Repeated nucleation of precipitates on dislocations in aluminum-copper

MISSING IMAGE

Material Information

Title:
Repeated nucleation of precipitates on dislocations in aluminum-copper
Physical Description:
viii, 208 leaves. : ill. ; 28 cm.
Language:
English
Creator:
Headley, Thomas Jeffrey, 1943-
Publication Date:

Subjects

Subjects / Keywords:
Aluminum-copper alloys   ( lcsh )
Dislocations in metals   ( lcsh )
Nucleation   ( lcsh )
Alloys -- Corrosion   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 204-207.
Additional Physical Form:
Also available online.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
Thomas Jeffrey Headley

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
oclc - 14079047
System ID:
AA00024750:00001

Table of Contents
    Title Page
        Page i
        Page ii
    Dedication
        Page iii
    Acknowledgement
        Page iv
    Table of Contents
        Page v
        Page vi
    Abstract
        Page vii
        Page viii
    Chapter 1. Introduction
        Page 1
        Page 2
        Page 3
        Page 4
    Chapter 2. Review of theory and previous work
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
    Chapter 3. Experimental procedures and materials
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
    Chapter 4. Experimental results and analyses
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
        Page 144
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
        Page 152
        Page 153
        Page 154
        Page 155
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
        Page 161
        Page 162
        Page 163
        Page 164
        Page 165
        Page 166
        Page 167
        Page 168
        Page 169
        Page 170
        Page 171
        Page 172
        Page 173
        Page 174
        Page 175
        Page 176
        Page 177
    Chapter 5. The repeated nucleation mechanism
        Page 178
        Page 179
        Page 180
        Page 181
        Page 182
        Page 183
        Page 184
        Page 185
        Page 186
        Page 187
        Page 188
        Page 189
        Page 190
        Page 191
        Page 192
        Page 193
        Page 194
        Page 195
        Page 196
        Page 197
    Chapter 6. Conclusions and suggestions for future work
        Page 198
        Page 199
        Page 200
        Page 201
        Page 202
        Page 203
    References
        Page 204
        Page 205
        Page 206
        Page 207
    Biographical sketch
        Page 208
        Page 209
        Page 210
Full Text
















REPEATED NUCLEATION OF PRECIPITATES ON DISLOCATIONS IN ALUMINUM-COPPER







By



THOMAS JEFFREY HEADLEY










A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA 1974
































Copyright by

Thomas Jeffrey Headley

1974






























Dedicated to my wife, Lynn















ACKNOW LED GMENTS



The author is deeply indebted to his Advisory Chairman, Dr. John J'. H-ren, who contributed unselfishly of his time,

and provided advice, encouragement, and stimulating discussion during the course of this research. He is indebted to his advisory committee for assistance, and to Dr. R. T. DeHoff

for many helpful discussions.

Thanks are due to Dr. R. W. Gould for providing alloy

materials; to the Sandia Corporation, Albuquerque, New Mexico,

for chemical analysis; to the Japan Electron Optics Laboratory, Boston, Massachusetts, for use of the JEOL 100B Electron Microscope; to Mr. E. J. Jenkins for assistance in the laboratory; to Mr. Paul Smith for assistance in the darkroom; and

to Mrs. Elizabeth Godey for typing this manuscript.

TLhe author's wife, Lynn, is acknowledged for her constant inspiration and support. His mother is acknowledged

for her lifelong encouragement.

Finally, the financial. support of the Atomic Energy Commission was deeply appreciated.















TABLE 0F CONTENTS


Page

ACKNOWLEDGMENTS........... .. .. .. .. .... iv

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

CHAPTER

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

2 REVIEW OF THEORY AND PREVIOUS WORK .. .........5

2.1. Theory of Heterogenieous Nucleation
at Dislocations......... .......5
2.2. Precipitation in the Al-Cu System . .10 2.3. Dislocation Climb..............17
2.3.1. Quenched-in Vacancies and
the Chemical Climb Force......17 2.3.2. Theory of Dislocation Climb ...18 2.3-3. Dislocation Climb Sources ...22
2.4. Repeated Nucleation on Dislocations ...25
2.5. Pertinent Electron Microscopy Theory . .28
2.5.1. Two-Beam Diffraction Contrast
Theory *... .... ... 28
2.5.2. Defect Identification from
Invisibility Conditions .......35
2.5.3. Imaging Precipitates in the
Electron Microscope .........37

3 EXPERIMENTAL PROCEDURES AND MATERIALS .......41

S.1. Specimen Materials ..............41
5.2. Heat Treatments.......................42
3.3. Electron Microscope Specimen
Preparation..................4
5.4. Electron Microscopy.............48

4 EXPERIMENTAL RESULTS AND ANALYSES ..........5

4.1. Introduction ..............................5
4.2. Nature and Source of the Climbing
Dislocations .. .. .. .. .. .. .. ...3
4.2.1. Dislocation Climb Sources . .53
4.2.2. Glide Dislocations Which
Climb................70

v









TABLE OF C(INTENTS Continued


CH A f, TF R Page

4 (Continued)

4.3. Identification and Characterization
of the Precipi tate Phase .. ......... ...77
4.4. Further Geometric Analyses .. ........ .94
4.4.1. Distribution of Precipitates
in Colonies at Climb Sources . 94
4.4.2. Geometry of the Precipitate
Stringer';.' *.................. ..98
4.4.3. Determination of the Burgers Vectors of Small Loops Within Precipitate Colonies .. ....... ..106
4.4.4. "Secondary" Climb Sources ... 111 4.4.5. A Climb Source on (100) .....118
4.4.6. Nucleation of Preferred 0'
Orientations During Segmented Climb ..... .............. 122
4.4.7. Displacement Fringe Contrast
in a Precipitate Colony ..... 127
4.4.8. Precipitate Colonies Associated
with Subboundary Formation ... 132
4.5. Effects of Experimental Variables on
Microstructure ...... ............. ..135
4.5.1. Effect of Time at Constant
Aging Temperature .. ........ .135
4.5.2. Effect of Solution Treatment
Temperature ... ........... .140
4.5.3. Effect of Temperature to Which
Samples Are Direct-Quenched . 147 4.5.4. Effect of Quench Rate ... ...... 154
4.5.5. Effect of Copper Concentration 166
4.6. Summary ...... ................. .176

5 THE REPEATED NUCLEATION MECHANISM .. ....... ..178

5.1. Nucleation of 0' Near Edge Dislocations 178
5.2. Comparison with Previous Repeated
Nucleation Mechanisms ... .......... 182
5.3. The Mechanism in Al-Cu ... ......... .. 184
5.3.1. Local Solute Buildup .. ....... ..186
5.3.2. Precipitate Stringer Formation 190
5.4. Criteria for Repeated Nucleation in
Al-Cu and Application to Other Systems 196

6 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK . 198

BIBLIOGRAPHY ......... ................... 204

BIOGRAPHICAL SKETCH ....... .................. .208
vi









Abstract of Dissertation Presented to the Graduate Council of the University of Florida Ln Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


REPEATED NUCLEATION OF. PRECIPITATES
ON DISLOCATIONS !N ALUMINUM-COPPER


By

Thomas Je f rey Headley

August, 1974


Chai rman: John J. Hren
Major Department: Materials Science and. Engineering


Results are presented of an investigation of a newly

discovered -propagation mechanism for the ai-*e' transformation in Al-Cu: repeated nucleation on climbing dislocations. It was found that during the quench, dislocations are generated and climb by the annihilation of quenched-in vacancies. Densely populated colonies of e' precipitates nucleate in the stress fields of the climbing dislocations. In this way, the distribution of the entire volume fraction of e' is established during the quench.

The climbing dislocations were found to be a/2<110>

type, falling into three categories according to origin:

(1) pure-edge loops on {110) habits nucleated at dislocation climb sources, (2) glide dislocations initially on {111}, and (3) pure-edge loops on {llOl formed by the collapse of

vacancy clusters.

The effects of solution treatment temperature, aging

temperature, quench rate, and solute concentration on the vii










repeated nucleation process we re determined. It was found that repeated nucleation OCc-u-,s during quenching from all temperatures within the solid solution range1y, to all temperatures in the -range room temperature to 300'C. it occurs during slow and fast quenching as well, but does not occur in alloys with concentration Clwt.% Cu.

Mechanisms of repeated nucleation proposed earlier for other alloys are not applicable to Al-Cu. Dislocation climb and precipitation were found to be independently controlled

-processes. The relevant criteria for repeated nucleation in

this system are:

(1) a precipitate phase which nucleates easily on

dislocations,

(2) a source of dislocations during quenching,

(3) a driving force for dislocation climb which is

independent of the precipitation process, and

(4) a climb -rate slow enough to permit nucleation

but -rapid enough to avoid pinning.

It is suggested that pipe diffusion along the moving dislocation provides the necessary solute enhancement for successive nucleations.













1J.i i













CHAPTER 1

INTRODUCTION



Some of the most important strengthening mechanisms in alloys result from the precipitation of a second solid phase from a supersaturated solid solution. The age-hardening phenomenon in many aluminum alloys is a well-known example. A -precipitation reaction is a nucleation-and-growth transformation. Hence, the rate of the reaction is dependent -upon

(1) the nucleation rate of precipitates, and (2) the rate of their growth. If either or both of these rates is low the reaction rate will be low. Consequently, it is important to understand how and where precipitate reactions nucleate, apart from the problem of growth. Much is known about the kinetics of growth, but not about nucleation, especially heterogeneous nucleation.

Precipitate reactions nucleate either homogeneously or

heterogeneously within the matrix. If both the volume misfit and interfacial energy between precipitate and matrix are small, the reaction can nucleate homogeneously at random sites throughout the lattice. Homogeneous nucleation is known to, occur in only a few alloy systems, e.g., the precipitation of cobalt particles from dilute solutions of cobalt in copper (Servi and Turnbull, 1966). In most


1






2


precipitate reactions, either the volume misfit or interfacial energy, or both, is sufficiently large so that only heterogeneous nucleation occurs at preferred sites within the lattice. These sites are lattice defects such as grain boundaries,-dislocations, stacking faults, point defects, and other particles. Presumably, a portion of the energy

associated with the defect is supplied to help reduce the activation energy for formation of the critical nucleus, resulting in a nucleation event which is otherwise energetically unfavorable.

In the case of heterogeneous nucleation at dislocations, it is the dislocation strain energy in the matrix which helps overcome the barrier to nucleation. If the misfit strain caused by the precipitate is large, dislocation-nucleation may be the only method of decomposition of the supersaturated solid solution. Kelly and Nicholson (1963) and Nicholson (1970), have given excellent -reviews of the evidence for nucleation on dislocations in a number of alloy systems. A well-known example of heterogeneous nucleation on dislocations is that of the metastable 81 phase in Al-Cu alloys.

