Cross slip, antiphase defects and work hardening in ordered Cu3Au

CROSS

SLIP,

ANTIPHASE IN

DEFECTS ORDERED

AND

WORK

HARDENING

Cu,Au*

B. H. KEAR? Superlattice dislocation and antiphase boundary structures have been examined in thin foils of deformed ordered Cu,Au. The observations point to the important role of forest intersection jogs in controlling the slip distance and work hardening of the ordered alloy. Jogs are considered to contribute to the frictional component of the flow stress through the generation of point defects and antiphase defects, and to the internal stress component through the trapping of glide dislocations by the jog mechanisms of dipole formation and ‘intermediate’ cross slip. Temperature dependent work hardening in the ordered alloy is discussed in terms of several different models. GLISSEMENT-CROISE, DEFAUTS D’ANTIPHASE DEFORMATION DANS LE COMPOSE

ET DURCISSEMENT ORDONNE Cu,Au

DE

Des structures de dislocations de sur-reseau et de frontieres d’antiphase ont 6th examinees dans des lames minces du compose ordonne Cu,Au deform& Les observations indiquent le role important joue par la foret d’intersections de crans dans le controle de la distance de glissement et du durcissement de deformation de l’alliage ordonne. Les crans sont consider& comme contribuant it la composante de friction de la limite Blastique par l’intermediaire de la production de defauts ponctuels et de defauts d’antiphase, et a la composante de tension interne grace au piegeage de dislocations en glissement par les mecanismes de m-an, de formation de dipole et de glissement croise “intermediaire”. QUERGLEITUNG,

ANTI-PHASEN-DEFEKTE UND GEORDNETEM Cu,Au

VERFESTIGUNG

IS

Die Anordnung der Uberstrukturversetzungen und die Struktur der Anti-Phasen-Grenzflachen sind in dunnen Folien einer verformten geordneten Cu,Au-Leigierung untersucht worden. Die Beobachtungen zeigen, da6 die durch Waldversetzungen erzeugten Durchschneidungssprige den Laufweg und die Verfestigung der geordneten Legierung entscheidend beeinflussen. Es wird angenommen, da6 die Spriinge infolge der Erzeugung von Punktfehlern und Anti-Phasen-Defekten zur Reibungskomponente der Fliel3spannung beitragen und infolge des Einfangens gleitender Versetzungen durch die Sprungmechanismen der Dipolbildung und der intermediaren Quergleitung die innere Spannungskomponente der FlieDspannung beeinflussen.

1. INTRODUCTION

In a previous

paper,(l)

account

for differences

crystals

due to ordering

on dislocation

was made to

in work hardening by correlating

configurations

with stress/strain

As in the earlier work, the present study has been

an attempt

and lattice

in Cu,Au

between motion

accumulating

as a result

of

work

in

to be associated

slip.

with the trapping The present

with

of high purity

was

PROCEDURE

stoichiometric

composition

CusAu

copper

and gold under vacuum

in a

graphite mould. Using this material a single crystal with dimensions $ in. x 4 in. x 6 in. was grown from the melt by the Bridgman homogenized annealing

method.

The crystal was

by heating at 900°C for several hours,

and fully ordered (S -

* Received April 15, 1965; revised November 18, 1965. t Advanced Materials Research and Development Laboratory, Pratt & Whitney Aircraft Plant N, North Haven, Connecticut. 1966

occurs at a critical The strongest work

in material with maximum

EXPERIMENTAL

An alloy

mine its role in work hardening.

VOL. 14, MAY

stress and

on the domain

was prepared by melting together the required amounts

cross

undertaken primarily to provide more evidence for intermediate cross slip in the superlattice, and to deter-

ACTA METALLURGICA,

of about 40 A.

is experienced

2.

of screw segments investigation

the yield

sensitively

order and largest domain size.

On the other

loops in intermediate

that

depend

A yield stress maximum

hardening

dislocation

in the ordered alloy appeared

dislocation

slip configurations.

of

established

hardening

size.(2-6)

between

and the grown-in domain structure.

domain diameter

in the primary

blocking

by the onset of conjugate

hand. work hardening of expanding

It has been

It was

alloy was due to elastic interactions

dislocations

slip planes

glide dislocations

crystals

data.

shown that the major part of the work hardening the disordered

so as to minimize effects due to interactions

observations

in the deformed rotation

restricted to material with relatively large domain size,

1 .O; domain size -0.1

at 350°C for several

hours,

,M) by

followed

by

slow cooling at intervals of a few degrees every 24 hr 659

ACTA

660

in the

range

350”-150°C.

sample of the annealed

Chemical

analysis

of a

crystal gave 25.1 at. y0 gold.

Spectrographic

analysis

purities

aluminum

silver,

METALLURGICA,

gave

as the

principal

and iron,

totaling

im0.015

wt. %. machine.

crystal was pulled in an Instron

The testing procedure

steps, as follows:

involved

three main

(i) the entire 6 in. length of crystal

was strained to marker 1 on the stress/strain 1, and, after unloading.

curve,

a 2 in. length

sample

14,

1966

operation several different operating reflections. it was possible dislocations The

to determine of each

samples

was

with

by

system.

back-

rotation

of the tensile axis,

1. 2 and 3 on the stress/strain

curve, was found to be in agreement lated rotation,

differently the

The data is given in the inset

of Fig. 1. The observed corresponding

contrast method.@) of the three

determined

reflection Laue method.

Thus, vector of

the Burgers

by the diffraction

orientation

strained

The electropolished

Fig.

VOL.

with the calcu-

assuming slip in the predicted

primary

In agreement with the X-ray lattice rotation

data, optical examination

of slip lines in specimens 1,

2 and 3 showed evidence for slip only in the predicted primary system.

The slip lines were long and straight

in the crystal face parallel to the Burgers vector, and they were short, diffuse and somewhat

wavy

in the

crystal face at right angles to the first, Figs. 2(a) and (b).

These particular micrographs

after unloading stress/strain

SHEAR

are for specimen 3,

and repolishing

at stage S on the

curve.

