Transmission electron-microscopic studies of twinning in Mo-Re alloys

TRANSMISSION

ELECTRON-MICROSCOPIC

OF TWINNING

IN Mo-Re

K. OGAWAt

STUDIES

ALLOYS*

and R. MADDIN:

Twins in MO-3.5 at. % Re alloys deformed at room temperature and in MO-18 at. % Re deformed at liquid nitrogen temperature were observed by transmission electron microscopy. Neither extended dislocations nor extended dislocation nodes were noted. Instead, a dislocation reaction between a slip Direct evidence of the operation of a dislocation and three twinning dislocations was often observed. pole mechanism for twinning was obtained. In view of these observations and of the theory of twinning recently proposed by Sleeswyk, (14) twinning mechanisms are discussed in detail. The present observations suggest that the critical stage of twinning is the dissociation of slip dislocations in { 112) planes into three twinning dislocations. Also direct evidence of the existence of emissary type non-coherent twin boundaries was obtained. The fringe contrast observed in non-coherent twin boundaries in these b.c.c crystals is interpreted in terms of the kinematical theory of electron diffraction due to stacking faults.(iO’ A new effect, oscillation of the intensities of electrons diffracted at non-coherent twin boundaries was found in the region where the absorption effect is prominent and the twinning dislocations are spaced closely. The effect of free surfaces upon the arrangement of dislocations was found to reach as deep as a few hundred A. ETUDES

SUR

LE

MACLAGE

D’ALLIAGES

ELECTRONIQUE

DE

Mo-Re

PAR

MICROSCOPIE

TRANSMISSION

Les auteurs ont examine par microscopic Blectronique de transmission les macles dans des alliages MO-35 “/u Re deform&s a temperature ambiante et d’alliages MO-18 % Re deform& Q la temperature de l’azote hquide. 11s n’ont pas note des dislocations dissociees ni de noeux de dislocations dissociees. Au contraire, ils ont observe une reaction de dislocation de glissement et trois dislocations de maclage. 11s ant, obtenu des preuves directes du fonctionnement d’un mecanisme de pole pour le maclage. Sur la base de ces observations et de la theorie de maclage recemment proposee par Sleeswyk,‘r4) les auteurs Les observations disponibles actuellement suggerent discutent en detail les mecanismes de maclage. que l’etape critique du maclage est la dissociation des dislocations de glissemont dans le plan {112} en trois dislocations de maclage. 11s ont de meme obtenu des preuves directes de l’existence de joints de macle 11s interpretent le contraste de franges observe dans les joints de non coherents du type “emissaire.” grains non coherents de ces alliages cubiques cent&s en fonction de la theorie cinematique de la diffraction Blectronique due aux fautes d’empilement. (lo) Les auteurs ont trouve un nouvel effet, l’oscillation des intensites des electrons diffract&s aux joints de macles non coherents, dans la region oh l’effet d’absorbtion est proeminent et les dislocations de macles sont peu espaces. 11s ont t)rouve que l’influence des surfaces libres sur l’arrangement des dislocations s’etend aussi profondement de quelques centaines d‘A. ELEKTRONENMIKROSKOPISCHE