For a precipitate reaction which is dislocationnucleated, the following problem arises whenever the initial dislocation density is low, as is often the case following quenching. How can the reaction propagate once the available nucleation sites on dislocations have been saturated, i.e., what is the mechanism for propagation of the nucleation? Currently there are two known mechanisms whereby the reaction






3


may propagate. One mechanism is autocatalytic nucleation, first proposed by Lorimer (1968), and similar to the way in which martensite propagates. The initial precipitates nucleate on dislocations and grow into the matrix. In so doing, they generate stress fields in the matrix which aid in the nucleation of new precipitates. Thus, the reaction propagates in bands spreading out from the original dislocations to fill the lattice. Lorimer showed that the ca-*' reaction in Al-Cu could propagate by autocatalytic nucleation. Before

the present work, this was the only reported mechanism whereby the e' -reaction propagates from a low initial dislocation density.

Secondly, nucleation of the reaction can be propagated if the dislocation can somehow free itself from the initial

-precipitates and move away under a chemical or mechanical stress. It then presents fresh sites for the nucleation of

more precipitates. Nicholson (1970) was the first to use the term "repeated precipitation on dislocations" to describe this process. Repeated nucleation on climbing dislocations was first observed for carbide precipitation in austenitic stainless steel (Silcock and Tunstall, 1964). Since that time it has been reported for only a few other alloy systems. Very recently, Nes (1974) published a paper on the mechanism

for -repeated -precipitation on dislocations which he implied was universal with the statement that his model "can be applied to repeated precipitation (or colony growth) in any alloy system."






4


During experiments in which Al-Cu alloys were quenched directly to aging temperatures, this author observed that precipitation of the 01 phase occurred exclusively by repeated nucleation on climbing dislocations. Further examination revealed that the -repeated nucleation in this system could not be explained by the mechanism proposed by Nes (1974). Therefore, the primary purpose of this research was to establish the mechanism for repeated nucleation of 81 on climbing dislocations in Al-Cu, and in so doing, to determine if there

are aspects of the mechanism which might apply to precipitation in other alloy systems.














CHAPTER 2

REVIEW OF THEORY AND PREVIOUS WORK


2.1. Theory of Heterogeneous Nucleation
at Dislocations


Nucleation theory employs the concepts of a critical

nucleus and an activation energy for nucleation. An assumption of the theory is that random thermal fluctuations lead to the formation of small embryos of the transformed phase.

Embryos having a size and shape smaller than some critical size and shape will on the average disappear, and those with a larger size will grow and become stable. This critical size and shape is defined as the critical nucleus. The activation energy is the minimum energy barrier which must be overcome before nucleation can occur and turns out to be the free energy of the critical nucleus. This energy barrier is a maximum with respect to size and a minimum with respect to all other variables. The importance of the free energy of the critical nucleus can be recognized from its appearance in the equation for the steady state nucleation rate, which

is written in general form as

N s AG*
j = Z c exp 'RT (2.1)
s






6


where J =nucleation rate,

Z =the Zeldovich factor,

=frequency which atoms add to the nucleus,

N s= number of available nucleation sites,

cs= composition of the nucleus,

AG* = free energy of the critical nucleus,

k =the Boltzmann constant, and

T = temperature.

AG* has the form


AG* K surf) 2 (2.2)
(AGd-riv)T

where K =a shape factor,

surf particle/matrix interfacial energy, and
AG drive -driving force for the reaction.

For homogeneous nucleation, Ns is hig assuring reasonable nucleation -rates. For heterogeneous nucleation, N sis low

and the nucleation rate is usually dominated by the exponential dependence on the free energy of the critical nucleus.

For precipitation in solids, there is a chemical free

energy change per unit volume tending to drive the transformation to the new phase. If the atomic volumes in the matrix and particle are different, there is a misfit strain energy associated with formation of the new phase. Thus the free energy of the critical nucleus can be written


AG* = K( uf) 3
[AG(chem)+AG(strain)1






7


AG(chem) is negative whereas a surf and AG(strain) are positive. For a given reaction, AG(chem) can be calculated from thermodynamic parameters by the method of Aaronson et al. (1970). Attempts have been made to calculate surf from atomic bond models, but in general, the binding energies are unknown. In the absence of a proven model, surf is often taken as the measured bulk interfacial energy. The validity of this approximation is questionable. AG(strain) can be calculated by the method of Eshelby (1957,1961).

If a nucleus forms in the stress field of a dislocation, an additional energy term arises from the interaction of the displacement field of the precipitate with the stress field of the dislocation. We can then write AG* as


AG* = K(asurf)) 32
[AG(chem)+AG(strain)+AG(int)2"

AG(int) is negative and acts to reduce the positive AG(strain) term, so that it represents a major part of the advantage gained from nucleation at a dislocation. If AG(strain) is large (i.e., the precipitate misfit is large), nucleation at dislocations may be the only way the reaction can initiate. In addition to the AG(int) term, a second advantage for nucleation at a dislocation arises from the pre-exponential

term in Equation (2.1). This term is the frequency with

which atoms join the nucleus and depends on solute diffusion to the nucleus and across the interface. Solute pipediffusion along a dislocation core is always faster than






8


bulk diffusion, so that $ iic-reases for nucleation at a dislocation. Also, solute diffusion to dislocations themselves enhances the local concentration (e~g., Builough and Newman, 1959).

The task of calculating AG(int) is difficult, which is the main reason why the theory of heterogeneous nucleation at dislocations is less advanced than homogeneous nucleation theory. In fact, there have been only six published attempts to calculate AG* for nucleation at a dislocation. Cahn (19S7) made the first calculation. lie assumed an incoherent precipitate, an isotropic material, and completely neglected any interaction term. Despite these simplifications, his model

was able to predict qualitatively some experimental observations of nucleation at dislocations. Dollins (1970) calculated AG* for coherent, spherical and disk-shaped nuclei at a dislocation in an isotropic matrix. His work was reexamined by Barnett (1971). Lyubov and Solov'Yev (1965) have given the most complete treatment for calculating AG* for a coherent nucleus at a dislocation. Ram~rez and Pound (1973) attempted to include effects of the dislocation core energy on nucleation, effects that were omitted from the other models which use linear elasticity theory. An excellent recent -review of the present status of calculating AG* for nucleation at dislocations has been given by Larchd (1974). None of the above treatments, however, have included effects of elastic anisotropy, principally because the calculations involved are extremely difficult. It can be concluded that









the presence of the dislocation stress field aids in reducing the energy barrier to nucleation, but a rigorous calculation oF the el-fect is not yet available to provide an explicit expression for the rate of heterogeneous nucleation at dislocations.

It is instructive, however, to examine the order of magnitude or the terms in AG* to estimate the catalytic effect of the dislocation. Typical values of AG(chem) are in the range l-Sx109 ergs/cm3 (20-100 cal/cm 3). Values of AG(strain) are in the same range as AC(chem) for particles with appreciable misfit. Values of o obtained from bulk measurements are almost certainly too large since they relate to incoherent interfaces, whereas critical nuclei whose sizes
0
are of the order of 10's of Angstroms should have coherent interfaces. Estimates of coherent interfacial energies are
2
in the range 20-50 ergs/cm

If we take AG(chem) = 2x109 ergs/cm 3, surf = 20

ergs/cm2 and AG(strain) = 2x109 ergs/cm 3, then a spherical
0
nucleus with a diameter of 20A would have a chemical free
-13
energy change and strain energy = 8x10 ergs each, and a surface energy = 24x10-13 ergs. Due to the problems discussed above, no calculated values are available for AG(int),

but it is estimated that it can be of the same order of magnitude as AG(chem) and AG(strain). Then if one assumes that the surface energy is overestimated, as is likely (Barnett, 1973), the interaction energy due to the presence of the






10


dislocation can have an appreciable effect of lowering the total free energy of the critical nucleus, whenever AG(strain) is large.




2.2. Precipitation in the Al-Cu System


The aluminum-rich end of the Al-Cu phase diagram is a eutectic system between the aluminum solid solution and 8-CuAl (53 wt.% Cu). Figure 2.1 shows the portion of the diagram containing the a--solid solution region. Upon quenching from the solid solution region and aging, the equilibrium precipitate is the b.c.t. 0-phase. The existence of three metastable, transition phases, Guinier-Preston (G.P.) zones, 0" and 0', was established by the early x-ray work of Preston (1938a,b,c) on the 4 wt.% Cu alloy, and by Guinier (1938, 19391942,195Oi952) on the 4 and 5 wt.% Cu alloys. The solvus lines for these three transition phases are shown in Figure 2.1. The positions of the 0" and e, solvuses are due to Hornbogen (1967). That of the G.P. solvus is due to Beton and Rollason (1957).

Guinier (1938) and Preston (1938a) determined that the G.P. zones are coherent, copper-rich clusters of plate-like shape which form on {i00) planes of the matrix. The most reliable lattice parameters of the 0" and a' phases are given by Silcock et al. (1953). e" is complex tetragonal with a = 4.04X and c = 7.81. It is coherent with the matrix and








700


600
54 8'

500 +


U
0 400


+*
300 -+e


20- 6+ol"! SOLVUS
0+ C
E


SOLVUS
1 00

100 0+ G.P Zones

I

1 2 3 4 5 6 7
Al
Wt.0/o Cu


Figure 2.1. The aluminum-rich end of the Al-Cu phase
diagram, including the solvus lines for
G.P. zones, o", and e' precipitates.






12


forms as platelets on {1001 planes of the matrix. 0' is complex tetragonal with a = 4.04A and c = 5.8 It also forms as platelets parallel to {lOOI matrix planes, and is initially coherent on its broad faces and semi-coherent on its edge. As it grows its broad faces become semi-coherent. The orientation relationship for both 0" and 0' is {100} p.t {10 I lOmatrix and <100> ppt 11 <100> matrix' The tetragonal unit cell of e' is shown in Figure 2.2. There are 6 atoms/unit cell. The a-solid solution is f.c.c. with a = 4.0 45. and has 4 atoms/unit cell. When the atomic volumes are calculated for these two unit cells and compared, it is found that the o.-*0' transformation involves a 3.95% volume contraction. The resulting transformation strain can be partially compensated if vacancies are generated by the growing precipitates and supplied to the matrix.

The early x-ray work established the following precipitation sequence for quenching and aging below the G.P. solvus:

G.P. zones V" - el -+ e(CuAl 2).

However, as suggested by the x-ray work and later confirmed by many transmission electron microscope (TEM) studies, several of the reactions can proceed concurrently depending on the quenching and aging procedures. In addition, TEM investigations have clearly established the homogeneous or heterogeneous nature of the various reactions. Nicholson and Nutting (1958) -resolved G.P. zones and 0" platelets in the 4 wt.% Cu alloy and found them to be homogeneously distributed in the matrix. It is now clear, however, that 0"





13



(100)AI (OOl) e' /1!
/ 1,






5.8 A









O Aluminum Atoms Copper Atoms Figure 2.2. The tetragonal unit cell of 6' (after
Silcock, Heal, and Hardy, 1953).