STRAIN-PERCENT

Fm. 1. Interrupted stress/strain curve and rotation of the tensile axis for a crystal of ordered Cu,Au.

was cut

from

the

crystal

using

(ii) the crystal was remounted an additional another

strain

jeweler’s

a

saw;

in the grips and given

to marker

2, and,

as before,

2 in. sample was cut from the crystal ; and

(iii) the remainder marker 3.

of the crystal

was strained

In each case, on reloading,

mation recommenced

in a discontinuous

little or no work hardening Some characteristics

to

plastic deformanner, with

for a few percent strain.

of this reloading effect have been

reported elsewhere.(7) Each after

sample

suitably

reflection

was mounted orienting

Laue method,

the

in a goniometer, crystal

by

and

the

back

$ in. thick sections were cut

parallel to the slip plane, and also perpendicular the slip plane, parallel to the Burgers vector. cutting

operations

Thin foils suitable

microscopy

These

were carried out using a jeweler’s

saw, with the sample firmly supported block.

to

in a plastic

for transmission

electron

were prepared from these bulk samples by

a two-stage electropolishing procedure.(l) The foils were mounted directly in a modified specimen holder for the Philips

EM

100-B

electron

viewed at 100 kV operating potential. trast conditions holder.

degrees about

cases the available

3. DISCUSSION

OF

The most characteristic

feature

slip plane was the elongation the direction

loops in

with the loops

consisting of straight segments in the screw orientation and somewhat orientations, work.(l) primary

wavy segments in the edge, or mixed Fig.

4,

in

agreement

with

previous

In a few cases the Burgers vector of the dislocations was confirmed by the g*b = 0

and

criterion,

other cases the orientation

one axis) was sufficient to bring into

of dislocation

of the Burgers vector,

con(-&6

of the dislocation

structure in thin foils of sections taken parallel to the

Optimum rotation

RESULTS

3.1 General dislocation structure

microscope

were achieved by tilting the specimen

In most

(b)

(a)

FIG. 2. Surface slip markings at stage S on the stress/strain curve; (a) edge bands, and (b) screw bands. x 250

using the 131 reflection,

Fig. 3(a).

In all

of the primary slip vector

in the micrographs was deduced from the known orientation of the foil in the electron microscope. A careful examination

of all micrographs

showed no

KEAR:

WORK

HARDENING

IN

ORDERED

ti61

Cu,Au

( bl

(0)

FIG. 3. Stereographic projections of the two different orientation thin foils examined; (a) parallel to the primary slip plane, and (b) perpendicular to the primary slip plane, parallel to the slip vector.

evidence

for classical

dislocation

pile-up

tions.

On the other hand, numerous

found

of fairly

orientation

uniform

dislocation

arrays

of edge,

dislocation

arrays

are shown

half of Fig. 4(c) for specimen (b) for specimens for neighbouring they

1 and 2. of the

lap of neighbouring

in the upper

the dislocation

in the inset of Fig.

tilt of the foil.

dislocations

Frequent

in a family

of the bursts of slip that invariably in an interrupted

Here the stopping

of slip planes.

3.5.

This interpretation

such groups, associated defects,

with

see section

contribute

predominantly Evidence

ally in specimen words,

appeared mentioned 7

see section

by the fact that are generally

activity

localized

primary

secondary

slip in specimen

effect of additional cause

dislocation

dislocation

of primary

dislocations

Figure 6(a) shows a region of 3.

slip

associated

slip in the secondary tangling.

with

It can be seen that the Figure

structure in the vicinity

system is to

6(b)

shows

the

of a region of the

foil where limited activity had occurred in a secondary system.

The very

superlattice

complex

dislocations

structure

of individual

in this micrograph

is not

understood. dislocation

dipoles

in various

tations were found in all three specimens.

factor

crystal

have their origin in

mechanism,

Fig.

15.

on the other hand, are considered

result of elastic interactions dislocation

loops

and

much

Screw

to be the

between newly expanding

screw

segments

by slip

in localized 1; in

systems

in stage II.

As

accompanying

cross slip,

previously

7(a) shows, at A, a stage in the overlap

secondary

earlier, the lattice rotation

dipoles,

superjog

were

Figure

deforming

to increase with prestrain

Edge dipoles probably

familiar

dipoles

that would

in specimen 3, occasionof

Fig. 4(a). the

orientation

by intermediate

for flexural glide to

slip, generally

or near edge

orien-

In general,

pinned

2, and not at all in specimen the

stage II.

antiphase

induced

of fairly uniform arrays of

regions, was found frequently other

drag,

avalanches slip

of jogs and

in the array, i.e.

in one system.

for secondary

intensive

therefore, must have remained

with that

shorter than screw dipoles ; cf. dipoles at A and B in

is the tendency

in a constrained

throughout

in for

edge

Another

to the trapping

edge dislocations develop

3.4.

compared

slip distance

is

is supported

observable

secondary dislocations, small

of slip exclusively

The average

1.

frictional

or dislocation

was indicative

system.

Fig.

considered to be primarily the accumulation dislocation

the primary

for the dislocations

point defects on all the dislocations an enhanced

the deformation

Superlattice

characteristic

occur on reloading

deformation,(7)

mechanism

over-

in a group, as at A in

Such groups may be the configurations a crystal

features

in these arrays show that

same sign;

Fig. 5(b), shows activity

slip planes.

Similar contrast

has been exaggerated

5(a) by an appropriate

or mixed

3, and in Figs. 5(a) and

dislocations

are mostly

contrast

were

segments in excess of one sign,

usually lying in a family of neighbouring Typical

configura-

examples

two near edge orientation of somewhat

arbitrary

see section

3.3. of

segments to form a dipole

shape by the jog mechanism ;

here the jog pair in the superlattice dislocation is indicated by the arrow. In thin foils of sections taken perpendicular

to the slip plane, parallel to the slip

vector, the edge orientation dipoles are visible as two pairs of dots lying in neighbouring (111) slip planes, as at C in Fig. 9(b).

Figure 7(b) shows an unusual case

of what

to be the approach

appears

of two

edge

segments of the same loop just prior to the formation

ACTA

METALLURGICA,

VOL.

14,

19G6

(b)

Fxa. 4. Changing

ctisloration structure w&h increasing prestrain soctiorls token parallel to the primary slip plane.

(epccimcns

J-3) in

KEAR:

WORK

HARDENING

IS

ORDERED

663

Cu,Au

(b) FIG. 5. Uniform arrays of primary dislocations

in specimens

(b)

(a) FIG. 6. Dislocation

1 and 2.

structure in regions of localized activity

in serondary

systems.

ACTA

664

METALLURGICA,

VOL.

14,

1966

on the loss and rearrangement foils of deformed after electrolytic have concluded

(a)

aluminium

of dislocations

thinning.

Wilsdorf

that electrolytic

in thicker

foils the dislocation

observations

have

In very thin foils evidence

in the

dislocations surface

line

energy

of the in the

foil.

by rearrangement

of to

Such

rearrangements

of

the

of

foil involved

or so, an entirely

consistent

taken

were reasonably

it should be mentioned

the

contrast

of a dipole. contrast

In these and other cases the fact that the the

dislocations

they have opposite

signs-in

all change in contrast of the almost

edge orientation wide variations dipoles

2.

changes from light to dark in opposite senses

on crossing

outside

1 and

is clear particular

evidence

that

note the over-

on going from the inside to the closed

dipoles

loop in Fig.

