Ni-50Al simulating
the Eshelby Twist effect was consdered. (a) atom position profile,

(b) simulation with twist.

Through focal series of HREM simulations for <111> screw dislocation
Ni-50Al. The foil thickness is 2.32 nm.

xviii

190

191

192

193

195

196

197

198

199

200

201

202

79 Thickness series of HREM simulations for <111> screw dislocation in 203
Ni-50Al. The defous value is -80 nm.

80 Core structure of an [010](001) edge dislocation in Fe-SOAI. Two extra half 204
planes (ED and PE in (b)) terminate at position D and B in (a).
In [011] and [011], the single extra half planes are observed.

81 Burgers circuit established on single layer projected images. 205
The Burgers vector of the superpartial dislocation are b1=1/2[111]
and b2=1/2[111]. The large dots represent Fe and the small dots
represent Al.

82. Comparison of core structures among the stoichiometric Co-50A1, 217
Ni-SOAl and Fe-50Al (from left to right).

83 Comparison of core structures among the oof—stoichiometric Co—48Al, 218
Ni-48A1 and Fe-40Al (from left to right).

84 Comparison of the ’ysurfaces between <100>[011 }, <100>{00} 219
and <111>{112} slip systems.

85 Comparison of the energy curves along the prefered directions 221
in various slip systems.

xix

1. Introduction/Background

1.1 Barriers to industrial application of B2 intermetallic compounds

Conventional superalloys are becoming less capable of meeting the growing
demands for lighter weight, higher temperature, high performance engine materials.
Recently, considerable research has been focused on suitable alternatives, such as interme-
tallic compounds (IC), metal matrix composites (MMC), intermetallic matrix composites
(IMC) and ceramic matrix composites (CMC). Among these, several intermetallic com-
pounds such as titanium aluminides, nickel aluminides and iron aluminides, promise to be
near-term replacement materials with distinguished properties (see excellent reviews [1-
4]). Compared to nickel based superalloys, having the B2 structure (fig. 1) CoAl, N iAl
and FeAl offer the advantages of lower density, higher strength at elevated temperature,
larger coefficients of thermal conductivity, higher Young’s modulus, higher diffusional
stability and better resistance to oxidation and corrosion. This makes B2 alumnides
potentially competitive and attractive materials for high temperature service necessary to
increase engine thrust-to-weight ratios.

Unfortunately, like most high temperature and high strength intermetallic com-
pounds, CoAl and MA] are extremely brittle at ambient temperature. This lack of ductil-
ity and low toughness limit the fabrication and application of these aluminides. Therefore,
most studies of BZ interrnetallics have been focused on understanding and improving
their poor ductility [1].

The low ductility of B2 intermetallic compounds may be attributed to intrinsic
and/or extrinsic brittleness. Intrinsic brittleness may be related to lack of sufficient slip

systems, low density of mobile dislocations, presence of high energy boundaries, impurity

2
scale, stoichiometry and texture. Poor grain boundary cohesion may result from high
ordering energies, large differencs in electronegativity, valence electron configurations
between transition elements (Co, Ni and Fe) and aluminium [1]. This lack of grain bound-
ary strength can sometimes be reduced by adding small amounts of boron [5], refining the
grain size [6], or eliminated by using single crystals. Microstructural control and microal-
loying with iron, gallium and molybdenum significantly improves the ductilities of most
B2 alloys [7,8,9]. Reducing the interstitial content or scavenging the interstitials through
certain alloying additions may help to avoid dislocation-point defect interaction and thus
increases the plasticin [1].

Extrinsic brittleness is mainly associated with environmental effects and pressur-
ization. The ductility of NiAl or FeAl is very poor when tested in air and increases dra-
matically in vacuum or oxygen envionments [10,11]. Hydrostatic pressure increases the
ductility in NiAl [12]. The high temperature strength of these aluminides can be raised by
adding ceramic particles, the precipitation of second phases and/or solid—solution harden-
ing by substitutional elements. However, these enhancements typically must be balanced
with decreases in ductility.

The mechanical properties of intermetallic compounds depend to a large extent on
dislocation mobility, especially at low to intermediate temperatures at which diffusion
rates are negligble. Dislocation mobility in turn is determined by the mobile dislocation
density, dislocation interaction and multiplication, and lattice friction. Therefore, under-
standing dislocation substructures and their corresponding mechanical behavior may be

one of keys to overcoming the barriers to industrial applications of B2 intermetallic com-

pounds.

3

1.2 Mechanical properties of B2 structure CoAl, N iAl and FeAl

Even though they have the same ordered bcc structures, the strengths and ductili-
ties of the B2 aluminides differ considerably. As cobalt, nickel and iron are neighbors in
the periodic table, and the electron structures of these elements have only one electron dif-
ference in their d-shells, their aluminides have the same crystal structure, almost identical
lattice parameters and similar material densities and melting temperatures (table 1). It
might be expected that these similarities would make the mechanical properties of these

materials similar, but large differences exist in the following areas:

1.2.1. Hardness

In one of the earliest examinations of the mechanical behaviors of B2 aluminides,
Westbook [13] studied the temperature dependence of the hardnesse of polycrystalline
CoAl, NiAl and FeAl. The order of hardness at room temperature is: FeAl>CoAl>NiAl;
at 773 K, the order is: CoAl>FeAl>NiAl and at 1073 K, the order becomes:
CoAl>NiAl>FeAl. The results indicate that CoAl has the best capability to maintain its
strength at elevated temperatures. The effect of composition changes on hardness at 1073
K is shown in Figure 2. Stoichiometric CoAl and MA] have the lowest hardness for their
respective systems. Small deviations from stoichiometry in CoAl increases the hardness
more significantly than for MA], whereas in FeAl, the hardness decreases continously

with increasing iron content.

1.2.2. Critical resolved shear stress
Slip begins when the shearing stress on the slip plane in the slip direction reaches a

threshold value called the critial resolved shear stress (CRSS). Selected CRSS values

4
determined at room temperature for various B2 aluminides are given in table 2. The CRSS
for <11 l>{110} slip in Fe-49Al [14] is smaller than that [15] of Co—50Al. This suggests
that <1 ll>{ 110} slip systems are more easily activated in FeAl and consequently this
material is less brittle than CoAl. However, even though the CRSS values for
<1 ll>{ 110} in FeAl are larger than those for <100> slip in MA] [16] at room temperatue,
it does not follow that NiAl is more ductile than FeAl. This is because there are only three
independent <100>{ 110} slip systems while <111>{ 110} slip results in more than five
independent slip systems. Consistent with the hardness behavior noted by Westbrook
[13], the CRSS varies with stoichiometry in FeAl. The CRSS for <111> slip in Fe-39Al is
much lower than that in Fe—49Al tested under the same conditions [14]. Information on

the CRSS-composition relationship is not available for CoAl and NiAl.

1.2.3. Ductility

CoAl is extremely brittle at room temperature. Chisel toughness is a simple mea-
surement of room-temperature toughness [17]. A steel chisel and either a light or a heavy
harmmer are used to define a four-level toughness scale as follows: level 0, broken on
cooling after casting or broken with a light tap of a light hammer; level 1, required
repeated sharp blows for fracture with a light hammer (160 g); level 2, required a sharp
blows with a heavy hammer (729 g); and level three, not fractured even with a heavy ham-
mer. The Chisel toughness of CoAl is zero [17]. This material displays no tensile elonga-
tion and exhibits less than 1% compressive plastic strain at ambient temperature [15]. As
the temperature is raised, CoAl displays limited but increasing compressive ductility.

Like CoAl, MA] is also very brittle. Stoichiometric NiAl displays 1-2% tensile elongation

5
at 297 K, while hypo-and hyper-stoichiometric changes in composition results in a loss of
this ductility [18]. In contrast, stoichiometric'Fe-SOAI displays zero ambient temperature

ductility, while Fe-rich deviations result in ductility enhancement.

1.2.4. Yield strength

The yield strength of these materials is affected by both temperature and composi-
tion. With increasing temperature, the 0.2% proof stress (0'02) continously decreases in
NiAl. Off-stoichiometric compositions have higher 002 values than the stoichiometric
composition in MA] [19]. This is reflected in compression tests [20], where stoichiomet-

ric compostions have lower values of flow stress at the temperatures below 1273 K. In

contrast, above 1273 K, Ni-SOAl is stronger than Ni-46Al and Ni-56Al.

1.2.5. Brittle-ductile transition temperature (BDTT)

Stoichiometric polycrystalline Co-Al has the lowest compressive BDTT value
(about 527 K) of Co-Al alloys. However, this value increases to over 827 K in both the
Co-rich and Al-rich sides of stoichiometry (fig.3) [21]. Thus the BDTT is very sensitive
to stoichiometry in CoAl. In contrast, the tensile BD'I'I‘ of polycrystalline Ni-50Al is 550
K [22]. A lower value (300 K) is obtained if the Ni-SOA] specimens are compressed (fig.
4) [23]. But in Ball and Smallman’s experiments [24], the BDTT of Ni-SOAl was found
to be 827 K, whereas the BDTT of Ni-51Al was found to be 727 K and the BDTT of Ni-'
48A] was found to be 627 K. The difference between Pascoe’s [23] and Ball’s [24] BDTT
observations may result from the effect of grain size and strain rate. However, it is inter-

esting that stoichiometry deviations increase the BDTT in CoAl but decrease it in MA].

6
In single crystal NiAl, the BDTT also depends on crystal orientation. Darolia [2] found

that the BDTT is 623-670 K in the <100> orientation and around 473 K in the <11 l> ori-

entation.

1.2.6. Creep strength

Hocking et a1. [25] first observed that single crystal CoAl has a greater resistance
to creep than single crystal NiAl at 1323 K (fig.5). Creep strain rates were found to be at
least 1.5 orders of magnitude greater for NiAl than CoAl tested at the same stress. Yaney
and Nix [26] examined polycrystalline materials using the strain rate change technique.
They concluded that NiAl, exhibiting pure-metal type behavior (dislocation slip deforma-
tion), is weaker than CoAl which undergoes a transition from pure-metal to alloy-type
deformation (dislocation climb deformation). Wittenberger [27, 28] examined the com-
pressive behaviors of these two alloys at slow plastic strain rates and results were consis-
tant with the results of Hocking e1 at. and Yaney and Nix (fig. 6). Deviation in
stoichiometry greatly affects the creep strengths of both CoAl and NiAl. Contrary to
hardness and BDTT experiments, where Co—SOAl is considered a “weak” composition, the
highest creep strength is obtained at this composition. Another feature of figure 6 is that
the creep strength of CoAl is much more sensitive to stoichiometry than that of NiAl. A
1% change in stoichiometry results in a 16-37% change in the creep strength of CoAl but
only a 4.4% change in the creep strength of MA].

The reason for the differences in the mechanical behavior of CoAl, MA] and FeAl
are still unclear. It is well known that the creep behavior of materials is mainly controlled

by dislocation and/or diffusion factors. At high homologous temperatures, the activation

7
energy for deformation in many materials is approximately equal to the activation energy
for lattice self-diffusion [26]. As the self-diffusion activation energy can be regarded
approximately as a linear function of the crystal melting point Tm [24] (Q = 34 (i20) Tm
), the QCoAl may be nearly equal to QNiAI because of their similar melting temperatures.
The diffusivities of Co60 in the two compounds are plotted as a function of temperature in
fig. 7 [29]. While the diffusivity of C060 in NiAl is markedly greater than in CoAl at tem-
peratures lower than 1300 K, the difference is quite small at 1300 K, the creep testing tem-
perature. This result was reinforced by a more accurate experiment measuring the
diffusivity of Ni°3 in NiAl [30]. These results suggest that the superior creep strength of
CoAl at 1300 K may not be related to the differences in diffusivities between CoAl and
NiAl.

Yancy and Nix [26] pointed out that any drop in elastic stiffness as temperature
increases will result directly in lower strengths at elevated temperatures. If the stiffness of
MA] were considerably less than that of CoAl at 1300 K, the difference in strength
between these two compounds could be easily understood. But this is not the case. The
Young’s modulus of CON and NiAl have been determined as a function of temperature
(eq.l and eq.2) and are given by the experimental relations:

E(CoAl)=327.88 - 0.167T ............ (1) [31]
E(NiAl) =199.80 - 0.040T ........... (2) [32]

At 1300 K, E(CoAl)=110.78 GPa and E(NiAl)=l47.8 GPa. This data does not
support the above stiffness assumption. Therefore, neither diffusivity nor stiffness can be

used to explain the difference in creep strength at 1300 K between CON and NiAl.

8

Another difficult aspect to understand is the disparity in room temperature ductility
between these alloys. Ductility is highly affected by structure, precipitation, grain bound-
aries, hydrogen concentration, impurity levels and texture. This difficulty can be more
simply addressed by examining single crystals. Fracture analysis [33, 34] has shown that
CoAl and NiAl single crystals tend to fracture by cleavage on {011} planes in <111> and
<110> orientations and on {112} planes in the <100> orientation. These cleavage planes
are the same as the slip planes of these aluminides (as will be discussed in the following
sections). Thus, it may be reasonable to relate the ductility and fracture differences to dis-
location slip in these materials. Assuming a dislocation mechanism, the lack of under-
standing of the DBTT and sensitivity to stoichiometry might be explained by the onset of
dislocation climb, thermally activated slip, unlocking of dislocations from vacancies, and
additional slip systems. All of these mechanisms are related to the mobility of disloca-
tions. Therefore it is reasonable to believe that the behavior of mobile dislocations control

the deformation processes in these 32 aluminides.

1.3 Dislocations and slip modes

The slip direction in bcc structures is almost always 1/2<111>, which corresponds
to the smallest perfect dislocation Burgers vector. The corresponding slip planes are
{ 110} { 112} and/or {123}. In B2 ordered bcc structures, 1/2<111> dislocation movement
produces an anti-phase boundary(APB) and increases the energy. This results in <100>
often becoming a more favorable slip vector. Selection of the operative slip system can
also depend on crystal orientation, temperature and composition. A single crystal speci-

men oriented to a <100> compression axis shows a macroscopic yield strength many

9
times higher than if it is oriented to a non-<100> direction. This is due to the fact that the
resolved shear stress for the “easy” <100> slip direction is zero in the <100> crystal.
Therefore, <100> oriented crystals are denoted as “hard” crystals and non-<100> oriented
crystals are referred to as “soft” crystals. Considerable research on the temperature and
composition effects on the slip systems and deformation mechanisms has been reported

for NiAl and FeAl, while information is very limited for CoAl.

1.3.1. Slip in CoAl

In 1971, Hocking et al. [25] first reported their observations of dislocations intro—
duced in single crystal CoAl by creep testing at 1300 K. Because the arrangement and
appearance of dislocations in CoAl were very similar to those in NiAl (discussed in 1.3.2),
the dislocations in CoAl were assumed to be <100> dislocations. In 1986, Nix et a1. [35]
observed <100> and <111> edge dislocations in polycrystalline Co-49.3 at%Al extruded
at 1505K. The corresponding slip planes for <100> dislocations were {001} and {110},
while <111> dislocations were observed on {110} planes. <110> dislocations were not
observed in their studies. Drelles [15] examined the dislocations in single crystal CoAl
deformed at room temperature. <1 11> screw dislocations were found for all orientations
remote from the <111> comer of the unit triangle. For orientations near the <111> comer,
the primary dislocations had Burgers vectors of [001] and were of a screw character. The
corresponding slip planes were {110}, {211} and {321} for the <111> dislocations and
{ 110} for the <001> dislocations. Dissociation of the dislocations was not observed by
the weak-beam technique [15]. The presence of <111> slip at room temperature is con-

trary to Yamaguchi and Umakoshi’s predication of <100> slip [36]. Research work on

10

dislocation structures in off-stoichiometric CoAl has not been reported.
1.3.2. Slip in NiAl

A large number of studies have examined the dislocation substructures involved in
the deformation of NiAl alloys. The observed slip systems in “soft” stoichiometric single
crystals NiAl are predominantly <100>{110} and <100>{001} at both ambient and ele-
vated temperatures [37-39]. However, <011> dislocations and <111> dislocations are
occasionally observed, presumely as a result of interection of two or three glide <100>
dislocations [40,41]. In “hard” stoichiometric NiAl, <111>{112}, <111>{ 110} and
<110>{ 110} slip systems are observed at elevated temperatures. <111> dislocations are
usually preferred at lower temperatures (77°K-600°K) and <110> dislocations at higher
temperatures (above 600°K) [2,42,43]. <110> slip is not activated at room temperature.
There are also a few reports that <100> crystals deformed in compression may deform by
an extremely localized glide of <100> dislocations (termed “kinking”) [44,45].

Deviation from stoichiometry affects the activiation of slip systems. {110} slip

planes disappear in favor of {001 } slip planes in [011] oriented N i-48Al and Ni-51Al
deformed at 600°K [46]. <111> dislocations are observed in nickel-rich Ni-42Al

extruded at 1023°K [47].

1.3.3. Slip in FeAl

At high temperatures (T >0.45Tm ), <100>{ 110} slip systems are observed in both
“soft” and “hard” orientations [51]. This suggests that <100> slip has a much lower CRSS
than <111> slip at elevated temperatures. The observed slip systems are generally not
affected by alloy stoichiometry with some slip systems being observed in both aluminum-

rich and iron-rich compositions. At room temperature, <111> slip is dominant [14,49].

11

However, Munroe and Baker observed <100> dislocations created through the interaction
of the <111> dislocations in iron-rich FeAl [53]. There is still controversy as to how the

aluminium content affects the activation of slip systems [48,52,53].

In summary [table 3], at high temperature and in soft orientation, the predominant
dislocations in all three B2 aluminides have <100> Burgers vectors. At high temperature
and in hard orientation, <110> or <l 11> dislocations are operative in NiAl while <100>
dislocations are active in FeAl. At room temperature and in any orientation, <111> dislo-

cations are favored in CoAl and FeAl, while <100> dislocations are activated in MA].

Analyzing the experimental results mentioned above, the following questions may

be raised:

Why is CoAl more brittle than MA] (with <100> slip) and why is FeAl more duc-
tile than NiAl at room temperature despite the fact that <111> slip is exhibited in both

CON and FeAl at ambient temperatures ?

Why does CoAl have the highest creep strength at elevated temperatures where

<100> slip dominates in all three materials ?

The answer might be a dislocation controlled deformation mechanism. In simple
binary single crystals, dislocation controlled deformation mainly depends on slip, cross
slip, climb, twinning, dislocation-point defect interactions, dislocation-dislocation interac-
tion and dislocation—planar defect interaction. Furthermore, the motion of dislocations is
mainly affected by lattice friction, crystal geometry, temperature and stress. In B2 single
crystals, for given testing conditions, lattice friction may play a very important role in
manipulating dislocation behavior. According to the Peierls-Nabarro model, lattice fric-
tion is caused by reluctant motion of dislocation cores. For this reason, it is necessary to
explore the core structures of dominant dislocations in B2 crystals in order to elucidate the

dissimilarity in mechanical properties.

1.4 Dislocation Cores

Many properties of dislocations are governed by the long range stress and strain
field of dislocations, such as dislocation-dislocation intersection and dislocation-grain
boundary interaction. However, some physical and mechanical phenomenon occur as a
result of interactions very close to the center of dislocations. For example, lattice resis-
tance and point defect-dislocation interactions depend on the atomic structure of disloca-
tions. Thus, in order to fully understand the dislocation slip and dislocation behavior of

the B2 aluminides, it is necessary to examine the dislocation core structure.

1.4.1 Brief history of core theory development

For a long time, metallic materials were treated as elastic continua. The effect of
dislocation cores on deformation has not been emphasized in studies of deformation
mechanisms. However, basic theory of the selection of slip systems cannot explain the
violation of Schmid’s law in bcc metals (slip is not confined to well-defined low index
planes [54]) and B-brass (both non-crystallographic and {110} crystallographic slip are
observed [55]). Nor can basic theories explain the temperature/orientation dependence of
the flow stress in most bee and B2 structures.

Theoretical research on core structures began much earlier than experimental
observations. The first models were presented by Frenkel and Kontorara[57], Peierls[58]
and Nabarro [59]. In their so-called semi-continuum models, only the atomic planes adja-
cent to the slip plane were treated discretely while the rest of the crystal was regarded as a
continuum. These models are suitable for planar and compact dislocation cores and there-

fore are only suitable for pure fcc metals.

13

Later, a large number of studies were conducted in bcc structures. It has been the-
orized that the cores of 1/2<11 l> screw dislocations in the bcc structures are not confined
to their slip planes but instead extend into several planes of the <111> zone (fig.8) [56].
This renders the dislocation sessile and provides a plausible explanation for the large
Peierls stress and the strong temperature dependence of the flow stress observed in bcc
metals, along with accounting for the slip asymmetry and complex orientation depen-
dence.

Theoretical studies on dislocation cores have been accelerated since 1970’s. So

far, various models for bcc [56,60,61], fcc [57,58,59], hcp [61,63], B2 [62,67,68], D03

[66], L12 [62,64] and D022 [65] have been established.

1.4.2 Construction methods of core models

Although there are a large varity of methods for modelling dislocation cores, all of
these models use the same general approach. The theoretical models are based on an
empirical interatomic potential by which a perfect lattice is determined. This perfect lat-
tice is then divided into an inner region with a surrounding border region as shown in
fig.9. In the inner region, a dislocation is introduced by imposing the elastic displace-
ments upon all the atoms corresponding to a dislocation in the center of the block. The
core configuration is then set by minimizing the total energy using a relaxation method
(static or dynamic method). During the relaxation, the positions of the atoms in the border
region are either kept fixed or modified in response to the changes which occur in the inner
region, i.e. fixed or flexible boundary conditions. Figure 10 is a calculation diagram for

static relaxation method with the fixed boundary condition.