DURCHSTRAHLUNGSAUFNAHMEN

ZWILLINGSBILDUNG

IN

VON

DER

Mo-Re-LEGIERUNGEN

Mit Hilfe van elektronenmikroskopischen Durchstrahlungsaufnahmen wurden Zwillinge in einer Moo35 at.-% Re-Legierung (verformt bei Raumtemperatur) und in einer in fliissigem Stickstoff verformten MO-18 at.- % Re untersucht. Es wurden weder aufgespaltene Versetzungen noch Knoten aufgespaltener Versetzungen beobachtet. Stattdessen wurde oft eine Versetzungsreaktion zwischen einer Gleitversetzung und drei Zwillingsversetzungen beobachtet. Es ergab sich ein direkter Hinweis auf die Betatigung eines Polmechanismus bei der Zwillingsbildung. Mechanismen der Zwillingsbildung -werden ausfiihrlich diskutiert im Hinblick auf diese Beobachtungen und die kiirzlich von Sleeswyk(i4’ vorgeschlagene Theorie der Zwillingsbildung. Die Beobachtungen lassen vermuten, da13 das kritische Stadium bei der Zwillingsbildung die Dissoziation von Gleitversetzungen in den {112}-Ebenen in drei Zwillingsversetzungen ist. Es ergaben sich ferner Hinweise auf die Existenz von emittierenden nichtkoharenten Zwillingsgrenzen. Der Randkontrast bei nichtkoharenten Zwillingsgrenzen in diesen krz. Kristallen wird auf Grund der kinematischen Theorie der Elektronenbeugung an Stapelfehlern gedeutet.(i@J In dem Gebiet, in welchem der Absorptionseffekt stark ist und die Zwillingsversetzungen dicht beieinander liegen, wurden als neuer Effekt Intensitatsoszillationen der an nichkoharenten Zwillingsgrenzen gestreuten Elektronen gefunden. Der Einflu6 freier Oberflachen auf die VersetzungsanIordnung reichte bis zu einigen hundert A Tiefe.

INTRODUCTION Easy twinning reported suggested

by

in MO-35 at.%

several

that

the

twinning in MO-35 at. yO Re alloys is due to a lowering Re alloys has been

investigators large

capacity

;(l--5) for

some

of the stacking fault energy on addition

have

mechanical

Using

* Received September 17, 1963; revised November 26, 1963. Sponsored by the Office of Naval Research. t Part of a thesis submitted by K. Ogawa to the Graduate School of Arts and Sciences, University of Pennsylvania in partial fulfillment of the requirements for the Ph.D. degree. Presently at Department of Metallurgy, University of Cambridge, Cambridge, England. $ School of Metallurgical Engineering and Laboratory for Research on the Structure of Matter, University of Pennsylvania. ACTA

METALLCRGICA,

VOL.

12, JUNE

1964

of rhenium to

molybdenum. transmission

electron

observed

a characteristic

coherent

twin

miscroscopy,

fringe

boundaries

in

contrast

b.c.c.

HuW in non-

crystals

and

interpreted the contrast in terms of twinning dislocations. Thus, according to his view, the analysis of fringe contrasts enables us to obtain information of individual twinning dislocations and hence the ease of twinning

in MO-35

twinning mechanism 713

at.%

Re alloys as well as a

can be more readily understood.

714

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PIG. 1. Two thin sheets of twin (Twin 1 and Twin 2) with a characteristic fringe pattern in &X+18 at. 72 Re alloy deformed 0.25 % at liquid nitrogen temperature. EXPERIMENTAL

PROCEDURE

Since the experimental procedure is detailed elsewhere, only a brief outline is necessary. Zoneleveled MO-IS at. y0 Re and MO-35 at. y0 Re rods were cold-rolled t#o 0.005-in. thickness and the resultant thin sheets were annealed in an electron-beam zonerefining apparatus. Vacuum was maintained in the range of lo-* to 10F5mm Hg throughout the operation. The annealed specimens were pulled in an Tnstron machine at a strain rate of 1.6 x 10m4see-l either at room ~n~perature or at liquid nitrogen temperature. The strained specimens were eleetro-thinned in concentrated sulfuric acid. EXPERIMENTAL

RESULTS

The zone-leveled polyorystalline No-18 at. y0 Re alloys deformed by slip at room temperature, but twinned at liquid nitrogen temperature, whereas the zone-leveled polyorystalline MO-35 at. o/o Re alloy deformed by twkming at room temperature. The twinning was accompanied by sudden load drops as well as audible clicks. Two thin sheets of oharac~ristically overlapping twins are shown in Fig. 1. We note the following features : (i) A typical fringe pattern characteristic of noncoherent twin boundaries.@) (ii) Slip dislocations associated with the termination of fringes (as observed frequently at the center of twin 2 and along the edge LM of twin I).