7(b).

in all micrographs

in equilibrium

F and G in Fig.

widths,

4(b).

The

exhibit

e.g. compare

No calculations

have

difference

between

for superlattice

anomalous

single

phenomena

have

that

observing

dislocations,

line

Such

analyzed

by

The

dislocation

structures

parallel

to the Burgers

relatively

long

orientation,

vector,

dislocation

dipole.(34) occurrence

Anot’her effect’ worth not’ing is the frequent of weakly contrasting

to t’he primary lines probably

lines inclined at 60”

slip vector, as at C in Fig. 4(a). These represent some special form of dis-

location debris produced locations, similar to that

by dragging jogs in disdescribed by Hirsch and

Steedscg) for copper crystals. Several workers(i0-i2) have

observations

thin

in

mainly the

Figs. 8 and 9, as would be expected

the observed

structures

of

screw from

in thin foils of sections taken

parallel to the slip plane, Figs. 4 and 5. In most cases, the

Burgers

In Figs. dislocations

vector

of the

dislocations

8 and 9, the segments

interesting 8(a), mixed

9(a).

dislocation

orientation

The middle (arrow)

(111)

are resolved

as

they have undergone (111) slip planes. An

case of cross slip is indicated

see also Fig.

was readily

using the

of the superlattice

in the screw orientation

pairs, which must mean that cross slip out of their original

superlattice reported

in the

consisted

segments

Figs. 3(b) and 10.

the

and

to the slip plane,

reflection,

narrower

contrast

Wilkens

observed

foils of sections taken perpendicular

the

the

to

3.2 Evidence for cross slip

by the g-b = 0 criterion,

slip planes

line

Hornbogen.(13)

confirmed

of the

frequently double

as opposed

contrast.

been

small tilts of

reflection,

been made so far, but it seems likely that the smaller separation

repre-

of the bulk sample.

Finally

loops and dipoles in specimrns

from to the

was taken to be evidence

structures

the foil, for a given operating

FIG. 7. Dislocation

was obtained

parallel and perpendicular

the observed

made

as will be shown

picture of the dislocation

slip plane, which correlation sentative

and pos-

in excess of 2000 A

in the deformed material

both sections

production

dissociation

In thin foils with thickness

that

foil,

nearly perpendicular

defects by dislocation

structure

study.

slip out of the

sibly by dragging jogs on dislocations, later.

(b)

Similar

has been found for (i) loss

by cross

into orientations

dislocations antiphase

are considered

sample.

under the action of image forces. and (ii)

reduction the

bulk

2000 A;

been made in the present

of screw dislocations presumably

only if

less than

patterns

of the

density

arrangement

of the foil becomes

be representative

of deformed

in dislocation

and to changes in the dislocation

to

and Schmitz(12)

thinning

leads to a reduction

the thickness

in thin

metals and alloys during or shortly

at A in Fig.

segment

is evidently

lying in the primary

of the in the

plane (ill),

KEAR:

WORK

HARDENING

IS

ORDERED

Cu,Au

(b)

Fra. 8. Dislocation and antiphase structures in the same area of a thin foil of a section taken perpendicular to the primary slip plane, parallel to the slip vector. since it is visible trace

(dotted

as a single line parallel

line), whereas

screw orientations opposite

dislocation slip plane,

apparently

are in

cross slip in

In this case the trailing

the superlattice in the original

the end segments

and have undergone

senses.

to a (111)

partial

is dissociated

since it lies parallel

(111) trace of the mixed dislocation

of

to the

Another

segment.

3.3 Jog mechanimls

Jbr CPOM slip

Some of t,he possible intersection

configurations

jogs in superlattice

orientation

are illustrated

in Fig. 12.

state for jogs in dislocations be visualized t,he jogs;

by rotating

of other orientations

for details see Hirsch.(15)

the so-called

sessile jog,(16) results

pinch together

which must be the

with Burgers

vectors

segment in the edge

whereas

case

between

dislocations

at a point (arrow),

orientation

lying

configurations superlattice mediate

of a dislocation in the

(111) primary

involving partial

cross

only,

slip

hereafter

Such inter-

glide

with

study,“)

was found

on

a

a reduction

so that

the

equilibrium

dislocation width;

Such

in energy,

the antiphase

pair

dependence

dislocation.

In Fig.

oriented

can

cross

cross slip may

since

boundary

see Flinn(14)

orientation

similarly

for intermediate

slip into the cube orientation. orientation

their

in the

cube

energy

is small.

assume

a larger

for details

on the

of the energy of a superlatticc

9(b),

at B, the unusually

width of the superlattice dislocation cross slip into the cube orientation.

strongly

large

suggests

the

other

dissociated

only

at 80” or

(b) the jogs can if they

become

to form a short segment

that can glide in the cube plane.

hand.

jogs

state.

cause the stair-rod direction

vectors

of type

dislocation

i.e. combine

edge dislocation

crystal,

evidence

constricted,

one another,

of intersections

with Burgers

In the configurat’ions

termed

Case (b), Fig. 12,

at 90” cut through

120”.

can

lines about

when dislocations

(a) is a consequence

leading

cross slip, seemed to be quite characteristic

of the material. In an earlier

involve

plane.

of the

of edge

The dissociated

the dislocation

case at B in Fig. 8(a) shows paired screw segments that point of emergence

for dissociated

dislocations

of t’ype (a) can

since

the

bowing

dislocations

of the slip vect’or.

glide

The

in the

segments

to zip-fasten actual

of On will

in the

result

of

dislocation intersection in the superlattice also depends on whether a given dislocation, say a glissile primary

dislocation,

dislocation, dislocation.

cuts through

a stationary

forest

or is itself cut by a moving secondary The former yields a parallel jog con-

figuration xith neighbouring jogs having the same glide plane, Fig. 13(a), whereas the latter gives an

ACTA

666

METALLURGICA,

VOL.

14,

1966

(b)

Frc. 9. Changing dislocation structure with increasing 1)restrain (specimens l-3) in sections taken perpendicular to the primary slip planr, parallel to the slip vet3tor.