14
1.4.3 Differential displacement tensor
Since a displacement field in a core is highly localized, a quantity which is large in
the core and vanishes far from the core is used to map this field. Vitek [61] first introduced
the differential displacement, a stress tensor, inside the core. The differential displace-
ment is drawn as normalized arrows along the dislocation line and described using the fol-

lowing equation.
dtDIr

(1,9113 :29. —Z dlr

iji rij 0er ........ (3)
iii |~ijl

 

Where;
01:15 is differential displacement tensor at the atom i

[:0] is the position vector of atom i relative to atom j

(X, B are the coordinates in x, y axis
9.- is the local atomic volume
¢ is the interatomic potential

1.4.4 Types of cores

In general, there are three types of cores: planar cores, non-planar cores and split
cores. In planar cores, core spreading is confined to certain crystallographic planes con-
taining the dislocation line. In non-planar cores, the core spreads into several non-parallel
planes of the zone of a dislocation line. Non-planar cores can be further divided into cross
slip cores and climb cores. A dislocation has a cross slip core if the Burgers vectors of
fractional dislocations or continuously distributed dislocations all lie in the planes of core
spreading. A climb core has the Burgers vectors of the dislocations possessing compo-

nents perpendicular to the planes of spreading. Split cores are termed as non—compact

15 -
cores. They are further divided into dissociated cores and decomposed cores. In dissoci-
ated cores, the superdislocations are dissociated into several superpartials with an APB
(anti-phase boundary), CSF (complex stacking fault) or other stacking fault in between,
for example, [GIT]:1/2[01I]+y+1/2[01I]. The stacking fault planes are often not the slip
planes of the original superpdislocations and thus the superpartials can be sessile. In
decomposed cores, one type of superdislocation can decompose into another type of
superdislocation without the formation of stacking faults, for example, [011]: [010]
+[001]. The slip planes of the so-formed dislocations may or may not be the slip planes
of “ordinary” dislocations. For example, both <100>{001} dislocations and <110>{001 }
dislocations have the same slip planes, while <100>{001 } dislocations have the different
slip planes from <110>{110} dislocations. Among these types of cores, the non-planar

cores and split cores will strongly affect the dislocation motion.

1.4.4.1 Core structures in the bee crystal structure
1.4.4.1.1 %< 111 > screw dislocation in bcc structure

Extensive experimental evidence indicates that many distinguishing features of the
low temperature plastic behavior of bcc metals are controlled by a special core structure of
l/2<111> screw dislocations. As the stacking fault energy is high in bcc structures, simu-
lations have found no dislocation dissociations. Instead, Vitek [61,69,70] found core
structures are clearly non-planar and are spread principally into three intersecting { 110}
planes (fig. 11 a and b). This non-planar l/2[1 l 1] core can be regarded as the sum of three
l/6[111] fractional dislocations with generalized unstable stacking faults on { 110} planes.

The cores of these l/6[111] dislocations can be further spread asymmetrically onto { 112}

16
planes resulting in a larger shear strain in the twinning than in the anti-twinning sense.
This asymmetry of l/2[111] dislocation cores can be used to explain the twinning-anti-

twinning asymmetry of slip in bcc metals.

1.4.4.1.2 Effect of stress on core structures of 1/2 <1 11> dislocations in bcc metals
Dislocation core configurations may change under the inflence of external stresses.

The transition behavior of a core depends on the interatomic potentials of the material and

the sense of the applied stress [93]. In the case of l/2[111] screw dislocations in bcc, there

are three core transformation modes resulting from stress [61, 93].

l. The transformation from one degenerate configuration to the other. For example, the

core structure in fig.1 1(a) can convert into the structure shown in figure 11(b).

2. The formation of extended multilayer faults on { 112} planes [6]]. As the stress is grad-
ually increased, the trailing fractional dislocation on the (110) plane disappears, while the
leading fraction dislocation on (T01) extends into the (01T) plane. Since the core is not

confined exactly to either the (T01) or (01T) plane, the dislocation establishes a multilayer

fault on the (112) planes.

3. The formation of an extended single layer fault on a {110} plane [61]
As the shear stress increases, the leading fractional dislocation extends itself on the
(T01 ) plane, leaving a single layer fault on this plane, while the trailing fractional disloca-

tion on (T10) is constricted towards the core center and the fractional on (0T1) is also con-

l7

stricted slightly (fig. 12 a). With further stress increases, fractional dislocations on (0T1)
begins to spread on (T10) plane in the opposite direction (fig. 12b). As the stress increases
further, the leading fractional spreads steadily on the (T01) plane, while two (T10) frac-
tionals become increasly constriced (fig. 12c). Finally, the whole dislocation moves freely
on the (T01) plane.

The application of an external stress significantly changes the core structure of a
dislocation before it moves. The unstressed dislocation core with non-planar spreading

can therefore be regarded as sessile.

1.4.4.1.3 [111](110) edge dislocation core in bcc

The structure of non-screw 1/2<111> dislocations in bcc metals is significantly dif-
ferent from the 1/2<111> screw cores. Chang and Graham [72] studied [111](110) edge
dislocations with a line direction [112] in bcc iron. The core atoms were moved one Burg-
ers vector according to the anharrnonic potential and Johnson potential [72]. A maximum
potential barrier (the Pererls barrier) of about 0.029 eV was obtained at the distance 1/4b
from the equilibrium position. The dislocation energy data in the region beyond a distance
of about 0.5 nm from the core center agreed well with those predicted from continuum
anisotripic elasticity theory. The calculated Peierls stress of a <1 1 1> edge core is 1.3-4.0
x 10'3tt, significantly lower than that of a <111> screw dislocation (27-29 x 10'3 1.1)

according to reference [61].

18 '
1.4.4.2 Core Structures in B2
1.4.4.2.1 <111> screw dislocations in B2
The B2 structure is one of the ordered bcc lattices (D03 as well) and in many
ways, the dislocation structures in bee and B2 are related. In B2 structures, only one type
of APB can exist on {110} and {112} planes, which is created by a £011) displace-
ment. No other stable stacking faults have been found [68]. Therefore, <111> disloca-

tions in B2 crystals may have a 2 fold dissociation:

a a
a0(111)=—2‘-’(111)+APB+7°<111> ............... (4)

Elastic calculations have found the APB either on { 110} or { 112} planes [62]
with the corresponding fault widths of 2 nm and 1.7 nm respectively. The 1/2<111> cores
with an anti-phase boundary on {110} planes have a lower energy than cores with the

APB on {112} planes.

1.4.4.2.2 <100> core in NiAl
<100> dislocations are frequently found in B2 alloys after high temperature

deformation. The edge <100>{001 } dislocations have two configurations as illustrated in
figure 13 [45,68]. The local stoichiometry of these two configuration are different. NiAl,
for example, can have one configuration with Ni atom at the termination of the extra half
planes (fig. 13a), while configuration “B” terminates with a Al atom . Configuration A
has a lOwer energy than configuration B in NiAl. The distortion of the core is spread in
compact planes of the type {110}. In NiAl, the minimum stress to initiate motion for this
edge core is high, 0018-0022 u (about 2580 MPa) due to non-planarity [68]. In contrast

to <001>{001} edge dislocations, <001>{011} cores are spread predominantly on {110}

l9

glide planes, although some non—planarity is present on {111 } planes. The stress required
to initiate motion of this core is nearly 90% lower, 0002-0003 u (about 320 MPa). In
Parthasarathy’s calculation [68], the <010>{001 } slip systems are the most difficult to ini-
tiate (mobility comparison in table 4). This is not in agreement with previous experimen-
tal results which show that the critical stress to move the <100> edge dislocation on the

{ 100} plane is comparable with that for motion on the { 110} plane. Therefore, there must
exist some factors not considered in the core models, such as out of slip plane displace-

ments, or the tendency of the core to spread on the {110} planes.

1.4.5 Core structures and potentials

Details of the core configuration of a dislocation depend sensitively on the inter-
atomic potentials used. For the same crystal, different core structures are produced when
different potential functions are employed. In early studies of the core structures of the
ll2<111> screw dislocation in bcc crystal, Vitek [61] used the Johnson potential [75,76] to
calculate the core structures and found that 1/2<111> dislocation cores have non-planar
degenerate structures, while Takeuchi [73] argued that a non-degenerate configuration of
the screw dislocaton may exist according to his calculation using a different potential.
Therefore, the accuracy of the interatomic potentials used to determine the interaction

between atoms is key to a successful computer simulation.

1.4.5.1 Summaries of potentials
There are two types of potentials currently used to simulate core structures: pair-

potentials and embedded atom (EAM) N-body potentials. The pair potentials can be also

20
divided into five catagories: empirical potentials, semi-empirical potentials, pseudopoten-
tials, tight-binding approximation and ab-initio pair potentials. These pair-potentials [74]

are briefly described below:

1 .4511 Empirical potentials

The functional form of the empirical potentials are arbitary and may be any rea-
sonable function which will fit a large number of physical parameters. The function coef-
ficients are usually determined by matching crystal structure, elastic properties, phonon
spectra, vacancy formation energy, stacking fault and APB energies, and alloying and
ordering energies. The typical type of empirical potentials are Johnson-I potentials [75]
that were developed for bcc in order to model tat-Fe. The short range elastic constants Cij

for a bee lattice can be related to the first and the second derivatives of the spherically

symmetric potential at the first and the second neighbor equilibrium sites.

2 6 , " 3 ’
(cu-en)“, = 375(71¢1+3¢2+-;2¢2) ............. (5)
2 ~ 2 , 3 ’
(C44)SR = E(O l+a¢l+g¢zj ............. (6)
2 .. 2 , " 2 ’
(B)SR -— 372(¢1-;;¢1+¢2-;—l¢2) ............. (7)
Where;

¢(r) is the spherically symmetric potential
c1], 012 and C44 are short range (SR) elastic constants
B represents the bulk modulus and r is the distance from origin.
The solution of the above differential equations gives the potentials for bcc metals

by two polynomial functions:

IA
‘r
IV
\

4 .5 2
11:04” +“3’ “’2' +“1"”0 ’n m ............ (8)

21

(l) = b4r4+b3r5+b2rz+blr+b0 r SrZr ............ (9)
where;
rm is chosen midway between the first and the second neighbor
distances
rc is chosen between the second and third neighbor distances
rn is chosen so that a potential ¢(r) results which contains a minimum
reflection point. a and b are constants.

These bcc potentials are fitted to the vacancy and interstitial formation energies
and give reasonable agreement with other properties, but were not fitted to the cohesive
energy. In addition to Johnson-I, the Johnson-H [76] potential was originally derived for
y—Fe. The Johnson-II does not hold the iron lattice at its equilibrium spacing. The physi-
cal values predicated by Johnson-II are good. In 1980’s, a new potential for transition
metals was created by March and co-workers [77,78]. They introduced the d-band elec-
tron theory into the potential function. The d-shells lead to considerably harder repulsive
core interactions than in simpler sp metals. De Hosson et a1. [79] investigated the use of
March’s d-band potentials in the simulation of the core structure of a 1/2<110> screw dis-
location in pure nickel and concluded that the potential based on the d-band force model

was quite reasonable for depicting core structures.

1 .4.S.1.2. Semi-empirical potential
For semi-empirical potentials, the functional form of a potential is deve10ped
based on theory and the few appropriate coefficients are determined by matching a small

number of physical results. One of the semi-empirical potentials is the Morse function

22
....... (10)
(i) (rij) = ¢0[exp {-2(l (rij- r0) } —2£’Xp {—01(rij—r0) }]
where;
or is constant with dimensions of reciprocal lattice
410 is equal to the dislocation dissociation energy

The energy of an individual atom is the sum of the interaction energies with N

neighbor atoms in sphere of influence, i.e.

N
E, = 24100.) .......... (11)
1' = 1
The Morse potential was used to calculate the atomic configurations for fee metals.

The disadvantage of semi-empirical potentials is that they are long-range and a lattice sum

consists of a large number of terms that requires long computation times.

1 .4.5. 1.3. Pseudo-potentials

In pseudo potentials [81], the strong potential inside an ion core is replaced by a
weaker potential in which the core electrons are only weakly disturbed by the ions. The
theory of the pseudo potentials has been frequently applied to the alkali metals. However,
in transition metals, because of their large incomplete d-shells, the d-band structures are
quiet different from free electron states. Therefore pseudo potentials are not suitable for
transition metal modeling.
1.4.5.1.4. Tight binding approximation and moments approach

The tight binding approximation was developed for defect calculations in transi-
tion metals. This model was used to explain the difference between the orientation depe-
dence of the Peierls stress for Ta, W and Mo. Masuda et. al. [82,83] calculated the Peierls

stress and the core energy of 1/2<1ll> screw dislocations in bcc metals using this

23
stress and the core energy of 1/2<111> screw dislocations in bcc metals using this
approach. It was found that the general behavior of screw dislocation motion in transition
metals strongly depends on the filling of the d-bands. Small differences in filling can

result in significant differences in dislocation core structures and Peierls stresses.

1.4.5.1.5. Ab-initio pair potential

The ab-initio pair potential model was developed by Willians, Kubler and Gelatt
[84] for metallic compounds. In this model, the roles of s, p and localized d-electrons in
the binding process are considered. The total energy is obtained from the independently
compressed atom calculation and the cohesive energy can be written as a sum of pair

interaction energies:

l
ET(rl) = 22ini¢(sir1) ............ (12)
where;
¢(r) is the pair potential

ni is the number of atoms in the i-th shell at a distance Ri=sir1, from
the atom of the origin.

ri is the nearest neighbor distance

Si is the atom coodinate

Given the value of ET as function of r], the pair potential can be found by inver-

sion.

1.4.5.1.6 Embeded Atom Method (EAM)

Though pair potentials have been used to calculate various types of dislocation

24
core structures, boundaries, phase transformations and cohensive energies, these models
have their own serious limitations.

The problem comes from their framework:

N
E .-.% 2 (1)000.) +U(p) ......... (13)
i: j = 1
where:
oi]. is the pair potential
U (p) is the density dependent part of the energy,
p is the average density of the material.

The models were constructed on the assumption of constant volume and may describe
the energy changes associated with the variation of atomic configuration at constant vol-
ume. But in intermetallic compounds, the difference between the atom sizes of constitu-
tional species can be large ( for example in the BZ alumnides rCo=0.126 nm, rNi=0.124
rim and r “=0. 143 nm). Thus the local volume change caused by core stoichiometry
change may introduce a large calculation error. To overcome this problem, the embedded
atoms method (EAM) [85] and N-body potentials (F-S) method [86] have been developed.
In this approach, the energy of the metal is viewed as the energy to embed an atom into the

local electron density provided by the remaining atoms of the system. In the EAM approx-

imation, the energy of the lattice is written as:

N N
E =% 2 $0.00.) + ZINE) ........ (14)

i¢j=1 i=1

where;
F, is the many-body interaction and/or embedding part of the
energy which replaces U(p)

(1)000.) 15 the pair part of the interaction

25
Pi is the local electron density which is calculated as a linear
superposition of atomic electron densities pl. = 2(1) (rij).
jati
The EAM and N-body potentials (F-S) remove some inadequacies of the pair
potentials and provide a better physical basis to compute atomistic structures of materials.
However, the local distortion near the core center is far from equilibrium conditions. As
the N-body potential must fit the materials parameters such as structure type, cohensive
energy and vacancy energy in the equilibrium condition, it might be questionable whether
its use can be extended to the non—equilibrium reality.
A severe problem of all the methods is that all the potentials were created for spe-
cific metals, mostly for pure elements. However these potentials have been widely used to
calculate the atomic configurations of crystal defects in other materials. The accuracy of

description of real situations in the other structures is therefore not guaranteed. For those

reasons, the theoretical models need to be verified and modified by experimental evidence.

1.4.6 High resolution electron microscopy

High resolution electron microscopy makes it possible to directly image some of
the details of the atomic structure of a dislocation core. So far, the experimental observa-
tions of dislocation cores have been sparsely reported in L12 [86, 94, 95], BZ [87, 88] and
L10 TiAl [96]. Technical difficulties are the main reasons for the limited studies. Crimp
[86] examined [T01] screw dislocations in L12 structured N i3A1. The screw dislocations
were dissociated into 2-fold '12- [TOll superpartial dislocations separated by an APB on
the (010) plane. The superpartials were further dissociated into Shockley 1/6[112] partials

with complex stacking faults (CSF) on the (111) primary plane or (111) cross-slip plane.

26
core dissociation remained unchanged. In L10 structural TiAl, Hemker, Vigwer and Mills
[87] found that the core of “ordinary” %(01T) dislocations are compact and that the
motion of these dislocations is inhibited by lattice friction and not by core dissociation. In
contrast, the core of a screw £010) superdislocation was dissociated in a non-planar
configuration. In B2 NiAl [88,89], <010> edge dislocations were found to be compact,
while <011> edge dislocations are highly split. Some of these dislocations were climb dis-
sociated, while others were decomposed into perfect <010> edge dislocations (shown in

the following relations).

Dissociation (011) = gnli] +APB+gtiiii ........ (15)
Decomposition (OlT) = (010) + (OOT) ........ (16)

These experimental results are in agreement with conventional TEM observations:
<010> type dislocations dominate the high temperature in the soft orientations, while
<011> slip corresponds to a high critical resolved shear stress in the hard orientations.

It is important to note that a HREM picture is significantly affected by defect
geometry, sample conditions and operating factors such as surface relaxation of disloca-
tion, kinks of dislocation lines, specimen thickness, surface contamination, magnetic
nature, defect interaction effects, residual stresses, beam damage, defocus values, astig-
rnism and beam misalignment. Therefore, interpretation of HREM images is not straight-
forward and needs the support of computer simulations. For example, the contrast
changes of several atoms in core regions were observed in HREM studies of Ni3Al and
TiA1[86,87]. These features were successfully explained after computer simulations pro-
duced the same phenomenon: stacking faults modulate the the local image contrast corre-

sponding to APB or ISF or ESF planes.

27
sponding to APB or ISF or ESF planes.

HREM computer simulations are performed using electron optics software. The
data files used in simulations are atom coordinates in a dislocation core. These can either
be atomic coordinates from core simulations or best-guess structures. These image simu-
lations allow direct comparison of experimental images with model structures. For a
number of resons, these comparisons may not result in a satisfactory match. One reason
may be that the potentials used in the simulations may not represent the the true atomic
bonding. Additionally, core calculations are usually performed at 0 K, whereas the exper-
imental images may reflect the core structure at either the deformation or observation tem-
peratures. Also, atomistic models are unable to account for climb dissociation which may
occur in real materials. Thus, mismatches between simulations and experimental observa-

tions are not necessarily unexpected.

1.5 General characteristics of CoAI

The cobalt-aluminum phase diagram, along with those for the N i-Al and Fe-Al
systems, is shown in fig. 14 [90]. It is very similar to the nickel-aluminum system, but
somewhat different from Fe—Al system. CoSOAl melts congruently at 2191 K, approxi-
mately 575 K higher than Ni-based superalloys. The single [3’ phase has the ordered
body-centered cubic crystal structure of cesium chloride or B2 type. It consists of two
interpenetrating primitive cubic cells, where cobalt occupies the comer sites and alumin-
ium occupies the body central sites (fig. 1). The B2 structure of {3’ phase is stable for
large deviations from stoichiometry. This wide field allows alloying for improvements of

mechanical properties without entering a two phase field.

28

l.6 Motivation of this research

It is difficult to elucidate some of the unusual mechanical behavior of B2 alum-
nides using general deformation and dislocation theories. The problems may be related to
core structures of those dislocations that play the major role in the deformation process of
the materials.

The effect of core structures on mechanical behavior has not been emphasized
until very recently. Traditionally, the resistance to dislocation slip has been dealt with as

the Peierles-Nabarro stress according to the form:
an? i '

Ip_nocGe ......... (17)

where;
G is the modulus of elasticity in shear
1‘”; is the Peierls stress

W is the width of a dislocation core,
for edge dislocation

 

W = l - U
a for screw dislocation

a is the interplanar spacing
b is the Burgers vector

This equation indicates that the Peierls stress for a given slip system decreases
with increasing interplanar spacing. But dislocation width is not simply a function of
interplanar spacings of slip planes. As shown in fig. 15, the spacing of slip planes (a) and
spacing of atoms (b) can be almost same while the dislocation widths (w) are distinctly
different. The dislocation width must be dependent on the atomic structure and the nature
of the atomic bonding forces. For example, when the bonding force is spherical in distri-

bution and acts along the line of atom centers, the dislocation width is large and conse-

29 .
quently the Peierls stress is small. By contrast, when the bonding forces are highly
directional (such as bcc), the dislocation width is narrow and the Peierls stress is corre-
spondingly large [91]. The equation of Peierls stress is too simple to consider the exact
shape of the displacement field around a core and core spreading geometry.

The equation (17) is too simple to explain the nature of the Peierls stress. Core
splitting, core dissociation, atomic row bending, core stoichiometry and the corresponding
displacement field are all related to lattice resistance. In addition to above intrinsic fac-
tors, core configurations may be changed by environmental factors, such as:

1. Temperature: this may lead not only to thermally activated core motion but may
also change the core configuration as well.

2. Stress: Vitek [61] predicted that core structure may change before slip occurs
when applying stress to the model crystal.

3. Heat Treatment and interstitial atoms: fast cooling after annealing of single crys—
tal NiAl increases its fracture toughness KQ dramatically from 2.8 to 15.6 (MPaMm)
[92]. This phenomena may be related to the interaction of interstial solute atoms with dis-
location core structures.

4. Deviations from stoichiometry: a small deviation from a stoichiometric compo-
sition may not change the core chemistry but may change local atom profiles.

From the above analysis, it is clear that the investigation of core-related behavior
is critical. Although previous work has already recorded some <100> and <110> cores in
NiAl, the effect of stoichiometry is still not understood. Furthermore, the core structures
of CoAl have not been examined yet. In order to thoroughly understand the deformation

mechanisms in B2 aluminides, it is necessary to investigate dislocation cores in other

30

alloys such as CoAl.