(iii) The fringes of twin 2 show a mirror image symmetry across the line XY. (iv) The characteristic fringes pile-up boward the tips of the twins 1 and 2. (v) Three different intensities of fringes are clearly seen in the lower half of twin 2. (vi) Fringes are less visible in the middle of twins 1 and 2 than near the edges (i.e. close to the surfaces of the specimen). (vii) Fringes near the surfaces of the specimen have a tendency to orient themselves toward the surfaces, (clearly seen near the center of twin 2). This effect is estimated to reach as deep as a few hundred A. Since the specimen was fairly thick (over 2500 A), a diffraction pattern of the area could not be obtained. A series of fragmented twins is shown in Fig. 2. The direction of the edges, e.g. AB, of the twin bands is identified as (111) (which is parallel to the twinning direction). This result is in agreement with Hull’s observations.(7) Some of the twin edges are associated with slip bands (P, $, R and S in Fig. 2), whose slip plane wa.s found to be (110). A large number of slip dislocations were observed inside the twins (Fig. 3). Crystallographic analysis {such as the determination of slip planes) with the aid of electron diffraction patterns shows that the slip planes of the dislocations observed inside the twin are planes of the type (110) containing the twinning direction.(*) Stepped twins are shown in Fig. 4. The same type of

OGAWA

FE.

2. Fragmented

A~TD

MADDIN:

TWINNING

IN

MO-Re

ALLOYS

twins and slip bands (P, Q, R, S) in MO-35 at. % Ke alloy deformed specimen is parallel to (10%).

FIG. 3. Slip dislocations

0.4 %.

inside a twin in MO-35 at. % Re alloy deformed

5 %.

The surface of the

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1964

Frc. 4. Twins stepped at P and Q and serrated along the edges A and B, in MO-33

twins

were

observed

previously

by

Votava

and

S1eeswyk.u’) We consider the steps at P and Q in Fig. 4 to be produced through

by the passage

the twin.

tip of the twin shown

in Fig. 5.

fringe terminating

Serrated

inside the foil is associated

with a

observed

MO-35 at.%

in deformed

and annealed

Re

and MO-1 8 at. o/o Re alloys. DISCUSSION

contrast

L{sir?(nts (TSY

edges are again

have never been

According

1 -

OF

to Hull’s interpretation twin boundaries

&)

+ sin2 &X $u) . cos 27~~s).

(1)

where t is the crystal thickness, s is the distance along the direction

t from the operating

reciprocal

lattice

point g to the reflecting sphere and CI= 2ng * R. The last term in the parenthesis of equation (1) gives rise to fringe contrasts.

RESULTS

-

+ 2 sin * CIsin(77ts -

This figure also shows that each

slip dislocation. Extended nodes and dislocations

non-coherent

of the foil, is

of slip dislocations

fringes are observed near the

(Fig. 4).

0.4 %.

shear R) at the distance z, measured from the center

The twin edges are serrated at A

and B and characteristic

at. % Re alloy deformed

R is i (111) for one layer twins in

of fringes due to

in b.c.c.

crystals,

the

b.c.c. crystals and 4 (111) for two layer twins and so

of the fringes either reverses or disappears

where twinning dislocations exist. This characteristic is clearly seen in Fig. 1, particularly in twin 1. The fringes observed in the lower half of twin 2 in Fig. 1 According to the show three different intensities. kinematical

theory of fringe contrast due to stacking

faults,(lO) the intensity beam through

of the transmitted

a foil with a stacking

electron

fault (producing

on. (111)

However, (= i

the shear 4 (111) is equivalent (111) -i

(111))

because

to -

in effect

z the

shear by a slip vector i (111) or its multiple does not result in any relative

displacement

in the crystal.

OGAWA

3%~. 5. A serrated

AND

MADDIN:

TWINNING

IN

Mo-Re

ALLOYS

edge of twin and perfect dislocations associated with the fringes ending inside the foil, in MO-35 at. % Re alloy deformed 0.4 %.