KEAR:

WORK

HARDENING

IN

ORDERED

667

Cu,Au

(b)

(a)

Fro. 10. Changing dislocation contrast with operating reflection in a section taken perpendicular to the primary slip plane, parallel to the slip vector, (a) 202 reflection, and (b) 111 reflection. In (b) the primary dislocations are invisible since g.6 = 0.

observed

dislocation

of intermediate on an expanding the points

structure in terms of nucleation

cross slip at random intersection dislocation

indicated

loop.

by arrows

on the loop

considered to be the sites where intersection just initiated

cross slip.

jogs

Thus, in Fig. 4(a),

The elongated

D are

jogs have loop

at E

represents a much later stage in the cross slip process, after extensive

glide of the leading jogs in each pair.

Intermediate

cross slip by the jog splitting mecha-

nism IO)

(bl

11. Illustrating orientation of Thompson’s’32’ FIG. reference tetrahedron ABCD for specif.ying the slip plane and Burgers vector of (a) a supeilattice dislocation pair, and (b) a superlattice dislocation pair with associated condensed vacancy dislocation loop. Burgers vectors are defmed after the manner proposed by Frank,‘33’ with the positive direction of the dislocation indicated by an arrow.

“oblique” tubular

jog configuration, antiphase

Fig. 13(b),

as pointed

and independently Figure

defect

by Vasil’yev

from

First,

orientation

for

crystal, the shear stress

dislocation,

apart of a jog

edge to screw.

dislocation

of the dislocation

It follows

that

if a

line assumes by chance

at a dragging jog pair, the

jogs may separate to yield an intermediate configuration,

inter-

in this particular

favourable

and Brown,(17)

in a superlattice

segment of mobile dislocation the near screw orientation

90”

section jogs, i.e. sessile jogs, for three reasons.

and Orlov.(ls)

14 shows that the distance

tends to increase as the orientation changes

particularly

which is the source of

in the slipping

out by Vidoz

pair (parallel or oblique)

seems

cross slip

as shown in sequence l-2 Fig. 15. It is

easy to envisage on this model the formation

of the

FAG. 12. Possible configurations for dissociated intersection jogs in a superlattice dislocation of edge character; (a) 60” intersection jog, (b) 90’ intersection jog.

x ,-\CTA

T”WW

METALLlTKGl(‘A,

VOL.

14,

1966

ANTLRLSE

_______

v----cr._-____-___ ,,-

..\ f

______

c____-_

___

CeLIWE JOG UMIFIGURATIZI

101

Ib,

FIG. 13. Parallel and oblique jogs in a superlattice edge dislocation pair. The oblique jog is a source of tubular antiphase defect in the slipping dislocation.“7~‘s’

in the cube plane is large, whereas that in the octahedral

cross slip plane is negligible.

trailing jog of the glissile constricted redissociate effectively

during anchor

one continues

slip

if the

process,

this

would

the trailing jog while the leading

its original motion.

of a slip induced orientation

the

Second,

pair happens to

antiphase

is a minimum,

Third, the energy

boundary

in the cube

so that the drag exerted on

the leading jog is a minimum. In sequence

2, Fig. 15(a), the trailing superlattice

I

*

,:I

*

I

FIG. 15. Illustrating possible slip motions for jogged superlattice dislocations. Sequence l-2 shows splitting of a jog pair to yield a pinned screw configuration, where neighbouring superlattice partials are dissociated in parallel slip planes. Sequence P5 shows the formation of a superlattice edge dipole by pivotal action at a stationary jog pair.

dragging

its jog along

with it.

The final sequence,

partial is shown to be parallel to the trace of cross slip

Fig. 15(a), shows that if the jog pair remains together,

generated

the advancing

by the leading

jog.

A variation

scheme

is that wherein

partial,

under the action of the applied

up the position the

the dissociated

on this

superlattice stress, takes

shown in sequence 4, Fig. 16(a).

intermediate

stage,

sequence

3, Fig.

In

16(a),

a

three-fold antiphase junction must be formed between the two Shockley partial dislocations, not constitute

As emphasized

final configuration superlattice

is a pinned

dislocation,

tials are connected boundary one. pinned

but this should

a serious obstacle to cross-over into the

final configuration.

since

together

previously,(l)

configuration

6he

for the

the superlattice

par-

by a strip of antiphase

that bends from one plane to a neighbouring

Figure

E(a),

sequence

configuration

eliminated

if the

3-4,

shows

that

for the screw segment trailing

edge

segment

the

(0,

FIQ. 14. Illustrating

by

formation

are believed

controlling

intermediate

slip

and

are several variations Thus, the movement

loop.

it is easily seen that there

on configuration

on the path

dipole

mechanisms

the slip distance of a dislocation

On further consideration depending

cross

to be important

taken

2, Fig. 15(a),

by the leading

jog.

of the jog may yield a segment

that bows out in the cube plane, such that the screw dislocation

pair takes up a configuration with maximum

corresponding

energy, width, in the cube orientation. Such behaviour

of minimum equilibrium

sequence 2, Fig. 16(b).

would account for the unusually large

may be

advances.

,bl

tendency for jog separation screw orientation.

dipole. Trapping of dislocation

segments

FIG.

I

segment may swing around to form a

stable edge orientation

in near

16. Some of the possible configurations that can result from cross slip of a superlattice dislocation. (a) Sequence showing the development of a pinned configuration for the superlattice screw dislocation, and (b) sequence showing dislocation multiplication by double cross slip via a cube plane.

KEAR:

widths of certain dislocation Another

possibility

WORK

HARDENING

pairs, as at B in Fig. 9(b).

is that the second jog follows the

IFi

ORDERED

Somewhat

669

Cu,Aa

similar behaviour

intersection

may occur also for 60”

jogs, at least in appropriate

path of the leading one, such that both segments tend

when the shear stress in the normal

to bow out in the cube plane.

is high, i.e. for crystal

frictional large,

stress,

slip in a cube

particularly

favourable

plane

may

such

as in

aplitt’ing

of superlattice

dislocations

sign in neighbouring at D, Fig. 9(b),

this manner.

slip planes.

Here the dotted line represents

of the

contrast

two

(light

the trace

Several

perpendicular

examples

are to be found

appears that a superlattice plane

to an adjacent

signs by

will be generated slip plane.

(arrows),

segments

and at E it loops from one

A third

case.

Fig.

17.

in

new

by

analysis

segments

cross slip plane,

regenerative

plane

cross slip at a dissociated

dislocation

the

Frank-Read

of the nucleation

Other mechanisms

for

by Fleischer,‘20)

and

been discussed and Seeger.(21)

In an earlier

paper, (l) it was suggested

slip may be nucleated

at points

that

of favourable

dislocation

loop and the

grown-in

structure,

and proceed

from

antiphase

these

domain

points

dislocation

nodes.

now considered

by

zip-fastening

of constricted

This mechanism

to be of doubtful

for cross slip is

significance,

evidence

has been found in this study

struction

of segments

The

most

antiphase

since no

for the

of the domain structure

of cross slip, as required

3.4 Antiphase

by the model.

defects important

boundary

parameter

contrast

associated

is the phase

vector and R is the boundary Antiphase frr,

contrast

occurs

with

angle,

a segment

the cube plane is necessarily happen

to

redissociate

assume

the

in the

bowing

constricted,

screw

original

out in

when

cc takes

Antiphaso boundary displacement vector, R

~

vector.(22) the

value

reflections.

