The correlation between stacking-faults and recrystallisation in impurity-doped copper

THE CORRELATION BETWEEN STACKING-FAULTS

AND RECRYSTALLISATION

IN

IMPURITY

-DOPED

COPPER

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WÉTENSCHAP AAN DE TECHNISCHE HOGESCHOOL TE DELFT

OP GEZAG VAN DE RECTOR MAG NI FICUS DR. R. KRONlG, HOOGLERAAR IN DE AFDELING

DER TECHNISCHE NATUURKUNDE, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN

OP WOENSDAG 26 FEBRUARI 1962 DES NAMIDDAGS TE 4 UUR

DOOR

FREDERIK EVERT VAN WELY SCHEIKUNDIG INGENIEUR GEBOREN TE ',-GRAVENHAGE

STELLINGEN

I

De berekeningen, waarbij de stapelf.outenergie wordt bepaald uit waarden v.o.or de verschuivingen der r~ntgenreflecties en de disiocatiedichtheid, worden thebretisch .onv.old.oende gemötiveerd.

R.E.SmalImarl en K.H,.Wètmàb:m, phil.Mág. 2 (1957j 669. K.NakajiIha. Sci. Rep. Res: fhst. Tohokb Uliiv. A-12 (4) (1960) 309.

TI

Het dislocatiem.odel, dät Jasw.on v.oorstelt v.o.or de vorming van martensiet, n.oudt geeti rekening met het feit dat een Burgers-vector ,varl I;tet ty~e

11

a <:: 112> geen slipvect.or is in het vlakken-gecentreerde rboster.

M. A.Jaswon iri "The mechanism of phase-transformations in metals" 1956. III

Het gebruik van ariisotro.oP. plaatrilateriaal in plaats van isotro.op plaatmateriaal bij dieptr~kkèn ben.oeft geen aanleiding te geven tot extra materiaaiverliézen; ddch kan in bepaalde gevallen de materiaal verliezen zelfs verminderen.

IV

Het magnet.o-chemisch .onderzoek van katalysatoren neemt in verschillende opzichten in belangrijkheid t.oe.

V

Het disl.ocatiemodel dat ten grondslag ligt aan Seeger's bereke-ningen van de stapelfoutenergie uit Tm w.ordt slechts benaderd in materialen met een lage stapelfoutenergie.

A.Seeger. R.Bernel' en H.Wolt. Z.f.Phys. 155 (1959) 247. VI

De vborspr.ong die de S.ovjet-Unie, .op s.ommige gebieden der h?-tüurwetenschapperi, heeft op de Verei1igde Staten, w.ordt niet

~lleEm ver.o.orzàakt dodr eeh mogelijkë naijver tussen de verscpil-lende researcH:'centhi ih de Verenigdê, Staten, maar tevens dbdr de organisatie van het .onöérwijs in de Sovjet-Unie;

VIt

Oe conclusie värl Èaii~y, dat rèkristaÜisatie iri

9b%

gewalst per ver.o.orzaakt wordt

äo

o

r

pölygàtiisàtie, is experimentee1 voldoende gemotiveerd:

J.A.Báiley iii Ptoc.Eur.Reg.Cöilf:El.Mit . (1!J6tlj 433.

ktJ-r\ ~"'

.on-Het is zeer twijfelachtig of het algemeen belang en de opleiding van technologen en academisch gevormde chemici gediend is met het instellen van de baccalaureaats studie voor chemische technologie aan de gemeentelijke Universiteit van Amsterdé'm.

IX

Voor het aantonen van een correlatie tussen walstextuur en sta-pelfoutdichtheid is het aan te bevelen de experimenten uit te voeren in een temperatuur gebied, waarin geen herstel van de

stapelfoutdichtheid of partiele rekristallisatie kan optreden. Hsun Hu. R.S.Cline en S.R.Goodman. J.Appl.Phys. 32 (1961) 1392.

x

Het door Rozen en Khorkhorina gegeven bewijs voor het me-chanisme van de extractie van uranylnitraat uit water met T. B. P. berust op een onjuiste interpretatie van de ligging van het even-wicht.

A. M. Rozen en L. P. Khorkhorina. Zhur. Neorganicheskoi Khimmii 2 (8) (1957) 1956. ver-taald als AERE Lib. Trans. 792.

-Aan mijn ouders Aan Atie

made possible by a grant of Delfts Hogeschool Fonds.

This work is part of the research progralllllle of the H.esearch group "Metals F.O.M.-T.N.O." of the "Stichting voor Fundamenteel Onderzoek der Materie"

(Foundation Ior Fundamental Hesearch of Matter

-F. O. M. ) and w~s also made possible by financial sup-port from the "Nederlandse Organisatie voor Zuivel·-Wetenschappelijk Onderzoek" (Netherlands Ol·ganization for pure Hesearch - Z. W.

o. ).

CONTENTS page Introduction ₇ Chapter I. Stacking-faults. ₉ 1. Introduction. ₉ 10 the 13 2. The formation of various types of stacking-faults.

3. The influence of deformation stacking-faults in F. C. C. lattice on the X-ray pattern.

4. Survey of measurements of intrinsic stacking-faults

in cold-worked F.C.C. metals. ~2

Chapter Il. Peak shifts measurements on pure copper. 2ö

1. Introduction. 26

2. Measurements. 27

3. The thermal elimination of intrinsic deformation

stacking-- faults in pure copper. 30

4. Discussion of the results. 33

ChapteI' lIl. The influence of impurities on the rate of

annealing of the peak shift. 41

1. Introduction. 41

2. Preparation of the specimens. .,.1

3. Measurements. .,.2

4. Discussion. +!

Chapter IV. The cube recrystallisation texture. 49

1. Introduction. 49

2. Recrystallisation theories. 49

3. The influence of impurities. 53

4. Experimental procedures. 5.,.

5. Experimental results. 5u

6. The suppression of the cube texture. 59

Chapter V. Electronmicroscopy. u ~

1. Introduction. u~

2. Experimental procedure.

u'"

3. Experimental results.

uS

4. Discussion. liS

Chapter VI. Conclusions. 70

Samenvatting. 'ï~

lNTRODUCTION

Af ter extensive rolling and recrystallisation copper shows a cube texture. Many workers have dealt with experiments and theoretical considerations for the explanation of the cube recrystal-lisation texture. Until a few years ago, two theories were used to explain annealing textures (1) the theory of oriented growth and (2) the theory of oriented nucleation. Bath conceptions, however, were not very successful in explaining the characteristics of the cube texture.

In 1957 Burgers and Ver.braak have proposed a new mechanism, based upon cooperative < 112> slip in the two components of the

{112} <111> rolling texture, for the explanation of the cube texture. The mechanism was analysed in detail by Verbraak (1.959). It was found that the different annealing textures of rolled copper single crystals could be explained very adequately.

It has been known for a long time th at impurities suppress the formation of the cube texture. Phosphorus seems to have the most olltstanding effect, whereas arsenic has a considerable, although much less pronounced influence (Phillips and Phillips 1952).

<112> slip is accompanied by the extension of a stacking-fault. Therefore, the mechanism of Burgers and Verbraak suggests a correlation between the influence of impurities on the behaviour of stacking-faults and the influence of the same on the recrystal-lisation texture. From the investigations described in this thesis the conclusions can be drawn that such a correlation actually exists.