The same feature can easily be confirmed by substitutSince the specimen shown in Fig. 1 showed very poor ing (a + 2n~) for u into equation (3 f where 9~.is a.n transparency, its thickness is estimated to be more integer. This substitution yields the same intensity than 2500 A. The minimum value of 6 E, for 100 kV electrons is about 1500 if for rnoly~de~urn.(‘2~ as a. Thus, 01 is reduced to a set of independent Therefore, the observation of the absorption effect is values, -- 3?f, 0; 4~. In general, the values of K, -37~ and -@ do not give the same maximum intensity this specimen is quite reasonable. Another in~resting feature of the fringe cont,rasts is because of the term sin(& - &x). Hence, three diRerent intensities are expected in the fringes. The seen in the area near the right hand tip of twin 2 in amplitude of the oscillation of intensities is given by Fig. I ; the intensities of fringes oscillate in the sin &Csin(& - &a). It can be seen from this expresmiddle of the twin sheet. Since this effect is prominsion that, fringes do not necessarily reverse the ent in the area where twinning disloca%ions are contrast where t,winning dislocations exist. Although closely spaced and the absorption effect is observed, no fringes are expected when a = 2nrr, faint fringes the oscillation of the intensities is considered to be do exist as seen in twin 2 (Fig. I). (When M= .%E,?T, caused by the interference of electrons diffracted at no fringes are expected from the dynamical theory).(lO’ neighboring twin boundaries. These faint fringes may be attributed to the very The cl-range in Lhe intensities of the fringes is existence af three of its mnltiple layer twins. observed where twinning dislocations exist (as When the thick~less of a specimen is greater than discussed at the beginning of this section). When the six times the extinction dista.nce, l,, corresponding to junction points between a slip dislocation and fringes an operating reflection g, the effects of electron are carefully examined in the a,bove view, it is found absorption are considerable.(ll~ The di~raction theory that three twinning dislocations are ~soci~~d with taking into account the absorption predicts that each slip dislocation. Each of the three twinning fringes are iess visible in the middle of stacking faults. dislocations lies in three adjacent (112) layers, whereas Indeed, this effect is clearly shown in twins 1 and 2 in the slip dislocation lies in one of the three adjacent Fig. 1. The thickness of good transparent specimens layers. of Mo-Re alloys is estimated to be 2500 L%or less.

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Consider the following notations :

where 1 and _LJ_L indicate a twinning dislocation u ith a Burgers vector of i (1 11> and a slip dislocation with a Burgers vector of 4 (I1 I}, respectively.

The first

matrix mdicates that there is one twinning dislocation in the first (top) (112) layer, another twinning dislocation in a second (middle) layer and the third twinning dislocation in a third (bottom) layer. The second matrix indicates that there is one slip dislocation in the middle (112) layer and nothing below or above the middle layer. From the law of the conservation of the Burgers vectors on each slip plane, the reaction between a slip dislocation and the resulting three twinning dislocation should be of the following form :

where 1 and 11 indicate a twinning dislocation with a Burgers vector of - i

(Ill)

and a complementary

dislocation(r3) with a Burgers vector

of f

(ill),

respectively. A set of dislocations described by the first term on the right side of equation (2) was introduced to conform with the conservation law of Burgers vectors on each slip plane. We refer to this set of dislocations as an emissary set (Sleeswyk(13) in his emissary dislocation theory). This emissary set does not have a long range elastic stress field owing to the cancellation of the Burgers vectors and hence cannot be observed in an electron microscope. When we assume the existence of an invisible emissary set, the fringes and the associated slip dislocations observed in twin 1 in Fig. 1 can be explained as follows. Twin 1 terminates along the line LN; on this line, a slip dislocation is found to be associated with every three twinning dislocations. These twinning dislocations and slip dislocations are schematically shown in the surface ABED and by t.he three-fold solid lines emerging from the junctions 2 and 5, respectively (Fig. 6). When the conservation law of the Burgers vectors is applied to each junction point, such as 1, 2, 3, 4 in Fig. 6, a set of dislocations shown in the surface of ABC in Fig. 6 is automatically introduced. The set of dislocations is immediately identified as an emissary type (Sleeswykoa)). The

C

-

:J_

---.

:-l-

=z==-_ :Tr zzSS :ll.L FIG. 6. Dislocation structure of twin 1 in Fig. 1. The line LM in Fig. 1 corresponds to the side ABC shown in this figure. The conservation law of Burgers vectors is satisfied at nodal points such as 1, 2, 3, . .....

emissary boundary (the surface ABC) is steep whereas the non-coherent non-emissary twin boundary (the surface ABED) is smoothly curved, primarily owing to the mutual repulsion of the twining dislocations. The fringes observed in twin 2 (Fig. 1) show a mirror image symmetry across the line XY. Hence, the shape of the twin must be lenticular or semilenticular. For simplicity, we assume the shape is semi-lenticular (Fig, 7). Since the fringes of the three different intensities behave as a unit, counting the darkest fringes (the most conspicuous ones) is sufficient to estimate the number of twinning dislocations. When this counting is done along the lower intersection of twin 2 with the specimen surface (Fig. l), POIC

FIG. 7. Dislocation structure of twin 2 in Fig. 1. The line XY corresponds to the line XY in Fig. 1. The eonserv~tion law of Burgers vectors is satisfied at the junction points B and C. Arrows along the dislocation lines indicate the positive direction of dislocation at each nodal point. Details me explained in the text.