14


must be nucleated on G.P. zones (Lorimer and Nicholson, 1969; Lorimer, 1970). If a sample is direct-quenched into the region below the e solvus but above the G.P. solvus (Figure 2.1), no 0" forms. However, if a sample is direct-quenched below the G.P. solvus and then up-quenched into this region and aged, 6" forms and its distribution is a function of the size distribution of G.P. ones present before the sample was up-quenched (Lorimer, 1970). Neither G.P. zones nor e" plays a role in the nucleation of 9'. Due to its misfit strain, 0' nucleates only heterogeneously in the presence of a stress field in the lattice. It nucleates either at dislocations (Nicholson and Nutting, 1958), in the stress fields of other 0' precipitates (Lorimer, 1968), or in the presence of a macroscopic stress applied to the sample during aging

(IHosford and Agrawal, 1974).

Numerous TEM investigations have confirmed the catalytic effect of dislocations for nucleating 6'. It was suggested early (Wilsdorf and Kuhlmarn-Wilsdorf, 1955; Thomas and Nutting, 1956), and later confirmed by TEM, that only certain 6' orientations will nucleate at a given dislocation. This is explained in terms of the misfit strain of the 8' platelet and the Burgers vector of the dislocation. In Figure 2.3, it is shown that the principal misfit around a 6' platelet is normal to the {100} plane of the platelet. In Figure 2.4, it is shown that a dislocation with Burgers vector a/2[110]

partially relieves the misfit strain around e' platelets on (100) and (010) whose misfits lie at 450 to the Burgers vector,











I



/ DIRECTION
0 OFMISFIT
I! !

PLATELET
a= b=4.04A c=5.8 aAl-Cu MATRIX
a: b: c: = 4.04A




Figure 2.3. Diagram showing that the distortion of (001)
planes around a 8' platelet is normal to the
platelet (not to scale).





LoTO] [100] COMPRESSION

MISFIT MISFIT [0
N*,/ MATRIX

G' on (010) f on (100) ORIENTATION


b=a/2[110]

TENSION



Figure 2.4. Diagram showing that a dislocation with
Burgers vector a/2[l10] relieves the misfit
around e' platelets lying on (100) and (010).
It does not relieve the misfit around a
platelet on (001).






16


but not for a 01 platelet on (001) whose misfit vector is perpendicular to the Burgers vector. Hence, the (001) orientation gains no advantage by nucleating in the stress field

of the dislocation. Likewise for a dislocation with F=a[1001, only the (100) orientation of el should nucleate in its stress field.

Many early TEM investigations of the 81 phase were conducted after long aging treatments at high temperatures in the a+e' field (Figure 2.1). The resulting microstructures contained a uniform distribution of large 81 platelets, and it was initially concluded that these 61 platelets were nucleated by a -random distribution of pre-existing 8". However, as it became clear that 81 nucleates at dislocations and not at e", the problem of how the -random distribution of e' could form by quenching and aging alone remained unresolved until the work of Lorimer (1968,1970). Lorimer showed that the a-*el reaction could propagate from an initially low dislocation density, introduced during quenching, by an autocatalytic nucleation mechanism. Early during the aging period, the initial dislocations become saturated with 0'. These platelets then grow into the matrix and produce their own stress fields which aid the nucleation of more precipitates. With long aging, the reaction propagates in bands spreading out from the dislocations to fill the structure with a uniform distribution of 0' platelets on all three {100} orientations. Until the present research, this was the only






17


-reported mechanism whereby the cx*e, -reaction was found to propagate from a low initial dislocation density.





2.3. Dislocation Climb

2.3.1. quenched-In Vacancies and the
Chemical Climb Force

It is now widely accepted that vacancies can exist in

crystals in thermal equilibrium with the lattice. The equilibrium concentration of vacancies increases exponentially with temperature according to the Arrhenius relation:


C 0 = A exp(-E f/kT)


where A =an entropy factor,

E f the activation energy for forming a vacancy,

k =the Boltzmann constant, and

T =temperature.

Large supersaturations of vacancies can be retained in the lattice by quenching rapidly from elevated temperatures. During and after the quench, the excess vacancies diffuse to

sinks such as surfaces, grain boundaries, and dislocations, or they may cluster and collapse into vacancy disks bounded by dislocation loops. The condensation of vacancies onto a dislocation causes it to undergo positive climb. The greater the supersaturation of vacancies, the greater is the driving force for climb. A simple picture of dislocation climb by vacancy annihilation is shown in Figure 2.5(a). Dislocations






18


can also climb by vacancy-emission (negative climb) and this is illustrated in Figure 2.5(b).

Christian (1965) has suggested that the vacancyannihilating climb of a/2 dislocations in f.c.c. lattices occurs easily only on the {111} and {l10} planes. A necessary condition for climb is that the Burgers vector has a component perpendicular to the plane of climb. Therefore there are two {lll} and five {l10} "planes of easy climb" for an a/2[l10] dislocation in f.c.c. Miekk-oja and Raty (1971) have considered the choice of climb planes in terms of the chemical climb force on each plane. This force arises from the supersaturation (or subsaturation) of vacancies (Bardeen and Herring, 1952). Its magnitude is proportional to (-xu), where Iis the Burgers vector and u is the dislocation line direction. Thus, according to Miekk-oja and Raty, a dislocation with F a/2[l10] is affected by the maximum climb force, F c,max'
on the {1101 plane perpendicular to F-. It is not affected at all on the {111} and {10} planes containing b. And it is affected by forces 0.82F and O.5F on the two {lll}
c, max c, max
and four {110} planes, respectively, which are inclined to E.


2.3.2. Theory of Dislocation Climb
In reality, dislocation climb is more complex than the

simple picture envisioned in Figure 2.5. The theory of climb

has been developed by Lothe (1960), Thomson and Balluffi (1962), Balluffi and Thomson (1962), Friedel (1964), Hirth





19






OOO00 O000000 000@000 OOO OO OO OO0OO OO~Oo oooooo0 1000000 0Q00O0 0000000 000000 000000 OOO OOO0 OOO OO OOO OOO0
OOO OO OO oOO OOO OOO
OOOOOO 000000 000000 000000 000000 000000
a




0000000 0000000 000@000 000@000 0000000 0000000

oooooo ooo ooo ooooOO ooo-qoo 00o0&00 0000 0 000000 OOOOOO 000000 000000 000000 000000
b



Figure 2.5. (a) Positive climb of an edge dislocation
by vacancy annihilation. (b) Negative climb by vacancy emission (after Reed-Hill, 1973).









and Lothe (1968) and a general review of the mi-echanisms has been given by Balluffi (196)).

Briefly, dislocation cLirib occurs by (i) the absorption of vacancies onto the dislocation core, (2) diffusion of the vacancies along the core to jogs, and (3) subsequent movement of the jogs by destruction of the vacancies. This sequence is illustrated in Figure 2.6 for climb of an undissociated edge dislocation (a similar model applies for climb by vacancy-emission). Then, according to Balluffi (1969), the dislocation climb velocity is

2 Dlb2 [c (R) -c]
V =

[kn(4I) A 7)

where D = vacancy diffusivity in the lattice,

b = magnitude of the Burgers vector,

c(R) = vacancy supersaturation at a large distance
R from the dislocation,

c = vacancy concentration maintained in the
lattice in equilibrium with the jogs,

z = mean migration distance of a vacancy along
the core before jumping off, and

= jog spacing.

Seidman and Balluffi (1968) surveyed the available experimental data on climb rates and concluded that, in the presence of moderate to large supersaturations, climb in aluminum appears to be highly efficient. In other words, jog production and motion is sufficiently fast that the climb rate is limited only by the diffusion of vacancies to the dislocation, and the dislocation acts as a perfect line sink.






21














VACANCIES

a






















C



Figure 2.6. Diagram of vacancy processes associated with
climb of the extra half-plane of an edge
dislocation. Vacancies absorb onto the core
(a) diffuse along the core (b) and annihilate
at jogs (c). Subsequent motion of the jog across the page moves the extra half-plane
up one atomic spacing.






22


2.3.3. Dislocation Climb Sources

The classical dislocation multiplication mechanism is

that proposed by Frank and Read (1950), whereby a dislocation, pinned at each end, expands in its slip plane by glide. Westmacott et al. (1959) observed dislocation sources in thin foils of Al-4 wt.% Cu by transmission electron microscopy, and interpreted them to be Frank-Read sources. Gulden and Nix (1968) have observed similar sources in Al-4 wt.% Cu3 wt.% Si. Analogous to the Frank-Read mechanism, a dislocation multiplication mechanism which operates by climb was

proposed by Bardeen and Herring (1952) to act as a continuous sink for excess vacancies. The Bardeen-Herring model for a dislocation climb source is shown in Figure 2.7. Initially, a straight dislocation between A and B has its slip plane normal to the plane of the paper. Hence, it can move in the plane of the paper only by climb. Condensation of vacancies onto this line would move the dislocation out through the sequence of positions shown. When the bottom segments of the loop meet, they annihilate and rejoin as shown by the dotted lines. The segment ABC is now free to repeat the process,

and there is left a vacancy loop outlined by the dislocation ring. As long as there remains a vacancy supersaturation in the region, this loop will expand, removing atoms from the lattice, and the operation can repeat removing an indefinite number of planes.

Dislocation climb source configurations were first observed by TEM in Al-Mg alloys (Westmacott et al. 1962;






23










































Figure 2.7. The Bardeen-Herring model of a dislocation
climb source. An edge dislocation, pinned
between AB, has its slip plane normal to the paper. It climbs in the plane of the paper, by vacancy annihilation, through the successive positions 1-4, rejoining at the bottom.
The portion ACB can then repeat the process
(after Bardeen and Herring, 1952).






24


Pmbury and Nicholson, 1963). Since then, dislocation climb sources have been identified in aluminum (Ldington and West, 1966) and a number of other aluminum alloys, including Al-Ag (Edington and West, 1966), Al-Ag ternary alloys (Passoja and Ansell, 1971), and Al-Cu (Boyd and Edington, 1971). They have also been observed in other systems, including silicon (Ravi, 1971) and NiAI (Marshall and Brittain, 1974). Often the dislocation climb sources observed by TEM have small particles at the center of the source loop. An example from the present work is shown in Figure 4.2. Although the particles are usually too snail to be identified, it is thought that they are insoluble particles existing at the solution treatment temperature. It is generally believed that vacancies diffusing to the particle interface activate the source which then operates to produce successive loops. The source itself is often thought to be a portion of a misfit dislocation at the particle/matrix interface.

The only reported observation of dislocation climb

sources in binary Al-Cu alloys is that of Boyd and Edington (1971). They observed source densities of about 3/grain. These sources generated pure-edge loops on {1101 habits with a/2 Burgers vectors.






25


2.4. Repeated Nucleation on Dislocations


The concept of repeated precipitation on climbing dislocations was first proposed by Silcock and Tunstall (1964) to explain the occurrence of planar colonies of NbC precipitates on stacking faults in austenitic stainless steels. In connection with the precipitate reaction, the stacking faults were found to grow by the climb of a/3<111> Frank partial dislocations bounding the fault. The transformation

to the NbC -phase involves a 23% volume expansion, so that the growing precipitates consume vacancies from the matrix in order to relieve the transformation strains. Silcock and Tunstall proposed that the Frank partial climbs by vacancyemission in order to feed vacancies to the transformation. Thus the driving force for the dislocation climb is this need to supply vacancies for the precipitate reaction. The principles of the Silcock-Tunstall model are outlined in Figure 2.8.