Since the important conception of the dissociation of a glide dislocation in partiaIs, separated by a stacking-fault ribbon, was put forward by Heidenreich and Shockley (1948), experimental and theoretical evidence have accumulated that the stacking-fault energy is an important parameter, influencing manyphysical and mechanical properties. It has not been possible, till now, to measure the stacking-fault energy explicitely. However, as pointed out theoretically by Paterson (1952), stacking-faults produce a displacement of the Debye -Scherrer lines in the powder diagram. Although all assumptions introduced in Paterson' s treatment will not be fulfilled in reality, peak shifts are actually found. The amount of the shift is proportional to the number of stacking-faults and thus gives qualitative information about the stacking-fault energy.

With the purpose to investigate whether there is a correlation between stacking-fauUs and recrystallisation in copper, we have made (1) peak shift measurements on scoured impurity-doped copper and (2) pole figures of rolled and recrystallised copper single crystals, doped with the same impurities.

In Chapter I the geometry of the different type of stacking-fauUs is discussed, together with the influence of intrinsic and twin faults on the Debye-Scherrer lines in the X-ray pattern.

in pure copper, introduced by scouring, is interpreted in terms of dislocation rearrangements. The annealing of the peak shift in copper, doped with smaU quantities of phosphorus, arsenic, silver and nickel is studied in Chapter lil. After a short survey on the current theories of recrystaUisation, the recrystallisation textures of roUed single crystals, doped with the impurities mentioned above, is given in Chapter IV. On the basis of the measurements it is proposed that an extra impurity-dislocation interaction is responsible for the outstanding effect of phosphorus on the recrystaUisation textures as weU as on the annealing characteristics of the stacking-faults.

Finally, electronmicroscopical observations on copperaluminium and copper foils are discussed in Chapter V.

. - - - -- - - - ~--~~

CHAPTER I

STACKING-FAULTS

1. Introduction

The ideal face-centered cubic lattice (abbreviated F. C. C.) can

be conceived as a régular sequence of close -packed planes. A

new plane can be placed in two different ways on a close -packed plane A, according to the two possible sets of hollows in the

A-plane (. and x in Fig. 1). The two placing possibilities • and x describe two planes Band C. An ABCABC stacking-sequence gives aF. C. C. structure, an ABAB sequence a hexagonal close-packed (abbreviated H. C. P.) structure. In the F. C. C. structure the planes are (111) planes, whereas in the H. C. P. structure

tne layers are (0001) planes.

Fig.l. Arrangement of atomie layers in the F.C.C. lattiee. The hollows in the A-layer

eorrespond to two plaeing possibilities (. and ,,) for the layers Band c.

A disorder in the regular sequence is known as a stacking-fault. Thus, a stacking-fault in the F. C. C. lattice is fault in the ABC sequence, with the restriction that two adjacent layers are always different.

A simple notation to describe the F. C. C. lattice is given by Nabarro (see Frank 1951). The sequence of two layers in the ABC direction is indicated by ~, and in the CBA direction by

'\1. According to this convention the sequence

ABCAB1BC

where the stacking-fault is indicated with an arrow, can be written

A twin can be described as

J.

ABCABACB

where the arrow marks the twin boundary, or, with the aid of

the "stacking-operators": ~~~~ '\l'\l'\l

The irregularity in the sequence of the. close-packed planes represents extra energy. In first approximation the energy of