OGAWA

TWINNING

MADDIN:

AND

IN

MO-Re

there are twelve of the darkest fringes in the left-hand

dislocation,

side of the line XY and sixteen in the right-hand

pole mechanism. According to

side,

719

ALLOYS

not the stage to initiate the operation of a

number of complete darkest fringes is twelve in both sides. The number twelve is a multiple of the number

the twinning mechanism recently proposed by Sleeswyk,(14) a three-layer twin is nucleated out of a slip dislocation of screw character. In the

of the incomplete

fringes,

present

number

together

four of which terminate

of fringes

symmetry

four.

The surfaces surfaces

strongly

image

suggests

the

structures

PQRS

of twin 2 in Fig. 1 are

terminates

and TUVW

of the specimen

foil.

inside

correspond

to the

reaction

described

seen at the junction

is considered

C and would

to have been produced

were one or more

way

cancelation

in principle

the

and hence

slip

the crystallographic

mechanism

means of transmission

could

In this

be tested

by

electron microscopy.

C.

(2) is

be at the

(4

dislocations

along

There

the line

of twin 2 in Fig. 1.

stress is high enough to cause the

in equation

(2) the segment

AB of the slip

dissociates into three twinning dislocations.

Thus a three-layer

twin is formed.

Then the three-

layer twin increases its thickness

by means of a pole-

mechanism.

during

expansion

In

other

words,

of the three-layer

of screw dislocations

twin

the

it may

meet

a

whose Burgers vectors

normal to the twinning plane of the

three-layer

Hence

twin.

the three-layer

glide up as it rotates around the pole. which is composed

(4

initial

have a component

twin would

The super pole,

of more than one screw dislocations

Arrangements of twinning dislocations after the dissociation of a slip dislocation suggested by Sleeswyk’s model (a) and by the present observation (b). FIG.

8.

One difficulty explain

the

arrangement

in the use of the Sleeswyk model to

present of

observations

the

three

and is able to take up more than one set of dissociated

which have been dissociated

twinning dislocations,

The arrangement

were observed in twin 2 (Fig. I),

where four sets of dissociated twinning

7, however, can be

of the line AB can be determined. Sleeswyk

be

of Burgers vectors.

A and B in Fig.

Twin 2 in Fig. 1 as follows.

OABD (Fig. 7) before the formation When the applied

number

located

not

to have been

by equation

B outside the specimen foil.

dislocation

owing to the mutual

could

(Fig. 7) is invisible

Since many twinning

C in Fig. 7 is considered

The dislocation

reaction

this mechanism the line AB

exist near the center of twin 2 (Fig. l),

the junction

clearly

because

orientation

the twin.

pushed from the center, 0 to the present position,

junction

observations

confirmed

The positions

shown in Fig. 7 where, for simplicity,

one set of fringes

dislocations

the mirror

of twinning.

The dislocation schematically

Thus, the

This result of the

with

across the line XY

pole mechanism

only

inside the twin.

disloca’tions

dislocations,

are moving

around

the Sleeswyk model.

one super

in Fig. (8a) is associated separation

Here we note that there are two distinct the course of the nucleation

stages in and growth of twins : the

dissociation

of a slip dislocation

dislocations

and the operation

The dissociation considerably

of a pole mechanism.

operated),

with

thick) ; simply dissociated

slip dislocations

have never

been observed in the present investigation. implies that whenever the dissociation of

This a slip

from a screw dislocation. to

Since the twinning dislocation with a stacking

fault,

between the twinning dislocations

The present observations super-pole

is a,lways found to be associated

the

B the

B and C

seems to be much smaller than that between A and C.

into three twinning

thick twins (say, more than ten layers

from

dislocations

is shown in Fig. S(a) according

or twelve

pole.