1.7 Expected impact of the project

The HREM examination of dislocation cores in BZ intermetallic compounds
CoAl, NiAl and FeAl will have an impact in both the basic understanding and practical
development of these alloys. First, it may provide some clarification for the differences in
both high temperature strength and room temperature ductility of these materials. After
this, an improved effort will be directed to obtain a better balance of strength to ductility
for these materials. Second, it will help to develop dislocation theory. Core structure is a
very weak link in the chain of dislocation theory. Experimental images of cores may sup-
ply some valuable new ideas and help to establish better theoretical models. Third, in the
near-tenn, the comparison of HREM observations with computer simulations will test the
accuracy of current theoretical models and the associated interatomic potentials. These
potentials are widely used in other research areas, such as the studies of grain boundary
structures. Finally, since the understanding of CoAl is not as complete as that of NiAl and
FeAl, the dislocation analysis and HREM core examination of CoAl will contribute to the

understanding of deformation mechanisms of this material.

31

 

 

 

 

 

 

 

 

Figure 1 B2 structure is the ordered bcc lattice. Two kinds of atoms (A and B)
occupy the corner positions or body center postion respectively.

32'

 

 

 

 

 

 

Hardness (Kg/mmz)
240
T=1073 K
200 CoAl
160
120
40 .
FeAl
H 4“]
0
46

47 48 49 50 51 52 53 54 55 56

Composition (Al)

O CoAl G NiAl (D FeAl

Figure 2 Hardness-composition isotherms in B2 intermetallic compounds. This figure
shows the high-temperature hardness and sensitivity to composition
deviation of fliese compounds.

33

Temperature °C

 

1000

800

600

200

 

 

 

0.2 0.1 0.0 0.1 0.2 0.3 0.4

Figue 3 Ductile-to-brittle transition temperature for binary Co—Al alloy [21].
The transition temperature is the lowest at stoichiometric Co-50A1.
Deviation from stoichiometry results in increase of the transition
temperatures.

34

00.2 (Kgf/mmz)

 

150

50

 

 

e +

 

 

 

0 100 200 300 400 500 600 700 800 900 1000

Temperature (k)

Figure 4 Temperature-dependent of the yield stress of stoichiometric NiAl single crystal
of soft orientation [23]. Brittle-to-ductile transition temperature is around
150 K.

35.

 

 

 

 

10'5
‘7 _.
6 _
5 .—
4 _
3 1—
2 _ NiAl
:37
M
E 10'6 ‘L
as
7 _ CON
6 ‘ o
5 _.
4 _
3 _
1 ' 1 1 1
10 20 40 6O 80 100

Stress, MPa

Figure 5 Creep resistance of CoAl and NiAl at temperature 1300 K [25]. CoAl has
significantly slower strain rates than N iAl.

36

Stress (MPa)
80

 

70 1300 K

_ _5 _1 CO-Al
6O 8-1x10 s

50

4o
30 @

CoNiAl
20 Ni-Al

59

10

 

 

0

 

42 43 44 45 46 47 48 49 50 5152

Atomic Percent Al

Figure 6 Creep stress of polycrystalline Co-Al and Ni-Al [27]. CoAl has higher
creep strength than NiAl. On the other hand, the creep strength is more
sensitive to composition deviation in CoAl than in NiAl.

37

Temperature °C

1400 1150 1000 850

 

-10

-11

-12

-13

Log DCo-60’ cmZ/s

-14

-15

-16

 

 

 

 

1/T x 103(°K'1)

Figure 7 Diffusivities of Co°0 in CON and in MA] [29]. Around 1000 K -l400 K
CoAl has comparable diffusion coefficients to NiAl.

38

 

Figure 8 Core strucuture of 1/2<111> screw dislocation in bcc structure [56].

39

 

Perfect Crystal

(based on interatomic potential)
Array of coordinates representing
the positions of atoms

1

Imperfect Crystal

 

 

 

 

Imposed a displacement field
corresponding a dislocation

1
Mr. 1.

fixed or

flexible
Relaxation
(static or dynamic method)

 

 

 

 

outer region

 

inner region

 

 

 

 

 

 

 

Minimizing the total energy of lattice

1

Atomic core structure
of
a dislocation

 

 

 

 

 

 

 

Figure 9 Diagram of computer modelling. Introduction of displacement field and
application of boundary conditions and relaxation method are key steps in
core modelling.

4O

 

11 atoms in the inner region
a m atoms in the outer region
total atoms S in the model

S=n+m

Determine coordinate of i-th atom and
the N neighbors

1

Compute forces
on this atom by

 

 

 

 

 

 

 

 

 

the N neighbors
d
F = d_¢ (r)
r

 

 

 

I

New coordinate of the atom
so that N

25:0
1

I '=i+1 I

 

 

 

 

 

l'lO

 

i=n

 

yes
STOP

Figure 10 Diagram of relaxation calculation. When the displaced lattice reaches its
equalibrium condition, the force upon an atom should be balanced.

41

1/6[lll]

l/6[111]
l/6[111]
l/6[1ll] 1/2[111]
1mm]
“611111 1/6[111]
(a) (b)

Figure 11 Two configurations of dissociated screw dislocation 1/2[111]. The arrow
directions indicate that the l/2[111] screw dislocation spreads on three
intersected planes.

42

('1'10)

 

 

(101) (101) ._ (101) (011)

(01 1)
(a) (b) (C)

Figure 12 Changes in core structure under influence of stress. The non-planar spreading
of 1/2<111> dislocation on (110) and (011) are contracted under the applied
stress. The process is shown from (a) to (c).

43

001

100
010

1).-.1001]

é = [010]

 

 

 

 

 

O O O 0 O 0

0

Be

ggg'ponooo

. U. D D
0.00.0 o. o .o
.0. o.D.o 0. D D
D D. .U , o. o
O .0\ a U D U
D D. o o o
o. oinuc D D D
D D. . c o. o
.o o. .o . U. D
D .0 D D .

.O .O O .O .O
.D .D D D .D D
.0 O o O O
.D D D D D D
O O 0 o O
U D D U U D
O O O O O
U U U U U U

 

 

 

Figure 13 Two configurations of simulated core structure of <100> edge dislocation

in BZ structure.

Temp (K)
2000

 

1800

l 600

 

1400

uné
1200

1000
930

800

700
600

 

 

 

 

 

Co 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 A1

 

at%

(a)

Figure 14 Phase diagram for binary B2 system. (a) Co-Al diagram [90] (82 structure (B)
can be found in the range of composition 0.45-0.55 A1 at% at room
temperatures), (b) Ni-Al diagram and [130], (c) Fe-Al diagram [131].

0

Temperature C

45

 

 

 

 

 

 

 

 

 

 

 

 

 

1800
L 1638
1400‘
+1395
15
1133
(B2)
1000
700
600
vs». 5
I , 1 1
Ni 20 40 60
A1 lat. %

(b)

Temperature ('C)

16m

15m

13m

1200

1100

§

§§§§§

46

Aluminium (wt.%)

30 40

50

8

70 80

90

 

0)

i

 

i
l

4— Fe Al,
4— FcAl,

1310'C

i
\ \\
1.95 \ \
1092’C\-
“101)
1022°C

52

To

700 c,
'. “a I
' 612‘C I «,0)
{552°C}
1

 

 

1215 'C
1164°C
1171°C

Q“

1157°c
[Ill
1'11
1'1'
111'
I'll
1'11
111'
1'11
1'“
“1'
1'11
t|1|
1'1|
I'll
I'll
111'
111'
1'1I
1'11
1'1I
1.1Il'

652°C

660.46 'C

99.1

 

 

47

:mB Set engages £23 segue—m6 028 5 mo Quezon—um 2 Roman

2: ac.
0

A3
K
O O 0
Q OOLQxx n Gui—q
f

NB 8.4 NB 8.4

ll"

 

 

 

llx

 

 

I'I'||'|l|||'lll'A

39:02 0 .
h p 3
H N) H
a q a .

 

3G

 

 

 

 

#1

4H

 

 

 

—0—-0-
«Ht-
_+—-0—

 

 

 

 

 

 

dbl—4p—
“0‘0—

 

 

48

Table 1 Physical parameters of stoichiometric COM and MM

 

 

 

 

 

Lattice
Parameter Melting Young’s D .
Material Structure (A) temperatue Modulus ensrty
at room (K) (GPa) (g/CC)
temp.
: = m

CoAl B2 2.86 1921 278 6.07
MM B2 2.88 1913 238 5.85

 

 

 

 

 

 

 

49.

Table 2 CRSS of some 82 aluminides

 

 

 

 

 

 

 

 

 

 

Material Slip System ((13:33 Reference
CoSOAl <i100>{ 110} 258 [15]
CoSOAl <111>{110} 272 [15]
C050Al <111>{112} 343 [15]
CoSOAl <111>{123} 324 [15]
Ni50Al <100>{ 110} 68.6 [16]
Fe50Al <111>{110} 202 [14]
Fe40Al <111>{ 110} 97.0 [14]

 

 

 

 

 

22-2 E has :5 ..
5:68:80 oEoEoEBSméO ”E EoEmoquU 050803305 ”a
oéfioqfioh Eoomum ”05:82”th swium ”oaaeoafioh. ”95,—.

50

 

 

 

 

 

 

 

 

 

 

 

 

 

<2 <2 327:5 327:5 <2 327:5 can 2
<2 <2 3:7:5 3:7:5 <2 5:7:5 us: a
7:5 <2 3:7:5 8:7:5 <2 8:7:5 .5: 2
<2 <2 <2 £8785 <2 327:5 com 2
<2 <2 <2 8:785 <2 3:7:5 com 2
7:5 <2 785 :8785 <2 8:7:5 com m
<2 <2 <2 A _ 5 <2 <2 ea: 2
<2 3:785 <2 725 <2 <2 .5: 2
<2 <2 <2 <2 8:7:5 eom :
Z5 <2 <2 8:785 <2 8:785 com :
785 8:785 :8785 :8785 <2 :8785 e8 :
5.20m 3362 .3242 5.32 5250 3580 5:23:35 “~th

 

 

 

 

 

 

 

 

.5... e5 22 .25 5 253% 35 m 2.3.

 

51

Table 4 Summary of the simulation results for the various
slip systems in the order of decreasing mobility [68]

 

 

 

 

 

 

 

 

C 't' 1 t
Slipsystem Dislocation type 11 rcazs ress
10 u
_ <001>{110} Screw 0.16-0.18
Edge 0.20-0.30
<111>{ 110} Screw 0.60-0.80
Edge 0.53-0.67
<111>{112} Screw 1.00-1.30
Edge 0.40-0.53
<110>{ 110} Screw >6.0
Edge >8.0
<010>{ 100} Screw >0.21
Edge 1.80-2.20

 

 

 

 

52

2. Experimental Method

2.1 Materials

The study was concentrated on single crystal Co-Al aluminides. Some joint
research on Ni-Al and Fe-Al aluminides with S. Tonn and D. Sharrott was also conducted.
CoAl crystals were obtained from the Naval Air Research Development Center (Waimis-
ter, PA) and Dr. D. Pope at the University of Pennsylvania. N iAl crystals were donated
by Dr. R. Darolia, GE Aircraft Engines, Cincinatti, OH. Single crystals FeAl were avail-
able from a previous study [14]. The nominal composition of the specimens were Co-
50at%Al (hereafter Co-50Al), Co-48Al and Co-52Al. The materials used for comparison

in the joint reserach were Ni-50Al, Ni—48Al, Ni-52Al, Ni-SlAl, Fe-40Al and Fe-50Al.

2.2 Specimen preparation

Single crystal slabs. were oriented to a specified direction using the back-reflection
Laue technique. A Cu x-ray tube was used at a voltage of 24 kV resulting in a tube current
of 35 mA. The exposure time was 4 minutes for Polaroid type 57 film.

Specimens for compression testing were electric-discharge machined (EDM) from
the oriented single crystals to a nominal size of 3x3x9 mm. In order to minimize end
effects and buckling, the height/width ratio was set at approximately 3. The EDM made
use of a wire saw and was set to produce a voltage of 180 V. The specimens were notched
in a upper-right comer to indicate orientation (fig. 16), and mechanically ground down to a
final size of 3x3x9 mm. These specimens were then electro-polished in order to remove
any surface scratches and mechanical polishing marks. Brittle materials, such as CoAl,

are very sensitive to surface defects. A smooth surface can avoid early fracture and more

53
clearly show slip lines. The polishing was performed by using a 10% perchloric methenol

solution with a current of 250 mA at -20°C.

2.3 Mechanical testing

The polished specimens were deformed in compression at a nominal strain rate of
2x10'4 /sec. The mechanical testing was performed under vacuum at the desired tempera-
tures using an MTS 810 servohydraulic load frame with a Centor vacuum furnace. The
strain was limited to 5% in order to introduce enough dislocations for TEM/HREM obser-
vation, but to avoid unwanted dislocation interactions. A1203 compression pads were
used to separate the specimen from the compression head and to reduce the friction. The
stress-strain data were recorded by an IBM-PC and plotted using the Excel software pack-

age.

2.4 Slip trace analysis

Slip lines on the surface of the deformed specimens were observed using optical
microscopy. Two-surface slip trace analyses was used to determine the slip planes
involved in deformation. Figure 17 represents a specimen where slip lines ab and ac con-
stitute the slip plane. After recording the slip lines on two orthogonal surfaces ABCD and
ABEF, the angles between the slip lines and the reference axis AB were measured. The
trace of plane abcd was then drawn 0t degrees from point B (south pole) and [3 degrees
from point B (east pole). The intersection of two traces is the normal of slip plane.

The intersection angle of slip lines depends on the surface orientation of a single

crystal specimen. If the surfaces are (100) and (01T), the intersection angle is 90° on the

54
(100) plane and 00 on the (OlT) plane. If the surfaces are not the (100) and (01T) planes,
the slip trace and intersection angle can be determined in a simple formula shown below.
Figure 18 is the coordinate system for [011] orientation. 0 is the rotation angle
between [100][01T][011] system and [ul v1 w1][u2 v2 w2][011] system. [x y z] is the
direction of slip traces in [100][01T][011] system, while [x’ y’ z’] is the direction of slip

lines in [ul v1 w1][u2 v2 w2][011] system.

cost) —sin0 0 x'
[XYZ] = sine 0059 0 y' ......... (18)
O O 1 z'

0050 sine 0 x
[X'Y'z'] = —sin9 c0590 y ......... (l9)
0 0 1 z

Ifthere are two sets of slip traces [x]’ y 1 ’ zl ’] and [x2’ y2’ 22’], the angle between

slip trace can be determined by the following formula:
[x1x2 +y1y2 +2122] ........ (20)
»./x1'2 + yl'2 + 21'2 0 4/Jc2'2 + y2'2 + z2'2

 

cosO =

 

 

The above method can be used to sort the slip traces associated with multi-slip sys-

tem and to confirm the results of trace analysis.

2.5 Transmission electron microscopy

After the slip plane was determined, TEM foils were sectioned parallel to the slip
plane by electrical discharge machining (EDM). Sections were sliced to an approximate

thickness of 500 pm. The thickness of the sections was reduced to approximately 250 um

55

by grinding with 400 grit metallographic paper, then 3 mm diameter discs were produced
by spark machining. These discs were further thinned to 150 mm by grinding with 600 grit
paper. Jet polishing was carried out using a Struers Tenupol Twin Jet polisher operated at
-30°C using an 8% perchloric acid in methanol solution with a flow rate setting of 4 and an

applied voltage of 10 V.

2.6 Dislocation analysis
2.6.1 g-b=0 analysis

Standard diffraction contrast analysis (g°b=0 method) was used to determine
Burgers vectors for dislocations observed under various deformation conditions. Screw
dislocations in elastically isotropic materials become invisible when b lies in the reflection
plane. After forming a series of images with two-beam conditions (g-vectors) and
0 <w<1.0 (w is dimentionless deviation parameter from the Bragg reflection) for individ-
ual reflections in different zones, two reflection vectors in which the screw dislocations are
out of contrast may be obtained. Therefore b must be the zone axis of these two planes,
i.e. b=g1xg2. Often edge dislocations are invisible only if the reflection plane is perpendic-
ular to the dislocation line u, that is gxu=0, or equivalently, g°b=0 and gObxu=0. With
anisotropic crystals, the dislocation may not be completely invisible even though g°b=0
and g'bxu=0 are satisfied. However the g°b=0 typically leads to reduced visibility and

can be used for a guide for simulation.

2.6.2. Computer simulation

Due to the fairly high anisotropic nature of CoAl, MA] and FeAl (table 5), it is some-

56

times difficult to unambiguously determine the Burgers vectors via the g-b=0 method.
For this reason, an image matching technique was sometimes used to confirm the Burgers
vectors. This technique is based upon computer simulation of a series of dislocation
images obtained with different operative reflections for the exact reflecting conditions.
The simulation program was adopted from Head et a1 [97]. In order to apply this
program, the reflecting vector g, beam direction B, deviation parameter s, dislocation
direction u, the thin foil normal F N and the foil thickness t are required. The Burgers vec-
tor b is varied until an experimental/simulation image match is obtained. All the input
data was measured from TEM micrographs and the corresponding diffraction patterns.

The details are given in Appendix 1.

2.7 High resolution electron microscopy

To directly resolve details of individual atomic arrangements in the core region of
dislocations, high resolution electron microscopy (HREM) was employed. HREM thin
foils were sectioned perpendicular to the line direction of the dislocations of interest in
specimens deformed under the identical conditions as for g°b=0 dislocations analysis (fig.
19). The thinning and jet polishing conditions were the same as for TEM specimens.
However, HREM foils need to be thinner and flatter than the regular TEM foils. Conse-
quently, fewer suitable foils were produced. These foils were then examined using a
JEOL-4000 EX operated at 350 kv at the University of Michigan Electron Microbeam
Analysis laboratory.

In HREM, dislocations must be imaged down the line direction. Generally speak-

ing, HREM requires (1) a low index zone, (2) the defect to be parallel to beam direction,

57

(3) displacements perpendicular to the beam direction. Therefore, only displacements
perpendicular to the optic axis are displayed, while the displacements parallel to the beam
direction cannot be resolved. For these reasons, edge dislocation cores are easily imaged,
while the screw dislocation cores are difficult to image. In mixed dislocations, the dis-
placements revealed in the core region only represent the edge components of the strain
field.

Although the JEOL 4000-EX has better than a 0.17 nm point-to-point resolution
and the lattice parameter of CoAl is 0.286 nm (NiAl: 0.287 nm, FeAl: 0.291 nm), not all
the dislocations can be imaged at the atomic level. This is because the lattice images pro-
vided by HREM are only two-dimensional projected pictures along the beam direction.
When the minimum projected atom column to atom column spacing is less than or close to
the instrument resolution, core examination becomes impossible. In the case of edge dis-
locations in B2 intermetallic compounds, the possible slip systems are <010>{001 },
<001>{ 110}, <100>{012}, {lll}{112}, <111>{123}, <111>{1T0}, <011>{011},
<1T0>{001}, <1T0>{ 111 } and <1T0>{ 112}. Table 6 lists the line directions of the edge
dislocations of these systems.

The projected lattice images and minimum atom to atom spacings of these disloca-
tions are shown in figure 20. Dnly in the line directions <100> and <111>, can the indi-
vidual atom spacings be resolved. Therefore, only <010>{001}, <011>{0T1) and
<1T0>{ 112} edge dislocations are reasonable candidates for HREM examinations in B2
alloys. In the case of screw dislocations, examination of the atomic structure is only pos-
sible for the <100> and <111> dislocations. However, since the Burgers vector is parallel

to the beam direction, the displacement field of a screw dislocation core cannot be

58

resolved. However, the shear strain field existing in the core region may change the con-
trast of the individual atoms. With the help of computer simulations, the screw dislocation
core structures may be solved. In contrast, core investigation in the <111> edge disloca-
tions and <110> screw dislocations is impossible. Based on the above reasons, the selec-

tion of dislocations for core examination is limited by the resolution of HREM.

In the present study, <010>{001 } edge dislocations were expected to be activated
in samples oriented to [011]. <011>{011} dislocations are expected when compression
specimens are either oriented to <100> hard orientations and deformed at room tempera-
ture or oriented to soft orientations and deformed at high temperature. <11 l> screw dislo-
cations are expected when specimens are deformed at room temperature or oriented to a
hard orientation and deformed at high temperature.

HREM employs phase contrast imaging in which the contrast depends on the
phase shift <I>(u) between Bragg-scattered beams and the transmitted beams and is given

by:

 

$04) = 2%‘(Csyz‘farm9‘22u ) .............. (21)

Here It is the position vector in reciprocal space and Af is the defocus value
If @(u) is an even integer multiple of 1t, atoms will appear bright and when (l>(u) is an odd
integer multiple of 1:, atoms will appear dark. Therefore the image contrast can be con-
trolled by defocusing. It is very important to locate the optimum defocus of the objective
lens to prevent improper interpretation of the images. A small negative defocusing is nec-
essary to give adequate and accurate HREM images.

The number of beams in the image is also important; too few will give rise to seri-

ous truncation effects in the image; too many may generate spurious contrast effects, due

59

to the inclusion of strong subcell reflections.

Thick specimens may cause multiple scattering and absorption of the electron
beam, preventing phase contrast imaging. A regular lattice image may become a superlat-
tice image with increasing thickness. Correspondingly, a <010> dislocation may be mis-
interpreted as a 1/2<011> dislocation (fig. 21). Therefore, the thickness in an analytical
area should not exceed 10 nm. In order to avoid being misled, the construction of a Burg-

ers circuit should refer to the diffraction pattern.

2.8 HREM image simulation

Because HREM images are highly sensitive to the instrument, operation and sam-
ple conditions, images can get hopelessly confused and are prone to be mis-interpreted.
Therefore it is necessary to employ computer-simulation techniques to interpret phase
contrast images. Matching of simulated images and experimental images over a range of
parameters (e. g. specimen thickness, specimen orientation, microscope focus) is at present
the most accurate method of image interpretation.