1

Phase angle x = 2~ g.R for different operating reflections g = I10

g = 701

g = 01i

+H

+ 277

n

-7r

0

+a

77

but should it

orientation

it

may

slip plane.

When this happens over a sufficient length the new segment could be

reactivated

process

as

a secondary

may be described

superlattice

dislocation.

source-the

as double

entire

cross slip for a

; [TOI]

The noteworthy

feature

of

such double cross slip is that the average

distance

of

; [loll

cross slip tends to be small, since slip in (100) is likely to be difficult. Dislocation multiplication by

; [Oli]

such a mechanism for

the

structure

(010)

of double cross slip would account

characteristic

fine

in the deformed

and

homogeneous

ordered alloy.dg)

slip

1

i[Oll]

1 1 i

7T

{-

2?r

(109) +?f

-i T

LX,

lattice

1 gives values of tc for all possible combinations TABLE

follows from the fact that

displacement

which is the case only for superlattice

Table

de-

at sites

given by CC= 2rg*R, where g is the reciprocal

multiplication

cross inter-

action between an expanding

of nucleation

FIG. 17. Jog mechanism for dislocation by double cross slip.

of

jog in the regular f.c.c. lattice

has been given by Hirsch.(15) also by Schoeck

of opposite

result octahedral

of

that

A detailed

mechanism.

In the event of mutual

dislocation

one.

in

cross slip have

to the primary 9(b)

possibility

the

shows

of such edge orientation in Fig.

with

multiplication

in the

such cross slip, short edge segments in directions

and the

will

in the normal

dark)

of screw segments

to

in

mechanism

dissociated

dislocations

superlattice

that they have opposite signs. annihilation

The

could be interpreted

of the original plane of one bowing segment, in overall

state

of the glissile jog pair, Fig. 12(a), cross slip by the jog

of opposite

change

[loo]

In this case, in view of the dissociated

under

circumstances,

to the attraction

or [ill].

plane

approaching

orientations

occur

arrangement

vicinity

or

stress for motion in the cube plane should be

but

response

The Peierls

orientations

octahedral

0

ACTA

6’70

METALLURGICA,

VOL.

14,

1966

the foil has been tilted so as to give contrast with the i01 reflection only, and the effect is to cause most of the

(010)

junction

(4

boundaries

to

disappear-the

three-fold

at A becomes an apparent two-fold

According

junction.

to Table 1 this must mean that the (010)

boundaries

have

displacement

vectors

parallel to (OlO), i.e. the boundaries shear type.(23) operating

Similarly,

reflection,

by appropriate

identical

for boundaries

Fig.

It may be concluded,

grown-in

domain

approximating low energy

have

in (001) and (loo),

structure

therefore,

consists

of

to cube orientations,

shear type,

are

choice

results

obtained 18.

that

are of low energy

e.g. see that the

boundaries

and mostly

in agreement

of

been

of

with previous

work,(1n22) In most antiphase

(b)

original

cases, new crystallographic boundary

segments

were found associated

grown-in

domain

these new antiphase

structure.

In

general,

defects were most prominent

the thinnest regions of the foil, and it appeared the majority ment 3.1).

or shortly

FIG. 18. Entire grown-in antiphase domain structure in a section taken parallel to the slip plane, as revealed by using two different operating reflections. (a) TlO reflection, and (b) Oli reflection.

of displacement available

vector

operating

foil, Fig. 3(a). superlattice in

reflections

a/2(110)

with

in an [111] orientation

It is clear from Table 1 that a single

reflection is not sufficient to give contrast

for all possible +2x

of the type

types

certain

reflections

of boundary,

cases;

are required

at

least

since two

u = 0 or

superlattice

to reveal the entire domain

Figure

19(a)

structure

shows

the

in a region

where contrast superlattice although

entire

grown-in

of an [ill]

orientation

is due to at least two

reflections.

somewhat

The

irregular

domain foil.

after electro-thinning defects

characteristic discernible

Again,

profusion

of antiphase

foil of specimen structure. antiphase

is no longer in

Fig. 21 shows another

example of a

defects in a particularly

3, with no recognizable

Careful examination

micrographs

structure

region of the foil (just

at top left of micrograph)

evidence.

thin

dislocation

of these and similar

shows at least two types of slip induced

defect.

Figure

19 shows ribbons

of anti-

phase defect (arrows) that have been formed tions ; here the are recognizable dot

dissociation

of superlattice

superlattice

partials

contrast

for

locations.

tend

many faintly contrasting

regular

simply disloca-

in Fig.

as single dot contrast,

boundaries, to be

(white traces parallel to

of the thicker

overlapping

in shape,

(see section

the edge of the foil, where the dislocation

double

domain

in the foil

clearly occurs only in the thinnest region near

by the complete

structure.

occurring

This is shown in Fig. 20, where a high concen-

t,ration of antiphase [iOl]

in

that

of them were formed by the rearrange-

and loss of dislocations

during,

of

with the

19(b)

as opposed

superlattice

to dis-

On the other hand, Figs. 18 and 22 show lines parallel to [iOl] which

oriented parallel to cube planes, e.g. the segments of

are considered

boundary

have been formed by dragging oblique jogs on super-

forming

approximately

the three-fold

parallel

to

junction

(OOl),

(100)

at A are and

(010)

lattice

to be tubular

dislocations,

Fig.

antiphase

defects that

13(b).(17*1s) This explana-

Marcin-

tion is consistent with the fact that antiphase defects

kowski(22) have reported much more crystallographic cube oriented boundaries in homogeneous, recrystal-

sometimes extend from top to bottom of the foil, and are not necessarily associated with the points of

tracts,

lized

Fig.

3(a).

polycrystalline

irregular material

domain

Previously,

material. structure

is a consequence

from the ideal stoichiometric be expected

Fisher

in a melt-grown

and

Possibly characteristic

of

localized

composition, crystal.

the of

more this

deviations which is to

In Fig. 19(b),

emergence primary vector

of dislocations. Further, as required for slip induced defects with displacement

a/2[iOl]

reflection,

Fig.

they become 22(a),

invisible

using the iO1

since the phase angle a = 2~,

see Table 1. Note that this contrast

effect tends to

KEAR:

WORK

HARDENING

IX

ORDERED

contrast

at

almost

superlattice

of Fig.

antiphase

(4

exactly

reflection,

inspection

671

Cu,Au

the

as

24(b),

in

Bragg Fig.

however,

angle

24(a).