arises

twinning

mechanism however,

(twin 2 in Fig. 1, where a is

believed

to

have

been

shows that twinning dislocations

are more or less equally spaced. ment of three twinning dislocations

Hence the arrangeshown in Fig. 8(b)

is more likely in the early stage of their dissociation. In this theory, (14) Sleeswyk

excluded

the dissocia-

occurs, the stress to have caused the is high enough to operate a pole mecha-

tion of an edge dislocation into three twinning dislocations in its single slip plane on the basis that the dissociation involves the creation of a stacking

nism. Therefore, we conclude that the critical stage of twinning is the process of the dissociation of a slip

fault of higher energy. If the dissociation occurs over the three layers of { 112) stacking as shown by equation

dislocation dissociation

ACT:%

720

AIETALLURGICA,

VOL.

12,

(2), however, no difficulty

would arise with the dissoci-

monolayer

ation of a slip dislocation

and the subsequent

or reported

of the three

t,winning

the atomic

dislocations.

configuration

thoroughly

The stability

of an edge

well as a screw dislocation

motion

under

dislocation

stresses

must

twins have not been either in connection

investigators.

agreement with our present observation: the formation of a three-layer twin from a slip dislocation and

be

with twin bands as

The

subsequent

However,

Sleeswyk

thickening

it is difficult

shown at P, Q, R and S in Fig. 2, whereas twin bands

more or less uniform

are not always associated

tions

are produced the

As three-layer

thickness

by

means

increase

near

the

boundaries.

In

tion

Therefore,

that the slip bands

as a result of twinning

opposite.

dislocations

with slip bands.

to conclude

than to conclude

twins

grow

in their

of a pole-mechanism, tip

of

order

to

the

stresses

non-coherent

release

the

mechanism(i3)

or

by

activating

slip

disloca-

dislocation

sources in the regions of high stresses. Since

the

believed

slip

the twinning relaxing these

dislocations

to have a Burgers direction

stress

concentration are

region.(15-16)

dislocations Judging

observed

near still

the

able

are

to that of method for

twin

edges),

to slip in the

We consider

that these are the

in the twinned

region (Fig. 3).

from the size of twins, Figs.

considered

1, 2 and 3 are

to show the process of the nucleation

growth of twins.

A three-layer

a slip dislocation

by the reaction

(2) and,

introduced

parallel

(the most effective

slip dislocations

twinned

thus

vector

subsequently,

twin is nucleated described

it increases

and from

in equation

its thickness

by

Two

basicadly

different

mechanisms

have

been

proposed for the nucleation mechanism(17-20)

and

of twins : (i) a dislocation (ii) the Orowan type homo-

geneous nucleation.(21322) tions

suggest

that

However,

twin

nuclei

dislocations,

the homogeneous

is considered

as unlikely,

since the observa-

are

related

nucleation

in b.c.c.

metals:

(i) Cottrell

and, (ii) Mueller and Parkero*) The Cottrell-Bilby dislocation

model

reaction,

;

Vlll

mechanism

at least in b.c.c. metals.

There are three models for the dislocation of twinning

to slip

mechanism and Bilby(l’)

and (iii) Sleeswyk.(14)

is based

on the following

i.e. +;[lll]

(3)

However, the present observations show that twinning is not related to the reaction shown in equation (3) but rather to that shown in equation (2). The Mueller-Parker model assumes the formation of a monolayer planes

twin

parallel

with

it is desirable

concurrent

to the twinning

slip in the direction.

(110)

However,

some

pole-mechanism.

1).

The dissociation

the

dislocaof a slip

described

in his paper.04)

to discuss the nucleation

by

Therefore,

and growth of

twins in a more general way. Consider arbitrary

the

dissociation

character

which is described conditions,

of a slip dislocation

into three

twinning

by equation

(2).

the atomic

Under

configuration

of

dislocations, certain

of a slip disloca-

tion in the { 112} pl ane is considered to become unstable and hence the slip dislocation dissociates into three twinning To

dislocations

obtain

an

instability,

as well

idea

about

it is useful

as an

the

emissary

conditions

to review

the

set.

for

the

experimental

results on twinning. Deformation metals

twins are commonly

when

they

are

deformed

observed at

low

in b.c.c. tempera-

tures,(23-25) at a highstrainrate(26~27)orafteraging,(2*,2g) or when they are alloyed.( 3~30~32) We note that yield stresses are raised under all these experimental conditions.