Repeated precipitation on climbing dislocations by this

mechanism has since been reported in a variety of systems, including different steels, an iron-vanadium alloy, a coppersilver alloy, superalloys, and semiconducting materials. The

phenomenon has been observed to occur on both partial and total dislocations. For the sake of brevity, the list of reports will not be given here, and the reader is referred to the complete list in the recent paper by Nes (1974). In every reported case to date, the precipitate phase has a larger atomic volume than the matrix, thereby consuming






26














XF


\\INbC~










a b C d e










Figure 2.8. The Silcock- Tuns tall model for repeated precipitation of NbC in austenitic stainless
steel. The precipitates nucleate on Frank
partials (a). Movement of jogs, J, provides
vacancies for the precipitates to grow (b)
with the consequent climb of the dislocation (c). The dislocation pinches off (d) and the
process repeats (e) (after Silcock and Tunstall,
1964).






27

vacancies during the transformation. In every case the dislocation climb has been reported to be vacancy-emitting in order to supply the necessary vacancies.

Nes (1974) has expanded the original model of Silcock and Tunstall (1964) into a more quantitative theory, which was intended to account for the various features of repeated precipitation in all the systems reported since 1964. The

fundamentals of the Nes theory are:

(1) Vacancies must be supplied to the transforming

particles in order to reduce the particle/matrix

mismatch.

(2) The subsequent particle growth causes vacancyemitting climb of the dislocation in order to

feed the transformation.

(3) The particle growth/dislocation climb sequence

between conservative nucleations is controlled

by balancing the rate at which vacancies must be supplied to the precipitates with the climb

rate of the dislocation.

(4) The particle is dragged some distance by the

dislocation before unpinning occurs.

(S) The rate controlling parameters in the kinetics

of colony growth are either (a) the atomic diffusion of the precipitating atoms, or (b) the core (interface) self-diffusion, depending on

which has the highest activation energy.






28


Nes implied that this mechanism is applicable to repeated precipitation on climbing dislocations in all systems, whereas in reality, it probably applies only when there is required a mass balance of vacancies between growing precipitates and

climbing dislocations.

There is one report of repeated precipitation on climbing dislocations which has not been attributed to the above mechanism. Embury (1963) observed that dislocations in Al-Mg alloys were drawn around M92 A 13 precipitate particles, pinched off leaving loops, and climbed away under the chemical force of a quenched-in vacancy supersaturation where the process repeated. However, this process is reported to occur only to a small extent.





2.S. Pertinent Electron Microscopy Theory


2.S.1. Two-Beam Diffraction Contrast Theory

In the transmission electron microscope, contrast arises from differences in intensity scattered out of the incident electron beam by Bragg diffraction from the crystal planes. The best contrast from defects occurs under so-called "twobeam" conditions. Owing to the large amount of tilt available in commercial goniometer stages, the crystal can be oriented so that the incident beam diffracts strongly only from one set of lattice planes. Then approximately 95% or more of the incident intensity is contained either in the






29


beam scattered in the forward direction (called the "transmitted" or "main" beam), or in the strong diffracted beam. The electron image is usually formed by placing an aperture around one of these beams and allowing it to pass through, while the other beam is blocked by the aperture holder (Figure 2.9). The unblocked beam is then magnified by successive lenses and projected onto the fluorescent screen. When the aperture is placed around the transmitted beam, the image formed is called a "bright-field" image. When it is placed around the diffracted beam, the image is called a "dayk-field" image. Contrast at defects arises in, say, the bright-field image because the strain in the lattice around the defect causes local distortions in the atomic planes which lead to local changes in the intensity scattered into the diffracted beam. This in turn leads to local variations in intensity in the bright-field image. This is illustrated for the case of a dislocation in Figure 2.10.

When a crystal of sufficient thickness is oriented very close to the Bragg condition for one set of planes, there can be a dynamic interchange of electrons between the two beams,

resulting from multiple scattering back and forth as the two beams pass through the crystal (Figure 2.11). In order to predict the intensities in the bright- or dark-field image, it is necessary to describe mathematically the physical processes which go on in this dynamic interchange. The two-beam dynamical theory of electron diffraction for a distorted crystal was developed by Howie and Whelan (1961). Their






30









INCIDENT BEAM










CRYSTAL



TRANSMITTED DIFFRACTE C

\D11
BEAM if BEAM


-OBJECTIVE
LENS PLANE





OBJECTIVE APERTURE

HOLDER












Figure 2.9. Method for forming a bright-field image under
two-beam conditions. The transmitted beam is
allowed to pass through the objective aperture
while the diffracted beam is blocked by the
aperture holder.






31





INCIDENT BEAM
















A All X






DIFFRACTED INTENSITY








TRANSMITTED INTENSITY




Figure 2.10. Diagram illustrating how contrast a-rises in
the transmitted and diffracted beams from
diffraction off the distorted planes around an edge dislocation. Planes to the left of the dislocation are tilted toward the Bragg angle. Planes to the right are tilted away
from the Bragg angle.







32











INCIDENT



BEAM












FOIL
THIC KNESS DIFFRACTING PLANES










DIFFRACTED
BEAM

TRANSMITTED BEAM








Figure 2.11. Diagram illustrating the dynamic interchange
of electron intensity between the two beams
resulting from multiple scattering events.






33


derivation is similar to the derivation of a two-beam theory for x-ray diffraction by Darwin (1914). The Howie-Whelan theory predicts the amplitudes T and S of the electron waves in the transmitted and scattered beams, respectively, at any point in the crystal. The formulation of the theory uses a column approximation, whereby the crystal is imagined to be divided up into parallel columns in the direction of the incident beam. Dynamic interchange between T and S is considered within a column, but not between neighboring columns. This is a valid approximation because the Bragg angles for high energy electron diffraction are small (-l/2).

The Howie-Whelan theory predicts the following coupled

pair of first-order differential equations for the variations in T and S with depth in the crystal:

dT = (Tri/ )T + (Ti/C )S exp(27risz+2Tig'*)


dS (ii/ o S + (Tri/ )T exp(-27isz-27ig.R)


where T = amplitude of the incident beam,

S = amplitude of the diffracted beam,

z = depth in the crystal in the direction
of the incident beam,

s = parameter measuring deviation from the
Bragg condition,

= the diffracting vector,

= the local displacement field at depth z,

o= parameter related to mean refractive index
of the crystal, and

= the extinction distance.
g






34


Each separate equation represents the variation in amplitude of the electron waves in that beam as it passes through the crystal. The first term in each equation represents the intensity scattered in the forward direction for that beam. The second term in each equation represents the intensity scattered into that beam from the other beam.

In order to account for experimentally observed effects

of absorption, it is necessary to replace the quantities l/ and l/Cg in the equations by the complex quantities (co+i/Eo') and (1/ +i/), respectively. One then obtains:

dT = ri(l/ o+i/C')T + Tri(l/ +i/Yg)S exp(2Tisz+27ig'7)
a T o g 9(~s+n~

dS= (l/ +i/E')S + rilWE +i/YT exp (-2risz -2'igR)


Multiplying the amplitudes T and S by their complex conjugates gives the relative intensities in the two beams at any point in the crystal. In particular, when the intensity is calculated at the bottom of all imaginary columns in the foil, it predicts the image projected onto the viewing screen, since no interaction occurs in vacuum once the beams exit the crystal.

In the absence of any displacement field (7=0), or in the presence of a fixed, rigid body displacement (7=constant), the equations can be solved analytically for T or S, and the solution predicts a uniform intensity over the bottom of the crystal. When the displacement field R7 varies with depth, as is the case around dislocations and other defects, the equations can no longer be solved analytically, and numerical

methods must be used to obtain T and S.






35


The validity of the Howie-Whelan equations in predicting intensities which correspond to two-beam images has been

overwhelmingly demonstrated by the success of computer simulation techniques for matching defect images (Head et al., 1973). (See for example Section 4.2.1.)


2.S.2. Defect Identification from
Invisibility Conditions

Although the solution of the two-beam equations is not straightforward for the case of defects with varying displacement fields, often the solution pfr se is not needed to identify the defect from its image. Instead, it is often possible to apply a simple criterion to identify defects in the electron microscope. This criterion is based on the fact that the term in the equations which gives rise to contrast is the product 9-7. The diffraction vector g is the reciprocal lattice vector normal to the diffracting planes,

so that the product -R samples the magnitude of the distortion created in the diffracting planes by the displacement field 7. If a defect happens to cause no distortion in the diffracting planes for a two-beam condition, then g-R=0 and the two-beam equations predict uniform intensity everywhere at the bottom of the foil. In other words, there is no contrast around the defect and it is said to be "invisible" for this diffraction condition. This criterion, applied to the identification of dislocations, can be described as follows. To a first approximation, the planes -parallel to the Burgers vector of a dislocation in an isotropic crystal are not






36


distorted. Then when the crystal is oriented so that one such set of planes is in the reflecting position, the dislocation will be "invisible" in the image. The diffracting vector is perpendicular to the diffracting planes, and therefore to the Burgers vector for this condition. Hence, the criterion for invisibility of a dislocation is the wellknown relation j.K-=O. To identify the Burgers vector of a dislocation, it is simply a matter of tilting the foil and selecting various two-beam conditions until two diffraction vectors, g, and 92,are found for which the dislocation is invisible in the bright-field image. The Burgers vector must be perpendicular to both g, and 92 so that it can be determined from their cross product, i.e., E-=( 9 x9. However, this technique is not capable of determining the Burgers vector unambiguously, i.e. whether it is +5 or -5b. Furthermore, the criterion B_=O for invisibility applies only to screw dislocations where, in the isotropic approximation, all sets of planes parallel to the Burgers vector are undistorted. This is not so for an edge dislocation. For a set of planes to remain undistorted by an edge dislocation, not only must 9-5=O, but in addition, g must be parallel to the dislocation line direction. Mathematically this is written 9-(ExY)=O, where a is the line direction. This is a very stringent condition which is seldom obtained in the microscope. Thus, edge dislocations, or dislocations with appreciable edge orientation, often exhibit strong "residual contrast" when -B_=O, due to the (Fxii) term. For






37


this reason, practical experience in recognizing "residual contrast" is necessary in order to identify dislocations from the invisibility criterion.

The criterion 9-57=0 for invisibility is valid only for total dislocations, where the product 9-F can be only zero or an integer (since it is the product of a reciprocal lattice vector and a real lattice vector). For partial dislocations, T-Fcan take on the non-integer values 1/3, 2/3, 4/3, etc., in cubic lattices. Howie and Whelan (1962) determined that partial dislocations are invisible when jT-b_=O or 1/3 and are visible for all other products. Silcock and Tunstall (1964) further determined that, for this to be strictly valid, the deviation from the Bragg condition cannot be too large.

The condition that a defect is "invisible" if its displacement field does not distort the reflecting planes can be applied to identify certain small precipitates. For example, in the case of el platelets in Al-Cu, the principal misfit in the lattice caused by the platelet is normal to the plane of the platelet (Section 2.2). If such platelets are too small to distinguish their shape, their orientation can still be determined since they will be invisible whenever g is perpendicular to the misfit vector.