a stacking-fault ~~~~'\l~~

is assumed to be twice the energy of a coherent twin

~~~~'\l'\l'\l

because in the first case two twin boundaries occur and only one in the second case. The so-called stacking-fault energy 'Y

is the energy of a stacking-fault per unit area. Until now, it has not been possible to measure the stacking-fault energy ex-plicitely. However, an indirect method, based upon the meas-urement of angles at the intersec'tion of twin boundaries and grain boundaries, was used by Fullman (1951). He found a val-ue of 25 for the ratio of grain boundary energy to twin bound-ary energy in copper. Assuming 500 erg/cm2 _{for the mean grain}

boundaryenergy, a twin boundary energy of 20 erg/cm 2 is

ob-tained, giving a value of 40 erg/cm2 for thestacking-fault energy in copper. As to the order of magnitude this value is in reas-onable agreement with theoretical predictions by Seeger (1955)

according to which monovalent met als like copper, silver and gold should have a low stacking-fault energy. It will be shown in the following section that the stacking-fault energy is an

important parameter which determines many physical properties

of F. C. C. metals.

2.

The

formation

of

various types

of

stacking-faults.

Stacking-fau1ts in the F. C. C. lattice can be formed in diffe-rent manners:

a. During the formation of the solid phase (growth or twin faults).

b. By slip on octahedral planes.

c. By dissociation of dislocations in extended dislocations.

d. By condensation of vacancies or interstitials.

a. GROWTH OR TWIN FAULTS.

The growth of aF. C. C. crystal by the addition of successive

(111) layers is governed by the rule that each new layer must be different from the last two. However, when a fault occurs the new layer is identical with the second last layer and we

have the sequence: ABCABCB or ~~~~~'\l

If further growth follows again the F. C. C. pattern the new layer

will be formed in the A position. Further growth will give the

~

sequence ABCABCBACBA or ~~~~~ '\l'\l'\l'\l'\l

In this sequence the two parts on either side of the fault plane (marked with an arrow) have a twin orientational relationship.

-11-growth, twin layers are formed. Because a mlmmum of three layers is necessary to decide whether two lattices are in a twin relationship, the thinnest twin is given by

l ~ .

ABCABCBABC or AAAAA \1\1 AA

where the arrows mark the growth faults. Stacking sequences of this type are called extrinsic faults. The attention is drawn to the fact that the name "extrinsic" does not tell anything about the way of formation of the fault. Clearly, with increasing

number of successive \1, a macroscopical twin layer will be

formed.

b. THE FORMATION OF STACKING-FAULTS BY SLIP ON OCTAHEDRAL PLANES.

Slip on octahedral planes in a <110> direction occurs by al-ternative displacements in <112> directions, resulting in a

zig-zag mot ion (Fig. 1.). An equal number of zig-zag movements

does not change the stacking-sequence but one additional zig (or zag) movement gives a stacking-fault. This signifies, in fact,

that a half dislocation with Burgers vector ~a <112> has swept

over the octahedral plane. When in the original sequence ABC ABC ABC

slip has occurred over ta <112> on plane BX

, the right -hand side

has changed according to C~A~B-C, and a deformation

stacking-fault of the type ABCABABCA or AAM \1 AAA

has been obtained. Stacking sequences of this type are called intrinsic stacking-faults. Again, the name "intrinsic" does not tell anything about the way of formation.

Twinning by deformation can occur also, as has been shown for copper by Blewitt, Coltham and Redman (1955). Although originally thought to be impossible (Cottrell and Bilby, 1951), a mechanism for the growth of F. C. C. deformation twins was given by Ookawa (1957). In Ookawa' s model a single Shockley dislQcation segment is connected with two screw dislocations emerging at different sides of the segment so that the Shockley

dislocation can sweep indefinitely around· the screw dislocations

at both ends of the segment. Venables (1961) has described a

modification of Ookawa' s model. We shall return to this in

Chapter IT.

c. THE FORMATION OF EXTENDED DlSLOCATIONS.

Heidenreich and Shockley (1948) have pointed out that in the F. C. C. lattice a dislocation of the type -}a<1l0> can dissociate into two half dislocations according to the e9uation:

ta[1l0]-ga[12Ï} + ta[211]

while a stacking-fault is formed between the two half (or partial or Shockley) dislocations .

Fig.2. The dissociation of a unit dislocation in two partial dislocations.

In Fig.2.!l XY is a dislocation with Burgers-vector ta[110], lying in (111). X and Y are dislocations nodes and are fixed. In part P the lattice above the plane (Ï 11) has slipped with regard to the lattice below that plane over tal110]. In Fig.2b dislocation XY has dissociated in two partial dislocations (1) and (2) with Burgers-vectors of respectively ~al12i] and tal211] (extended dislocation). This means that also part R between the half -dislocations has_ slipped over the lattice below (111), how-ever only over la[121j. Necessarilya stacking-fault of the type ABCABABCA has been formed between the two partial dislo-cations . The area of the stacking-fault between the partial dis-locations is determined by the stacking-fault energy 'Y.

The energy of a dislocation per unit length is given by E = f. G. b2

in which f is a numerical factor depending upon the elastic model employed, G the shear modulus and b the Burgers -vector. As b for a Shockley dislocation is ia

YB

and for a ta r11 0] dis-location ta V2, 2. E₁₁₂

<

E 110 and dissociation can occur. The

area of the stacking-fault is given by the balance between the repulsive force between the half -dislocations and the surface tension of th~ fault. Clearly the area of the fault increases if the stacking-fault energy decreases.

The formlltion of a stacking-fault has a considerable influence upon the glissile character of screw dislocations. Dislocations only glide in the plane defined by Burgers -vector and disloca-tion line. This means that a screw dislocadisloca-tion of the type ta[11D] can glide in the two octahedral planes (l11) and (1Î1), which intersect in 110]. However, when dissociation occurs in two partial dislocations, slip is only possible in the plane

of the fault.

d. THE FORMATION OF STACKINÇ-FAULTS BY CONDENSATION OF VACANCIES OR INTERSTITlALS.

A mechanism for the creation of stacking-faults from va-cancies or interstitials has been described by Read (1953). We consider aF. C. C. lattice with a relatively large concentration of vacancie~. Suppose that these vacancieH will cluster on octahedral planes, so that part of an octahedral plane is elim-inated (Fig.3a). Now the adjacent octahedral plancs ean move

-13-together in the [111] direction (Fig.3b) changing the sequence

!

ABCABCABC into ABCABABC, where the arrow marks the

eliminated plane. The intrinsic stacking-fault will be surrounded

by a partial dislocation with Burgers -vector ~a[lll] (Frank dislocation) .

a

-~~-l.

Fig.3. Sequence of octahedral planes in the F. C. C. lattlee. In a) part of an octahedraJ

plane is missing. In b) an inmnsic fauJt has been formed surrounded by a Frank

partial. In c) an extrinsic fault has been formed.

Condensation of interstitials results in the formation of an

extra octahedral platelet. Now the neighbouring planes will bow

out in the [1111 direetion. (Fig.3e). Again a staeking-fault is formed surrounded by a Frank fa[1111 disloeation~loop. Within the loop the sequenee ABCABC has ehanged to ABCBABC, where the arrow marks the inserted extra plane. Clearly, the stacking

sequenee in the loop is of the extrinsie type.

Finally, the stacking sequences of the different types of faults

eonsidered here are shown in Fig.4.

3.

The

influence

of

deformation

stacking-faults

in the

F.

C. C.

lattic

e

in the X-ray pattern.

It was first suggested by Barrett (1952) that eold work eould

produee staeking-faults in a F. C. C. lattiee. In an important

eontribution Paterson (1952) has pointed out theoretieally th at

staeking-faults have an influenee on the X-ray pattern. Sinee

th at time numerous observations have been made on the powder

patterns of deformed F. C. C. metals.

All methods for handling the staeking-fault problem make use