The effect

threefold:

of alloying

rise in flow stress in the stacking

elements.

owing

to

elements

by solution

fault energy

stability

of the atomic

of alloying

fault energy and instability

configuration

tion in the (112) plane. with

regard

low

temperatures

planes

to

operate

observed

the

be

and instability

a supersaturation

Stress, stacking

may

hardening,

of phases could be factors which predominate

over the

of a slip disloca-

Also we note the observations

operating where

as twinning

slip

planes;(5,33)

twinning planes;

occurs

at (112)

little or no slip is

on these planes.

When the atomic configuration of a slip disloca,tion on the (112) pl ane becomes unstable, the slip dislocation may dissociate into three twinning dislocations critical

+121

a

spacing of the twinning

(2)) was excluded

of phases

MECHANISMS

by

shows

other than a screw (generally

decrease

means of a pole-mechanism. TWINNING

equation

model

for his model to explain

in twin 2 (Fig.

dislocation

twin

stresses,

are created either by the emissary

here

by any other

of

its

it is more reasonable

observed

with twinning

as

examined.

Slip bands a.re always associated

1964

section,

as described

by equation

stage for twinning the three-layer

(2).

as discussed

Since this is a in the previous

twin nuclei will easily increase

in thickness by operating a pole mechanism. number of twinning dislocations increases,

As the greater

force is available to propagate the leading twinning dislocations because of the pile-up effect (which is clearly seen in twins 1 and 2 in Fig. 1). Quick propagation of twins is attained in this manner despite the poor mobility of individual dislocations.

OGAW.4

MADDIN:

AEFD

TWINNING

The pile-up effect, which plays an important the

propagation

character,

of

twinning

is not expected

dislocations

role in of

edge

to act in the case of screw

dislocations since they are expected to cross slip easily. Hence, we predict the growth rate of twins to

IN

MO-Re

in the early portion

ing

discussions

than that, parallel to the twinning direction.

Thus, the in the

of twins should be rod-like extending

shape

twinning

direction

as observed

by several

invest,igator~.(l~~~~~~~~~~)

with

of a slip dislocation

twinning dislocations (2) The analysis

was frequently

into three

of a pole mechanism

by which

the increase in its thickness is attained. (3) The critical stage of twinning is concluded the processof

the dissociationofa

(112]

into

plane

three

evidence

twinning

(5) A twinning

mechanism

are

the atomic

configuration by

instability

of

formed

nucleated

becomes

cont,rolled

mechanism. type

nonco-

was suggested.

Three-

from slip dislocations of slip dislocations

unstable. stress,

The

The

mechanism.

Quick

is attained

may

be

energy

and

twins

thus

three-layer

their thickness

dislocations

fault

when

in (112)

instability

stacking

phases.

increase

ofa pole

not

was obtained.

layer twins planes

in the

dislocations,

of an emissary

herent twin boundary

to be

slip dislocation

the stage to initiate the operation (4) Direct

by means of a pole

propagation

of

the

twinning

with the aid of the pile-up

effect upon the leading twinning dislocations. (ti) The fringe contrasts observed in non-coherent twin boundaries

were successfully

of the kinematical

interpreted in terms

theory(lO) of a diffraction

contrast

due to stacking faults. (7) The effect reduction

in the visibility

intensities

of

the

absorption’ll)

(i.e.,

the

of fringes in the middle of a

A new effect, transmit~d

oscillation

electron

of the

beam

was

found in the region where the absorption effect is prominent and twinning dislocations are closely spaced.

(8) The effect, of free surfaces upon the dislocation arrangements hundred

was found

Kimura

Stimulatare

greatly

appreciated. REFERENCES 1. R. I. JAFFEE, C. T. SIPASand J. J. HARWOOD, P&r~see Proceedings, Vienna. Springer-VerIag (1959). 2. J. M. DICKINSON and L. S. RICHARUSON, Trans. Amer. sot. &let& 51, 1059 (1959). 3. A. LAWLEY and R. MADDIN, Truns. Amer. In&. Min. 4. E. VOTAVA, Acta Met. 10, 745 (1962). 3. H. W. SCHADLER and A. LA~LEY. Trans. Amer. Inst. Min.