2.5.3. Imaging Precipitates in the
Electron Microscope

Precipitates can be imaged by one or more of several mechanisms in the electron microscope. A good description






38


of these mechanisms is given by Hirsch et al. (1965, p. 336). Those pertinent to this research will be outlined below.

(1) Strain contrast in the matrix. All coherent and

semicoherent precipitates, and most incoherent precipitates, cause some strain in the matrix. These strain fields therefore give rise to diffraction contrast effects in the matrix.

This can be the only mechanism for imaging very small precipitates whose sizes are less than the resolution limit of the microscope, but whose long-range strain fields are

greater than this limit.

(2) Misfit dislocation imaging. Semicoherent precipitates have misfit dislocations over their semicoherent interfaces. The strain fields of these misfit dislocations can cause strain contrast just as for isolated dislocations in the matrix. Weatherly and Nicholson (1968) have investigated the conditions for imaging misfit dislocations. Often small platelets viewed normal to the platelets are imaged by the misfit-dislocation loops around their edges. This is referred to as "dislocation-ring" contrast.

(3) Structure factor contrast. According to Ashby and Brown (1963), this contrast arises whenever a coherent precipitate has a different structure factor from the matrix, and thus a different extinction distance. A particle of thickness Lt then increases the effective foil thickness in columns -passing through the particle, giving rise to an intensity change relative to columns in the matrix. Depending on the depth of the particles in the foil and the






39


relative values of the extinction distances in the particle and matrix, the particles can appear either lighter or barker than the surrounding matrix. Structure factor contrast arises only within the limits of the particle boundary.

(4) Orientation contrast. This contrast mechanism

arises whenever a foil is oriented such that a certain set of lattice -planes in the precipitate is diffracting strongly, whereas the matrix is diffracting weakly, or vice versa. The contrast is of a uniform light and dark nature, typically dark precipitates in a light matrix. Orientation contrast can arise only when there is appreciable difference in crystal structure between the precipitate and matrix, i.e., when the precipitates are semicoherent or incoherent. For example, when the electron beam is parallel to the thin dimension of large precipitate platelets, often certain lattice planes in the precipitate will also be parallel to the beam. In this case, the precipitate diffracts strongly. If the matrix is not oriented for strong Bragg diffraction, the bright-field image will show dark precipitates in a light matrix.

(5) Displacement fringe contrast. Displacement fringe

contrast arises when there is an abrupt change in the phase of the transmitted and diffracted waves as they encounter a thin sheet of precipitate which displaces the matrix planes in opposite directions on either side of it. This displacement IT around a typical semicoherent precipitate platelet is normal to the plane of the platelet, and its magnitude is given by






40


1 R A I nIF n I


where At = thickness of the platelet,

6 = precipitate misfit,

n = number of misfit dislocations at the
periphery of the platelet, and

= Burgers vector of the misfit dislocations.

When this displacement is substituted into the equations of the dynamical theory, the intensity of the transmitted beam is found to oscillate with thickness (Whelan and Hirsch, 1957). Thus, when the precipitate platelet is inclined to the electron beam, a fringe effect is observed. The socalled stacking fault fringes are the limiting case of displacement fringe contrast.














CHAPTER 3

EXPERIMENTAL PROCEDURES AND MATERIALS



3.1. Specimen Materials


The four Al-Cu alloys used in this work were obtained

as rolled sheets from a previous research project. They were prepared from 99.99% aluminum and 99.99% copper by double melting in an induction furnace using a graphite mold. After solidification, the billets were alternately cold-rolled and

annealed to reduce them to sheet form.

The target compositions were the 4, 2) 1, and 1/2 wt.% Cu alloys. The nominal copper concentrations of the four alloys were 3.85, 1.96, 0.99, and 0.5 wt.%, based on starting weights before melting. The impurity content in the 3.85 wt.% Cu alloy was determined by x-ray spectrographic analysis by the Sandia Corporation, Albuquerque, New Mexico. The impurity levels are given as ranges in Table 3.1. The barium level is suspect as it was determined from only one line. The impurity levels in the other three alloys were not determined. However, since all four alloys were prepared from the same starting materials, the other three probably had the same impurity levels as the 3.8S wt.% Cu alloy.

The 1 wt.% and 1/2 wt.% Cu alloys were obtained as

rolled sheet, 0.038 inch and 0.034 inch, respectively. They 41






42


Table 3.1

Impurity Levels in the A1-3.85 wt.% Copper Alloy


I purity Weight ppm

Fe 5-25

Pb <10

Si 1-10

Mo <10

Mg 5-20

Ca 1-5

Ga <10

Ba 10-40




were then cold-rolled to 0.005 inch for heat treatment. The

3.85 wt.% and 1.96 wt.% Cu'alloys were obtained as rolled sheet, 0.004 inch thick. They were not reduced further before heat treatment. Samples for heat treatment were cut from the rolled foils to the approximate dimensions 1/8 x 1/2 x 0.004 inch. This was found to be a suitable size for preparing electron microscope specimens after heat treatment.





3.2. Heat Treatments


All samples were solution treated for one hour at a

temperature in the a-solid solution range (Figure 2.1). Next, they were either (1) direct-quenched to an aging temperature






43


above the G.P. solves, or (2) quenched to a low temperature. The samples given direct-quenches were aged for various times from approximately one second to 24 hours, and then quenched into room-temperature water. Samples quenched to low temperatures were either prepared for electron microscopy without further treatment,, or they were up-quenched to a temperature above the G.P. solves and aged for various times. They were then quenched into room-temperature water.

The solution treatments were conducted in a vertical furnace in air. The temperature in the heat zone was controlled to within 2'C. One end of the sample was clamped in a stainless steel alligator clip attached to the bottom of a one-half inch diameter stainless steel tube, and this was inserted into the heat zone of the furnace. Before each treatment, the temperature in the heat zone was determined by inserting a thermocouple into a dummy stainless steel tube

suspended in the heat zone.

Quenching was achieved by dropping the specimen-stainless steel tube assembly out of the bottom of the furnace into the quench bath. For direct-quenches to the aging temperature, the specimen was dropped into a Lauda Constant Temperature Oil Bath, maintained at the aging temperature, to within 0.2'C. A schematic diagram of the apparatus used for solution treatment and direct-quenching is shown in Figure 3.1. For quenching to low temperatures, the specimen was dropped into one of several low temperature baths in place of the oil bath. Following the quench to low temperatures, some






44





CLAMP -STAINLESS STEEL TUBE




INSULATION- VERTICAL
FURNACE




ALUM IN UM -SPECIMEN
BLOCKALLIGATOR CLIP









DROP 18INCHES
QUENCH MOTOR





CONSTANT
OIL TEMPERATURE
dub OIL BATH
HEATER STIRRER






Figure 3.1. Diagram of the apparatus used for solution
treatment and direct-quenching. The specimen,
attached to the stainless steel tube for weight,
is dropped from the solution treatment furnace
into the constant temperature, aging bath.






45


sampDles were immediately up-quenched into the constant temperature oil bath maintained at the desired aging temperature. Due to the wide variety of solution treatment temperatures, aging temperatures, and aging times employed in this research, no table of heat treatments will be given here. Instead, the specific heat treatment information will be given either in the text or in the figure captions.





3.3. Electron Microscope Specimen Preparation


Electron microscope specimens were prepared from the

heat treated strips by electropolishing in a solution of 5% perchloric acid in methyl alcohol. A polishing potential of 18 volts d.c. was used with a stainless steel cathode. The electropolishing setup is shown in Figure 3.2. The beaker containing the polishing solution was immersed in a bath of dry ice and acetone to slow down the polishing reaction. The solution was circulated at a slow speed with a magnetic stirrer to keep it cold. Under these conditions, the polishing bath was maintained at -45'C.

The specimen strip was held with locking tweezers and polished by dipping the bottom end (approximately 1/8-3/16 inch) into the solution at a dipping rate of about 1/second. Dipping was found to reduce edge attack and to give a relatively uniform polish. The voltage dropped to about 12 volts during immersion. Total polishing time to obtain a suitable







46










18B VOLTS d.c. TWEEZERS











50/. PE RC HLO RIC SEIE
ACID IN METHANOL
!STAINLESS STEEL CATHODE (2 HALVES)














MAGNETIC
STIRRER









Figure 3.2. The electropolishing setup for preparing thin
foils for electron microscopy. Polishing is
accomplished by dipping the bottom end of the
specimen into the solution.






47

thin area was about 1S minutes. When it was determined (by experience) that the specimen was nearly thin enough, the stirring was stopped to avoid damaging the thin area. The

last 20-30 seconds of polishing was done by immersion and agitation instead of dipping, since dipping to the last was found to sometimes etch the thin foil edge. Polishing was continued until the bottom edge appeared very ragged or until small holes had broken through. Then the power was switched off and the specimen was rapidly removed and plunged into a beaker of cold acetone (99.8% pure) immersed in the dry iceacetone cooling bath. It was agitated for about 10 seconds and then immediately placed under a stream of room-temperature

acetone from a wash bottle. After washing for about 30 seconds, it was allowed to dry in air. The initial wash in cold acetone was necessary to remove most of the electrolyte which rapidly etched the polished surface if allowed to warm to room temperature.

The thinned, bottom portion of the sample strip was cut

off with an X-acto razor knife and mounted in a 3 mm, 7S mesh, locking, double copper grid for viewing in the electron microscope. Several more specimens could then be polished from the sane sample strip, if desired. However, the remaining bottom part of the strip was already polished quite thin. To avoid etching this polished surface, the specimen was agitated for about one minute in the small beaker of cold acetone prior to repolishing.






48

3.4. Electron Microscopy


The thin foils were examined in a Phillips EM 200 electron microscope operated at 100 Kv potential. A goniometer stage with 45' and 300 tilt on two orthogonal axes was used.

Two-beam diffraction conditions were established for taking all micrographs. To obtain two-beam conditions, the foils were oriented close to one of the low index poles shown on the Kikuchi line map for an f.c.c. crystal in Figure 3.3. Use of this Kikuchi line map during specimen tilting, as described by Head et al. (1973), enabled diffraction vectors

to be determined unambiguously in every case.






49













10 0 D200 --0












13T








Figure 3.3. Kikuchi line map over two adjacent stereographic triangles for a face-centered cubic
crystal (after Head et al., 1973).














cJii'PTR 4

EXPERIMENTAL RESULTS AND ANALYSES



4.1. Tvatroduction


Evidence for repeated nucleation of the 6' phase on dislocations was first observed in this research when the Al-3.85 wt.% Cu alloy was quenched directly to aging temperatures above the 6"' solvus. Figure 4.1 shows a typical inicrostructure resulting from direct-quenching and aging.