A

c

Fig.4. The stacking-sequence of a) a twin. b) an extrinsic fault and c) an intrinsic fault.

elementarx ~oncepts of the reciprocal lattice.

Let Al ~ ~

!Je

the primitive translations of the

crysta!..lat-tice and BI B2Ba th0..êe of t1.!.e r~ciprocal lé!!tice. T.!.J.en BI js

perpend!.cular to both A2 and A3' B 2 to both Aa and Al and B3

to both Al and Ä_{2 . These relations give the following equations}

in vector notation:

o

The magnitude of the reciprocal vectors is defined by

BI Al

=

Ë2A2

=

B3Aa 1

This means that for rectangular coordinates IB11 is the reciprocal

of the spacing of the (100) planes in the crystal lattic~ IBal

the reciprocal of the spacing of the (010) planes and IB31 the

reciprocal of the spacing of the (001) planes. The plane (hkl)

in the crystal lattice is represented by a point (hBI' kHz, lB₃)

in the reciprocal lattice.

The vector

r

_hkl connecting the point (h~, kB2' IEa) with the

origin of the reciprocal lattice is perpendicular to the planes (hkl) in the original crystal lattice; its magnitude is equal to the reciprocal of the spacing between these planes.

An elegant geometrical construction to find the reflection

con-ditions has been described by Ewald. The points in Fig. 5 re-present the reciprocal lattice points (hkl). The Ewald

construc-tion is the following: from the origin 0 a vector is drawn with

-15---0

Fig.5. The Edwald construction.

Around P a sphere with radius

t

is constructed, which intersects the plane of the drawing as a circle. If any point R of the reci-procal lattice lies on the sphere, a diffracted beam arises from the corresponding lattice planes, whereas PR gives the direction of the diffracted wave-normal. Because

OR 2sin®

À

and

OR

I

r~kl

I

~hkl

we have 2d: sine

=

.À

the condition for Bragg reflection.

The mentioned considerations hold for crystals without

deform-ations. In a deformed crystal the lattice planes are bent and the reciprocal lattice points are extended, so that reflections

will be broadened. In the following we will deal with the influence of intrinsic and twin deformations faults on the reciprocal lat-tice points of F. C. C. met als .

According to Paterson (1952) intrinsic faults produce a sym-metrical line broadening and a peak shift, whereas twin faults

produce an asymmetrical line broadening and a negligible peak

shift. For intrinsic faulting the same result was obtained by Warren and Warekois (1955). In a recent review paper Warren (1959) has described the influence of intrinsic and twin faults

on the X-ray reflections of F. C. C., body-centered cubic (ab-breviated B. C. C.) and H. C. P. metals. The derivation given be-low folbe-lows, with some modification, Warren' s treatment for F. C. C. metals ol.

To handle the stacking-fault problem the following assumptions are made:

a. Only one crystal is considered and in that crystal stacking-faults occur on only one set of octahedral planes.

b. The stacking-faults traverse the whole crystal; stacking-faults bounded by Shockley or Frank partials are not considered.

c. The stacking-faults occur independently and at random. To perform a sommation over layers it isconvenient te .i.ntro-duce hexagonal axes Al1\2A3 instead of the cube axes al

a

₂

a

₃. Al and A₂ lie in the octahedral plane on which faulting oc -curs, and A3 is perpendicular to these planes. We have the following transformation equations (Fig. 6):

/ ' / ' I I I 1

IJ

_1/

)L---~-'"

~ ./'" 2

Fig.6. The relation between cubic and hexagonal axes.

Al al + ~ H h + k 2 2 2 2

-

_{k 1} A₂ a2 + ~ K + 2 2 2 2 A3 al + a~ - + a:] L h + k + 1 0) Tilc: aUllJOr is illuebrcu to Dr. J.13ouman for many hclrrlll u iSClissiol1s.

-17-The scattered intensity is given by

I .... f2 E E E E, E, E, exp {271i (8-8₀ ) (R_{m,- Rm)}} mI m2 m3 mI m2 m3 À

where f is the atomie scattering factor and So and

s

are '!!lit

vectors in the direction of primary and diffracted beam. RIJl defines the position of atom ~ m2. in _{layer m 3 . When a fault} has occurred, layer m;l has been displaces over a distance '0 in the layer. Then

-R _{m mI I} A- _{+ m 2} A-_{2 +} m3

A

3 + -6

3

For each plane L we have

Iplane-f2 E E E, E, exp {

2~i

(8-8₀) (m{ÄI + m

2

A_{2 - mlÄ I - m 2 Ä 2 )}} mI m2 mI m2

"-Uqing the formula for the sum of a geometrie al progression we get

*)

where NI and N 2 are the number of atoms in the Al and 1\2 direction. The total intensity over all layers is given by

{ 21Ti - - [ Ä - -

J}

1= Iplane.E E,exp - ( s - s o ) (m~-m3) ~+ (6'-6)

m3 m3 À 3

Let m'3 -m 3 = m, then mÄ 3 is the distance of two layers. 3

6" -

ö

= {j (m) gives the relative displacement in the plane of the layers, if a fault has occurred.

V{e ..!!o~ introduce the reciprocal lattice BI B2B3 corresponding to Al A 2A3 ' and the :re~ation

s-so

=

HBI + KB₂ + LB3

Introducing N as the A-umber of layers having a mth neighbour and <Ö(m) >A~ as the corresponding average relative displace-ment, as in Warren' s treatdisplace-ment, we get

1_ EmNmexp{21Ti(HBI + _KB2 + _{LB3) (m A3} + <Ö(m» )}

3 Av

The introduction of <Ö(m)

>

requires the assumption that

fault-Av

ing occurs independently and at random. Because

and where

B3:i\

=

1

I -. 1::

exp(211"im~)NJIl

<expi._m > Av m (2)

is the extra average phase difference as a result of faulting. H-K

This phase difference is equal to 0 or t 211" -3- for two layers in a A ... A, A ... B, A ... C relationship respectively.

The next problem that has to be solved is to find the prob-é'lbility that two layers, mapart, obey to the above mentioned relationships. This has been treated in detail by Gevers (1954). Suppose that intrinsic and twin faults are formed with probabilities a and

f3

respectively. Using the expressions derived by Gevers, the probability

p!

of finding an A atom in the mth layer, when both types of faults occur independently and at random, turns out to be

1

where t = (3 - 6

f3 -

12a)2, m>O and a and

f3«

1 .).

If p~, p:n and P~ are the probabilities that relative to the zero layer the layer m is the same, or one ahead, or one behind the ABC sequence, we get for the boundary conditions

p~ 1

pO 0

1

From these boundary conditions follow the constants b_l and b_{2 ,} and finally

po

m

! {I

+ (1-

t)

(-(1-f3) + it)m + it 2

(3)

We now return to equation (2). For random intrinsic and twin faulting we have

P~

=

p~

=

t(1-P~)

.) The attention is drawn to the fact that in the derivation given by Gevers the definition of the probabilities is different from the one used here. For that reason a and

f3

in this derivation correspond to

f3

and (I-a) in the Gever' s treatment.

-19-. po

+

(I_pO )COS21T H-K

< expl" m > Av = m m 3

For H-K = 3M, in which M is an integer, <expi" m > Av = 1, and there is no effect of faulting.

For H-K = 3M

t

1

<expi"m>Av t(3P~ - 1) (4)

Combining equations (3) and (4) and substituting the value of

<expi"m > ~v so obtained in (2) in the way described by Warren

(1959), (2) becomes

I ... EN Zlml {cos21Tm (L-l _ a'/3) +

~

sin21Tlml (L-l _ a\f3)} +

m m 3 41T

V3

3 41l

+ EN Zlml {cos21Tm (L+l + aV3)

m m 3 41T

_ .f

_V3

Sin21Tl m l (L+l + ₃

a~}

_4tt

(5)

where Z ;.: 1 - 1,5 a -

f3.

This fin al expression for the intensity contains a eosine series and a sine series. This latter one contains the coefficient

!Js«

land thus causes only a modulation of the eosine functions. For a value of L which produces a peak in the upper eosine series for reflection (HK.!:-h_ the lower eosine series shows a peak for -L for reflection (HKL). In both reflections a peak shift AL occurs and an asymmetry due to the sine terms. The up-per expression has a peak at L+AL, where L=3N+l, with a peak

shift corresponding to AL =

3a:; .

For this value of L, the Iower

eo-sine fundion vanishes, because the function has to be summed over m. Near L=3N -1 the lower wression shows a peak, whereas the

shift is given by AL = - 3a_4Tt3. This means that the displacement

of the reciprocal lattice points (HKL) and (HKL) due to intrinsic

faults will be in opposite direction. Thus the points move in the

same direction with respect to the plane L=O (see Fig. 7), i. e.