Stadelmann’s EMS software package [98] was used to generate the HREM simu-
lations using a Sun workstation based Unix system. Images of dislocation cores were sim-
ulated using atom positions of cmputed cores as input data. These atom positions which
were the result of ABM calculations of dislocations in B2 aluminides, were provided by
D. Farkas at Virginia Polytechnic and State University.

The EMS program uses the multislice method to calculate the wavefunction of an
electron in the crystal. As shown in figure 22, the electron wavefield exiting the bottom of

the specimen W, is calculated by considering the successive interaction of the incident

6O
wavefield ‘1’0 with the crystal potential (DP of each slice.

W1 = [W0®P1]'Q1 ............... (22)

‘Pn = [‘Pn_1®Pn]OQn ........... (23)

Here Pn is free space propagator between the [n— 1 ]th and nth slices and the symbol
8) represents a convolution. Qn is the transition function of the nth slice and is a function
of crystal potential (Pp:

......... (24)
Q, = ..,,[,. . mi
Where;
0' is the relativistic electron interaction constant,
(Pp is the crystal potential per unit length projected along
the beam direction;
52 is the thickness of each slice
If the crystal is perfect, (DP will repeat periodically along the beam direction so that Qn is
constant as a function of thickness. If crystal contains a dislocation (or other defect), (Pp
is no longer periodic in the beam direction, and the variation of (PP is discretized into slabs
of constant thickness.

The simulation path is shown in figure 23. The data files containing atom positions
from Prof. Farkas were converted into supercell files by a conversion program ( given in
appendix 2). In the supercell, the x and y axes are perpendicular to beam direction, while
the z axis is parallel to beam direction (dislocation line direction ) (fig. 24) and a>>t, b>>t
as shown in figure 25. The dislocation line is always at the center of the supercell.

The SC subroutine is then used to generate the phase object function (POF)

(xxxxxxpof) and the Fresnel propagator function (FRE) (xxxxxx.fre). The POF is calcu-

61

lated directly in Fourier space by calculating the structure factors at the (h,k,0) sampling
points. The .pof and .fre files are used by the multislice interation.

The major problem of the multislice method is the selection of the right slice thick-
ness and sampling of the projected potential. When the slice thickness is too large, the
phase object approximation fails and when the sampling is too coarse, the projected poten-
tial could possibly become complex or negatively valued. In order to check the validity of
the calculation of the projected potential, a unitary test program (UT) is used to test the
number of sampling points and the slice thickness of the .pof file. If the supercell height is
too large, it is necessary to slice the unit cell in the beam direction into several thinner sub-
slices. Figure 26 is the map for “slice” program.

The SC subroutine is applied to each of the subslice files to generate a .pof file.
_When the .pof file passes the unitary test, the multislice interation is performed in the man-
ner shown in figure 26. The first subslice is iterated with the second subslice and so on.
After each individual iteration, a new wavefunction is produced. This new wavefunction
continues to interact with the POP in next subslice to give another new wavefunction. The
procedure is controlled by a so-called “autorun” script program in a C-shell (given in
appendix 3). The MS program was kept “on” until a desired foil thickness was reached.

The IM subroutine is used to calculate the HREM images. These images are dis—

played through the subroutine “PR”.

62

‘_ notch

 

 

 

 

 

 

Figure 16 The size of compression specimen is 3x3x9 and a notch was made at
upper right comer.

63-

 

 

 

 

 

 

 

 

Figure 17 Slip trace analysis. The angles a and B were measured on the surface
and the normal of slip plane was determined using a Wulff net.

64

011

 

 

/ 6/ W

ul V] w]

100 u2 v2 w2

Figure 18 Coordinate system for [011] oriented single crystal Co-Al. The angles
between slip traces depend on the coordinate system. Slip traces in
[100][011][01 1] system can be easily identified. Slip traces in the other system
can be determined using eqs. 18 and 19.

65

HRTEM foil

 

dislocations \

 

-—‘,‘1 TEM foil \

TEM foil

 

d
"o
‘
"
"
’

 

’
"
"
‘

I. ........ __
,L O

L/l/l77/

end-on dislocations
o

\ o

 

 

 

 

 

HRTEM foil

Figure 19 HRTEM foil section, and end-on dislocations. The TEM foils were
sectioned in the direction parallel to the slip plane while the HREM foils
were sectioned in the direction perpendicular to the dislocation line.

66

if) 6:..
@flfifififlfififi
%®%%®%®@@
®®®%%%%®$
®®%®®@%®®
figflfifififififi
semeeoeee
®%®®3$®®@
:3 o

(a) (b)

 

 

”one
GOG
®€3®C3®cag
GUQGGQ"
30.635366
.3063

(c) (d)

 

Figure 20 Projected lattice for dislocation lines corresponding to various zones.
For some zones (<1 10> and <1 12>). projected atom spacings of the lattices
are below the resolution of the high resolution transmission eletron
microscope. (a) <100> (b) <110> (c) <11 l> (d) <l 12>.

0000 OO O M

O o O
0000 CONGO.
O o O o. o e

O 0 GOOD.

                     
   

OO
O.

 

 
     

 

 

67

Figure 21 (a) Regular lattice: schematic core structure of [010] dislocation.

(b) Superlattice: schematic core structure of [010] dislocation.

68

(b0 Incident Wavefield

 

Crystal Potential (pp

 

 

 

.1

0-0.20 nm

 

(p1 Output Wavefield

Figure 22 Schematic representation of the multislice principal. The incident wavefield
interacts with the crystal potentials, resulting in a modified output
wavefield.

 

DATA file

 

 

 

i

 

 

69

 

SC

 

 

 

Phase objective

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Supercell file '—‘> Function
xxxxxxocel .Sll .Fre .POt
Convert
Program; FT * UT
. No TEST
Subshce
Program ‘_' .POF DIM
Subslice‘ sub00i.ce| M8; Yes
.Multislice waillhsllfifin
Loop .wav .bea
.wav 1M1
3
. > Calcugrtetion
.ima
TV;
Dis 13y TV Prepare
0?] <—— image for
Screen print anctll display
.ae

 

 

 

 

 

 

PR

 

 

Print

image

 

Figure 23 Simulation path for multislice calculations. Phase objective function, wave
function and image calculation are key steps in HREM simulation.

 

7O

 

 

   

Y
dislocation [in

 

 

 

 

I; a 4

 

Figure 24 Representation of a supersell used for image simulation. The supercell was
made with a and b borders much longer than its thickness.
Note: the z direction corrsponds to the beam direction.

 

l

l

71

 

 

Supercell.cel

 

 

l

 

 

82=tlm

 

 

l

l

 

subl.cel

 

 

 

sub2.cel

 

 

 

sub3.cel

 

 

 

 

l

 

 

SC program

 

 

 

Unitary Test

l

YES

To MS Program

1

 

 

subm.cel

 

Figure 25 Slice program map. The number of slices should be large enough in order

to pass the unitary test.

 

sub 1

sub 2

sub 3

sub 4

sub 1

 

Figure 26 Iteration diagram illustrating iteration procedure. The exit wavefunction
of the previous subslice was regarded as the incident wavefunction of the
current subslice.

73

Table 5 Elastic constants of Co-Al, Ni-Al and Fe-Al

 

 

 

C11 C12 C44
W

Ni-SOAl [128] 203 134 116

Fe—50A1[129] 181 114 127

 

 

 

 

 

 

74-

Table 6 Edge dislocations and the corresponding
line direction in BZ structure

 

 

 

 

 

 

 

 

 

 

 

 

 

gzctgoerrs Slip Plane Dilrelgfion
010 001 100
001 110 110
100 012 021
111 110 112
111 112 110
111 123 541
011 0T1 100
110 001 110
110 111 112
110 112 111

 

 

 

 

Chapter 3 Results and Discussion

In the following sections, results of the experimental studies will be presented.
These results will be analysed and compared with the previous studies in B2 alloys section
by section. A comprehensive discussion that intergrates deformation behaviors, slip sys-
tems, dislocation activation and core structures is not included in this chapter. It will be

presented in Chapter 4.

3.1 Mechanical behavior of Co-Al alloys
3.1.1 Deformation of Co-Al under high temperature compression

Representative true stress-strain curves for three [011] oriented Co-Al alloys with
different compositions compressed at a stain rate of 2x10‘3 3’1 at 1300 K are presented in
figure 27. The curves (a), (b) and (c) show the results for Co-50Al, Co-48Al and Co-52Al

respectively. The deformation features are summarized in the following paragraphs.

Off-stoichiometric Co-52Al and Co-48Al both exhibit significantly higher stress
levels for corresponding strains than stoichiometric Co-50Al, with the aluminium rich
Co-52Al displaying higher strength than the cobalt rich Co-48Al. This is consistent with
the hardness-composition data for Co-Al of Westbrook [13] and Whittenberger’s slow
strain rate creep compression experiments for polycrystalline Co-Al [27]. Similar yield
strength vs. composition trends have also been observed in the Ni-Al system (Ni-51A],
Ni-50Al and Ni-49Al) deformed at a strain rate of 1.41x10‘3 5'1 at temperatures below 673

K [99]. However, this trend disappeared at 1273 K [99,100]. This comparison indicates

75

76
that Co-Al is more sensitive to stoichiometry deviations than Ni-Al with respect to defor-

mation behavior at high temperatures around 1300 K.

The observed compressive stress-strain curves (fig. 27) of Co-Al are indicative of
B2 alloy deformation behavior [26,99,100], in which the stress-strain curve increases rap-
idly during the first 0.8-1.0% deformation and then remains more or less constant with
respect to stress. Co-52Al and Co-48Al exhibit different strain-hardening behavior than
Co-50Al. As shown in figure 27, the work hardening exponent is very low for Co-50Al.
In off-stoichiometric Co-Al, this work hardening exponent (0.174) is significantly higher
than that of Co-50A1. Because the observed dislocation densities in off-stoichiometric
Co-Al are lower than in stoichiometric Co-50Al (discussed in 3.2), dislocation interaction
is not likely in this work hardening. Therefore, the difference in yield strength strain-hard-
ening behavior may be related to differences in the mobility of dislocations in these mate-

rials.

Comparison with Wittenburger’s previous compression results [26] for polycrys-
talline Co—Al shows that the true stress levels in single crystal Co-Al are lower than those
in corresponding polycrystalline Co-Al. This may be explained by the fact that the com-
pression axis is a soft orientation for slip in single crystals, while the compression axis
varies between soft and hard orientations in polycrystals. Secondly, deformation in poly-

crystal requires grain boundary compatibility.

A true stress-strain curve for the [001] oriented Co-50Al, compressed at a strain
rate of 2x10'3 sec'l is presented in figure 28, and compared with a curve for [011] oriented

Co-50Al. An interesting deformation phenomenon was noticed in [001] oriented Co-

77
SOAl: the strength drops after yielding and continues until a minimum stress is reached,
beyond which the strength slowly increases. Macrosc0pic examination of the deformed
specimens reveals that they were deformed via kinking and/0r bending. This phenomenon
is known as strain-softenin g. Whether or not strain-softening is followed by strain-hard-
ening depends on the nature of the material. Strain-softening also exists in N iAl
[42,100,101] and has been explained by kinking mechanisms [101]. Strain-softening can
occur irrespective of the prior uniform deformation and is dependent on testing conditions.
Corresponding to the kinking phenomenon, much higher deformation resistance occurs
when the compression axis is parallel to the [001] crystal orientation as compared to the
[011] orientation. This high strength in [001] oriented CoSOAl may be related to the criti-
cal resolved shear stress (CRSS) values for initiation of predominant slip systems and will
be discussed in detail later. In N iAl [99], the difference in yield stress caused by orienta-
tion is significant at temperatures below 700 K, but not obvious at temperatures above 800
K. Since the operative slip systems are <011>{011}/<011>{111} at higher temperatures
and <111>{011}/<111>{112} at lower temperatures in [001] oriented NiAl, it seems that

the CRSS of <011> dislocations may drop more rapidly as the temperature increases.

3.1.2 Mechanical behavior of Co-Al and Ni-Al at room temperature

[011] oriented single crystal Co-SOAl, Co-52Al and Ni-50Al were compressed at
room temperature with the resulting stress-strain curves being given in figure 29. Co-
50Al and Co-52Al crystals displayed completely elastic behavior and fractured at an early
stage of deformation. Co-52Al crystals were more difficult to deform elastically than Co-
50Al, possibly reflecting the effects of stoichiometry shifts on the atomic bonding

strength. Examination by electron microscopy did not reveal any deformation-introduced

78
strength. Examination by electron microscopy did not reveal any deformation-introduced
dislocations, indicating a high CRSS values for the dislocations. In contrast, N i-50Al
crystals have significant compressive plasticity at room temperature and do not fracture
during deformation.
Compression tests were also performed at 673 K and 1000 K. Due to an interface
problem, the computer could not receive the data from MTS. Therefore the mechanical

behaviors under those conditions were not successfully recorded.

3.1.3 Slip trace analysis

Figure 30 illustrates slip lines on the surfaces of a [011] oriented Co-50Al speci-
men deformed at 873 K. Two sets of slip lines intersect each other on the surfaces. The
intersection angle of slip lines depends on surface orientation of single crystal specimen.
If the specimen surfaces are (100) and (011) and the slip planes are (001) and (010), the
two sets of slip lines intersect at 90 degrees on the (100) face and 0 degrees on the (011)
face. If the surfaces are not the (100) and (Oil) planes, the slip traces and intersection
angles can be determined in a simple formula shown in section 2.4

The slip planes corresponding to the slip traces shown in figure 30 were deter-
mined to be (010) and (001) by using a stereographic projection, indicating the existance
of “cube” slip. Figure 31 and figure 32 displays the slip lines on [011] Co-48Al and [011]
Co-52Al deformed at 873 K respectively. Obviously, the slip lines observed on Co-52Al
specimen are less dense than those on Co-50Al, indicating deformation is more difficult
in Co-52Al. This also explains the premature fracture of the specimen during the 1300K

compression. However, the observed slip planes in both Co-48Al and Co-52Al are also

79
(010)/(001), indicating cube slip. This fact suggests that internal friction of the slip sys-
tem plays an important role in Co-Al plastic deformation.

Recording slip traces at 1300 K was not as successful as at 873 K. Due to high
temperature oxidation, the surface slip lines are too faint to be clearly indentified. One
exception is shown in figure 33. The slip traces on [01 l] Co-50Al specimen after 1300 K
compression are faint but still discernible. These slip lines indicate “cube” slip is opera-
tive. This suggests that raising testing temperature does not change the selection of slip

planes.

3.2 Dislocation analysis

Dislocations were introduced during the compression tests under various condi-
tions of temperature, orientation and composition. The Burgers vectors of these disloca-
tions were determined using the g-b=0 analysis method, while the line directions of the
dislocations were determined using trace analysis. In selected cases, these diffraction con-
trast studies were supplemented with dislocation image simulation and matching. The

experimental results are outlined in following sub-sections.

3.2.1 As-grown single crystal Co-50Al

The dislocation densities in the as-grown Co-50Al thin foils are generally very
low. Most of the areas in the foils are dislocation-free and the majority of the dislocations
are observed in a few locations. This indicates that the dislocation distribution is not uni-
form. A typical area containing dislocations is shown in figure 34. The dislocations are

divided into two groups according to line orientations and are marked “a” and “b” respec-

80

tively. The projected line directions of dislocations and the corresponding configurations
vary with the electron beam directions. For example, dislocations “a” are straight under
the beam direction near [TIT] (figure 34a), but they appear curved when the beam direc-
tion is near [lOl] (figure 34b). Therefore the average direction of dislocation lines will be
considered. Since the projected line direction of the dislocations “a” is [020] under the
beam direction [001], [011] under the beam direction [011], and [121] under the beam
direction [1T1], the true average line direction of these dislocations is roughly [010] (see
the sterographic projection diagram in figure 35). However, dislocation “b” is highly
curved and its line direction is not well defined. With the g=(011) (fig. 34c) and g=(020)
(fig. 34d), dislocations “a” are either out of contrast or show weak contrast. Thus the
Burgers vector of these dislocations is b=[100], according to the g'b=0 invisibility crite-
rion. The dislocation labeled “b” is in contrast at g=[101] (fig. 34a), g=[101] (fig. 34b)
and g=(011) (fig. 34c), and out of contrast at g=(020) (fig. 34d), g=(200) (fig. 34c) and
g=(T10) (fig. 34f). Thus the Burgers vector of the dislocation labeled “b” is b=[001].

Because the line direction of dislocations “a” is perpendicular to the corresponding Burg-

ers vector, these dislocations are of edge characters and have slip plane of (001).

3.2.2 [123] oriented Co-50Al deformed at high temperatures

3.2.2.1 [123] Co-50Al deformed at 1300 K

The deformation substructure resulting from deformation at 1300 K was found to
contain a relatively low dislocation density. An example of the structure is shown in
figure 36. Many different types of dislocations were observed, but no dislocation dissoci-

ation or anti-phase boundaries were seen. Generally, the dislocations exist individually

81
and are straight or slightly curved in nature. However, some dislocations appear as junc-
tions among groups of dislocations and some dislocation loops were observed as well.
Three types of dislocations [011], [111] and [100], marked “a”,”b” and “c” respectively in
fig. 36(a) have been analyzed by diffraction contrast and computer simulation experi-
ments. The details of these studies are outlined below.

Figure 36(b and c) show the results of a diffraction contrast analysis of dislocation
type “a”. These dislocations are visible in the (lfi) reflection (fig. 37a), but are weak or
invisible with the (200) (fig. 37b) and (211) reflections (fig. 37c). Thus the dislocations
have the Burgers vector b=[011]. These “a” type of dislocations are observed both as iso-
lated dislocations and in networks. The average dislocation line direction, determined
using trace analysis, is [100]. Thus, these [OIT] dislocations are of edge character. Figure
37 shows an analysis of a dislocation reaction observed in a different foil sectioned from
the same deformed specimen. Two sets of dislocations with different type <100> Burgers
vectors intersect one another, forming a junction dislocation b=[01l] resulting in a
decrease in elastic energy. Similarly, many studies [3,6,25] of dislocations in NiAl have
found the short segments of <011> dislocations arising from the interaction of two gliding
<001> type dislocations in the manner:

[001] + [010] =[01T] ........ (25)
These dislocations are usually considered to be sessile [3,6,25]. But Miracle [l3]
and Dollar [14] have recently reported the occurrence of active <011> slip in MA]. The
observations in the present study cannot rule out the possibility of either active <011> or
inactive <011> slip in CoAl. However, based on the overall low number of <011> dislo-

cations in this material, it is reasonable to conclude that these dislocations contribute to

82
plastic strain on a relatively small scale.
Dislocations of type “b” lie roughly in the direction [423,3] (close to [010]) in

fig. 36a. It was not possible to completely characterize the dislocations labeled “b” using
conventional invisibility criteria. For a fairly anisotropic material such as CoAl, disloca-
tions may display strong residual contrast even though the g°b=0 and g¢bxu=0 conditions
are satisfied. For example, dislocations “b” appear somewhat weak and display dotted
contrast using the (1T0) reflection in fig. 36c. Assuming this condition is near invisibility,
the g°b=0 criteria suggests [111], [111], [110] and [001] as possible slip vectors. Figure
38 contains computed images for these possible Burgers vectors for the diffracting condi-
tions g=(lT0), g=(0ll) and g=(121). The appearance of the dislocation simulations is
described in table 7. The experimental image of the dislocation with g=( 1T0) in figure 38
is characterized with many segments whose orientations deviate from the line direction of
the dislocation. Both b=[l 11] and b=[111] simulations match this feature. However, an
alternative contrast fluctuation along the dislocation line can be observed at the reflection
vector (0T1) in fig. 38. The simulation under this condition shows that only the b=[11 l]
simulation matches the experimental image. When this dislocation was imaged at

=(121), it appers as a long straight line. Again, the simulation for the Burgers vector
[111] is close to the experimental image (fig. 38). Therefore only b=[l 11] consistently
matches the experimental images for different conditions. Because this Burgers vector is
neither parallel nor perpendicular to the line direction, the [111] dislocation is of mixed
character. No evidence of any dislocation networks involving [111] dislocations was
observed. In contrast, dislocation reactions between <1 11> and <100> dislocations are

readily observed in FeAl [10,102,103].

83

Most of the dislocations produced in CoAl deformed in non-<100> orientations
are expected to be <001> dislocations based on the theory of self-energy and relative
mobility [16] as well as the anisotropic elasticity theory [26]. Due to elastic anisotropy,
the dislocations labeled “c” in fig. 36a are only completely out of contrast for one reflec-
tion, g=(01l) in fig. 36c. Therefore images of [100], [011] and [I] 1] and [111] disloca-
tions were simulated at the diffraction conditions g=(OTl), g=(110) and g=(121).
Comparison of these simulations and corresponding experimental images are presented in
fig. 39 and table 8. For example, using the condition g=(0Tl) (fig. 40), the computed
image for the Burgers vector [011] has double image feature, contrary with the experimen-
tal image. For the [T11] Burgers vector, the simulation shows that ends of the four seg-
ments are visually indented while the experimental image does not. At the condition

=(1T0), the simulations for b=[Tl l] and b=[l l l] are significantly different from the
experimental image, while both b=[100] and b=[011] simulations are close to the experi-
mental condition. However, under the two beam condition g=[121], the simulation for

=[011] (as well as b=[Tl 1] and b=[111]) fails to match the experimental image. Hence,
it is reasonable to conclude that the type “c” dislocations have the Burgers vector b=[100].
The line direction of these dislocations, measured using the stereographic analysis, is
[010]. Thus these [100] dislocations are edge in character and the slip plane can be deter-
mined to be (001) from the cross product of the line direction and Burgers vector.