(Metall.) Engr.s 221, 650 (1961). Fifth International Congressfor ElectrmzMicroscopy, Now York, 1962. rlcademic Press. 7. I). HULL, Conference on Deformation Twin, University of

Florida, 1963. 8. K. OGAWA, Ph.D. Thesis, Cniversitg of Pennsylvania (1963). E. VOTAV~ and A. W. SLEESWYK, Actn Met. 10,965 (1962). 1:: Mtl. J. WEELAN and P. B. HIRSCH, Phil. Mug. 2, 1121

(1957).

11. H. HASHIMOTO, 9. HO~IE and M. J. WHELAN, I)?&

5, 967 (1960).

Mng.

Transmission Electron &~icrascopy of Metals, John Wilev. A. W. SL&SWYK. Acta Met.“lO. 705 (1962). A. W. SLXESWYK; Phil. Mqm8; 1467’ (196&. A. W. SLEESWYK and C. A. VERABRAAK, Acta Met. 9, 917 (1961). C. H. MATKEWSON and G. H. EDMUNDS, Trans. Amer.

12. G. THOMAS,

New York, 1962.

13. 14. 15. 16.

Inst. Min. (Metd.)

Engm 80, 311 (1928). Phil. Mag. 42, 573

17. A. H. COTTRELL and B. A. BILBY,

(1951).

18. F. 0. MUELLER and E. R. PARKER, Technical Report, Series No. 27, Issue No. 21, Material Research Laboratory,

Institute of ~~~neer~g Research, University of California, Berkely. 19. N. THOMPSON and D. J. MILLARD, Phil. &fag. 43, 422 (1952). 20. J. A. VENARLES, Phil. Mag. 6, 379 (1961). 21. R. L. BELL and R. W. CAHN, Proc. Req. 800~. A289, 494 (1957). Dislocations in Metals, New York, 1954. 22. B. O&WAN, AIME. 23. C. J. M~HA~~GuE, Trans. Amer. Inst. Miv~. (Metall.) Engrs 224, 334 (1962). 24. F. S. DE~~ONJA and M. GENSANIER, Tmns. Amer. Sot. Metals 51. 666 (19.59). 25. J. S. ERKXSON &d i. R. Low, Jr., Acta Met. 5,405 (1957). 26. M. A. ADAMS, A. C. ROBERTS and R. E. SMALLMAN, Acta Met. 8, 328 (1960). 27. C. G. DUNN and E. F. KOCH, Acta Met. 2, ,548 (1957). 28. W. D. &a~ and P. L. PRATT, A&a. Het. 6, 694 (1958). 29. J. HOLDIN, Acta Met. 8, 424 (1960). 30. C. S. BARRETT, G. ANSEZ and R. F. MEHL, Trans. Amer. --r

of electron

foil) was observed.

H.

6. D. HULL,

observed.

of a thin sheet of twin strongly

suggests t,he operation

Dr.

(MetdZ.) Engrs 224, 573 (1962).

SUMMARY

(1) Tht! dissociation

to Dr. N. Brown and Dr. D.

for helpful discussion.

be much smaller in the direction normal to the twinning direction

of this research is acknowledged.

The authors are indebted Kuhlmann-Wilsdorf

721

ALLOYS

to reach as deep as a few

A.

218, 634 (1960). J. 0. STIEGLER

and Dr. A, Lawley

(Met&)

Engm

and C. J. MCHARGUE, J. Metals 227, 91 (1963). 33. H. W. SCRADLER, Trans. rlmer. Inst. Min. (Metall.) Engm 32.

218, 649 (1960). 34. H. B. PROBST, Trans.

Amer. Inst. Min.

35. V.

Amer.

221. 741 (1961).

ACKNOWLEDGMENTS

The aid of Dr. R. E. Smallman

&XL Metals 25, 702 (1937).

31. E. HO~NBOC~EN, Trans. Amer. Inst. Min.

E.

WbLFF,’ Trans.

224, 327 (1962).

(Metalt.) Engrs

Inst. Min. (Metnll.) Engrs