both towards or both from that plane. Therefore for the deter-mination of the direction of the peak shift in the powder pattern only the positive values of L need to be considered. L=3Mtl corresponds to shifts to higher and lower angles respectively. As can be seen from equation (5) the same arguments hold for the asymmetry.

The relation between AL as a result of intrinsic faulting and

A2® is given in Fig. 7. ~ is the angle between Ë 3 and HEI + KB 2

1

Fig. 7. The relation between the diffraction vector and the peak shift. /Ar*1

=

A (2sin®) '"

IB3IAL.cos~

À

With the relation

I

B3

I

= 2 sin®

~

cos

~

À L

we get A(2®) 2tan®cos 2 ~--AL ( ±)2tan® cos 2 ~ _ _

3a.V3

_

L 41l-L

or in degrees A(2®)

=

(t) tan®cos2~. 270'{3 (6)

where (r) corresponds to L = 3N t 1

For the {111} reflection 3 out of the 4 (111) planes are

ef-fective in producing a peak shift, because for (111) L = 3N;

for the other (111) planes L = 3N+1, so that intrinsic faults

produce a peak shift to higher angle.

For the {200} reflection all (200) are effective. Because

L = 3N -1 the peak shifts in a direction of lower angle as a

result of intrinsic faulting (Fig. 8) .

I I I

!

J (111)(111) (lil) (11 i)

.. e

I I I I 0(0((1 I I I .. 9{200}

- - -

-

-21-In case twin faults occur, the reflections are broadened

asym-metrically. Assuming for reason of simplicity a=O, the

asym-metry can be deduced by plotting the cosine and sine functions given in (5). In Fig. 9 both functions are drawn schematically

for reflections {11l} (L=3N+1) and {200} (L=3N-l). It can be seen

that the {111} and {200} reflections in the powder pattern are extended to higher and lower angles respectively. The attention is drawn to the fact that in the powder p'attern intrinsic faults themselves produce an asymmetry of the {111} reflections also,

because one -quarter of the diffracted intensity is not shifted.

This asymmetry is opposite in direction to the twin fault asym-metry.

Warren' s theory outlined above has been developed for intrinsic

and twin faults. The faults were assumed to occur on only one

set of octahedral planes. In practice, however, deformation

{lil} ,

,

_ 1

-

-___ ---'N+I . . L / / / / / /

----{200}

--~ L

Fig.9. The asymmetry of the reflections L = 3N + 1 and L = 3N - 1 due to twin faulting. stacking-faults occur on more than one set of (111) planes (ex-perimental evidence will be given in Chapter V,

Electronmicros-copy). In first approximation the measured values of Cl. are

as-sumed to be the sum of the faulting probabilities for the different sets of octahedral planes (Warren and Warekois 1955, Warren 1959), but a rigorous proof has not yet been given.

The twin fault probability {3 can be obtained by analysing the

line profiles by Fourier methods. The theoretical background

is given in the review paper by Warren (1959). The experiment al

determination of {3, however, is rather inaccurate as aresult

of the overlap of the tails of the reflections by deformation

A doubtful point is the influence of extrinsic faults. Formally extrihsic faults are the smallest twin faults which are conceivable. From this point of view it might be argued that extrinsic faults produce an asymmetry like twin faults, as suggested by Wagner (1957). On the other hand it seems improbable that intrinsic faults produce a peak shift and extrinsic faults an asymmetry only. We made an attempt to treat the influence of extrinsic faults in a similar way as has been described above for intrinsic and twin faults, but this has not been successful as a result of the difficulties in the determination of po. Because of the lack of detailed knowledge about the influencf1 of extrinsic faults the asymmetry of the reflections has been attributed to twin faults or thin twin layers.

A second point, which has not been clarified at the moment, is the influence of extended dislocations . It has been discussed by Christian and Spreadborough (1957) that it is physicallyimpro-bable that extended dislocations might cause a peak shift like intrinsic faults traversing through the whole crystal, because of the fact that the mean dis placement of the layers beyond the immediate neighbourhood of the dislocation is a whole lattice vector. Evidence that faulting must extend over large distances was deduced by Houska and Averbach from.experiments on faulted cobalt. In hexagonal crystals stacking-faults produce a broaden-ing of the reflections and no peak shift (see e. g. Warren 1959). However, reflections of the type H-K=3N are not influenced. This was confirmed experimentally by Houska and Averbach (loc. cit.), indicating that stacking-faults, and not extended dis-locations were responsible for the observed effects . If a large number of extended dislocations had been present, the reflections of the type H -K=3N should be broadened by internal strains.

Nevertheless, after drastic cold work by filing or scouring a large number of dislocations certainly will be present. Based on the idea that peak shifts are caused by the stacking-faults of extended dislocations, stacking-fault energies have been cal-culated from peak shifts and data on dislocation density, obtained from line broadening (Smallman and Westmacott 1957, Nakajima 1960). At the moment, however, these calculations lack any theoretical basis, because it was assumed in the theory on the influence of faulting on the X -ray pattern that stacking-faults traverse the whole crystal. We shall, therefore, interprete our results, described in the following chapters, in terms of stacking-faults rather than extended dislocations .

4. Survey of measurements of intrinsic stacking-faults in cold-worked F. C. C. metals .

To introduce a measurable peak shift, a heavy deformation is necessary. Because the shifts are small it is essential to make accurate measurements of the line profiles. Present-day

-23-scintillation counter diffractometer measurements are capable of giving good results .

The usual way i~ to determine the sum of the peak shifts of two reflections, each shifting to different sides. The combination {111} - {200f suits the purpose fairly weIl. From the peak shifts ct can be caiculated according to equation (6).

In the following the results, given in literature, are put to-gether.

a. PURE COPPER.

Even before Paterson (1952) predicted on theoretical grounds that intrinsic faults give rise to a peak shift, Greenough and Smith (1955) measured the shifts of the {331} and {420} reflec-tions on copper filings, produced at room temperature. They found a value of 6. 10-3 _{for the intrinsic stacking-fault}

prob-ability ct. For the same material, Smallman and Westmacott (1957), using Paterson' s method, found ct=3, 3.10 -3 for copper filed at room temperature whereas copper filed at -196° C and measured at this temperature gave a value of 13.10-3 . The peak shifts decreased at room temperature: af ter 10 hours ct diminished to 3.10-3 . Wagner (1957) found a value of 12.10-3 forO. F. H. C. copper filings obtained at -160°C, whereas 5 hours at room temperature were sufficient to "anneal out" the peak shift almost completely. The measurements of Wagner agree well with those of Smallman and Westmacott.

b. ct -COPPER ALLOYS.

Peak shift measurements on ct-brass filings, obtained at room temperature, of different compositions have been made by Warren and Warekois (1955). The peak shifts increased with increasing zinc content, in accordance with measurements of Smallman and Westmacott (1957). ct-Brass filings with 10 and 30 at.

%

Zn gave ct-values of 5.10 -3 and 24.10-3 respectively. The peak shifts annealed out in the temperature traject of 150-3000

C. Wagner (1957), however, found values of 16.10-3 _{and 40.10-}3 _{for alloys} of the same composition, filed at -196°C, whereas the peak shifts annealed out in the temperature range of 50-2000_{C. The}

differences in the measured values of ct are probably due to the rise in temperature during the preparation at room temperature of Warren and Warekois' s filings. Moreover, the authors have used different methods for the determination of the peak posi-tion. We will return to this in Chapter Il.

The increase in peak shift af ter deformation with increasing zinc content is in agreement with observations by Barrett (1950) on a deformed ct-copper-silicon alloy, for which the "non-Laue streaks" could be interpreted as stacking-faults. In this case the F. C. C. copper-silicon alloy changes into a H. C. P. phase at higher silicon content. Barrett therefore assumes that the difference in energy between the two phases decreases with in-creasing silicon content of the F. C. C. phase.