A brief description of the features and evolution of this microstructure (with the facts to be established in this chapter) is as follows. Dispersed throughout the foil are densely populated colonies of small e' precipitates. The colonies are bounded either totally or partially by dislocations, some of which are out of contrast in this image. The dislocations were generated and climbed during the quench From the solution treatment temperature. As they climbed, they nucleated and dispersed the e, colonies in their paths. All dislocations climbed during quenching and all nucleated precipitate colonies. The precipitate colonies may (1) be planar, (2) lie on smoothly curved surfaces, or (3) lie on corrugated-shaped surfaces, depending on the climb paths of the dislocations.



50






Si







01

16


























1A4










Figure 4.1. Typical microstructure resulting from quenching the Al-4 wt.% Cu alloy directly to the

of mal 8'precipitates, bounded by dislocation. (eattreatment: S.T. 1 hour, quench
to 200. ae Sminutes.)






?


The primary goal of this research was to determine the

mechanism by which repeated nucleation of 0' occurs in the Al-Cu system. However, since this work is the first reported observation of the phenomenon in Al-Cu alloys, a secondary goal was to characterize thoroughly the various features of the microstructures observed. The geometrical analyses are reported in detail here.

The material in this chapter is developed much in the

way in which the experimental analysis was performed. First, in Section 4.2, the nature and sources of the climbing dislocations are established. Next, in Section 4.3 the precipitate is identified as 0' and characterized as to distribution of orientations in the colonies. Section 4.4 contains descriptions of the various geometries and some of the diffraction effects. Finally, Section 4.5 describes results of experiments designed to determine the effects of different parameters on the repeated nucleation process. Most of the analyses for identification purposes were conducted on the

3.85 wt.'O Cu alloy. Accordingly, all micrographs in this chapter are from this alloy, except those in Section 4.5.5. In addition, most micrographs in this chapter are from samDles quenched directly to aging temperatures. For the sake

of brevity, the copper concentration of the alloys is listed in the figure captions as either 4, 2, 1, or 1/2 wt.%.






S3


4.2. Nature and Source of the Climbing Dislocations


The dislocations which climbed during quenching can be classified mainly into one of two categories according to origin: (1) those generated at dislocation climb sources, and (2) glide dislocations which subsequently climb (a third category found in alloys quenched into oil or water at room temperature will be discussed in Section 4.S.4).


4.2.1. Dislocation Climb Sources

Figure 4.2 shows micrographs from fOilS direct-quenched to 220'C and aged for short times before quenching to room temperature. Present in the microstructures are configurations consisting of concentric dislocation loops. When viewed edge-on, the loops are seen to be coplanar Since their traces are Straight lines, as at points A in Figure

4.2(c). Tilting the foil confirms that these straight lines are traces of coplanar loops. Concentric loops sectioned by the thin foil leave straight-line traces with the foil surfaces, e.g., at B-B in Figure 4.2(b) and (c). Often small particles were observed at the center of the loops as in Figure 4.2(b). The operation of dislocation sources has been

discussed in Section 2.3.3 and will not be repeated here. It will now be established that these are climb sources, and the Burgers vectors and habit planes of the loops will be identified.

A typical source is shown in Figure 4.3. Several loop habits have been generated at the source. We are concerned






54



















a b

















J A4


C



Figure 4.2. Dislocation sources in Al-4 wt.% Cu directquenched from 550'C to 220'C and aged for
8 seconds in (a) and (b) and one minute in (c).






55

















a b

~ 41 9 ii i:'i ,,i! i









C d












e



Figure 4.3. Series of micrographs for determining the
geometry and Burgers vectors of the source
loops. The beam direction is close to [101]
in (a), (b), and (c), to [112] in (d), and
to [001] in (e). (Heat treatment: S.T.
1 hour 550'C, quench to 220'C, age 8 seconds.)





56


in this analysis with the outermost ioop and the one inner loop which lie totally within the foil. The plane of the

foil was analyzed to be very close to (101) so that this loop habit must lie on or very close to (101). Consider first the three images (a), (b), and (c) taken about the [101] beam direction. In each image the source loops on (101) exhibit weak, residual contrast typical of "invisible"~ images of edge dislocations for which 9-BY=0, but 9-(bxT) O (Hirsch et al., 1965, p. 261). Those loop segments lying approximately parallel to the 9 vectors, where g. (ExiT>0-, are invisible. The loops are everywhere visible for the two reflections, g=131 and 220. From this analysis, the source loops are identified as pure edge-dislocation ioops lying on (101) with F-=a/2[101]. Since the Burgers vector is normal to the plane of the loops, the loops must expand in this

plane by the process of climb. The sources are therefore dislocation climb sources of the type observed by Boyd and Edington (1971) in Al-265 wt.% Cu.

The ioop habits of climb sources in these alloys were observed always to be {110} (with one exception to be discussed in Section 4.4). The typical source produced loops on more than one {1101 habit. Loops lying on as many as five of the six possible 1110} habits were observed at one source. The typical source also generated more than one loop on each habit. As many as five or six loops on one habit were commonly observed, although the average number varied with the heat treatment.






S7


When a given foil was first examined, a technique was

used for rapidly determining if the dislocation sources were indeed climb sources with {1101 habits, or if some or all of them might be dislocation glide sources which are known to operation the {1111 slip planes in AI-Cu alloys (Westmacott et al., 19S9). This technique was to tilt the foil to {0011, {1111, and fl0l) orientations and, in each orientation) to determine the number of different source habits viewed edgeon together with the angles between these habits. For example, when a foil was tilted to the (001) orientation, two edge-on habits at 90' apart were observed, Figure 4.4(a). Since the [001] pole is parallel to two {110} planes at 90' to each other., and not to any {111} planes, those sources are identified immediately as {110} climb sources. Likewise, when viewed in the (111) orientation, three edge-on habits at 600 apart were seen, Figure 4.4(b). Again, since the [111] pole is parallel to three {110} planes at 60' to each other and not to any 11111 planes, the sources are identified as climb sources. However., neither of these cases rules out the possibility that other sources seen inclined to the beam in these orientations might be glide sources lying on 1111 planes. Therefore, it was necessary to tilt to a {1011 orientation. The [101] pole is parallel to two {1111 planes at 70.S' and to only one fllOj plane. In this orientation, only one habit was ever seen edge-on, as shown in Figure 4.1. There was no evidence that any of the sources found in these

foils were glide sources.






58





120

220













a
)MI




















b

Figure 4.4. (a) Two edge-on habits of climb sources at 900
to each other in an (001)-oriented foil.
(b) Three edge-on habits at 600 to each other
in a (111)-oriented foil. (Heat treatments:
S.T. 1 hour 5500C, quenched to 2200C, aged
5 minutes.)






59


Occasionally, when viewing edge-on habits in the (001)

orientation, it was observed that two different habits did not lie exactly at 90' to one another, although the habits of other sources in the same field of view appeared to be perpendicular, Figure 4.5. It is concluded that climb of the loops is not necessarily confined strictly to the {1101 planes. This angular measurement between two adjacent habits is more accurate for determining if the loops lie exactly on {1101 planes than are measurements made from the rotation calibration between directions in the diffraction pattern and those in the image.

It has now been established that the dislocation sources in these foils are climb sources. However., the climb of pure-edge dislocations can be either vacancy-annihilating or vacancy-emitting. The former case removes lattice planes from the crystal whereas the latter case adds interstitial planes. It remains to be shown whether the source loops climb by vacancy annihilation or emission, although intuitive arguments favor vacancy-annihilating climb. For instance, it is known that quenching produces large vacancy supersaturations, but negligible concentrations of interstitial. As the temperature drops during quenching, the need for the excess vacancies to diffuse to sinks would promote the growth of vacancy loops and tend to annihilate any interstitial loops. Therefore, one would expect that the large climb sources operate by vacancy annihilation during quenching, but this is not a sufficient proof. In fact, in the past






60






















Figure 4.S. Two edge-on habits of climb sources lying
slightly off 900 from each other in an (001)oriented foil. (Heat treatment: S.T. 1 hour
5500C, quench to 220'C, aged 5 minutes.)























Figure 4.6. Climb source inclined through the foil. Two
loops are sectioned leaving dislocation arcs.
The arc at A was selected for computer matching to determine its Burgers vector. (Heat
treatment: S.T. 1 hour S500C, quenched to
2200C, aged 4 seconds.)






61


only intuitive reasoning has been used to show that climb sources in aluminum alloys operate by vacancy-annihilating climb.

In the present work, the technique of computer matching of dislocation images (Head et al., 1973) was employed to establish that these loops climb by vacancy annihilation, thereby removing planes locally from the lattice. This technique is capable of determining unambiguously the Burgers vector of a dislocation line segment, i.e., whether the

Burgers vector is +B- or -F.

Figure 4.6 shows a climb source in a sample directquenched to 220'C and held only four seconds. This source has generated two loops on a {1101 habit inclined through the

foil, so that each loop is sectioned and leaves two arcs of dislocation. The segment of the outermost loop at A is reasonably straight and was selected for the computer matching experiment (the oscillations in the image are contrast effects arising from the inclination of the dislocation through the foil). From invisibility conditions, the Burgers vectors of these loops were determined to be either a/2[0111 or a/2[0111. The loops are pure-edge and lie on (011). By stereographic analysis, the line direction of segment A was determined to be very close to [100] in (011), and the foil

normal was determined to be [3131.

Six experimental images of segment A are shown in Figure

4.7 along with the corresponding computed images for 5-=a/2[011] and 5-=a/2[011]. These six images represent






62
























d,





e




S..... . ...




b=a/2E [TT] b a/2EO11]


Figure 4.7. Six experimental and computed images of dislocation A in Figure 4.6. The line direction is [100], the foil normal is [313], and the beam
direction is close to [101] in (a) and (b), to [112] in (c) and (d), and to [111] in (e)
and (f).






63


reflections from three non-coplanar beam directions, a necessary condition for uniquely identifying a dislocation by computer matching (Head, 1969). From the rotation calibration of the electron microscope, the exact orientation of the g-vector was marked on each experimental image. Also, from the known geometry of the computer program, the orientation of the g-vector was marked on each computed image. Thus the direction of the j-vector serves as a basis for comparison when matching the features of the computed images with those in the experimental images. Now for a given diffraction vector 'g, the image of a dislocation with Burgers vector +U7 is identical to that of a dislocation with Burgers vector -F5 after a rotation of 1800 (Head et al. 1973, p. 382). Clearly it can be seen from Figure 4.7 that the Burgers vector of Segment A of the loop is a/2[011] and not a/2 [011].

By convention, the positive direction of the dislocation line in the computer program is always taken to be acute to the foil normal. Thus for the foil normal [313] the positive direction of Segment A is [100] and not [100]. Also, the computer program employs the finish-to-start, right-hand (FS/RH-) convention for establishing the direction of the Burgers vector with respect to the positive sense of the dislocation line, Figure 4.8. Thus, from the (PS/RH) convention, and the absolute Burgers vector and positive line direction of Segment A, the geometry of the two 1oops in Figure 4.6 can be established, and this is illustrated






64







o -* 0 0 0 e
o 0o0o 0 0 0 00 0

0 000 0 0 0 000 0

0 0 0 0 0 0 00 ()0
O F O 0-S 0
0S0 0000 F6 000

a b

Figure 4.8. Schematic representation of Burgers circuits
taken in a cubic lattice around an edge dislocation (a), and in perfect crystal (b), illustrating the FS/RH definition of the
Burgers vector. The positive sense of the
dislocation line is out of the paper afterr
Head et al., 1973).