Considering the Schmid factor of 0.21 and 0.25 for [100](001) and [100](011)
respectively under the [123] compression axis, the resolved shear stress for those two slip
systems is very close. With respect to dislocation slip in MA] [26], both <100>{011} and

<100>{001} systems have been observed at low and high temperatures (<0.45Tm and

84
>0.45Tm respectively), indicating the critical resolved shear stress (CRSS) is similar for

both systems. Thus it may be deduced that the CRSS of [100](011) is higher than that of
[100](001) in CoAl deformed at 1300 K. On the other hand, Yancy et al. [35] tried to the-
oretically determine the directional instability of a dislocation in extruded polycrystal
CoAl using an inverse Wulff plot. In the resulting plot, the inverse of the line energy of a
dislocation, is plotted in polar coordinates as a function of the angle between the Burgers
vector and the dislocation line. If dislocations are in a high energy orientation, a zig-
zagged shape should be expected. Yaney’s calculation shows that <100> dislocations on
[011} planes are unstable about both pure edge and screw orientations, whereas <100>
dislocations on {001} planes are unstable only about the screw orientation. This result,
along with present experimental observation that the [100] dislocations do not exhibit the
sharp bends (fig. 36-39), may help to explain why <100>{001} slip dominates the defor-
mation at 1300 K.

Ball and Smallman [37] have predicted the operative slip directions in B2 com-
pounds, based on the dislocation self-energy (E) and mobility parameters (S) using aniso-
tropic elasticity theory. Their calculations for compounds NiAl, Cqur and CsBr are in
good agreement with the slip directions observed in these materials. Drelles [15]
extended the analysis of Ball and Smallman to include CoAl (table 9), showing that <001>
type dislocations have the lowest value for a combination of E and S. The experimental
results of the present study support this approach: [100] slip, which is much easier than
[111] slip and [011] slip, dominates the plastic deformation.

If the data in table 9 are considered, it is expected that <011> slip would be the sec-

ond most likely slip mode to contribute to the plastic deformation. However, in NiAl,

85

where the same would be expected, <1 11> slip has been reported at low temperatures in
[001] oriented crystal [35] while <011> has only been reported to occur at high tempera-
tures [44,104,105,106,107]. Potter [104] suggested that the atomic ordering places restric-
tions on certain slip systems. The operation of <011> slip causes like atoms to become
nearest neighbors at the half slipped position, which increases the total energy of the lat-
tice. Thus, even in [001] MA], [011] slip is less likely to operate. Therefore, in the

present study, it appears that <011> slip is more difficult than <100> slip and <111> slip.

3.2.2.2 [123] Co-50Al deformed at 1000 K

In order to examine the effect of temperature on the selection of slip systems in
single crystal CoAl, additional compression tests were carried out at 1000 K. Trace analy-
sis shows the operation of (001) and (010) cube slip planes. Figure 40a illustrates the dis-
location arrangement in foils sectioned parallel to the (001) slip plane. There exist five
types of dislocations labelled “a” ,”b” ,”c” “d” and “e”. Burgers vectors and line direc-
tions of these dislocations were determined in the same manner as described in 3.2. 1, from
which a three-dimensional distribution of active dislocations was determined (fig. 40b).
Dislocations “a” are [010](001) edge dislocations; dislocations “b” are [100](001) edge
dislocations; dislocations “c” are [001](010) edge dislocations and dislocations “d” are
[100](001) edge dislocations. Dislocation loops lableled “e” were not identified in this
study. This distribution is in good agreement with the slip trace analysis and dislocation
projections onto the micrograph (fig. 40b). At this temperature, only <100>{001} slip
was observed. <111> slip and <011> slip, which was observed in 1300 K, was not found.

This result suggets that the CRSS of <111> slip and <011> slip increase relative to the

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CRSS for <100>{001} slip as the temperature decreases. As it has been reported [15] that
only <111> slip is observed in deformed single crystal CoAl at room temperature, it is
likely that the operative slip systems in CoAl are temperature dependent and a transition

temperature is expected.

3.2.3 [011] Co-Al deformed at elevated temperatures
In this section, dislocations and the corresponding slip systems analyzed in [011]
oriented Co-48, 50 and 52A] deformed at 873 K and 1300 K will be summarized. The

effect of stoichiometry and temperature on selection of slip systems are discussed.

3.2.3.1 [011] Co-Al deformed at 873 K
3.2.3.1.1 Co-50Al

Slip lines are clearly observed on the Co-50Al specimen surfaces after deforma-
tion at 873 K. The operative slip plane determined by the two surface trace analysis corre-
sponds exactly to {100} type slip (fig. 30). Foil sections cut parallel to the { 100} slip
planes exhibited a large number of dislocations (fig. 41a). Three dislocation types exist in
terms of their configurations. Dislocations marked “a” and “b” appear to be lying near
plane of the foil. Dislocations “c” appear as “dots” with line direction is perpendicular to
the foil. Dislocations (“a” and “b”) lie in the same direction and are located in the slip
bands. There are only a few dislocations between slip bands. Both g=(110) and g=(200)
satisfy the g-b=0 invisibility criterion for dislocations “a” (fig. 41b c) and hence b=[001]
is the Burgers vector. Unlike dislocations “a”, dislocations “b” do not lose contrast at

g=(110) (fig. 43b). Instead they only have weak contrast (near invisibility) at g=(101) (fig.

87
41d) and disappear at g=(200) (fig. 4 la). Therefore the Burgers vector of dislocations “b”
is [010]. Line direction analysis reveals that both dislocations “a” and “b” to be [100].
Because the Burgers vectors of these dislocations are perpendicular to their line direction,
both dislocations “a” and “b” are edge dislocations. This helps to explain the limited
invisibility. Both disloctions “a” and “b” display minimum visibility when g=u satisfying
the g'b=0 and g°bxu=0 criterion for edge dislocations. The end-on dislocations “c” are
analyzed in the same manner as mentioned above. These end-on dislocations are weak
with g=(110) and g=(200) (fig. 41b,c). Therefore, the corresponding Burgers vector of the
end-on dislocations is [001]. The line direction of these end-on dislocations is [010], indi-
cating edge character. Figure 42 is a schematic showing the three-dimensional distribu-
tion of the dislocations in the thin foils (end-on dislocations and dislocation loops are not
included in this drawing).

Dislocation reaction and interaction were not observed under this deformation

temperature.

3.2.3.1.2 Co-52Al

Figure 33 shows the surface slip traces on Co-52Al deformed at 873 K. These slip
lines are less dense than observed for Co-50Al, indicative of the difficulties in plastic
deformation of Co-52Al. However, as in Co-50Al, the active slip planes in Co-52Al are
{001} type-

The dislocation distribution in Co-52Al is similar to that in Co-50Al. Figure 43(a)
shows two types of dislocations labeled “a” and “b”. The Burgers vector analysis was per-

formed as follows. When (200) is the operative reflecting vector (fig. 42b), both disloca-

88

tion types are in poor contrast, while dislocations “a” are out of contrast at g=(l01) (fig.
430) and dislocations “b” disappear at g=(110) (fig. 43d). Therefore, the Burger’s vectors
of the dislocations are b=[010] and b=[001] for dislocations “a” and “b” respectively.
Trace analysis indicates both of these dislocations have the average line direction of
u=[100], thus both dislocations “a” and “b” are of edge character. In addition to the dislo-
cations inclined in the thin foil, a limited number of dislocation loops and the end-on dis-
locations are also observed. For the reflection planes (200) and (110), some of the loops
and end-on dislocations lose their contrast, defining the Burgers vector to be b=[001],
indicative of edge nature of end-on dislocations with respect to their line direction of

[010]. Dislocation reactions or interactions were not found in this foil.

3.2.3.2 [011] Co-Al alloys deformed at 1300 K

In order to examine the core structures of the dislocations generated by deforma-
tion at 1300 K, it is necessary to first perform a TEM substructure analysis. Unfortunately,
due to the higher temperature, surface oxidation of the deformed specimens made it
extremely difficult to identify the activated slip planes. Hence, no “slip plane” parallel
sections could be made. However, sections perpendicular to the deformation axis were
taken so that g0b=0 analysis could be performed. These sections were not as convenient

but still produced foils that allowed a substructure analysis to be performed.

3.2.3.2.] [011] oriented Co-SOAI
On the oxidized surfaces of the Co-50Al deformed in the [011] orientation, slip

lines were faint but still discernible and featured cube slip of (010)/(001) (fig. 34). Figure

89

44 shows a typical dislocation structure observed from this material. The structure was
generally characterized by <100> dislocations. However, the other dislocations were also
observed. In the example shown in figure 44, four types have been analyzed. Figure
44(a)-(d) show detailed examples. The dislocations labeled “a” are invisible with g=(200)
and g=( 1T0) (fig. 443,b) and therefore have a Burgers vector of [001]. The average line
direction of dislocations “a” is [100]; hence these dislocations are edge in character. Dis-
locations “b” are out of contrast at g=(200) and g=( 101) (fig. 44a, c), and therefore have 3
Burgers vector of [010]. Dislocations “c” are out of constrast only at g=(Oll). The cor-
responding Burgers vector has the possibilities of [100], [111] and [011]. Regarding to the
slip plane (001) and dislocation line direction [010] of these dislocations, the “c” type of
dislocations most likely have [100] Burgers with edge character. The dislocation loops
labeled “d” have prismatic shape. The parallel borders of these loops are invisible or in
weak contrast at g=(200) and g=(0Tl) respectively, resulting in [011] Burgers vectors and
edge character (fig. 44). The reason why no operative g vectors can make the loops com-
pletely disapper can be given by the g-bxu=0 criteria. These loops have line directions of
[100] and [0T1] (fig. 44). Only those g-vectors whose direction is perpendicular to Burg-
ers vector and is parallel to the line direction, can make dislocation completely out of con-
trast. The [011] edge loops may be generated by vacancy disc collapse.

Dislocation reactions were also observed at this foil. At the positions labeled R
and Q, the short junctions of dislocations were determined to be [fil] Burgers vector

because these dislocations disappears at both g=(1l0) (fig. 44b) and g=[101] (fig. 44c).

This dislocation reaction have three possibilities.

90

[HI] = [100] + [0T0] + [001] decomposition ......... (26)
[100] + [010] + [001] = [T11] interaction ......... (27)
[100] + [Oil] 2 [1T1] interaction ......... (28)

<1 1 l> dislocation discomposition is less likely because it would cause the elastic
energy of the dislocations to increase at least according to isotropic linear elasticity. The
other reason is that at the temperature of 873 K, only <100> type of dislocations were
observed. It is reasonable to believe that higher temperature increases the interaction
opportunities for thermally activated <100> dislocations. On the other hand, dislocation
interaction between <100> dislocations and/or between <100> dislocations and <011>
dislocations are both energetically favorable. This result is in agreement with the obser-
vation of <111> dislocations in [123] Co-50Al deformed at 1300 K (section 3.2.2.1).
However, the [123] orientation resulted in free <111> dislocations, while [011] orientation

resulted in sessile <111> node dislocations.

3.2.3.2.2 [011] oriented Co-48Al

The dislocation density in [011] Co-48Al deformed at 1300 K is visually lower
than that in Co-50Al deformed under the same conditions. An example of this is shown in
figure 45. Dislocations labeled “a” are lying roughly in the [200] direction; dislocations
“b” are aligned in the [020] direction. Here dislocations “a” have a [010] Burgers vector
due to the invisibility with g=(101) and g=(200) (fig. 45 a,b). Dislocations “b” are invisi-
ble at g=(01T) and g=(020) (fig. 45 c,d), and therefore their Burgers vector is defined as
[100]. Therefore dislocations “a” and “b”are all edge in character.

In addition to the <100> dislocations, there are many dislocation reactions in Co-

91
48A] than Co-50Al. The dislocation reactions in Co-48Al featured by forked disloca-
tions. A dislocation fork with the branch labeled u,v and w is analysed in figure 45.
Branch u is almost out of contrast at g=(200) (fig. 45b) and in weak contrast at g=(020)
(fig. 45d), indicating b=[001]. Branch v is invisible at g=(101) (fig. 48a), indicating
=[010]. Branch w is in weak contrast at g=(200) (fig. 45b) and g=(01l) (fig. 45c), indi-
cating b=[011]. Therefore the dislocation reaction is formulated.
[010]+[001]=[011] ......... (29)
This <100> dislocation interaction is also energetically favorable according to lin-
ear elasticity. However, [011] dislocation is less mobile than <100> dislocations. They
may inhibit the glide motion of <100> dislocations. Thus the deformation structure may

be indicative of a balance bwtween glide and lowering the dislocation energy.

323.23 [011] oriented Co-52Al

The observed dislocation density in [011] oriented Co-52Al (deformed at 1300 K)
visually is the lowest of three compositions investigated in this study. Deformation of Co-
52Al generated two types of dislocations, as shown in figure 46a. The first type, labeled
“a” in figure 46 may be the [001] dislocations which are invisible at g= (200) (fig. 463)
and in contrast at g=(002) and g=(10l)(fig. 46 b and (1). Figure 46b and 46c shows that
dislocations “b” are out of contrast at g=(002) and g=(011), therefore having a Burgers
vector of [100]. Because dislocations “a” have the approximately projected line direction
[200] under the beam direction [010], and [200] under the beam direction [011], indicat-
ing the line directioin u=[100]; Dislocations “b” have the projected line direction of [002]

under the beam direction [010], and [0T1] under the beam direction [011], indicating

92

[010] line direction. Hence, both dislocations “a” and dislocations “b” are of edge char-
acter. In figure 46, some dislocations have the same line direction as dislocations “a”, but
have different contrast. They may have different Burgers vectors. Unfortunately, the
Burgers vector can not be determined using the existing g-vectors.

In figure 46a-d, there appears to be a dislocation reaction at the position labeled
R. However, when the foil was tilted, two complete dislocations were observed (fig. 46e
and f). Therefore the “interaction” in position R, is only the image of of two dislocations
contacting each other. Because the nobs of these dislocations do not move when the foil
was tilted, the dislocations may intersect and lock each other. The gap pointed in fig. 46f
is due to the local contrast change which results from the strain field compensation
between two dislocation perpendicular to each other. Lack of dislocation interaction in

Co-52A] may be due to the low density of <100> dislocations.

3.2.4 [001] Co-Al deformed at high temperatures
3.2.4.1 Dislocation structures in [001] oriented Co-50Al

As shown in section 2.1, [001] Co-SOAI has a much higher compressive strength
than the [011] Co-SOA] (figure 28) and the former also displays a kinking phenomena. In
general, kinking is a process which happens when normal plastic deformation is difficult
due to . Due to the high temperature oxidation, slip lines could not be readily observed on
these samples. Dislocations observed in [001] oriented CoSOAl foils are distributed uni-
formly and are in good contrast at g=(TOT) (fig. 47a). However, the observed dislocations
“a” in the area of view are in extremely poor contrast at g=(020) and g=(OIT) (figure 47b,

c); the others marked “b” disappear at g=(200) (figure 47d) and are in weak contrast at

93

g=(020) (fig. 47b); dislocations “c” are out of contrast at g=(TOT) (fig. 47a) and g=(200)
(fig. 47d). Hence the dislocations “a” have a [100] Burgers vector; dislocations “b” have a
[001] Burgers vector; and dislocations “c” [010] Burgers vector.

Because the dislocations have the projected line direction of [020] for dislocations
“a”, [200] for dislocations “b” and [1—10] for dislocations “c” under the [001] beam direc-
tion; [020] for dislocations “a”, [101] for dislocations “b” and [121] for dislocations “c”
under [T01] beam direction; [011] for dislocations “a”, [200] for dislocations “b” and
[211] for dislocations “c” under [0T1] beam direction, the average line directions of the
dislocations are [010] for dislocations “a”, [100] for dislocation “b” and [101] for disloca-
tions “c”. Therefore, dislocations “a”, “b” and “c” are all of edge character.

A question might be raised after the Burgers vector analysis: why are <001> dislo—
cations activated under zero resolved shear stress (the Schmid factor is zero for
<100>{001} system under <010> stress orientation)? To investigate further, more foils
were examined. Figure 48 is a typical example.

The majority of the deformation structure is composed of three sets of dislocations
lying roughly perpendicular to each other (fig. 48a). Dislocations labeled “a” have the
projected line direction of [110] under the [001] beam direction, [211] under the [111]
beam direction and [Til] under the [011] beam direction. Therefore, the dislocation line
direction is [1 1T]. Dislocations “b” have the projected line direction of [0T1] under the
[001] beam direction, [1T2] under the [T11] beam direction and [1T1] under [011] beam
direction, indicating that [1T1] is the true direction of these dislocation lines. Dislocations

“c” have roughly the same line direction as the dislocations “a”. Dislocations a are out

of contrast at reflection vector g=(01T) (fig. 48b) and are in weak contrast at g=(200) (fig.

94

48b), defining their Burgers vector as [011], while the dislocations labeled “b” disappear
at both g=(101) and g=(020) (fig.48d and e), and therefore have a [T01] Burgers vector.
Dislocations “c” disappear at g=(101) and are in weak contrast at g=(OlT) and g=(1—I0).
Their corresponding Burgers vector is b=[T1 1]. Since the burgers vectors of both “a” and
“b” dislocations are perpendicular to the corresponding line directions, these dislocations
are of edge character and glide on (21I) and (121) plane respectively.

Substantial evidence of dislocation reactions were found in this foil. The disloca-
tions labeled “c” are involved in typical examples. One of the interacted dislocations
which is labeled “f” is determined as [T00] dislocation because it is invisible at g=(01T)
(fig. 48b) and g=(020) (fig. 48c). Unfortunately, rest of the interacted dislocations can not
be indentified using the existing g-vectors. Therefore, the reaction shown in figure 48 is a

<111> -related dislocation interaction. Three possible reactions are listed below:

[711] = [T00] + [011] .......... (30)
['1‘11]=[T00] +[010] +[001] .......... (31)
[T00] + [011] = [T11] .......... (32)

The first two reactions are dissociations of <111> dislocations. Although these
seem unfavorable in term of dislocation elastic energy, the dissociation may occur under
certain conditions. One of conditions is the anisotropic nature of B2 materials, such as
CoAl and MA]. It was reported that <1 1 1> dislocations decomposed into three <100> in
MA] extruded at 1505 K [40]. The other condition is that lack of plasticity in [001] CoAl
increases strain energy in the material. Decomposition of <111> dislocations will release
the strain energy because <100> dislocations are more mobile than <111> dislocations.

When the decrease in strain energy is larger than the increase in dislocation elastic energy,

95

the <111> decomposition occurs simultaneously.

Interaction between <110> dislocations and <001> dislocations are also possible
because this interaction is energetically favorable.

The above mentioned analysis shows that in the [001] orientation, single crystal
Co—50Al is deformed under compression stress via <011>{211} slip. Since the activation
of this slip system is much more difficult than that of the <100>{001} system, the com-
pressive stress is very high (fig. 28). As the deformation continues, the slip planes are
rotated toward the [001] orientation. This reduces the resolved shear stress on the active
slip system <011>{211} and further deformation becomes harder and harder until the
kinking of the specimen occurs. Kinking changes the orientation of the single crystal
locally and the <100>{001} slip systems are then favored. Therefore after kinking, the

<100>{001} slip as well as <010>{ 101 } slip dominates the deformation process.

Summary

In Co-Al system, <100>, <110> and <111> type dislocations are all generated,
depending on temperature and orientation. Alloy stoichiometry does not have much influ-
ence on the selection of slip systems. Above 873 K, no matter what orientation is chosen,
<100> slip dominates the deformation. However, a large number of non-<100> disloca-
tions were also observed. <111> and <110> dislocations were observed in Co-50Al and
Co-48Al deformed at 1300 K as the reaction products of <100> type dislocations. In
[001] oriented Co-50Al, <110> dislocations dominate the deformation before kinking,
while <100> dislocations dominate the deformation after kining. Therefore <100> dislo-

cations play the most important role in the high temperature deformation of Co-Al single

96

crystals. Understanding core structures of dislocations is the key step to understand the
dislocation behavior in Co—Al aluminides. The HREM results are presented in subsequent

sections.

3.3 Core structures of <010> edge dislocations

For the most part, Burgers vector analysis was performed on the thin foils sec-
tioned parallel to the observed slip planes and revealed the active slip systems in high tem-
perature deformation. In order to elucidate the strength and ductility of B2 Co-Al alloys
at a deeper level, it is necessary to examine core structures of dislocations. To do this, one
has to view a dislocation along its line direction. To this end, foils for HREM were sec-
tioned perpendicular to the dislocation line directions and the resulting “end-on” disloca-
tions were investigated. Since the plastic deformation was limited to about 5% in this
study to avoid possible dislocation intersection, the dislocation density in thin foils is rela-
tively low. Additionally, in order to achieve usable lattice images, it is necessary to work
at magnification in excess of 600,000 x. At these enlargements, the relative spacing of lat-
tice positions becomes discemable. Often poor contrast under the many-beam image-
forrning condition can result in extreme difficulty in locating and identifing the end-on dis-

locations.

3.3.l Co-50Al
Figure 49a is a HREM image of a [010](001) edge dislocation core in Co-50Al
projected in the [100] direction. It is a white atom image, meaning the white spots repre-

sent lattice locations. The B2 ordering characteristics (ordered bcc) are clearly seen in fig-

97
ure 49a. It is impossible to differentiate Co from Al lattice positions in this picture.
However, the comer atoms in the “apparent" fcc square lattice (projected images of B2
structures in the [100] direction) is arbitrarily assigned reliably as cobalt and the central
one as aluminium. Though the overall resolution is very good, there exists a darker area
very near the core center. This may be caused by a weaker exposure dose that is related to
diffraction changes associated with the local strain field. A Burgers circuit around the dis-
location core is illustrated and the closure failure of the circuit gives the Burgers vector
[010]. This matches the results of the dislocation analysis on deformed Co-50Al in the
previous section. The lattice distortion in a dislocation core is more clearly seen by
observing the image from different orientations. This inspection is usually performed in

the [001] direction (front view), [010] direction (side view), [011] and [0T1] directions

(450 view) using either perspective or compressive viewing methods. In the perspective
method, the scanned image is tilted 70-80 degrees, while in the compressive methods, the
scanned image is squeezed to 1/3 of its original size so that small displacements are mag-

nified. In order to observe the extra half planes more clearly, the HREM image was

scanned into a TIFF file format and tilted 75° using the “TILTER” program to produce a
perspective view. The core is characterized by two extra half planes (one is the Co atom
plane and the other is the Al atom plane) in figure 49b. The two extra half planes that are
indicated by arrows in fig. 49b, terminate on (001) planes, and the atoms rows on these

planes are continuous in the core center (fig. 49c). A single extra half plane terminates at

the point on A, while second plane, 900 away, terminates on B (fig. 49d and e). Because
the points A and B are adjacent each other, this core has a compact nature. Correspond-

ingly, the (001) plane is the slip plane of this [010] edge dislocation.