with tin, germanium and aluminium show, after deformation, an analogous increase of the peak shifts with increasing content of the second component. In the equilibrium diagram of all these alloys B. C. C. and H. C. P. phases occur beside the F. C. C.

phase. This means that near the boundary of the a-phase the energy difference between F. C. C. and H. C. P. diminishes and therefore the stacking-fault energy decreases.

lf the equilibrium diagram shows only one F. C. C. phase (complete solid solution) it may be expected that the. second component will have a small or r.o effect on intrinsic deforma-tion faulting. In agreement with these predicdeforma-tions, Smallman and Wcstmacott (1957) have found that the value of a for copper-nickel filings (50 at. %) is almost the same as for pure copper filings.

C. OT HER METALS AND ALLOYS.

Peak shifts for aluminium, silver, nkkel and gold filings obtained at low temperature, have been measured by Wagner (1957, 1958, 1960). Aluminium filings showed no trace of peak displacements . This agrees wUh the fact that the stacking-fault energy of aluminium is known to be high compared with other F. C. C. met als . The values of a for silver and gold filings are almost equal to the value for copper filings. Therefore, Wagner (1960) concludes that the stacking-fault energies for copper, silver and gold should be nearly the same.

The value of a for nickel filings lies between that found for aluminium and the copper-silver-gold group. Qualitatively this agrees wUh the fact that nickel has a relatively high stacking-fault energy.

Measurements on extended nickel-cobalt specimens have been made by Broom and Barrett (1953). Cobalt shows an allotropic phase transformation from H. C. P. to F. C. C. at 400°C. The transformation temperature is lowered with increasing nickel content, until at about 30 at. % Ni the transformation temperature is 20°C. In aF. C. C. alloy of this composition many stacking-faults may be introduced by relatively slight deformation. Ac-cording to Christian and Spreadborough (1957) nickel-cobalt al-loys in the range of 0-70 at.

%

Co show an increased peak shift with increasing cobalt content, in agreement with the measure-ments on a-copper alloys.

Recent measurements on platinum filings (Taranto and Brotzen 1961) show that this metal belongs to the copper-silver-gold group. Measurements on lead, lead-silver (0,1 at. % Ag), lead-indium (10 at.

%

In), aluminium and 70-30 a-brass, deformed by scratching at 4, 2 oK, have recently been performed by Bolling et. al. (1961). For lead a value of 13.10-3 _{was obtained for} the intrinsic stacking-fault parameter. The question arises, however, whether the degree of deformation after scratching with a pointed tooI is comparable with that after filing.

Finally, the results given in the literature have been combined in table 1.

-25-Table I

Material Composition Def. Temp. a.1O- 3 _Authors

Cu O.F.H.C. 20°C 6 Greenough & Smith (1955)

Cu pure

..

3 Smallman 8i. Westmacott (1957)

Cu pure 770_{K 13}

..

"

Cu O.F.H.C. 770_{K 12 Wagner (1957)}

a-Brass 10 at."!o Zn 20°C 5 Warren & Warekois (1955)

..

20 at."!o Zn

..

16

..

..

..

30 at."!o Zn

..

24

..

..

..

35 at.,,!o Zn 770_K 39

..

..

..

10 at.,,!o Zn 16 Wagner (1957)

..

20 at."!o Zn

..

25

..

..

30 at."!o Zn

..

40

..

..

35 at."!o Zn 2ÖOC 50

..

14 at."!o Zn 7 Smallman & Westmacott (1957)

..

27 at."!o Zn

4~2oK 20

..

..

..

30 at."!o Zn 34 BOlling et. al. (1961)

Cu-Al 5,7at.,,!oAI 20°C 11 Smallman & Westmacott (1957)

..

11 at. ,,!o Al

..

29

..

..

..

17 at.,,!o Al

..

40

..

..

4,2 at."!o Al

..

4 Christian and Spreadborough (1957)

..

8,5at.,,!oAI

..

13

..

..

..

12,8 at."!o Al

..

31

..

..

..

17 at.,,!o Al

..

51

..

_..

Cu-Ni 50 at. ,,!o Ni

..

5 Smallman & Westmacott (1957)

Cu-Si 2,5at."!oSi

..

6

..

..

..

4,5at."!oSi

..

15

..

..

..

7,1 at. ,,!o Si

..

34

..

..

Cu-Ge 2,5at.,,!oGe

..

5

..

..

..

5 at."!o Ge

..

15

..

..

..

7,2 at."!o Ge

..

35

..

..

Al pure 770K

--

Wagner (1957)

Al pure 420_{K 3 BOlling et. al. (1961)}

All 99,95 ,,!o Ag 770K 16 Wagner (1957)

Nl pure

9ÖoK 4 Wagner (1958)

Au 99,99 ,,!o Ag 12 Wagner (1960)

Pt 99,99 ,,!o Pt 20°C 16 Taranto & Brotzen (1961)

Pb pure 420K 13 Bolling et. al. (1961)

Pb pure 770K 11

..

Co-Ni 69 at."!o Co 50°C 15 Broom & Barrett (1953)

..

50 at."!o Co 20°C 6 Christian and Spreadborough (1957)

..

65 at."!o Co

..

19

..

..

..

69 at.,,!o Co

4:'2oK 22

Pb-Ag O,lat."!oAg 11 BOlling et. al. (1961)

Pb-In 10 at."!o In 4,2oK 2

..

List of intrinsic stacking-fault prob-abilities obtained from peak-shift measurements. In all

cases the temperature of the measurement was almost equal to the deformation temperature.

All measurements were performed on filings, except those of BOlling et. al. (scratched

PEAK SHIFT MEASUREMENTS ON PURE COPPER.

1.

Introduction.

The shifts of the {111} and {200} reflection of a deformed cop-per specimen are of the order of a few hundredth of a degree. Therefore it is necessary that the angle 2 ® of the reflections can be determined extremely accurate and reproducibly.

The peak shifts first described in the literature have been found by photographic analysis of Debye-Scherrer diagrams (Broom and Barrett 1953). This method, however, is not very accurate and several precautions have to be made to take into account shrinking of the film. Much better results are possible in case a diffractometer with Geiger or scintillation counter is used. Modern diffractometers are capable to record the line profiles continuously. Because of the mechanical inertia of the recording mechanism line profiles have to be recorded with a low speed. The high recording time makes it necessary that an adequate stabilisation of X-ray and counter feed is present.

To avoid positional errors two reflections shifting to different directions are recorded in a single run. The difference in

angle of both reflections is compared with the corresponding dif-ference for an annealed specimen. In this way small changes in lattice parameter are partially compensated, whereas the sum of the displacements is obtained. From the sum t::,. the value of the intrinsic fault parameter a can be determined directly by means of equation (6). For the {111} reflection cosr=~, and for {2001 cos~= ~

v'l.

UsingÀ = 1,39 Ä (Cu-K(3 radiation) and a= 3, 61 Ä

for {he lattice parameter, we get

t::,.(2®2oo-2®m)o= 5,0 a (7) To get a measul-able peak shift the copper specimen must be deformed severely. Therefore the usual way is to measure on a briquet of pressed filings. In this way a random specimen is obtained. The disadvantage is, however, that the degree of cold-work can not be controlled.

With a diffractometer one can only measure reflections of the planes (hk!) parallel to the surface of the specimen. Thus, measuring {111} and {200} reflections, stacking-fault densities of two types of crystallites are compared, e. g. crystallites with (111) and (200) planes parallel with the surface of the specimen. For high degree of deformation it is assumed that in all crystallites the stacking-fault probabilities will be the same. Of course, this assumption is not necessary if different orders of one reflection are compared.

-27-The recorded line profile has a maximum at 2®. An annealed specimen and a narrow receiving slit would give a sharp reflec-tion. As a result of extension of the reciprocal lattice points due to deformation a cold-worked sample will give a line profile be-tween 2®- ó and 2®+ó. For large ó, any texture of tbe specimen may possibly change the line profile because of the change in the number of reflecting crystallites in the recorded interval. For the determination of the twin fault probability (3 the texture of the specimen may play a role because (3 is influenced especially by the tails (large ó) of the reflections. For the determination of the intrinsic fault parameter from the peak shift, the influence of deformation texture will be negligible, because the position of the top is hardly affected. Possibly in the case of an extreme sharp texture the top will be displaced.