(011) PLANE
SOURCES

5a/,- [OTT]I




Figure 4.9. The geometry of dislocation climb source loops
in Al-Cu as indicated by the absolute sense of
the Burgers vector determined from computer
matching. The pure-edge loops expand in their
habit plane by vacancy-annihilating climb.






65


schematically in Figure 4.9. Clearly the loops are pure-edge, vacancy loops which climb in their habit plane by vacancy annihilation. It is concluded that these climb sources operate during the quench to act as sinks for the excess, quenchedin vacancies.

Now that it is established that the source loops climb by vacancy-condensation onto the loops, one further experimental observation must be explained. The vacancy-annihilating climb of a/2<110> dislocations in f.c.c. lattices is generally believed to occur easily only on {1111 and {110} planes, removing one and two atom planes, respectively (Christian, 1965, p. 363). Stacking faults were never observed within these climb loops, even though the same loops were examined on many different reflections, e.g., Figure 4.3. The stacking of {110} planes in f.c.c. is ABAB (Figure 4.10). Removal of a single {1101 plane by vacancy condensation behind a climbing a/2<110> dislocation would create a stacking fault. Two adjacent fllO} planes must be eliminated to avoid a stacking fau t. It appears, therefore, that the source loops climb by condensation of vacancies onto two adjacent f1101 planes. Since the stacking fault energy in dilute aluminum alloys is high, it appears to be energetically favorable for the loops to expand in this manner. A schematic cross-section through a climb source is shown in Figure 4.11.

The nature of the source particles is undetermined.

Occasionally, sources were observed that nucleated at very






66











Lool]






















thr pln dow liA i A poiios Reoa







Figurof 41.Daga sgleg plae ofacBiatoms crates aitak


ing fault, A on A.





67












(110) PLANES
000000 A OO OOQOOOA
000;0 O00000O0O 000000 B
0OOOO 0000000000 OOOOOA
5'a b/2[110 SOURCE@ A F.Q
OOO@ ..OO OOOOO OOOO-,Buu
0000000000050000 H00000
OOOOO 000 OOOOOOA
00 00 00000 B







Figure 4.11. Schematic diagram of the cross-section through a climb source loop on (110). The pure-edge
loops with b=a/2[110] climb by vacancy condensation onto two adjacent (110) planes, thereby
avoiding creation of a stacking fault.





68


large sphei-oidized particles ( l/1O l/211 diameter), Figure

4.12. These particles were large enough to be analyzed on a JEOL l00B Analytical Electron Microscope using a finefocused electron beam (approximately l,OOOA diameter) and a non-dispersive detection system for fluorescent analysis of the emitted x-rays. The analysis of these large spheroids

identified them as pure lead. It is not known how lead entered the sample material. However, such particles were observed in only a few foils and nucleated only a small fraction (1<]%) of the climb sources present. The typical. source particle was so small as to be barely visible or not visible at all, Figure 4.2(b). Such particles were too small for the x-ray analysis, but they are most probably not lead. The chemical analysis of the 3.85 wt,% Cu alloy (Section 3.1) showed no appreciable concentration of any single impurity which would suggest a guess at the particle nature.

Although the chemical. composition of the source particles is unknown, some observations were made about their distribution. rIh1e climb sources were dispersed randomly in most portions of the foils. Occasionally, local high densities of sources were observed. In a few instances, sources were observed evenly spaced in a straight line (Figure 4.13), suggesting that the source particles were part of an impurity stringer produced when the original cast alloy was rolled down.

The density of active climb sources in these foils varied with heat treatment (Section 4.5) In the only other reported







69




















Figure 4.12. Climb sources generated at a large, spherical
lead particle. (Heat treatment: S.T. 1 hour
550C, quench to 220C, aged 1 minute.)





20
1)-0















Figure 4.13. Climb sources aligned in a row. (Heat treatment: S.T. 1 hour 550'C, quench to 2000C,
aged 5 minutes.)





70


observation of climb sources in Al-Cu alloys, Boyd and Edington (1971) observed a source density of about three per grain in Al-2.5 wt.% Cu (although it is not stated, most probably measured in the volume of a grain sectioned by the foil; grain size not reported).- Source densities many orders of magnitude higher than this were observed in the present foils. The maximum density was produced in a sample quenched from 550'C to 180'C,, A micrograph of this foil is shown in Figure 4.49(e) From this micrograph and the average grain size (approximately 2S5% diameter) the active source density was estimated to be approximately 6x10 sources per grain.


4.2.2. Glide Dislocations Which Climb

In addition to loops generated at climb sources, other dislocations were observed which had climbed during quenching and nucleated precipitate colonies. Examples are shown in Figure 4.14. Gene-rally, these dislocations were long and either smoothly curved or irregular-shaped, depending on their climb paths. The micrographs in. this section were taken from foils aged long enough so that the precipitate colonies are -readily visible, thereby delineating the climb paths of the dislocations. F7or the present, it is assumed that the precipitate colonies were nucleated by the climbing dislocations (this will be proven in Section 4.3). In Figure

4.14(a), the dislocation exits the foil surfaces at A and C, and the trai Iing precipitate colony intersects one foil






71



























414


B"




Fiue4.4 rciiaecoois ulaeda ogcib



in isoaios Tedslctini ()i









Figureou of14 coniptast along ABc.ete (Hat treatment:b

S.T. 1 hour 550'C, quenched to 220'C, aged
S minutes.)~





72


surface along the trace ABC. In Figure 4.14(b), the dislocation lies along ABC at the upper edge of the precipitate colony, where it is "invisible." Some residual contrast can be seen, however. The source of these dislocations is unknown. They could be (1) grown-in dislocations, (2) glide dislocations which existed at the solution treatment temperature prior to quenching, or (3) glide dislocations which were generated at some source, probably grain boundaries, at the onset of quenching. It is thought that most, if not all, fall into categories (2) and (3), i.e., they were a/2<110> glide dislocations on Ml} planes prior to climbing. Figure 4.1S, for example, shows two images of a precipitate colony nucleated by one such long dislocation. In (a) the precipitate colony is inclined through the foil. The curved dislocation has been sectioned twice by the foil, leaving two arcs, AB and CD, at the ends of the precipitate colony. The Burgers vector of this dislocation was determined to be a/2[101]. The micrograph in (b) was taken after the foil was tilted to the (111) orientation. Here the precipitate colony is viewed edge-on and appears as a curved, dark line. This indicates that the dislocation climbed on an irrational, smoothly curved surface normal to the (111) plane. Since (111) is a glide plane, it is reasonable to assume that it was a curved, glide dislocation on (111) prior to climbing.

Such long glide dislocations were observed often to

have cllmbod on smoothly cut'ved suTfacos. This was easily recognized by the curved. intersections which the asSoci-Ited






73





















a




















b
Figure 4.15. Precipitate colony nucleated by climb of a
glide dislocation, initially on (111), with
FIa/2[101]. The dislocation has been sectioned
twice by the foil, leaving arcs AB and CD in
(a). The beam direction is close to [011] in
(a) and to [111] in (b). (Heat treatment: S.T. 1 hour 550'C, quenched to 220'C, aged
5 minutes.)





74


precipitate colonies made with the foil surfaces, Figure 4.16. Similarly, Miekk-oja and R~.ty (1971) observed repeated nucleation of silver-rich precipitates from solid solutions of silver in copper behind dislocations which were shown to be a/2<110> glide dislocations on 11111 planes before climbing. They foune. that these dislocations subsequently climbed in one of two different ways: (1) off the slip plane on smoothly curved surfaces, similar to -that described above, or (2) into a crooked shape so that different segments of the dislocations climbed on different low-index -planes intersecting the original slip plane. They further showed that these low index planes were of the typos {1101 and'11111, i.e., the planes of "easy climb" (Section 2.3.1) on which the chemical climb force, from a subsaturation of vacancies, was the greatest.

In the present research, the shapes of precipitate

colonies behind certain glide dislocations suggested that

different segments of these Jislocations had climbed on separate crystallographic planes also. The term "segmented

climb" shall be used here to refer to this mode of climb. Micrographs of precipitate colonies apparently resulting from segmented climb are shown in Figures 4.17 and 4.14(b). In Figure 4.17, the dislocation between AB has climbed through the lattice From left to right. The precipitate colony nucleated by this dislocation is separated into bands of precipitates. This effect is thought to be associated with

the climb of adj acent dislocation segments on separate





75











'*:o
-4%






t* 0"0




Figure 4.16. precipitate colony exhibiting Curved traces
of intersection with the foil surfaces, indicating a curved climb path of the nucleating dislocation. (Heat treatment: S.T. 1 hour

550C, quenched to 220'C, aged 5 minutes.)
0.C'



















Figure 4.17. Banded precipitate colony nucleated by "segmented climb" of the dislocation AB from left
to right through the foil. (Heat treatment

S.T. 1 hour 550C, quenched to 220'C, aged
5 minutes.)






76


crystallographic planes. The resultant precipitate colony has a corrugated shape. No precipitation Occurred in areas between the bands, e.g., at C. Such precipitate-free areas can also be seen in the climb path of the dislocation in Figure 4.14(b). For some reason the dislocation is ineffective in nucleating precipitates in these regions of its climb path. A possible explanation is that precipitation Occurs readily on those segments of the dislocation which climb on the separate crystallographic planes, but not on those curved arcs of the dislocation which bridge the gaps between these planes. This will be discussed further in

Section 4.4.6.

The segmented climb of initial glide dislocations was observed only in the AI-3.8S wt.% Cu alloy. An attempt was made to determine the planes upon which segmented climb occurred by trace analysis of the intersections of the precipitate colony with the foil surface, but this proved to be impractical for two reasons. First, as pointed out by Miekk-oja and My (1971), the possible planes of easy climb can be numerous, i.e., six {1101 and four {1111 planes, so that the trace analysis is best accomplished by using single crystals cut to special orientations. Such crystals were not available in this research. Secondly, the traces of the intersections of the bands of precipitates with the foil surfaces were never well defined, a condition which leads to poor accuracy in the stereographic analysis.





77


There is evidence that the tendency for glide dislocations to climb either on smoothly curved surfaces or to segment and climb on different )lanes depends upon the line direction of the dislocation before climb began. For example, in Figure 4.18 the curved dislocation along ABC has nucleated a smoothly curved precipitate colony between A and B, and a corrugated colony between B and C. Presumably, the initial line direction of the dislocation segment between B and C was favorable for rapid climb onto the different planes of easy climb.