98

Figure 50a is another example of a core in Co-SOAI. In the front view (fig. 50b),
the two extra half planes terminate at positions aduacent to one another, a feature consis-
tant with a compact core. However, when the core is examined in the [0T1] direction (fig.
50c), a single extra half plane is found at the position “A”: when the core is examined in
the [011] direction (fig. 50d), a single extra half plane is found at the position “B”. Obvi—
ously the position “A” does not coincide with the position “”.B This indicates the exist-
ence of a finite dissociation in the dislocation core. After exposure under high energy
electron beams for additional four minutes, the core structure was recorded and is dis-
played in figure 51. The core structure looks unchanged in the front view (figure 51b).

However, the distance between the two termination locations of the extra half planes in the

450 views is almost coincident now (fig. 51c and d), showing that the dissociation width is
decreased after energy input. Comparison of two subsequent images of the same disloca-
tion core indicates that core dissociation is a metastable state and it is transferred to a com-
plete edge dislocation under the assistance of external energy.

Based on the above two examples, one can conclude that in Co-50Al, atoms in the
core region are rearranged under the beams and the rearrangment results in a complete

compact core.

3.3.2 Co-48Al

A dislocation core structure in deformed Co-48Al is shown in Figure 52. The clo-
sure failure of the Burgers circuit (fig. 52a) confirms the [010] edge character of this dislo-
cation. This dislocation was considered an active dislocation by dislocation analysis in

the 1300 K compression deformation experiment discussed in a previous section 3.2.3.2.2.

99
Unlike <100> cores in Co—50Al which always have compact appearance in the
front view, the atomic arrangement in this core structure is more complicated (fig. 52b).
Although the atom rows parallel to the (010) planes are well aligned and continuous in the
side view (fig. 52c), the atom columns have slightly more distortion in Co—48Al than in
Co-50Al. However, instead of being a compact core, the extra half Co plane is separated
from the extra Al plane by a finite distance in the front view (fig. 52a). However, it is dif-

ficult to locate these extra half planes in the [100] view direction. The single extra half

planes are more easily observed in the 450 directions. In this case, one single extra half
plane terminates at point “A” in the [0T1] perspective (fig. 52c) and the other extra half
plane terminates at point “B” in the [011] perspective (fig. 52d). The distance between
“A” and “B” is a three atom spacings, i.e, 3x0.286=0.858 nm. This dissociation width is
less than the resolution of weak beam TEM and therefore this dissociation cannot be
determined via diffraction contrast transmission electron microscopy. Two separate Burg-
ers circuits are built around the two extra half planes, indicating the possible partial dislo-
cations 1/2[011] and 1/2[01T], or 1/2[T11] and 1/2[11T] respectively (fig. 52 f). Because
the l/2<110> is not an atom to atom translation, the 1/2<111> is regarded as the superpar-
tial dislocations. Because the l/2<111> superpartial dislocations may have screw compo-
nents which cannot be obsvered via HREM, the dislocation nature (edge, screw or mix)
cannot be determined by the displacement observed on HREM micrograph. Therefore it

is more likely that a [010] edge dislocation core is dissociated into two 1/2<111> partial

dislocation cores.

(010)—->%(Ill)+APB+%(lll) ......... (33)

Since the dissociation direction is [010], perpendicular to the slip plane, this type

100
of dissociation is also termed climb dissociation. After dissociation. the [010] edge core
can not glide on the (001) plane because the slip planes of partial dislocations are not
(001) planes. Therefore, atom reorganization may be required before the core moves

under the applied stress.

3.3.3 Co-52Al

Co-52Al specimens have the highest compression strength and the lowest
observed dislocation density among the Co-Al alloys studied. Core structures of this
material are given special attention.

Figure 53a is an example of a dislocation core observed in a Co-52Al thin foil.
Generally, the atom arrangement recorded had good resolution except for the left side of
the core, here the point resolution is reduced to line resolution because of beam damage,
twisting or strain.

A Burgers circuit was constructed around the core center and the resulting [0'10]
displacement vector matches the Burgers vector analysis results in section 3.2.3.2.3.
Viewing along the [010] direction (fig. 53b), the atom rows are found to be distorted more
significantly than those in either Co-50Al or Co-48Al (fig. 49-52). The atom columns are
well aligned in area away from the core center, while they are highly distorted near the

core center. The extra half planes are difficult to identify in the front view because of

image contrast fluctuation. Therefore it is necessary to use 45° views to completely char-
acterize the core. In the [011] directions, one single half plane is found at position
“A”(fig. 53c) and the other single extra half plane is terminated at position “B” (fig. 53d).

Position “A” and “B” represent the locations of two partial dislocations of this core in the

101

front view, and the distance between “”A and ““B is the width of the dissociation band and
is equal to 4-5 atom spacings (1.144-1.430 nm). Similar to the climb dissociation

observed in Co-48Al, the dissociation in Co-52Al occurs on the plane which is perpendic-
ular to the slip plane. This means that the core is climb dissociated. Figure 54 is a HREM

image of the same core structure taken after two minutes of beam exposure. With the help

of 45° views, the Co atom extra half plane is found to terminate at point “A” (fig. 54b) and
the Al atom extra half plane is found to terminate at point “B” (fig. 54c). Obviously the
distance of “A” and “B” (14 atom spacing or 4.004 nm) is larger than that in figure 53a
(1.144 nm). This means that energy input (high voltage electron beams) can assist in the
development of climb dissociation and illustrates the need to be aware of anti-defacts.
Since the dissociation plane is not on the original slip plane (001), the climb dissociation
is non-planar. Figure 54d schematically represents two separated Burgers circuits around
“A” and “B” (fig. 54d), giving the Burgers vector of the partial dislocations 1/2[11T] and

1/2[T1 1] (eq. 34).
[010]=%[111]+APB+%[111] ......... (34)

Climb dissociation is a vacancy-related thermal activated process. In off-stoichio-
metric Co-Al alloys, there exists high concentrations of vacancies and anti-lattice defects
[118,119]. This high concentration of point defects may promote the core transformation
and dissociation via diffusion.

Figure 55 is another example of a dislocation core structure in Co-52Al. This core
also has 3 Burgers vector of [010] (fig. 55a). Viewing along <011> direction, single extra

half planes are found to terminate at the positions “A” and “B” (fig. 55d and e) respec-

102
tively. When “A” and B are marked in the experimental photo (fig. 55a). the core is
found to be climb dissociated at a distance of four atom spacings (1.14 nm). Its (001)
planes are more highly bent near the core center than in any other cores displayed thus far
(figure 55c). Thus when core motion is needed, atoms on the (001) planes will have to
follow a wavy path which combines glide and climb. This mode requires more energy

than the pure glide mode in both Co-50Al and Co-48Al.

The core width is usually defined by the displacement range —2 < w < Z on its co—

sponding slip plane [129]. Currently, precise measurement of core width is difficult
because individual atom coordinates can not be precisely determined via digitization. The
main problems are non—uniform illumination and irregular atom images. The core width
of the dislocation shown in figure 55a is visually smaller than any of the other cores dis-
played in this chapter; the (010) planes are severely distorted in the narrow region
(-Zao~+2ao) (see fig. 55b). Abrupt changes of orientation of (010) planes result in high
stress concentrations in local areas and strongly scatters incoming electrons, resulting in
darker contrast.

In addition to climb dissociated cores, a different type of core configuration is also
observed in Co-52Al. The core structure shown in figure 56a is neither simply climb dis-
sociated nor glide dissociated. Separation between the extra half plane of Cobalt atoms
and Aluminum atoms is three atom spacings in the [010] direction and two atom spacings
in the [001] direction. This combination of glide dissociation and climb dislocation is
referred to as mixed dissociation. Movement of a dislocation with a mixed core structure

needs a larger driving force than that required for either pure glide dissociation or pure

103
climb dissociation. Observing the core in the side view (fig. 56b). the slip planes are found
to be discontinuous. Corresponding to points ““E and ““,F extra half planes are observed
in the [010] direction. Since the two extra half planes have opposite sign. no net displace-
ment is produced. Figure 57 is the schematic drawing of the dislocation dissociation.
This kind of core is unusual and its relationship to deformation remains unclear. This core
may be immobile.
Summary:

The previous sections compared and discussed the core structures of <010> edge
dislocations investigated in the various compositions of CoAl. Generally speaking, dislo-
cations in stoichiometric Co-50Al have the simplest core structure, while non-stoichio-
metric compositions Co-48A1 and Co-52Al introduce more complicated core
configurations. Climb dissociation of dislocation cores is found in both Co-48Al and Co-
52Al. Mixed dissociation of [010] cores is observed in Co—52Al. The non planar nature
of these cores retards activation and/or movement of <100> dislocations. Since <100>
edge dislocations dominate the high temperature deformation in Co—Al alloys, these core
structure play the key role in controlling the mechanical behavior of these materials.

As seen in the HREM micrographs, the appearance of the dislocation core images
is affected by various electron optic and specimen conditions, such as defocus value, foil
thickness, specimen tilt, astigmatism, spherical aberration and beam damage. Addition-
ally, the core images presented are [100] projections of real crystal defects. In other
words, different dislocations, such as <110>, could appear as those observed. Hence,

computer simulation of these cores must be perfomed to accurately qualify the HREM

observations.

104

3.4 HREM Image Simulation Of Core Structures

A critical issue in HREM is how to interpret the experimental images. It is well
established that images can be misleading. i.e. they may not be readily interpretable in a
simple fashion. Thus it is necessary to compare experimental images with calculated
images in order to interpret the results. All of the simulated images in the following sec-
tions are based on EAM models from Farkas and calculated by the multislice method

using the full non-linear image calculation of Stalemann’s EMS software.

3.4.1 Simulation of core structures for Co-Al system
3.4.1.] <010>{001} edge dislocation

For the binary system Co-Al, only <100> edge dislocations have been modeled.
Figure 57(a) shows a typical image simulation of a <100>{001) edge dislocation core.
This core has a compact structure: it is neither dissociated nor decomposed. Two extra
half planes (one Co and the other A1) terminate at the core center. Using the “co” subrou-
tine of EMS, the atom positions (Al small dots and Co large dots) of the supercell have
been superimposed onto the HREM image simulation (fig. 57b). The extra aluminium
half plane extends lower than the extra nickel half plane by an amount of 3?- of the lat-
tice parameter. It should also be possible to construct a core in which the Co half plane
extends lower. The lattice distortion parallel to the slip plane is more significant than per—
pendicular to Burgers vector. Viewing in the <011> directions, single extra half planes

and corresponding lattice distortion are observed. The two single half planes in the two

<011> directions terminate at the point which coincides with the bottom of the two extra

105
half planes in the front view ([100] direction). This feature illustrates the compact nature
of this core. Figure 57 visually match well with the experimental observations and char-
acterize the main features of the core structure of the [010](001) edge dislocations (fig.
49).

Because the HREM image characteristics can be affected by factors such as foil
thickness, defocus and other microscope and sample parameters, it is necessary to exam-
ine the effect of these variables on the simulations. These effects are illustrated in the fol-
lowing paragraphs.

Figure 58 shows a through focal series of image simulations for the <100>{001 }
edge dislocation in a Co-50Al crystal 3.3 nm in thickness. The defocus ranges from -40
nm to -95 nm with steps of 5 nm. The details of the image change significantly as the
defocus changes. The image contrast is too weak and difficult to seeat df=-4O am. From
df=-50 nm to df=-55 nm, both atom types display essentually the same brightness, while
from -65 nm to -80 run, one atom type is weaker than the other. The approximate atom
positions are represented by white or bright contrast (white atom images) for defocus val-
ues imaging from -60 nm to —80 nm. Conversely, for defocus values less than ~85 nm and
greater than -60 nm, the atoms are dark, and the tunnels between the atom columns appear
as bright apots (white tunnel images). That is, there are contrast reversals at -60 nm and -
85 nm for this thickness. These reversals will occur at different defocus values for differ-

ent specimen thickness.

Figure 59 shows the effect of thickness on image details. The crystal thickness
increases from 1.1 nm by 1.1 nm steps with a constant defocus value of -70 nm. In very

thin areas, both Co atoms and A1 atoms are clearly observed (white atom image), with Al

106
atoms displaying lower intensity than Co atoms. As the thickness increases, the intensity
of the Al atom columns become weaker. This is to say. a regular lattice image becomes a
superlattice image as the thickness increases. In the present case, a bcc or bcc-based B2
structure image degenerates into a simple cubic lattice structure image. Thus, the image

analysis can be misleading if thickness effects are ignored. To further complicate the

analysis, some Al atoms in the central core region become visible again as the thickness
nears 10.2 nm (this figure is not included in figure 59). Therefore, both experiment and
simulation should avoid thick crystals. In addition, the thickness effect varies with defo-
cus value. Under the condition df=-60 nm (figure 60), two Co atoms at the dislocation
center display lower intensities than the surrounding Co atoms in the thin crystal, and
these atoms are completely out of contrast for thicknesses greater than 3.3 nm, forming a

dark hole.

Temperature also affects HREM and must be considered when simulating images.
The Debye-Waller factor is a measurement of the thermal vibration of an atom and is a
function of temperature. A large Debye-Waller factor means that atoms strongly scatter
the incoming electrons and thus affects the images. Reference [111] provides the Debye-
Waller factors for all the elements at three specific temperatures. The D-W factors of Co,

Ni, Fe and A] are listed in table 10.

Based on table 10, aluminium atoms have the largest Debye-Waller factor
(nearly 2 times as large as the other elements). This may explain why the Al atoms
look dim to some degree in simulations and in experimental observations. The Debye-
Waller factors increase with temperature increases. Temperature effect was studied

through simulation using different D-W factors and the results are presented in fig. 61.

107
The image intensity of Al atoms is too weak to be seen in fig.61(c). which corresponds
to the temperature at which the microscopy was performed. This is contrary to the
experimental images which clearly resolve the Al atom columns in the microscope. It
seems that the temperature effect on experimental images is not as large as predicted
by simulation. That is, the experimental images reveals clearly resolved A1 and Co

columns at room temperature.

3.4.1.2 <010>{0fi} edge dislocation

The [100](01T) edge dislocation simulated in the present work is coordinated in a
[100]-[01T]-[011] system (fig. 62). The line direction of this dislocation is [011] and the
slip plane is (OIT). Since the so-defined lattice has a repeat length of 0.4054 nm in the
multi-slice direction (Z direction), there is a potential that a large slice thickness may
introduce errors in FFT calculations. Stalemann recommends [112] a slice thickness of 0.2
nm for light atoms, while a slice of thickness of 0.05 nm is preferable for heavy atoms (i.e.
periodic table mass). The supercell with the [100](01T) dislocation was cut into two sub-
slices (fig. 63). The wave functions were then calculated using the multislice program plus
a script program that alternatively serves individual subslice data files one at a time to the
multislice program. A typical simulation of an [100](01T) core is presented in figure 64.
The core only shows its superlattice structure because the projected distance between Co
and Al atoms in the <011> direction is smaller than the microscope resolution. Therefore,

experimental studies of [100](01T) cores are limited by current microscope technology.

108

3.4.2 Simulation of core structures in the N i-Al system
3.4.2.1 <010>{001} edge dislocations

Figure 65a shows a simulated core structure of an [010](001) edge dislocation in
Ni-50Al. This simulation matches the main features of the experimental observation of
Crimp, Tonn and Zhang [1 16] for the [010](001) core structure. However, the significant
lattice distortion in the direction of Burgers vector on the experimental image [116] is not
reflected in the simulation. This indicates that many factors that may affect the core struc-
ture, such as surface effects, may not be accounted for in the simulations. On the other
hand, the core simulation is visually identical to the simulation of the Co-50Al core with
the same Burgers vector. Superposition of the CoAl supercell (dots) onto the NiAl simula-
tion shows a perfect match (fig. 65b). Since the mechanical properties are significantly
different between CoAl and NiAl and the observed experimental core structures are also
dissimilar to each other, it appears that the potentials or modelling techniques used do not
satisfactorily reflect the differences in atomic bonding beween either Co-Al atoms or Ni-

Al atoms.

Off-stoichiometric compositions can be formed by either anti-site defects (for
example nickel atoms replace aluminum atoms, or visa versa) or vacancies. The anti-site
situations can be further divided: local chemical composition change (one atom type
replace the other at the core center) or random anti-sites (atom type replacement on ran-

dom sites) . The following simulations test these conditions individually.

A model core structure with a local chemical change N i-anti site defect is shown in
figure 66a. To reveal the atom arrangement at different layers in one unit cell, a viewing

direction of [l l 20] has been chosen. This is a slight deviation from [001] direction. An

l ()9

aluminum atom is replaced in the lower level by a nickel atom and therefore the local
chemical composition is Ni-rich. In a multislice image simulation, the Ni-anti-site defect
will be repeated in each slice. resulting in Ni enrichment along the entire dislocation line.
A simulated HREM image corresponding to this model is displayed in figure 66b. The
core structure has the same features as the core in figure 66a though the aluminum column
with nickel substitutions appears brighter than the other columns. Therefore except slight
intensity changes, the local atom replacement does not affect the core configuration to any
noticeable degree. Neither do Al-rich anti—site defects (fig. 67a). The possibility of an Al
atom exchanging position with a Ni atom at the core is illustrated in figure 68. Although
the local chemical composition does not change, the bonding condition is changed
locally. However, the element exchange does not affect the core configuration to any

noticeable degree.

It is well known that vacancies can significantly affect dislocation behavior in
crystals. The situation considered in figure 69(a) is that two nickel atoms are missing
leaving two vacancies instead. This results in an Al-rich structure. The corresponding
image simulation is shown in figure 69(b). Right in the core center, the image contrast at
the two nickel atom positions is less than that at the regular nickel atom positions. This is
because there is only one nickel layer at these positions and electrons are strongly scat-
tered by the non-periodical potential field around the two vacancies. Except for the local
contrast change, the right-in-core vacancies do not change the core structure and lattice

distortion.

In non-stoichiometric alloys, it may be a more energetically favorable situation if

the atoms being substituted for are not limited to the core center but occur randomly.

110

Ni48Al can be regarded as 2% Al randomly replaced by Ni (fig. 70'). To describe the
replacement in three-dimensional space, a large supercell file was constructed. In the z-
direction, there are five layers and the atom arrangement on each layer is displayed in fig—
ures 70(a) through figure 70(e). Each layer defines one supercell and the stacking of
supercells were processed by the multislice program. The simulation result (fig. 70f) indi-
cates no significant changes in core structure occur. Figure 71 shows the result from
another random distribution of excess Ni atoms. Figure 72 shows simulations for Ni-
52Al with two differenct distributions of excess aluminum atoms. Again, no significant
changes in core structure are revealed. Similarly, atom exchange of Ni and Al atoms at
random positions does not affect the core structure of a dislocation (fig. 73). None of the
calculations for off-stoichiometric compositions are able to explain the fact that significant
changes in core structure with composition changes are observed experimently. Crimp,
Tonn and Zhang [116] found significant distotions both parallel and perpendicular to
Burgers vector in Ni-48Al. Additionally, the results presented in the present study show
significant core changes with stoichiometry in Co-Al alloys. It may be that not only the
point defect location changes, but also interatomic potential changes due to vacancy or

anti-site defects need to be considered in model construction of core structures.

3.4.2.2 Simulalted core structures of <111> screw dislocations

<111> screw dislocations exist in B2 COM and NiAl under the certain conditions
[113, 114]. Core structures of these <111> screw dislocations may affect the deformation
behavior of these alloys. However, experimental observation of core structures of the

screw dislocations is very difficult. Because the Burgers vector of a screw dislocation is

ll 1
through the local image contrast changes. Therefore, computer simulation is necessary to
interprete the HREM images of screw dislocation cores. For these core simulations, vari-
ous theoretical models are used to generate the core images via the EMS software until a

good agreement between the simulated and experimental images are reached.

Figure 74 is a HREM micrograph of a <1 11> dislocation in Ni-50Al provided by
Sun [121]. The dislocation was imaged along its <111> line direction, resulting in a pro-
jected hexagonal lattice image pattern. Careful examination reveals that one particular
bright spot is significantly brighter than the surrounding atoms and shifted slightly from

the periodic position. This is where the dislocation core is suspected to be.

A screw dislocation core was simulated using a data file provided by Farkas et
al.[122]. These atomic positions were calculated from a core model of a straight <111>
screw dislocation. Even though the atom positions in the data file (fig. 75a) match well
with those in the experimental image (fig. 74), the brightness contrast between the central
spot and surrounding atoms, along with the spot shift, in the observed core structure are
not seen in the simulation (fig. 75b). This indicates that the model of straight <111>
screw dislocation is not able to describle the true configuration of the screw dislocation

COI'C.