Our measurements have been carried out on flat specimens,

8 mm wide, deformed by scouring on emery paper. The advan-tage of this method is th at the specimen remains flat af ter de-formation. Moreover it was found experimentally that a repro-ductive concentration of stacking-faults is introduced af ter scouring for a few seconds. Because of the short time necessary for deformation, the development of heat is reduced to a minimum, preventing self-anneal. The reproduction of the measurements allows the conclusion that the deformation texture is too weak to influence the peak position.

The line profiles have been recorded with a stabilised X-ray apparatus with precision goniometer and scintillation counter (type Philips PW 1010). Characteristic Cu-Kp radiation has been used. Although the intensity of the Kp radiation is much lower than that of Ka, this disadvantage is largely compensated by the fact that Kp is a single line and not a doublet. Thus inaccurate graphical resolving methods are not necessary. All line profiles have been recorded with a speed of 0,010

/ tmin. per 2,5 mm on

the chart. Unless mentioned otherwise, the recording.s have been made at room temperature.

2. Measurements

.

Two methods have been described to define the posltion of the reflections. Warren and Warekois (1955) used the centre of gravity. In order to use this method it is necessary to record the line profile together with some background at both sides of the profile. The base of the prvfile is then given by interpolation of the background. The reflection is assumed to occur between 2®-ó and 2®+ó (Fig. 10a). The base is divided into equal parts. Now the X-coordinate of the centre of gravity is defined by

x

"

where Yi is the recorded intensity minus background at the point

xi. The inaccuracy of the method is caused by the difficulty to separate the tails of the reflection from the background.

a b

fig. 10. The definitions of the position of a reflection with

a) the centre of gra vity and

b) the top of the reflection.

The second method involves the determination of the position of the top (Xt), as described by Smallman and Westmacott (1957) and Wagner (1957). The top is found by extrapolation of the mid-points of the width of the line profile at different intensity levels (Fig. lOb).

Both methods do not give the same results as will be shown in following. The shifts of the {111} and {200} reflections of copper, cold-worked by scouring, have been determined in both ways. The specimen was then annealed at 1800

C and the shifts were measured again. In Fig. 11 the results are given as a function of the time of annealing. Curves (1) and (2) have been obtained using the centres of gravity and the points at maximum intensity respectively. fig. ll. 1Q2_{t. (28} 200-28111 ) 0

I:

3 2 20 _{- - -___ minuto} ' 40 60

Isothermal annealing curves (T=1800_{C) of the {}

UI} -{

_{200} peak shifts in copper.}

deformed by scouring at room temperature. (1) obtained from the centres of gravity (2) obtained from the top of the reflections.

-29-Fig. 12. Line profiles of the{200}reflection. upper line: immediatel y af ter scouring.

middle line: af ter annealing for a few minutes at 180°C. lower line: af ter annealing for 15 minutes at 400°C.

The marked difference between the curves (1) and (2) is caused by the asymmetry of the {200} reflection af ter annealing for a few minutes only (Fig. 12). Because of this asymmetry there is a dif-ference between the position of the centre of gravity and the position of the top. The asymmetry occurs for all specimens after an annealing treatment at relati vely low temperatures. At higher temperatures recrystallisation sets in, and the asymmetry disappears together with the line broadening. The asymmetry of the \. 200} reflection (extension to the low angle side) corresponds to the asymmetry caused by twin faults (see Chapter I). Thus for the determination of the intrinsic fault probability the position of the top has to be used rather than that of the centre of gravity, because the latter is influenced by twin faults too (Van Wely 1961). In their measurements on a-brass filings Warren and Warekois (1955) used the centre of gravity as a reference for the peak position. In our opinion this is the reason of the

difference between the measurements of Warren and Warekois

(1955) and Smallman and Westmacott (1957), the latter using

the top of the reflections.

The position of the top of the reflections from deformed'

cop-per could be determined with an accuracy of

t

0,5 mmo The

in-accuracy is caused by the statistical errors of the counter, the width of the line recorded on the chart and slight differences in the deformation process. With the used recording conditions

of 0,01°/2,5 mm the accuracy in 2® becoomes t 0,002°, thus

for the difference 2® 200 -2 ® 111

±

0,004 • For an annealed

specimen 2® 200 -2® 111 can be determined by using the mean of

several measurements. Putting this to t 0, OOI, ~(2® 200 -2®111 )

can be obtained with an acuracy of t 0, 005 .

3. The thermal elimination of intrinsic deformation

stacking-faults in pure copper.

The peak shift ~(2 ® 200-2 ® 11M decreases after annealing in

the temperature range of 100-150 C. This is shown in Fig. 13;

the values are obtained by annealing the cold-worked specimen

in an oil thermostate for 15 minutes at each temperature. From

the curve the temperature Tt can be found at which the peak shift is reduced to the half of the original value. According to

Fig. 13, Tt = 115 COfor pure copper cold-worked by scouring

at room temperature. 102A(2~-2elll) 0 3 2 O~ ____ ~ ______ ~~ __ -L~=A __ ~

o

SC 100TI,A.z ISO 200 - - - _ .. _ CC

Fig. 13. Isochronal annealing curve of the {11]} -{200 }peak shift for pure copper. deformed

by scouring at room temperature. t=15 minutes.

The results given in Fig. 13 differ in two ways from the data

in the literature:

a. The peak shift after deformation. Measurements on copper filings obtained at room temperature have been performed by

-31-for the sum of the shifts of the {111} and {200} reflections. It must be kept in mind, however, that filing is a drastic defor-mation, evolving much heat. As a result of the rise in tem-perature "self-anneal" may occur, decreasing the peak shift. b. The half-way temperature. Values for Tt, for copper cold-worked at room temperature, are not yet available. From the data of Wagner (1957), however, Tt

=

300e can be deduced for copper filings prepared at low temperature (-1960 _C).

The question therefore arises whether the deformation tempe-rature has influence on the rate of annealing of the stacking-faults. This is actually the case. Measurements have been per-formed on copper specimens scoured at low temperature. The experimental procedure was as follows: the specimen was cooled in liquid air, and after this scoured on emery paper for a few seconds. During the contact with the emery paper some ri se in temperature may occur. However, the average deformation tem-perature is believed to be below -1000

C. During the measurement a stream of dry, cold air was blown against the specimen, keeping the temperature at about -200

e,

to prevent annealing during the measurements·). An isothermal annealing curve for

1000

C and an isochronal curve for 15 min. have been determined. The results are given in Fig. 14 (curve 1) and Fig. 15. For comparison, an isotherm al annealing curve for 1000e for a specimen scoured at room temperature is given as curve (2)

in Fig. 14. As can be concluded from a comparison of Fig. 13

and 15 and curves (1) and (2) in Fig. 14 the rate of annealing

Fig. 14.

102_{6 (2e}

200 -26111) 0

30 60 90 120

- - -__ .. minuta

Isothermal· annealing curves of the {U1}- {200} peak shifts for pure cop~er. deformed by scouring at (1) low temperature and (2) room temperature. T=100 C • • ) It was found experimentally that at room temperature the peak shift in copper. scoured at low temperature. disappeared in about 24 hours. whereas the peak shift in copper deformed at room temperature did not change even in 7 days. Therefore in the latter case cooling during the measurements was not necessary.

3 2

-32-

o~----~----~~----~~----o

50

_{- - - -___ • oe}

ISO

Fig. 15. Isochronal annealing curve of .the{ 111 }{ 200} peak shift for pure copper. deformed