4.3. Identification and Characterization
of the Precinitate Pfihse


Figure 4.19(a) is a difFraction pattern in the exact (001) matrix orientation taken from the group of precipitates shown in Figure 4.19(b). The image quality in (b) is poor since the exact (001) orientation is a many-beam condition. The geometry in Figure 4.19(b) is as follows. The foil has sectioned three ll] 0 habits of dislocation cli-mb sources, numbered 1, 2 and 3. These habits are viewed edgeon in this orientation. Habits 1 and 2 lie on (110) while habit 3 lies on (i0) Small precipitate platelets are dispersed over the three habits. Two orientations of precipitates are present lying parallel to the (100) and (010) matrix )h1anes. The p:recipitate reflections in the diffraction pa":tern are streaked in the <100> directions owing to






78


























CN



V44




Figure 4.18. A glide dislocation which climbed on a
smoothly-curved surface between A and B, and underwent segmented climb between B
and C. (Heat treatment: S.T. 1 hour
5150C, quenched to 2200C, aged 5 minutes.)






79


































a"










b


Figure 4.19. (a) (001) diffraction pattern showing precipitate -reflections, taken from the area of the
foil shown in Nb. (Heat treatment: S.T.
1 hour SS00C, quenched to 220'C, aged 30
minutes.)






80


the relaxation of the Laue condition along the thin dimension of the platelets. The diffraction pattern can be analyzed

on the basis of three superimposed patterns shown in Figure

4.20(a)-(c), where we consider only the lower right-hand quadrant of the pattern. The patte-rn in (a) is the (001) matrix pattern. The pattern in (b) is indexed on the basis of two el orientations parallel to (100) and (010) matrix planes, using the lattice parameters of 4.04A and SAX for el (Section 2.2). The remaining reflections in (c) are due to double diffraction from the matrix {2001 and {2201 beams. Double diffraction is a common occurrence in foils containing

precipitates with dimensions much smaller than the foil thickness. The composite pattern, shown in (d), matches the experimental pattern. Thus the precipitates are positively identified as the of phase, in agreement with the known fact that a' is the only metastable phase which nucleates on dislocations in Al-Cu.

In the present research, conditions were chosen to insure that the e' phase was the only precipitate phase present after heat treatment. Its distribution was always associated with the climbing dislocations.

The appearance of the precipitate colonies at high

magnifications is shown in Figure 4.21. These are typical colonies nucleated on dislocation climb sources. The colony in (a) was nucleated on the (101) source habit in the plane of the foil. In (b), five different {1101 habits were generated at the same source particle and have nucleated






81





O00M 020M O00M 002
00-one. (0)
I OP' 20%(

1 1~

o2 00 0
e 0
200M 220M 103G
a b







oooM O00M

S- 0(D



I I





c d


Figure 4.20. Analysis of the lower, right-hand quadrant of
the diffraction pattern in Figure 4.14(a).
(a) (001) matrix pattern; (b) precipitate
reflections from e' platelets lying parallel
to (010) matrix planes (0j), and to (100) matrix
planes (01); (c) double diffraction from matrix
200 and 220 reflections; (d) combination of
(a), (b), and (c). Compare with Figure 4.14(a).






82











A04











a




~b

cooie en ated on. th -10 hbts
b s.a S
~B










S..1hu 55,qece t 2,ae
mi e


020



C


b

Figure 4.21. (a) and (b) Appearance of typical precipitate
colonies generated on the f11O1 habits of
climb sources. (c) and (d) Schematic diagrams
illustrating the geometry of the colonies.
See text for description. (Heat treatment: S.T. 1 hour 550'C, quenched to 220'C, aged
5 minutes.)






83






VIEWING DIRECTION., NORMAL TO (101)





5=2/2[1011











c


VIEWING
DIRECTION, NORMAL TO (101)














(f of)


SECTION OF THIN FOIL

d


Figure 4.21. Continued.






84'


precipitate colonies. One habit lies in the plane of the foil at A, one habit is viewed edge-on at B, and three other habits at C, D and E are inclined through the foil. The geometries of these sources are shown schematically in Figure

4. 2 1 (c) and (d) .
Often the best condition for imaging the precipitates in a colony was also a condition for "invisibility" of the dislocation loop bounding the colony, e.g., Figure 4.21(a). This was particularly true when examining colonies on dislocation climb sources where the best projected view of a colony was obtained with the beam oriented approximately normal to the colony, and hence to the bounding source loop. However, since the source loops are pure-edge with their Burgers vectors normal to their habit planes, any two-beam reflection selected to view the precipitate colony in this orientation has its g-vector perpendicular to the Burgers vectors of the loops. Thus the loop will be "invisible" when viewed normal to its habit plane. This is the case in Figure

4.21(a) where 9-F=0 for the loop bounding the precipitate colony and only residual contrast due to the pure edge-nature

of the loop is detected.

Likewise in Figure 4.21(b), the dislocations bounding

the colonies at A, C and D are invisible, whereas the one at E is visible. A consistent interpretation of the geometry of this source array is as follows. The beam direction is close to [101] and g=lli for this image. Habit A lies on the (101) plane of the foil (see Figure 4.21(d)). The






85


Burgers vector of its source loop, being pure edge, is a/2[101]. Thus the loop is invisible for g=lll. The source loops bounding the habits C and D are also invisible. These dislocations must have the other two a/2<110> Burgers vectors which cause invisibility for the lli reflection, namely, a/2[011] and a/2[liO]. Habit B lies on the (101) plane parallel to the beam and is viewed edge-on. The Burgers vector of its source loops must be a/2[iOl]. The source loop bounding habit E must have one of the two remaining a/2<110> Burgers vectors, namely, a/2[110] or a/2[Oli], both of which would be visible for the lli reflection. The dislocation is visible at E.

It is difficult to determine whether the smallest precipitates in these colonies are imaged by strain contrast in the matrix or by structure factor contrast (Ashby and Brown, 1963). The larger precipitates in a colony are imaged by the dislocation loops bounding the periphery of the platelets

(Section 4.4).

In Section 2.2) it was pointed out that because of dislocation strain effects, only two el orientations will nucleon any given a/2<110> dislocation. The missing orientation has its principal misfit (normal to the plane of the platelet) perpendicular to the Burgers vector of the dislocation so that its strain field is not relieved by the stress field of the dislocation. Careful examination of a number of precipitate colonies at dislocation climb sources revealed that only two 61 orientations were present in any given colony.





86


The missing orientation was always that (100} orientation whose misfit would be perpendicular to the Burgers vector of the source loop bounding the colony. This is illustrated in

Figures 4.21(b) 4.22 and 4.23.

First, Figure 4.22 shows bright and dark field images of several precipitate colonies on climb sources in a foil whose normal was close to [1011. The foil was oriented with the electron beam close to [101]. The dark field image was taken from a precipitate reflection from the (010) 01 orientation parallel to the beam. Climb source A (and its precipitate colony) lies on (101).' and its source loops, being pure edge, have Burgers vectors a/2[101]. At B, two other source habits lie on f1101 planes inclined to the foil. The Burgers Vectors of their source loops were not determined but they cannot be a/2[1011. Now, if all three {1001 orientations of el were present in the colony at A, the orientation imaged in the dark field would be observed throughout source A as in the sources at B. The misfit of this missing (010) orientation is perpendicular to the a/2[1011 Burgers vector of the source loops at A (which are "invisible" in this image). The few precipitates on (010) in the middle of source A in the dark field image were found to lie within small source loops lying on other T1101 habits, when this source was

examined in another orientation.

Next, in Figure 4.21(b), the source habit at B lies on the (101) plane and is viewed edge-on. The Burgers vectors of its source loops, being pure edge, must be a/2[101].





87































Figure 4.22. Bright-field and dark-field images of precipitate colonies on dislocation climb sources.
The colony at A lies in the (101) plane of the
foil. The colonies at B are inclined through
the foil. The dark-field was taken from a
precipitate reflection from the (010) 0' orientation lying parallel to the [101] beam direction. (Heat treatment: S.T. 1 hour 5500C,
quenched to 2200C, aged 5 minutes.)






88


The (010) 01 orientation, which is parallel to the beam direction and also viewed edge-on, is not present in habit B, although it is easily detected in habits C and E. Again, this is the 01 orientation whose misfit is perpendicular to the a/2[101] Burgers vector of the source loops bounding

habit B.

The fact that el platelets lying parallel to the beam

can indeed be seen if present in precip itate colonies viewed edge-on is shown in Figure 4.23. This micrograph was taken with the beam oriented near [001].. The two edge-on habits at A and B lie on (110) planes so that the bounding dislocation loops have Burge-rs vectors a/2[1101. Both the (010) and (100) orientations of 6' platelets can be clearly seen dispersed along the habits. Note that these are the two e' orientations whose misfits are not perpendicular to the Burgers vector of the bounding dislocation loops and are therefore favored to be nucleated by the loops.

All three 81 orientations were never observed in a given precipitate colony. As pointed out above, the missing orientation was always that whose nucleation is not aided by the stress field of the dislocations bounding the colony. This was true for precipitate colonies generated by both climb sources and glide dislocations which climbed. This evidence leads to the important conclusion that the precipitates must have nucleated in the stress field near the dislocations as they climbed through the lattice, and not at some later time when the influence of the dislocation was no longer present,






89































Z2.44






Figure 4.23. 0' precipitate colonies on climb source habits
A and B which lie parallel to the beam. Two
edge-on orientations of e' platelets, (100)
and (010) are clearly visible in colonies A and B. The beam direction is close to [001].
(Heat treatment: S.T. 1 hour 550'C, quenched
to 2200C, aged 30 minutes.)





90


e.g., during aging. Since the dislocation climb sources are known to have operated during the high-temperature part of the quench, the precipitates must have nucleated during quenching.

Further evidence to support this conclusion was obtained by in situ aging experiments in the electron microscope. The results of these experiments are shown in the micrographs of Figure 4.24. These are images of a foil from a sample solution treated for one hour at SSO'C, quenched into oil at 220'C and held only four seconds at 220'C, then water-quenched to room temperature. After electropolishing, the foil was placed in the heating stage of the microscope. The micrographs in Figure 4.24(a) and (b) Were taken prior to heating. In (a), a dislocation climb source is viewed normal to its

(011) habit of source loops which are "invisible" in this orientation and imaged by -residual contrast. Since this is a climb source, we know that these dislocations climbed during quenching. A-long, crooked dislocation, which was most probably a glide dislocation prior to quenching, is shown in (b). 'Its crooked shape is the only indication that it may have climbed during quenching. Now, if nucleation of the 01 precipitates does occur as the dislocations climb through the lattice during quenching, then the precipitates must already be present in the foil in (a) and (b). However, the four-second aging time at 220*C was insufficient to cause the precipitates to grow to visible sizes. The foil was then heated to 230'C in the microscope. After nine minutes at






91




















oil

(a)





















(b)

Figure 4.24. (a) A dislocation climb source, imaged by
-residual contrast, and (b) a long glide dislocation in a sample quenched from 550*C to 220*C and held only 4 seconds before quenching to room temperature.






92







++ %,-B,+


00








.1+ A,' I
44




~ 4
(c)








I -zr4 q
,+ p++- : ++.s ...
4A,





lip B





(d)

Figure 4.24. Continued. (c) and (d) Micrographs of the
same dislocations in (a) and (b) after aging
9 minutes at 230'C in the electron microscope.
The random precipitation at B has occurred at the foil surfaces. The precipitate colonies
associated with the dislocations are now
clearly visible at A.