Careful

shows

that

large deviations

where in fact structure

the contrast

has actually

anomalous

contrast

from the Bragg at the grown-in

disappeared. effect

is

is a micrograph

understood.

of the micrographs

and antiphase

contrast

the motion

24, the fact that the dislocation

an obstacle

exhas

In Fig.

segment at A appears itself around

boundary

indicates

to dislocation

motion,

a seg-

that the latter is which

is to

when the dislocation

in Fig. 24, the fact that

location antiphase

at B correlates boundary

dislocation/domain

cuts through it.

t’hc kink in the dis-

with the presence loop

suggests

of a closed

some

kind

interaction.

Fro. 19. Antiphase domain structure in a section of specimen 2 taken parallel to the slip p&m. (a) Two overlapping superlattice reflections, (b) 101 reflection. In (b) one set of boundaries lying approximately parallel to (010) is not visible since the phase angle a = 271.

rule out an alternative

explanation

in terms of the formation by screw dislocations

of the phenomenon

of diffuse slip traces, or tracks

escaping

through

the surface of

the foil. Antiphase

defects

regular dislocation the

foil,

were found also associated structures

indicating

structures

that

in the thicker

in these

were representative

Figure 23 shows antiphase to terminate dislocation location,

at points

areas

of the

defects (arrows) that appear

in sequence

3, Fig.

high concentration

defects at the bottom

right-hand

correlates

As mentioned oblique

an

of

jogs

when

on glide

dislocations

mechanism

contrast the

of

foil

(b).

suggests that an of

is an important

in the superlatltice.

of antiphase was

In

dislocation

in micrograph

drag due to the accumulation

stopping

Optimum

15(b).

of antiphase

corner of micrograph

avalanche

earlier, this correlation

frictional

dislocation tained

with

in near edge orientation

enhanced

defect’ sample.

loops, i.e. at the sites of jogs in the disas illustrated

segments

the

of cross slip in segments

Fig. 24 an unusually (a)

with

regions of

bulk

oriented

defects for

was obdiffraction

be

since energy must be supplied to create a step

in the boundary Again,

boundary

of glide dislocations.

to be in the process of wrapping ment of domain

in both

shows many

amples where the presence of antiphase influenced

A

the latter

of a region to the right of Fig. 24(b).

A careful examination dislocation

angle, domain

The origin of this

not

similar effect is shown in Figs. 5(b) and 25;

expected

the

defects are still just visible under conditions

of relatively

(b)

for a

Fra. 20. Concentration of antiphase defects (bottom right of micrograph) near the very thin edge of a foil of specmnen 2.

of

ACT.4

672

JIETALLURGICA,

14,

1-OL.

this

1966

case has been developed

recently

by Vidoz,(24)

and the results show that such a conclusion As mentioned curve at 77°K the

briefly elsewhere,t7)

shows much less work hardening

corresponding

StoloP25)

curve

have confirmed

have shown that tinuously

result is indicative Vidoz

to a maximum

of a diminishing model

activated

of secondary

ljrimary

dislocations

conThis

slip distance

foi

On the by

of localized secondary mainly by primary

process;

the low work hardening

inability

increases at 350°K.

can be explained

that the penetration

is a thermally

and

and moreover

temperature.

this

than

Davies

this result,

slip into the crystal deforming 77’K

298°K.

loops with increasing

and Brown

assuming

at

the work hardening

from 77°K

dislocation

is justified.

the stress/strain

slip

in other

words at

is identified

with the

dislocations

to cut through the

and form oblique

jogs in them.

Davies and Stoloff,(25) on the other hand, suggest that as a dislocation PI(:. “1. High &n&y of a&phase defects in u particularly thin foil of specimen 3.

that cross slip will occur, so that a

barrier

as in sequence

is formed,

increase explained Vidoz and Brown(l’)

have proposed

rapid rate of work hardening alloy,

compared

disordered produce

jogs for

cations the

that

in

antiphase

the

defects

in superlattice

antiphase

that

the

studies(‘)

in the

wake

of an

since nucleation

pre-strain

in the disordered

value for the coefficient which is comparable difference

are jogs on anelastic frictional

proportionally

CusAu,

of the frictional

for ordered and disordered

coefficients

for the

in stage

I1

Cu,Au.(l)

The specific model proposed

by Vidoz and Brown

slip in at least two intersecting in thin

component

with the value of -G/750

Burgers

of

The measured

in the ordered alloy is -G/1000.

in work hardening

appropriate

with the

but is independent material.

(a)

indi-

the dislocation

vectors.

In this

systems study,

foils has been obtained

ih

with direct

for an in-

creasing activity in secondary systems throughout stage II, but in amounts small compared with that in the

primary

system.

To reconcile

this

observation

with the intersection jog model, therefore, it must be argued that even relatively small amounts of slip in secondary t,he primary

systems system.

have a profound The mathematical

effect on slip in treatment

foi

FIG. 12. Chang_ in antiphase contrast with operating reflection. (a) 101 reflection, (h) overlapping 101 and 110 reflections.

is

increasing

of

previous

roughly

in ordered

of the work hardening

with

of the defects

have shown that

rp, increases

evidence

in terms

of forming such barriers

The

In agree-

production,

Furthermore,

pre-strain

requires

simply

16(a).

corresponding

dislocations.

defect

sources

dislocations.

stress,

quite

4, Fig.

with temperature

in the deformed ordered

ment with this model, evidence has been found in this study

likelihood

in the work hardening

alloy, is due to the extra energy required to tubular

oblique

with

that the more

loop expands in the slip plane there is

a finite probability

of

KEAR:

WORK

HARDEKING

(4 FIG. 23. Antiphase

ORDERED

Cu,Au

673

(b)

and dislocation

structures in the same area of a thin foil of specimen 2.

(a) FIG. 24. Antiphase

IN

011: reflection.

(b) and dislocation

structures in a thin foil of specimen 2.

Oli reflection.

ACTA

674

METALLURGICA,

VOL.

section their

14,

1966

jogs, since these jogs are constricted glide

motion;

60” intersection

favorable sites for vacancy condensation dissociated

state.