Ideally for HREM imaging, dislocations will be straight, normal to the thin foil,
and oriented along a low index zone axes. However, in practice dislocations may not
remain normal to the foil because non-screw dislocations can often lower their energies by
taking up a more screw like orientation.- This is balanced by the minimization in disloca-
tion line length (and energy) offered by remaining normal to the foil. A pure screw dislo-

cation in a thin foil does not tend to move from the screw orientation. However, beause of

112
tion line length (and energy) offered by remaining normal to the foil. A pure screw dislo-
cation in a thin foil does not tend to move from the screw orientation. However. beause of
the unbalanced shear stress on surface, there exists a torque about the dislocation line. A
screw dislocation is therefore twisted in a thin foil (fig. 76). This twist displacement was
calculated by Eshelby [123] and verified by Tunstall et al. [124]. Because the dislocation
configuration in bulk material may become more complicated when it is located in a thin
foil, it may be useful to consider the so-called Eshelby twist effect when the core structure

of a screw dislocation is simulated.

To simulate the twist imposed on the <1 1 l> screw dislocation core structure in
MA], the dislocation was sliced into nine slabs of constant thickness. In each slab, the
dislocation twist was simplified to a straight line and the data file of Farkas et al. was
rotated. These data files which were based on the straight dislocation were then used to
produce supercells. The twist displacement was also added into the displacement field of
the dislocation through a modified “convert” program. The transmission function was cal-

culated continuouly via combination of “MS (option c)” and “autorun” programs.

The Eshelby twist effect on the atom arrangement in the core region is illustrated
in figure 77(a) for a left hand screw dislocation. The central atom is not displaced, while
the rest of atoms are shifted in the circumferential direction. Figure 77(b) is a correspond-
ing HREM simulation of the left hand screw dislocation with an Eshelby twist. Figure 78
and 79 show the focal series and thickness series. Simulations at 2.32 nm thickness dis-
play the effect of defocus value on images (fig. 78). The white atom images are observed
only when are defocus values 70 nm and 80 nm, with 70 nm defocus resulting in the best

defined core structure. The thickness is also important. If the foil is too thin (such as 0.58

 

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nm), the Eshelby twist feature is not obvious, whereas it is easily recognized when the
thickness is greater than 2.03 nm (fig. 79). The most apparent feature of these images are
a higher intensity spot that is located in the center. This spot should represent the central

atom in fig. 74.

Simulations of the <1 11> screw dislocation with Eshelby twist gives better inter-
pretation of the experimental HREM image of this dislocation. However, Eshelby twist
can not explain the slight displacement of two atom columns away from their lattice posi-
tions in the core center. This indicates that in addition to Eshelby twist, there may exist
other factors influencing core configurations of <111> screw dislocations, such as local

strain field distribution and relaxation at the free surfaces.

3.4.3 Simulation of core structures in Fe-Al system

FeAl exhibits the highest duality and lowest room temperature strength of the B2
aluminides considered in this study (CoAl, N iAl and FeAl). In many regards, the mechan-
ical properties of FeAl are more similar to NiAl than CoAl, while the dislocations acti-
vated in deformation are more similar between FeAl and CoAl, i.e., <111> dislocations
are activated in low temperature deformation while <100> [125] dislocations are activated
in high temperature deformation. <100> dislocations are more easily activated in FeAl
than the other two alloys, even when the deformation axis is near <100>. This means that
the CRSS of <100> dislocations is very low in Fe-Al. This characteristic of Fe-Al may be

expected to be reflected in the core structures of <100> dislocations.

114

3.4.3.1 <010>{001} edge dislocations

Simulated [010](001) cores in FeAl visually have the same appearance as those in
CoAl or NiAl. A typical example is shown in figure 80. For FeAl. two extra half planes
in the [001] viewing direction and a Burger's circuit on (001) plane results in a [010] Burg-
ers vector for the dislocation with a line direction of [100]. The glide plane is therefore
the (001) plane. However, in the [022] or [022] directions, single extra half planes can be
observed. The single extra half plane AB terminates at atom B (aluminum) and plane CD
at atom D (iron) (see figure 80b). These two end atoms are also the bottom atoms of two
extra half planes in the [100] viewing direction. This coincidence reflects the compact
nature of this core. These simulations match the experimental images of [010](001) core
structures in FeAl [117]. Unfortunately, core structure calculations for off-stoichiometric
compositions are not available. In Fe-40A1, an apparent dissociation is observed experi-

mentally [117] and more work on core models is needed to understand these differences.

3.4.3.2 <010>{101} edge dislocations

Since the minimum projected atom spacing in the [1‘01] direction (distance
between corner atoms and central atoms in the B2 unit cell ) is smaller than the resolution
limit of the instrument used in this study, no experimental images are available. The pro-
jected profile from the data file provided by Farkas et al. [122] was used for analysis
instead. As shown in figure 81, the [010](01T) core is dissociated along the (OIT) slip
plane. The superpartial dislocations are located at position A and B respectively with an
APB in between. An extra Fe half plane is separated from an extra Al half plane by dis-

tance of approximately 4 atom spacings. The Fe planes in the upper part of the core

115
(above the slip plane) align with the A1 atom columns in the lower part of the core. Burg-
ers circuits constructed around two extra half planes reveal the dislocation is dissociated
into two l/2[100] dislocations. It should be recalled however that only edge components
of dislocations are revealed using HREM. Likewise, figure 81, being a two dimensional
representation, only illustrates the edge components and does not reflect screw compo-
nents along the line direction (into the image) of the dislocation. In fact, the EAM simula-
tions of Farkas et a1 reveal that the atoms along the APB are in fact displaced 1/2[011]
relative to each other. That is, each superpartial dislocation has a 1/2[011] screw compo-

nent. The resulting dissociation scheme is

£010]=%[T]1]+APB+%[111-] ........ (36)
Such a scheme is reasonable as 1/2[010] is not an atom-to-atom traslation, and conse-
quently is expected to be a high energy position, while 1/2<111> is in fact an atom to atom
translation and results in a stable APB. However, according to linear elasticity and
Frank’s rule, such a dissociation would not be energetically favorable. Thus, non-linear
and/or anisotropic elasticity effects may be responsible for the dissociation. It should also
be noted that HREM evidence for a similar dissociation mechanism has been observed for

climb dissociated <010>{110} dislocations in NiAl [88] and FeAl [117].

In CoAl, simulations indicate that the core was compact with no evidence of glide
or climb dissociation. The reason there is no dissociation of this <100>{011} dislocation
in CoAl may be the higher APB in CoAl relative to FeAl. Evidence for a higher APB
energy in CoAl comes from the fact that weak beam microscopy cannot image the super—
partials of <111> superdislocations, while in FeAl, the 1/2<1 l l> superpartials can be

imaged [86] at least in Fe-rich alloys.

116
In summary, simulations of core structures of the <010>{ 001 } edge dislocations in
B2 aluminides have successfully interpreted the HREM images of dislocations for stoichi-
ometric compositions. However, dissociation of a <010>{001 } cores in off—stoichiometric
alloys can not be simulated by modelling. The effect of point defects on potentials and

modelling procedures may be a key to solving this problem.

117

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Figure 30 Slip traces on two perpendicular surfaces of Co-50Al. The specimen was
oriented in the [011] direction and deformed at 873 K.

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Figure 31 Slip traces on two perpendicular surfaces of Co-48Al. The specimen was
oriented in the [011] direction and deformed at 873 K.

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Figure 32 Slip traces on two perpendicular surfaces of Co-52A1. The specimen was
oriented in the [011] direction and deformed at 873 K.

 

Figure 33 Slip traces on two perpendicular surfaces of Co-50Al. The specimen was
oriented in the [001] direction and deformed at 1300 K.

124

 

(a)

 

(b)

Figure 34 Analyis of dislocations in as-grown single crystal Co-50Al.
There exist two types of dislocations labeled a and b.
(a) (IIT) zone, (b) (TOT) zone, (c) (1T1) zone, ((1) (001) zone,
(e) (011) zone, (f) (001) zone.

125

 

(C)

 

(d)

 

 

126

 

(e)

 

(f)

 

127

line direction
of dislocations “a”

 

 

Q beam direction 0 projected line direction

Figurre 35 Dislocation line direction determination by trace analysis for dislocations in
fig. 34. Both the beam direction (bi) and the projected line direction (Pi)
are lying on the same great circle. The intersection of two or three great
circles give the true line direction of the dislocation.

128

 

(a)

 

 

 

(b)

Figure 36 Dislocation analysis in [123] oriented Co-50Al that was deformed at
1300 K. Three types of dislocations labeled a, b and c were characterized.

129

 

(C)

 

(d)

130

 

(e)

131

 

 

(b)

Figure 37 Dislocation reaction in [123] oriented Co-50Al deformed at 1300 K.
Two <100> dislocations form one <110> dislocation.

132

 

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(a)

I,

ompression Axis [123]

 

 

 

 

 

 

 

 

 

 

 

 

 

75b
b
/c it)
fb a b
c
/b
d
TEM micrograph

 

 

 

100
(b)

Figure 40 Dislocations observed in [123] oriented Co-50Al deformed at 1000 K.
(a) Arrangement of dislocations in single crystal compression sample.
(b) Schematic illustration of appearance of dislocation distribution
in a (001) foil.

136

I) .3li git-w ' '

 

 

(b)

Figure 41 Dislocation analysis for [011] oriented Co-50Al deformed at 873 K. Inclined
dislocations, end-on dislocations and dislocation loops were all observed.

137.

 

(d)

138

001

 

 

 

 

>010

 

 

 

 

100

Figure 42 Three dimensional schematic illustration of the distribution of dislocations
observed in [011] oriented Co-50Al deformed at 873 K.

139

 

 

(b)

Figure 43 Dislocation analysis for [011] Co-52Al deformed at 873 K. Inclined
dislocations, end-on dislocations and dislocation loops were observed.

140

 

 

141

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3*

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(b)

Figure 44 Analysis of dislocations in [011] Co-50Al deformed at 1300 K. Dislocations
labeled “a”, “b” and “c” were identified. Dislocation reactions were
also observed in the foil.

142

 

(d)

 

143

419 31.77)
’

 

Figure 45 Dislocation analysis for [011] Co-48Al deformed at 1300 K. Dislocations
labeled “a” and “b” were identified.

144

 

145

 

(a)

 

(b)

Figure 46 Dislocation analysis for [011] Co-52Al deformed at 1300 K. Dislocations
labeled “a”and “b” were characterized.

146

 

(d)

147

 

(f)

 

(b)

Figure 47 Dislocation analysis for [001] oriented Co-50Al deformed at 1300 K.
<100> dislocations were observed.

149

 

 

(b)

Figure 48 Analysis of dislocations in [001] oriented Co-50Al deformed at 1300 K.
<110> dislocations were found.

151.

 

152

 

(e)

 

153

Table 7 Description of image features in figure 38.

 

Images

Charateristics

 

 

 

 

Experimetal image at g=[ 1T0]

many segments whose orientations
deviate from the dislocaton line direction

 

simulation for Burgers vector [001]

double image

 

simulation for Burgers vector [110]

double image

 

simulation for Burgers vector [1 1T]

same features as the experimental image

 

simulation for Burgers vector [111]

same features as the experimental image

 

 

Experimetal image at g=[01T]

continous dislocation with contrast
fluctuation

 

simulation for Burgers vector [001]

contrast fluctuation is not obvious in the
middle of the dislocation

 

simulation for Burgers vector [110]

same feature as above

 

simulation for Burgers vector [1 II]

no contrast change

 

simulation for Burgers vector [111]

same as the experiemental image

 

 

Experimetal image at g=[121]

long straight dislocation without
contrast change

 

simulation for Burgers vector [001]

discrete segments at both ends

 

simulation for Burgers vector [110]

dislocation is wavy at both ends

 

simulation for Burgers vector [11]]

contrast is high at both ends

 

 

simulation for Burgers 'vector [11]]

 

same feature as the experimental image

 

 

154

Table 8 Description of image features in figure 39.

 

Images

Charateristics

l

 

—

 

Experimetal image at g=[0T1]

four segments whose orientations devi-
ate from dislocation line direction.

 

simulation for Burgers vector [100]

same feature as the experimental image;
slightly higher contrast

 

simulation for Burgers vector [011]

double image segments which are paral-
lel to the line direction of the dislocation

 

simulation for Burgers vector [T11]

head ends of the four segments seem to
be indented

 

simulation for Burgers vector [111]

high contrast and double image seg-
ments

 

 

Experimetal image at g=[ 1T0]

long dislocation with a small segment at
end

 

simulation for Burgers vector [100]

same feature as the experimental image

 

simulation for Burgers vector [011]

same feature as the experimental image

 

simulation for Burgers vector [I11]

two segments at both ends

 

simulation for Burgers vector [ l l 1]

doube image

 

 

Experimetal image at g=[121]

two descrete segments

 

simulation for Burgers vector [100]

same feature as the experimental image

 

simulation for Burgers vector [01]]

no segments

 

simulation for Burgers vector [T11]

two segments are connected by a faint
arc

 

 

simulation for Burgers vector [111]

 

double image; one segment is much
larger than the other

 

 

Filll =11 ,LI 1.1711 Fig lilAIlIlArllLl I -

 

155

Table 9 Calculation of Dislocation Energies

and Mobilities for COM [14].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Burgers slip system type Ex10-9 leO;1 S
vector Screw-Edge (J/m) (N/m )

am) (1101 3 23.68 W
a<l 11> { 110} E 36.36 1.48 0.536
a<111> {211} S 23.68 0.96 0.711
a<111> {211 } E 36.36 1.48 0.727
a<111> {312} S 23.68 0.96 0.605
a<111> {312) E 36.36 1.48 0.736
a<110> { 110} S 17.36 1.06 0.533
a<110> {110} E 22.11 1.35 0.390
a<010> { 101 } S 11.30 1.38 0.482
a<010> { 101 } 1:. 11.38 1.39 0.478
a<001> { 100} 11.30 1.38 0.652
a<001> { 100} E 11.05 1.35 0.661

 

 

 

 

 

 

 

E: Dislocation energy

S: Dislocation mobility parameter

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(a)

Figure 49 Core structure Of an [010] edge dislocation in Co-50Al deformed at 1300 K:
(a) HREM micrograph and Burgers circuit,

(b) perspective view (front view) along [001] direction,
(c) perspective view (side view) along [010] direction,

(d) perspective view (45° view) along [0T1] direction,
(e) perspective view (45° view) along [011] direction.

157

 

(b)

 

158

 

(d)

 

 

159

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(a)

Figure 50 Core structure of an [010] edge dislocation in Co-50Al deformed at 1300 K:

(a) HREM micrograph and Burgers circuit,

(b) perspective view (front view) along [001] direction,

(c) perspective view (45° view) along [0T1] direction,
(d) perspective view (45° view) along [011] direction.

160

 

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Figure 51 Core structure of an [010] edge dislocation in Co-50A1 deformed at 1300 K:
(a) HREM micrograph and Burgers circuit,
(b) perspective view along [011] direction,
(c) perspective view along [0T1] direction,
((1) perspective view along [011] direction.

163

 

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Figure 52 Core structure of an [010] edge dislocation in Co-48Al deformed at 1300 K:
(a) HREM micrograph and Burgers circuit,
(b) perspective view (front) along [001] direction,
(c) perspective view (side) along [010] direction,
(d) perspective view along [0T1] direction,
(e) perspective view along [011]direction,
(f) Burgers circuit on partial dislocations.

166

 

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Figure 53 Core structure of an [010] edge dislocation in Co-52Al deformed at 1300 K.
(a) HREM micrograph and Burgers circuit,
(b) perspective view along [010] direction,
(b) perspective view along [011] direction,
(c) perspective view along [0T1] direction.

 

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Figure 54 Core structure of an [010] edge dislocation in Co—52Al deformed at 1300 K:
(a) HREM micrograph and Burgers circuit,
(b) perspective view along [011] direction,
(c) perspective view along [0T1]direction,
(d) schematic drawing of core structure of [010] edge dislocation
in Co—52Al.

173

 

 

 

 

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Co-52Al deformed at 1300 K:

(a) HREM micrograph and Burgers circuit,

(b) perspective view (front) along [001] direction,
(c) perspective view (side) along [010] direction,
((1) perspective view along [0T1] dorection,

(e) perspective view along [011] direction.

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deformed at 1300 K:

179

 

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(b) Atom positions superimposed onto the HREM image simulation. Large

dots represent Co and small dots represent Al.

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Figure 61 Effect of temperature on HREM simulations is shown at the conditions
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001 01]

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Figure 62 (a) Unit cell configuration used for <100>{001 } dislocation image simulations.

(b) Alternate unit cell used for <100>{011} dislocation image simulations.

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Figure 66 Effect of off-stoichiometric composition change on the core structure in
Ni-SOA]. (a) Supercell of [010](001) edge dislocation core in Ni-rich Ni-Al.
Large spheres are Ni while small spheres are Al. (b) Simulated HREM

image of core structure of [010](001) dislocation in Ni-rich Ni-Al.

I90

 

(b)

Figure 67 Effect of stoichiometry deviation (Al rich) on core structure.

(a) Supercell of [010](001) edge dislocation core in Al-rich Ni-Al. Large
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Figure 68 Anti-site defect in core structure (a Ni atom exchanges position with a Al atom).
(a) Supercell of [010](001) edge dislocation core in Ni-Al. Large spheres
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the arrows.
(b) Simulated HREM image of core structure of [010](001) dislocation
in Ni-Al.

 

(b)

Figure 69 Effect of right-in-core vacancies in core structure in N i-Al
(a) Two vacanies exist in dislocation core (indicated by arrows).
(b) HREM image simulated at df=-7O nm and thickness=2.2 nm.

193

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Figure 72 Simulated HREM images of core structures using random A]
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Figure 73 Image simulation of core structure of [010](001) edge dislocation in Ni-SOAl

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306 .

Table 10 Debye-Waller Factors [111]

 

 

 

 

 

 

 

Element D (20 K) D (93 K) D (293 K)
Co 0.002 0.045 0.275
Ni 0.001 0.030 0.180
Fe 0.003 0.060 0.350
Al 0.005 0.110 0.640

 

 

 

 

 

4. Further Discussion

The differences in the mechanical properties of the B2 aluminides CoAl, NiAl and
FeAl are significant. However, the reasons for those difference are still not clear. In this
chapter, an attempt will be made to rationalize the differences by making comparative
studies of the mechanical testing results. dislocation analysis and core structures obtained

by experimental examination.

4.1 Mechanical Properties
4.1.1 Mechanical Properties of Co-Al At Elevated Temperatures

The compressive behavior of the [011] oriented Co-48, —50 and- 52A] are pre-
sented in section 3.1. The 0.2 percent off-set yield stresses are obtained from the corre-
sponding stress-strain curves. The slip trace analysis indicates {001} slip planes for all
three compositions, while the primary Burgers vector has been determined using TEM
contrast analysis to be <100>. The cirtical resolved shear stress (CRSS) which is a mea-
surement of the minimum shear stress need to initiate slip on a certain slip system can then

be calculated for <100>{001 } slip in these alloys. The CRSS can be calculated using the

Schmids law:
PS
In” = Xeosflcoso .............. (37)
where;

PS is the load at yielding

A is the true cross-section area

207

208
0 is the angle between the slip direction and the compression axis.
and q) is the angle between the slip plane normal and the compres-

sion axis.

The term cochosQ) is termed as the Schmid factor.The Ps/A values were determined from
the 0.2 percent offset yield stress and the angles 9 and ¢ were measured using a stereo-
graphic projection of the single crystal compression samples. The calculated CRSS val-

ues are listed in table 11.

[001] oriented Co-SOAl has the much higher yield strength than [011] oriented Co-
50Al (fig. 28). The dislocation analysis presented in section 3.4 shows <011>{112} oper-
ative slip systems before kinking and <100>{001} operative slip systems after kinking.
The Schmid factor is 0.28 for <011>{ 112} slip system in the [001] orientation. The CRSS
has been determined using the Schmid law and is listed in table 11. It is clear that
<011>{112} slip system has much higher CRSS value than <100>{001}.

Table 11 indicates that the CRSS of <100>{001} depends on stoichiometry. The 2
at% off-stoichiometric deviations in composition raise the CRSS values. These differ-
ences might be explained by the core structures which occur with changes in stoichiome-
try. Recalling section 3.3, the [010](001) edge dislocation cores are compact or
undissociated in Co-SOAI, while the dislocation cores are significantly climb dissociated
in Co-48Al and Co-52Al. The complicated core configurations in off-stoichiometric Co-
Al make core movement difficult. Since the displacement field in the core region is an
elastic strain field, the difference in core structures may be related to some measurable
parameters that are indicative of interatomic potentials. Young’s modulus is one of those

parameters. That is: Young’s modulus is believed to reflect the atomic bonding strength. It

209

means that the difference in Young’s modulus should be in agreement with the difference
in core structures between Co-Al. The measurement of Young’s modulus ( 296 GPa for
Co-Al and 320 GPa for Co—52Al) [31] supports this argument. Therefore the difference
in core structures due to stoichiometric deviations may result in the difference in CRSS
value among Co-48, -50 and 52Al.

In addtion to potentials, slip plane bending in the core center may affect core
movement. Minimum distortion of slip planes in the core center is found in Co-SOAI,
while the maximum distortion is observed in Co-52Al, which corresponds to the lowest

CRSS in Co-50Al and the highest CRSS in Co-52Al.

4.1.2 Mechanical properties of other B2 alloys

Compared to Ni-Al and Fe-Al (see section 2.2), Co-Al has the highest strength and
hardness at elevated temperatures (fig. 6). Additionally, the mechanical behavior of Co-Al
is more sensitive to stoichiometry deviations than Ni-Al and Fe-Al (fig. 2 and 6). These
phenomenon may be explained by characteristics of the dislocation core structures in
these alloys.

<100>{001 } edge dislocations dominate the plastic deformation process in [011]
oriented Co-Al and Ni-Al [46, 114, 115]. This slip system is also observed in [001] ori-
ented Fe-Al [116]. Comparison of core structures of <100>{ 001} edge dislocations in Co-
50Al, Ni-SOAl and Fe-SOAl (fig. 82) shows that all of the dislocation cores are compact or
have minimal dissociation. However, the simulations of Farkas at a]. show that the com-
pact <OlO> cores usually have non-planar spreading. For example, <010>{001} cores in

Ni-SOAI structures spread on three { 110} planes [62,68]. A core with non-planar spread-

210
ing requires a larger applied stress to slip than a core without non-planar spreading [table
4]. This larger stress is necessary to compress to core into a planar configuration. How-
ever, it has not been possible to measure any significant non-planar spreading of a disloca-
tion core from experimental HREM micrographs of dislocations in the stoichiometric
alloys.