by scouring at room temperature. t=15 minutes.

of the peak shift increases with decreasing deformation

temper-ature. From the isochronal curve in Fig. 15 Tt

=

850

C is

obtained for copper deformed at low temperature Moreover the

peak shift after deformation at low temperature is somewhat larger than after deformation at room temperature (Fig. 14 at t= 0).

The asymmetry of the {200} reflection shown in Fig. 12 oc-curs in all specimens af ter elimination of the peak shift. This leads to the conclusion that intrinsic deformation

stacking-faults are transformed into twin stacking-faults. A similar suggestion

was made by Wagner (1957) based on annealing experiments on silver filings.

An explanation for the disappearance of intrinsic faults and

the formation of twin faults might beo given in terms of

re-crystallisation. Experiments by Garber et. al. (1960) on

poly-crystalline copper, deformed in compression at 4°K and 20oK,

have shown that recrystallisation, or at least grain boundary

migration, can occur at low temper'ature. Moreover it is known

from many experiments on the recrystallisation of copper that annealing twins occur frequently. Combining, these experimental facts might lead to the conclusion that the asymmetry of the {200} reflection should be caused by the annealing twins, formed by recrystallisation at low temperature.

Serious objections can be made, however, if this theory is used for the explanation of our results. First, the broadened line profiles of our specimens show no indication that total recrystallisation has occurred. Secondly, the observations of Garber et. al. on the movement of grain boundaries at room temperature have been obtained after deformation at extremely low temperatures. Copper, deformed at liquid air temperature,

-33-does not show any recovery of the mechanical properties after warming up to room temperature (Molenaar and Aarts 1950), although it must be kept in mind th at the degree of cold-work in the latter case is much less than in Garber' s experiraents. Thirdly, if recrystallisation actually takes place at room tem-perature, it is not clear why annealing twins should disappear at 300-400° C, whereas it is known from experiments on rolled copper that such twins are formed during recrystallisation at about 400° C. A fourth argument against the suggestion gi ven above can be deduced from some experiments which we carried out on silver. The peak shift in high-purity silver, scoured at room temperature, anneals out at room temperature af ter a few hours, while the same asymmetry of the {200} reflection occurs. Recrystallisation certainly does not occur so quickly.

The difference in the rate of annealing of the faults between copper and silver can be accounted for when vacancies play a role. .According to Manintveld ~1954) vacancies introduced by plastic deformation "anneal out' in the rangeof -70 -

oOe

for silver and -40 - +400_{Cfor copper. Moreover' it is known from}

the experiments of Adams and Cottrell (1955) on the work-softening of copper that dislocation rearrangements can occur at low temperatures under the influence of stress. Therefore, in the following paragraph a tentative explanation will be given, based 0:1 the idea that intrinsic faults are transformed into twin

faults by vacancy mechanisms and/ or dislocation rearrangements.

4. Discussion of the results

'

).

Since the well-known experiment of Molenaar and Aarts (1950) on copper and silver it is known that there Ó.re two types of lattice defects: (1) those ha ving a marked influence on mechani-cal properties (dislocations) and (2) those having a small or neglibible influence (vacancies or interstitials). The beha viour of the latter type of defects can be determined by measuring a suitable physical property, e.g. the electrical resistivity.

The increase of the electrical resistivity after cold-work is due to a contribution of point defects and dislocations. Af-ter deformation at sub-zero temperature the point-defects dis-appear in several steps at temperatures below the recrystal-lisation or polygonisation temperature (see e. g. Seeger 1955). Although many contradictory suggestions have been given for the mechanisms of the observed annealing steps, we can conclude at any rate that point defects will have areasonabie mobility. For this reason it seems possible that point defects may cause the conversion of intrinsic faults to twin layers.

A second possibility for the formation of twin faults from intrinsic faults might be dislocation rearrangements. It was thought originally that rearrangement of dislocations in copper was hardly possible because polygonisation occurs scarcely even

af ter prolonged annealing at 1000oC, whéreas aluminium polygo-nises at much lower temperatures (300°C). Cottrell and Stokes

(1955) showed that dislocation rearrangements in aluminium

strained at liquid-air temperature are even possible at very low temperatures. Similar experiments were performed by Makin

(l958) on copper. In these experiments single crystals are

strained at low temperature, unloaded and strained again. The

yield stress required to resume plastic flow after unloading" is

initially greater than the flow stress immediately before un-loading, and a sharp yield point and a yield drop is observed.

It is essential that straining is performed up to a point in stage

Il or III in the stress-strain diagram, indicating that dislocations

on the second slip system play a role. The effect is ascribed

to locking of dislocations on the first slip system by interaction

with dislocations on the other slip system. Analogous interpre-tations have been used in a recent paper by Birnbaum (1961). The stored energy increases with decreasing deformation tem-perature. This is known from direct calorimetrical measurements (Pervakov et. al. 1961). whereas the same conclusion can be drawn from the increase of the line broadening with decreasing deformation temperature (Paterson 1954). Garber et al. (1960) have given a similar suggestion for the explanation of the low temperature recrystallisation phenomena of copper. Thus after

deformation at a lower temperature.TI a smaller temperature

activation energy will be necessar:y to enable some dislocation

movement than after deformation at a higher temperature T_{2 •}

Therefore, besides vacancy mechanisms, temperature activated rearrangements of dislocations might be assumed in order to explain the formation of twin layers.

It is brought back in mind that the following results were

obtained from the measurements ?f the {111} and {200} reflections of scoured copper:

a. Af ter annealing" of the peak shift the {200} reflection is

clearly asymmetrical.

b. The peak shift as well as the rate of annealing of the peak

shift increases with decreasing deformation temperature.

We first consider mechanical twin formation. A mechanism for mechanical twinning in the F. C. C. lattice has been given by Ookawa (1958). A modification of Ookawa' s dislocation model was described recently by Venables (1961). Both mechanisms start with a ta[110] dislocation. Part of the dislocation in plane (d) (=(111» may dissociate (Fig. 16a) according to

!a[110]

----=-.

~a[I11] + ~a[112]

(8)

or + óB

-35-DB=~Q[1I0]

DB .. ~a [110)

Fig. 16. Dissociation of a ia [110] dislocation segment in (111). See text for discussion •

o

c

A

B Fig. 17. Thompson' s teuahedron of Burgers vec;tou.

The Shockley partial óB bows out under the influence of an ap-plied stress causing an intrinsic /ault. After half a revolution the partials meet on neighbouring slip planes (Fig. 16b). The in-teraction between the partials tnay be overcome by their 'dynaml -cal energy, as suggested by ::)eeger (1956), so that the following revolution can be made.

In Ookawa' s model the Shockley dislocations rotate about their accessory pole dislocations emerging on different sides of plane (d). It is unlikely, however, that all Shockley dislocations have sufficient energy to overcome their stress fields dynamically. For these partials an alternatlve mechanism has been sugges-ted by Venables (loc. cit.). Thin twin layers might be formed by repeating on neighbouring slip planes the mechanism described above for intrinsic faulting. This might be possible if af ter the rejoinmentofthe Frank and Sbockley partials the res1,lltant ta[UD]