Figure

lattice dislocation tion of vacancies boundary. 6A-t

jogs

during are less

owing to their

11(b) shows that a super-

may become

pinned by condensa-

on its connecting

The dislocation

loop

strip of antiphase with vector

DA can react with the inner Shockley

of the dissociated

superlattice

sessile dislocations,(26-28) loop probably

dislocation

Fig. 26.

will occur

Dd + partials

to form

Nucleation

of the

on that partial giving the

lowest energy sessile configuration,

e.g. on the inner

partial B6 in Fig. 26(a) to give a stair-rod dislocation with vector

AB/yB.

The attractive

feature

of this

mechanism is that pinning can occur along three (110) directions

in the slip plane, so that the expansion

the entire dislocation

loop may be inhibited.

the slip distance may be controlled temperature

dependent

fluctuations

FIG. 25. Dislocation avalanche exhibiting deep cusps (arrows) in individual dislocation segments of near edge Note also faintly contrasting lines lying character. parallel to the slip vector.

could be important

constriction

should be thermally

assisted.

tions for temperature as follows:

required

for

cross

of intermediate

between

glide

and

cross slip, Fig. 15(a), (ii) in promoting

of superlattice

Fig. 16(a) sequence

4, spontaneously

excess

neighboring

slip plane, thereby

defect/oblique

jog

in Figs. 11(b) and 15(b).

mechanisms,

together

densation

frictional

Figure 15(b) shows that the

stress may be enhanced

of excess vacancies

with that

temperature

dependent

sources of antiphase

disloca-

one to retain the attractive

even at

hardening,

This mechanism

low vacancy

should

supersaturations,

BC-BB W-Do uIc+

+ +

**c +

ac as+*a

y*+z,a yD

+ns/,a

(al FIG. 26. Illustrating condensed vacancy

The

latter

illustrated

two

in Fig.

as proposed

in one system, and allows idea of antiphase

defect

by Vidoz and Brown.07)

To

be more specific, the source of antiphase defects in the

at least for 90” inter-

DA)rt)B +

IBC+*M

be important

and

strain hardening under condi-

tions of slip predominantly

tion.

constricts

creating an antiphase

arrangement.

this may transform them to oblique jogs and therefore in the slipping

dipoles

1 l(b), are of particular interest, since they can explain

by con-

on parallel jogs, since

defects

screw dislocation

follows a different path from the leading one into the

point defects generated by the dragging jog or dislocation coalescence mechanisms. Two cases are illustrated dislocation

the

antiphase defects, and (iii) in causing a modified form

work hardening are

dislocations

thermal

of double cross slip, wherein the trailing screw segment,

First, the slip distance may be influenced by

interactions

Thus,

(i) in determining

in such a manner as to form oblique jogs and associated

slip

Other possible explana-

dependent

by some form of

slip.

frequency of dislocation pinning by the jog mechanism annihilation

the dislocation

cross

of

Second,

.!.C-SBB+BC mcOo+.a ~BC+Dl\)r88+DS

lBc+aorac+n6+2ss

tb)

+ap. +BD,.~

nc-4a+ec DA-D,%-SA I&z+DbWa+d

+2.a

I&+Ao)-BC+Eo+2~o

(cl

products of dislocation reactions involving a dislocation loop and a superlattice dislocation.

KEAR:

slipping dislocations of point

defect

dipoles,

WORK

HARDENING

may be considered to be the result

interaction,

or double

annihilation

cross slip, rather

of screw

than

dislocation

IN

ORDERED

The

preceding

intersection

discussion

jogs

dislocation

675

C&Au

has

acquired

shown

by

loops can have a profound

slip process.

Thus,

it is considered

through the

mechanisms

of dipole formation

tion

slip (section

3.3), and also through

following

dislocations.

the

motion

It follows that

of the

a back

on the source will soon develop as successive tions get held up, and therefore tions

will emerge

stress

from

the

relatively

source

builds up to the point

disloca-

few disloca-

before

where

stress

the back

the source

on the

control the average slip distance

locations

will impede

effect

jogs on dis-

phase defects in the slip plane by the leading dislocaa source

forest

primary

that

intersection, as originally proposed. In this connection, it should be mentioned that the formation of antifrom

how

expanding

point defects and antiphase

and intermediate

of

defects, and interaction

of

these defects with glide dislocations. expression

cross

the generation

A simple general

for the flow stress that takes these factors

into consideration

is

can

no longer operate, which is in accord with the relatively small slip offsets observed. dislocations

course, another oriented

slip

direction

Interactions

and slip induced

dislocations.

mostly

Evidence

for

the creation

[iOl] in this particular defect

Fig.

double

micrograph

cross

there

CusAu.

for double

slip of the

At present,

from tensile

work

cross slip, probably

involving

much more experimental At

elevated

location/point important

the

of anti-

defect interaction

deformation,

and

FlinnZo4) who also emphasized

more

sources

extensive

This point was recognized

possible.

dis-

should become

tend to become

climb first by

that the climb process

favourable-the

lowest

energy

parallel

trapped

mechanisms. that

the

Previous

anelastic

con-

by the different

work(‘)

dislocation

(TV + TV’) accounts

for about

Moreover,

has shown

frictional

a similar

contribution

to the

from observed

densities after various pre-strains of -l/3

explanation

for this

discrepancy

although

it does seem possible that 7Q may have been

underestimated. densities

This

be offered

in stage

of the flow

No satisfactory can

stress

Q of the flow stress

flow stress from 7. has been estimated dislocation

stresses in neigh-

stress set up by

in the crystal

combined

in stage II.

and ho the

dislocations

bouring slip planes, i.e. the interaction dislocations

is

because

at

this

the

time,

dislocation

in the thin foils may not be representative

of the bulk sample. temperatures

To be more specific,

some of the narrower

at ambient

edge dislocation

dipoles may anneal out by climb and unstable dislocation

dipoles may annihilate

Interactions induced

between

point

scribed of

since dislocations

is energetically

dependent

work.

as well as sinks for vacancies, becomes

for

of the details will require

temperatures

for nearly

to be explained.

in ordered

creation

on the dislocation,

stress

it is believed that the experimental

Clarification

considered)

stress,

(both long- and short-range

in

tests will be

to account

hardening

stress”

frictional

drag due to the presence

No

it seems clear that

of mechanisms

of jogs and defects “passing

dislocation

frictional

This leaves a component

shown above.

where 7p is the intrinsic 7p’ the additional

II.(l)

defect interactions,

evidence favours some type of temperature phase defects.

cross

from thin foil observations

evidence

dependent

type

form discussed

In sum, therefore,

is no shortage

temperature

are considered to be

dislocation/point

but some indirect

in its

but it is not clear whether this

evidence has been obtained

discussed later.