The effect of composition on the mechanical behavior of the three B2 alloys can be
explained by core structures of the <100>{001} edge dislocations. The extra half planes
in <100>{001 } edge dislocation cores in Co-48Al and Co-52Al are significantly separated
(fig. 52-56), whereas such seperation is very limited in Ni-48Al and Fe-40Al (fig. 83).
Seperation of extra half planes is also termed as dissociation and it will result in two
superpartial 1/2<111> dislocations plus anti-phase boundary in between. These superpar-
tial dislocations can not glide on the {001} slip plane. Hence, movement of a dissociated
core needs a high external stress to push the separated extra partials together. The wider

the separation, the higher the initiation stress.

4.2 Dislocations in Co-Al, Ni-AI and Fe-Al
4.2.1 Dislocation density in Co-48Al, Co-SOAI and Co-52Al

As shown in section 3.3, the majority of the dislocations observed in the deformed
Co-Al (except [001] compression samples) are <100>{001 } edge dislocations. However,
the density of dislocations observed is dependent upon alloy stoichiometry. Even though
the dislocation density has not been measured quantitatively due to time limitations, qual-
itatively the density of dislocations in Co-SOAl is the highest among the three composi-

tions. The lack of active dislocations may be one of the main reasons for lack of the

211

plasticity in the off-stoichiometric Co-Al. On the other hand, the core structures of the
dislocations may to a large degree determine the dislocation activiation under the condi-
tions of stress, temperature and orientation. The <010> dislocations in Co-50Al have
compact cores, while the <010> dislocations in Co-48Al and Co-52Al have dissociated
cores. Furthermore, the dislocation cores in Co-52Al are more complicated than those in
Co-48Al. If core dissociation plays a more impertant rele in dislocation initiation than
core spreading, the difference in dislocation density due to stoichiometry may be
explained by core dissociation. Dislocation cores in Co-50Al display minimal dissocia-
tion and the corresponding dislocation density is the highest; dislocation cores in Co-52Al
have complicated dissociations (climb dissociation and mixed dissociation), and the corre-

sponding dislocation density is the lowest.

4.2.2 Dislocation density in Ni-Al and Fe-AI

Typical dislocation structures in Co-SOAl, Ni-SOAI and Fe-50Al deformed at 673-
873 K are shown in figure 41 and else where [116,117]. <010>{001} edge dislocations
dominate the deformation process in Co-Al and Fe-Al. In addtion to <010>{001} disloca-
tions, <010>{ 101 } edge dislocations are also observed in Ni-SOAI [127]. The dislocation
density is lower in Co-Al than in either Ni—Al or Fe-Al when these images are compared.
Furthermore, this difference is more dramatic when off-stoichiometric Co-Al, Ni-Al and
Fe-Al are compared.

The core structures of the <010>{001 } edge dislocations may influence these dif-
ferences in dislocation densities. In stoichiometric Co-SOAl, Ni-50Al and Fe-SOAl, the

core structures of the <010>{001 } edge dislocations are similar experimentally and theo-

l‘J
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retically. However, the simulations show that in N i-50Al, the compact core of
<100>{001 } edge dislocation spreads in three {011 } planes. If this argument is true, the
non-planar spreading of the dislocation core may determine dislocation activation under
the testing conditions. Increases in applied stress and temperature will overcome the bar-
rier of non-planar spreading of dislocation cores.

In non-stoichiometric Co-Al, Ni-Al and Fe-Al, dislocation dissociation may play a
key role in slip initiation. The dislocation densities observed in the compression speci-
mens are a result of dislocation generation versus motion (fig. 42) [116,117]. If disloca-
tion generation is difficult and dislocation movement is easy, the corresponding
dislocation density should be low; if dislocation generation is easy and dislocation move-
ment is difficult, the corresponding dislocation density is high. The core structure should
affect both generation and motion of dislocations. Recalling the slip trace density on the
compression specimens, Co-SOAl has the highest slip line density, while Co-52Al has the
lowest slip line density. It is reasonable to say that dislocation core structure influences
the dislocation initiation more significantly than the dislocation movement. The larger the
dissociation, the lower the activated dislocation density. Co-52Al has a more complicated

dislocation dissociation, and its dislocation density is the lowest.

4.3 Core structures
Comparison of the core structures of various B2 aluminides will be performed in
this section. The local lattice distortion, spreading and dissociation of the cores will be

emphasized.

213
4.3.] Core structures in stoichiometric B2 alloys

Compactness is the common feature of <100>{001} cores in CoSOAl and Ni-SOAl
(fig. 82). However, simulations indicate there exists non-planar spreading on {110}
planes which is not readily observed by HREM. This non—spreading nature of a compact
core is explained in detail as follows:

A necessary condition for dissociation of a dislocation core into partial disloca-
tions is the existence of a stable planar fault which corresponds to the local minima of the
7 surface. In B2 Ni—Al, there are no stable planar faults except for an APB on { 110} and
{ 112} [62,65]. This is why there is no dissociation of the core into partial dislocations
except 1/2<11 1> superpartials in N i-Al. However, the yenergy increase on 7 surfaces may
not be uniform in all the directions. In some directions, the energy increases at slower rate
than other directions. Therefore the core tends to spread along these directions. These
directions are also termed corridor directions [115]. Figure 84a is the (110) 7 surface on
which [110] is the corridor direction. Figure 84b shows the (100) 7 surface and the planar
fault is completely symmetric. This means that no corridor direction can be defined in
this region. Figure 84c shows the (111) 7 surface and three l/2<112> vectors are corridor
directions. Figure 85 compares the energy curves along the preferred directions along
each plane, indicating <100>{ 001 } slip requires more initiation stress than the other slips.
From previous analysis on BZ NiAl, [010] edge dislocations with line direction [100] and
slip plane (001) dominate deformation process. However, a [010] diSplacement vector can
not spread on its slip plane because the energies for planar faults on this plane are high.
Therefore, the displacement field is most likely to spread on the (011) and (011) planes

along the corridor directions [011] and [0T1]. In contrast, a <100>{011} core can spread

214
on its own slip plane and therefore is planar. According to model calculations, the activa-
tion stress of a non-planar core is ten times as high as that of a planar core [68]. Accord-
ing to this point of view, <010>{ 101} edge dislocations should have a CRSS lower than
<010>{001} edge dislocations. However, no <010>{101} edge dislocations were found
in [011] oriented Co-Al and Ni-Al except [011] Ni-SOAl. There are two possibilities for
lack of <010>{ 101} slip: (1) the Schmid factor for this system (0.35) is not large enough
to activiate <010>{ 101 } edge dislocations; (2) <010>{ 101} edge dislocations are activi-
ated and sweep out of the crystal due to high mobility, leaving <100>{001} edge disloca-
tions in the crystals. For the second possibility, <010>{001} slip would be a slower
process than <010>{ 101 } slip, and then would become a dominating factor in plastic
deformation. However, recalling the slip traces observed on the compression specimens,
only {001} slip planes are involved in plastic deformation. Therefore, it is reasonable to
regard <100>{001} as the primary slip systems in Co-Al. Additionally, the dislocation
interaction between <100> dislocations, which forms <110> and <111> dislocations, also

reduces the mobility of <100> dislocations.

4.3.2. Core structures in off-stoichiometric 82 alloys

Characteristic of the core structures of <010> edge dislocations in B2 Co-48Al,
Co-48Al, Ni-48Al and Fe-40Al is their dissociation. Climb dissociation and mixed disso-
ciation exist in off-stoichiometric Co-Al (fig. 83a), while the corresponding dissociation
in nickel rich Ni-Al and iron rich aluminides Fe-Al is minOr. Figure 83b is an example of
<100> core with edge character in Ni-48Al. The extra Ni half plane is separated from the

extra A] half plane at the distance of two atom spacings in the [010] direction. Therefore,

215

this is a case of slight glide dissociation. Shown in figure 83c is the core structure of
<1()()> edge dislocation in Fe-40Al. The extra Ni half plane and the extra Al plane are
adjacent to each other, indicative of the compact nature. Recalling the core structures of
<100> edge dislocations in Co-48Al and Co-52Al, the climb dissociation width is over
four interatomic spaces. Hence, the differences in core dissociation between Co-Al, Ni-
Al and Fe-Al can be characterized by two issues. One is the dissociation type. Ni-48Al
has glide dissociation, while Co-48Al and Co-52Al have climb/mixed dissociations. To
compress a glide dissociated core only requires glide motion of atoms, whereas to com-
press a climb dissociated core requires the climb motion of atoms. The latter process is
more difficult than the former process. The second issue is the extent of dislocation disso-
ciation. The extra half planes are only separated at one or two lattice spacings in Ni-48Al
and are not separated in Fe-40Al, while this separation is more significant in Co-48Al and
Co-52Al. These two factors make motion of the Co-Al core difficult to initiate. There-
fore, core structures play a very important role in mechanical behavior of B2 aluminides
Co-Al, Ni-Al and Fe-Al.

Stoichiometric deviations do not necessarily directly change the local chemical
composition in the core region. Therefore, the core dissociation may not be directly
related to core chemistry. However, off-stoichiometric composition creates numerous
structural vacancies in these materials. Vacancies are very active at high temperature.
Generation, segregation, migration and interaction of the structural and thermal vacancies

may have significant influences on core structure and dislocation mobility.

216

4.3.3. Simulations of core structures

The simulated images agree well with the compact core structures. However, the
simulations do not depict the minor differences in core structures between Co-Al, Ni—Al
and Fe-Al. By carefully examining the simulated core structures of these alloys, one will
find that each core configuration is exactly the same as the others because the potentials
used for simulations are all similar for CoAl, MA] and FeAl. The simulations also do not
describe the climb dissociation of a dislocation core. Although vacancies and anti-site
defects were set in the different locations of the core area during simulation, the simulated
images do not changed visually. This can be attributed to the fact that the models do not

utilize the composition dependent potentials, vacancy and interaction characteristics.

217

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(b)

Figure 84 Comparison of the 7 surfaces for <100>{011}, <100>{001}
and <111>{112} slip systems

220

 

 

 

 

[11—2] ]

 

 

 

 

 

 

 

 

 

 

(C)

221

 

—‘—' “-101 In (110)

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Figure 85 Comparison of the energy curves along the prefered directions in
various slip systems [115].

222

Table 11 CRSS of [011] Co-Al and [001] Co-SOAI

 

 

 

 

 

 

 

. 7. Schmidt CRSS

Slip system factor 30.1 (Mpa) (Mpa)
<010>{001 } =i
in [011] 0.50 50 25
Co-SOAl
<010>{001}
in [011] 0.50 60 30
Co-48Al
<010>{001}
in [011] 0.50 70 35
Co-52Al
<011>{ 112}
in [001] 0.28 240 69

Co-50Al

 

 

 

 

 

5. Conclusions

Oriented B2 Co-Al alloys were mechanically tested at high temperatures and the
corresponding slip planes were determined by slip trace analysis. The deformation-intro-
duced dislocations and the dislocations in their as-grown state were analyzed using the
g-b=0 method. Core structures of <100>{001 } edge dislocations were carefully exam-
ined using HREM. Image simulations were performed to interpret experimental results.
A comparative study of the mechanical behavior, dislocation density and their core struc-
tures were conducted. Based on all the experimental results and analysis, conclusions are
made as follows:

5.1 Mechanical properties

At room temperature, Co-Al is much more brittle than Ni-Al. At high tempera—
tures, Co-48 and Co-52Al are significantly stronger than Co-50Al. In the [00]] “hard”
orientation, C050A1 exhibits much higher deformation resistance and displays the kinking
phenomenon.

5.2 Dislocations and slip systems

<100>{001 } cubic slip systems were observed in all the orientations, compositions
and testing temperatures, indicating that the <100>{001 } slip systems are easiest to be
activated. <110> dislocations and <111> dislocations were also found in [123] oriented
Co-50Al and [011] oriented Co-SOAl and Co-48Al deformed at 1300 K. However, these
dislocations were not activated at the lower temperature of 1100 K. In the [001] orienta-
tion, both <110> and <100> dislocations were seen in CoSOAl deformed at 1300 K. <110>
slip has much higher CRSS than <100> slip and therefore greatly lifts the compressive

strength of the [001] oriented Co-50A1 in the initial stage of deformation. After kinking,

224

the local orientation is shifted to non-<100> direction. the <100> slip is then predominant
in deformation. Therefore the <100> edge dislocations are the most important disloca-
tions in high temperature deformation of B2 aluminide Co-Al.
5.3 Core structures of <010> edge dislocations

Core structures of <100> edge dislocations in Co-50Al are characterized by com-
pactness with non-planar spreading and/or slight dissociation. Dislocation core structures
in Co-48Al display climb dissociation. Dislocation core structures in Co-52Al exhibit
both climb and mixed dissociation.
5.4 Computer simulations

Computer simulations based on Farkas’ core model match the experimental obser-
vations of core structures in CoSOAl. The simulated core structures are always compact
when the vacancy and anti—site defects are considered. Simulations of core structures in
off-stoichiometric B2 alloys are not in good agreement with experimental images. The
main reasons may be that the role of vacancies in core structures is not clear.
5.5 Mechanical behavior and core structures

Mechanical properties of B2 Co-Al, Ni-Al and Fe-Al are related to the
<100>{001 } edge dislocation core structures in these aluminides. In stoichiometric
alloys, non-planar spreading of the <100>{001 } edge dislocation cores plays the key role
in dislocation slip initiation. Co-50Al cores may have more non-planar spreading than Ni-
50Al and Fe-50A1. This may be responsible for the higher strength of Co-50A1 than Ni-
50A1 and Fe-50Al. In off-stoichiometric aluminides. core dissociation may strongly influ-
ence the CRSS of <100>{001 } edge dislocations. Co-48Al and Co-52Al have climb/

mixed dissociated core structures, while Ni-48Al and Fe-40A1 have glide dissociated

l J
J
'JI

cores. Dissociation type and dissociation degree makes off-stoichiometric Co-Al stronger

and more brittle than off-stoichiometric Ni-Al and Fe-Al.

226

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[129]. T. Godecke and W. Koster, Z. Metallkule, 77, (1986), p. 408.
[130]. EN. Rhines and J.B. Newkirk, Tmas., ASM, 45, (1953), p. 1029.

[131]. Kubaschewski and Ortrud, Iron-Binary Phase Diagrams, Germany, Springer
Verlag Berlin/Heidelberg, (1982).

Appendices

Appendix 1 The parameters used in computer image simulation (Head’s program)

Elastic constants: C11=2.705 C12=1.073 C44=1.397

Anomalus absorption coeffient : ANO=0.07

LU is direction of dislocation line

LBM is electron beam direction

LFN is foil normal

W is deviation from Bragg condition

Thick is foil thickness

12. Parameters used for simulation of dislocation “b”

 

 

 

 

 

 

 

 

 

 

 

13.31353... g=(0Tn g=(1T0) g=(151)
b=[001] LU=[4 23 3] LU=[4 23 3] LU=[4—23 3]
LBM=[] T19] LBM=[2 2 57] LFN=[26 9 25]
LFN=[26 9 25] LFN=[26 9 25] LBM=[ 5 6 7]
W=0.82 W=0.82 W=O. 15
Thick=3.75 Thick=3.67 Thick=7.07
b=[] 10] LU=[4 23 3] LU=[4 23 3] LU=[4—23 3]
LBM=[] 1—19] LBM=[2 2 57] LFN=[26 9 25]
LFN=[26 9 25] LFN=[26 9 25] LBM=[ 5 6 7]
W=0.82 W=0.82 W=O. 15
Thick=3.75 Thick=3.67 Thick=7.07
b=[11T] LU=[4 23 3] LU=[4 23 3] LU=[4—23 3]
LBM=[] T19] LBM=[2 2 57] LFN=[26 9 25]
LFN=[26 9 25] LFN=[26 9 25] LBM=[ 5 6 7]
W=0.82 =0.82 W=O. 1 5
Thick=3.75 Thick=3.67 Thick=7.07

 

 

235

Table 13 Parameters used for simulation of dislocation “c”

 

 

 

 

 

 

 

 

 

 

 

D"‘3§f“°“ g=(1T0) g=(0Tl) g=(121)
== ==

b=[100] LU=[T 19 1] LU=[T 19 1 LU=[T 19 1]
LBM=[2 2 57 ] LBM=[5 4 4] LBM=[5 7 6]
LFN=[26 9 25] LFN=[26 9 25] LFN=[26 9 25]
W=0.62 W=0.82 W=O.390
Thick=3.0 Thick=6.07 Thick=1.05

b=[110] LU=[T 19 1] LU=[T 19 1 LU=[T 19 1]
LBM=[2 2 57 ] LBM=[5 4 4] LBM=[5 7 6]
LFN=[26 9 25] LFN=[26 9 25] LFN=[26 9 25]
W=O.62 W=0.82 W=O.390
Thick=3.0 Thick=6.07 Thick=1.05

b=[]11] LU=[1'19 1] LU=[T 191 LU=[T191]
LBM=[5 4 4 ] LBM=[5 4 4 ] LBM=[5 7 6]
LFN=[26 9 25] LFN=[26 9 25] LFN=[26 9 25]
W=O.62 W=0.82 w=o.390
Thick=3.0 Thick=6.07 Thick=1.05

 

 

Appendix 2 Conversion program

C

Program Convert

implicit rea1*8 (a-h,o-z)

character*2 a1,ni

open (unit:10,file=’Ni50Al’,status=’old’)

open (unit=1 1,file=’msm001cel’,status=’new’)

open (unit=12,fi1e=’msm001.atom’,status=’new’)

al=’Al’

ni=’Ni’

fe=’Fe’

co=’Co’

nzal=l3

nzni=28

nzco=27

nzfe=26

dwa1=0.005

dwni=0.001

dwfe=0.003

dwco=0.002

one=1.

izero=0

ir=0.1

ik=1O

write(6,*) ‘type in lattice parameter’

read(5,*) xlat

write(6,*) ‘type in primitive crystal vector along dislocation ‘
write(6,*) ‘line; put a decimal point in each number and separate’
write(6,*) ‘them by a comma or a space’

read(5,*) x,y,z

az=sqrt(x*x+y*y+z*z) * xlat

write(6,*) ‘type in the minimum and maximum values in the’
write(6,*) ‘x-direction; put in a decimal point in the’
write(6,*) ‘numbers and separate them with a comma or space’
read(5,*) xmin.xmax

write(6,*) ‘numbers and separate them with a comma or space’

read(5,*) ymin,ymax

write(6,*) ‘so that I know where the file ends type in the’
write(6,*) ‘first three numbers of the last line of data’
write(6,*) ‘put a decimal point in each number and separate’
write(6,*) ‘them by a comma or a space’

read(5,*) xl,y1,zl

write(6,*) ‘type in the stream number you have assigned the’
write(6,*) ‘data file to’

30

10

read(5,*) nin
write(6,*) ‘type in the stream number for the output’
read(5,*) nout
write(6,*) ‘thankyou’
ax=xmax-xmin
ay=ymax-ymin
zmax=az/2.
zmin=-az/2.
xninety=90.
write(nout,30)
format( 10h;supercell)
write(nout,20) ik,ax/10,ay/10,az/10,xninety,xninety,xninety
format( 1 x,i2, 1 x,6f8.4)
read(nin,*)
natoms=0
kount=0
read(nin,*) x,y,z,xa,ya,za,kat
if(x.eq.xl.and.y.eq.yl.and.z.eq.zl) then
write(6,*) ‘dunnit’
write(6,*) ‘number of atoms in output fi1e=’,natoms
write(6,*) ‘cell sides=’,ax,ay,az
write(12,1000)natoms

1000 format( 1 x,i3)

stop
endif

if(x.1t.xmin) goto 10

if(x.gt.xmax) goto 10
if(y.1t.ymin) goto 10
if(y.gt.ymax) goto 10
natoms=natoms+1
=x+xa
Y=Y+Ya
z=z+za
x=x - xmin
y=y - ymin
x=(x+xa)/ax
y=(y+ya)/ay
if(z.lt.0.) z=z+az
if(z.gt.az) z=z—az
z=z/az
if(kat.eq.1) then
write(nout,100) x,y.z,one.dwa1.ir.izero,izero
endif
goto 10

100 fonnat(1x,2hAl,lx.8f8.4)

end

Appendix 3 Autorun in C-shell

#lfbin/csh

# Purpose: Automate repetitious execution of ems-msl program with
# slightly varying input files.

# File Requirments: subconstant files must end last line of text with a

# return. newax files should begin with a new001 file
# previously created by msl run manually.
if ($#argv < 4) then

echo ‘ ‘

echo -n ‘Usage: autorun ems_program iterations data_file_constant’
echo ‘ input_file_constant’

echo -n ‘ ie: autorun msl 10 subconstant’
echo ‘ new [showtmps]’
echo ‘ ‘
exit(1)
endif

set showtmps = false

if ($#argv == 5) then

if ($5 == ‘showtmps’) set showtmps = true
endif
@ i = 1
while ($i < $2)

@ constcnt = 0

foreach file ($3*)$l < $inputfile > tmpout$$.$i
if ($showtmps == ‘false’) /bin/rm -f $inputfile
@ i++

endif

end

end

exit 0

@ constcnt++

if ($i <= $2 && ($1 != 1 ll $c0nstcnt 1: 1)) then
set inputfile = tmpinp$$.$constcnt
cat $fi1e > $inputfi1e
if($i < 10) then

echo $4’00’$i >> $inputfile
else

echo $4’0’$i >> Sinputfile
endif

111111111111|1111111111111111111111111

 

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