possibly

defect

lines parallel to

Evidence

17, or the modified

for supperlattice

dipole

The deep

of annihilation,

contrasting

trails.

slip has been discussed, represents

(110)

screw

of an antiphase

The many faintly

antiphase

of

at B in Fig. 5(b) seems to be a

screw dipole in the process wake.

is, of

of a highly

consisting

has already been mentioned.

cusp in the dislocation involving

defects

reason for the development structure

configurations

between glide

antiphase

defects

as a dynamic

therefore,

glide

dislocations

represent

what

and

may

significance

slip

be de-

source of work hardening,

of permanent

uous deformation.

screw

by cross slip.

and

only in a contin-

If the deformation

is interrupted,

so as to allow the excess point defects to be eliminated completely

by diffusion,

location

sources

structure

should

glide,

at

least

on reloading

developing

from

experience

the new dis-

the

a reduced

temporarily,

and

pre-existing resistance

the

to

dislocation

figuration for an edge dislocation pair with slip vector a (110) is with one segment above the other in

velocity and slip distance will be enhanced. The slip distance and dislocation velocity will be reduced to

neighbouring

the original value characteristic

slip

planes.

A

reduction

in

energy

would be achieved also by the mechanism illustrated in Fig. 26. where glissile u (110) type superlatt,ice dislocations with

are

t,he shorter

t’ransformcd slip

vector

to

sessile

n 1100).

dislocat,ions

only after

a burst

priate excess concentration required frictional drag. explain

the repeated

of the applied stress

of slip has recreated of defects Such

yielding

the approto give

behaviour

phenomenon

the

would observed

676

in the yield

interrupted point

through

deformation,

representing

the crystal

consistent

also

Fig.

a burst

1, with

as a Luders front.

with

the

each

of slip spreading

absence

This model is

of the

reloading

neighbouring

dislocations

phase and point latter

point,

avalanche

defects.

consider

and the presence

of anti-

As an illustration

of this

the

in Fig. 4(c).

case

effect at 80”K, and the fact that it makes its appearance only after a few minutes ageing at room temperature.“)

lished

It

10M8 cm,

be

mentioned,

also,

process at room temperature

that

the

may involve the elimina-

tion of some of the slip plane debris unstable

dipoles and antiphase

of course, diminish good reason defect

consists

one-half

defects.

This would,

avalanches,

In the limiting

or bursts

translation

In principle,

can be eliminated

distance

therefore,

by

in the slip

an antiphase

by diffusion

of

case, an antiphase

of a single row of atoms displaced

a complete

direction.

in the form of

both rF’ and TV, which is another

for dislocation

slip on reloading.

recovery

defect

of a single vacancy

along its entire length. Previously,(l)

that

the flop

stress in the deformed ordered alloy may be expressed in the form

ho -

7F

by -4

musb also be acting account

for this

is the

dislocation

Gb/L is th e critical

stress

and

In sum, therefore, stress

formula

The

present

importance

of intermediate

work

cross slip in the

mation process, but no clear indication for a diminishing model, effect

except

L with pre-strain, perhaps

in dislocation

4(c) and 5(b). correlation expected,

for some

avalanches,

the defor-

has been found

can influence

segment

L, and (ii) other factors influence the bowing pinning points, such

the bowing

out of a dislocation

in the slip plane.

Finally,

it’ should discussion

perhaps

and involves

ordered

(X N 0.8)

the motion

In the disordered

be stressed phases

of the

alloy,

of superlattice

dislocations.

alloy, where slip is very coarse and motion

of many

type,

dislocations

the decisive

and short-range

recent theoretical

the

fine and homogeneous,

slip process seems to be the interaction dislocations

that

applies only to the fully ordered,

order.

of the

factor

in the

between

glide

According

to a

study of this problem by Cohen and

Cottrell,(31)

e.g.

of this

compare that

Figs.

a definite

can hardly

be

slip to give an observable besides the line tension

out of a as elastic

since it does not take

Fine,(2g) based on earlier work by FishercN) and also

L and pre-strain cross

stress must be involved.

as required by the

since (i) not all the jogs on the dislocation

loop will nucleate

7c and the

indication

It is now recognized

between

confirms

60

In other

other factors besides the line tension

dissociated

slip in a

segments

calculated

is inadequate,

into consideration

group

loop.

between

3

stress

it now seems clear that’ the bowing

ordinary

cross

x

value

opposing

configuration.

from other sources of internal

involves

of intermediate

This

shear stress in specimen some other

where slip is characteristically

stress to bow out the glissile

dislocation

7 kg/mm2.

on the dislocation

cases, t,he discrepancy

or partially

frictional

,u. From pub-

flow stress is larger, so that even greater contributions

edge (or mixed) segments of average length L between at points

7e -

particular

the

jogs

is ~0.25

1O’l dyn/cm2 and b = 5.3

x

gives

kg/mm2, so that

preceding 7 = Tp + Tc

where

G = 3.3

which

falls short, of the operative

that

it has been proposed

data

dislocation

The average width of the glissile

edge segments in the avalanche

should

of the

can

segment between interactions with

the leading

dislocat’ion

in a sequence,

group should occur in pairs, and the spacing pa.irs should

increase

because

passage

the

for successive of a sequence

across a slip plane in a material order causes oscillations

pairs.

or

of the This

is

of dislocations

containing

short-range

in the local order across that

plane, which are large initially but get progressively smaller-about 6-8 dislocations through a region bring3 the value for local order to it)s final value.

The

KEAR:

driving

force

accelerating

the lead dislocation, numbers,

successive

therefore,

second,

etc.

release, Figure

in the deformed

in striking

agreement

rapidly

the third

arrangements

disordered

short-range

must

above

more extensive partly

have

T,,such

clarified

material

of dislo-

directions,

have not been with

minimum

order following a rapid quench from above

is believed,

T,. It sample

in

of

analysis.

the groups

by arrows. Such groupings

previously(l)

to

alloy that are

cations at A and B are moving in opposite as indicated

to the

less rapidly

with the theoretical

It follows from the model that

observed

to

gets less with increasing

27 shows

dislocations

HARDENIXG

dislocations

i.e. the second is accelerated

first by t,he energy the

WORK

therefore,

that

been imperfectly

that

the local

than

usual.

by further

this

particular

quenched

order developed

This point

investigation

from was

needs to be

on quenched

and

ordered alloys. ACKNOWLEDGMENTS

The

author

is indebted

to Dr.

many

helpful

discussions.

and to Mr. M. E’. Horn-

S. M. Copley

for

becker

for valuable

assistance. REFERENCES

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IX

ORDERED

Cu,Au

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