Preferential growth of annealing twins in copper

Scripta

METALLURGICA

Vol. 4, pp. 1 0 0 9 - 1 0 1 4 , 1970 P r i n t e d in the U n i t e d States

Pergamon

Press,

Inc.

PREFERENTIAL GROWTH OF ANNEALING TWINS IN COPPER

E.C. Parkinson, G. Van Drunen and S. Saimoto Department of Metallurgy, Queen's University Kingston, Ontario, Canada

(Received

October

26,

1970)

Introduction Recent and continued interest in recrystallization textures has centred its attention on the parameters which govern grain boundary migration (I).

These parameters are (a) the

spatial orientation relationship between two grains, (b) the orientation of the boundary, (c) the role of impurities and (d) the nature of the driving force.

In their most thorough

studies Aust and Rutter (i) used striation or lineage boundaries as the driving force with the inherent uncertainty of matrix orientation.

Moreover, the low driving force permitted experi-

ments only at temperatures near the melting point, T m.

On the other hand growth-selection exper-

iments (2,3,4,5) have used moderately deformed single crystals in which some uncertainty of matrix orientation results due to asterism associated with lattice rotation and large local misorientation near deformation bands (6).

Furthermore, most studies have been carried out with annealing

temperatures near T m and very few near 1/2 T m. Recently Van Drunen and Saimoto (7) have observed that [001] oriented crystals do not manifest slip bands or characteristic glide bands upon etch pitting. random etch pit arrays are found on all {lll} planes.

Instead homogeneous, almost

In this note results of growth-selection

experiments carried out on such [001]. crystals are reported. Procedure and Results [001] oriented crystals with {ll0} faces were grown in chlorine purified graphite molds. This method as previously described (7) did not detectably degrade the initial purity {American Smelting & Refining Company 99.999% Cu) as checked by spectroscopic analysis.

The resistivity

ratios (R296oK/R4.2OK) which were measured for three crystal melts A, B, C, were 1500, lO00, and 1200 respectively. The as-grown crystals (3 x 3 x i00 mm) were all pulled in tension to a shear stress of 4.2 Kg/mm 2 with a corresponding dislocation density of about 4 x 109/cm 2.

Using Wolfenden's

stored energy data, the driving force is estimated to be about 3 x 107 ergs/cm 3.

(8)

If held for

1 hr. at 5000C, this value would decrease by about 40% (7). Artificial nucleation was performed either by shearing in the direction of single slip or of coplanar double slip or by twisting 1009

1010

PREFERENTIAL GROWTH OF ANNEALING TWINS IN CU

Vol.

4,

No.

12

TABLE I R e c r y s t a l l i z a t i o n Results on Defomed [001] Copper C r y s t a l s Type of nucleation and amount of shear

Specimen

Annealing conditions

Recrystallization characteristics

Grain no. 10

21"

1 T1

54 34

122

9.8

25.6

105

26.8

8.6

2 T2

48 48

109 120

22.8 11.8

12.6 23.6

not

determined

not

determi ned

T4

$2 20 21 47 46

116 112

15.8 19.8

19.6 15.6

S T5

51

113

18.8

16.6

49

114

17.8

17.6

large s i n g l e gra i n outgrew one short grain

6 7

56

114

17.8

17.b

twinned b i c r y s t a l

8

T8

49 48

ll0 116

21.8 15.8

13.6 19.6

9 T9 TT9

29 46 52

I16 116

15.8 15.8

19.6 19.6

AI

s i n g l e s l i p yffil.l

500°C for 1 hr.

small g r a i n s , a grain at matrix i n t e r f a c e

A2

s i n g l e s l i p yffi3.7

420°C for 1 h r . ; plus 3 hrs. at 500"C

small grains in shear zone only

A3

s i n g l e s l i p yffil.4

500°C for 1 hr.

twinned b i c r y s t a l

A4

double s l i p yffiO.60 400"C for I# hr.~ no r e c r y s t a l l i z a t i n n 500°C for 3 hrs. twinned b i c r y s t a l ad ditional ~=0.55 double s l i p ~ffi0.93 420°C for 1 h r . ; plus 3 hrs. at 500"C

AS

small gra i ns in shear zone; short twinned b i c r y s t a l m u l t i - c r y s t a l , few short twinned b i c r y s t a I s

A6

double s l i p yffil.5

500OC for I hr.

A7

twist

Ymax=2-3

420°C for 1 h r . ; no r e c r y s t a l l i z a t i o n ; subsequent 500°C growth of 2 gra i ns to about 4m long with common parent for 1 hr.

twist

500°C for 1 hr.

A8

3 T5 T3'

twinned b i c r y s t a l

4

¥maxffi2-3 A9

500°C for 1 hr.

twist

twinned b i c r y s t a l

Ymax=3-1 81

500°C for 1 hr.

twist

Ymaxffi2.3 squeezed

82

CI

500°C for 1 hr.

slip cluster

Minimum Angle of Deviation from angle of r o t a t i o n 131.8 ° [ 96.4 e I r o t a t i o n about <012>

600°C for I hr.

twinned h i c r y s t a l

34

* a l l grains smaller than width of sample.

about

<111> a x i s * ,

{111} plane f r o m 4 00 ° t o per

hour

after

by spark

for

The results preferential

cutting.

600°C for

and hold

growth

one end of

various one hour

These times. at

place

crystals

deformed were

The normal

crystal

annealed procedure

in

was notched vacuum at

was to

parallel

to

temperatures

slowly

a

ranging

heat

at

about

It

is

evident

200°C

500°C.

and experimental took

a 3cm l o n g

particulars

by forming

twin

are related

outlined bicrystals

in Table with

I. the

twin

plane

almost

* During preliminary tests it was found that artificial nucleation by squeezing or using the grip section followed b y heating in a steep temperature gradient in the manner described by Y o s h i d a et al (3) was not as p r o d u c t i v e as the m e t h o d described above. O f 12 crystals attempted by immersing in a lead bath or tube furnace, only 2 resulted in long twin-related bicrystals.

Vol.

4,

No.

12

PREFERENTIAL

GROWTH

OF A N N E A L I N G

TWINS

IN Cu

I011

TII

4 ~T8 / J 705; T9~6e07rs./' OT2 T 20

r~I T

Oi 0 OT3' 010

/

9

TI

• e

OOl

012

OI

001

0

FIG. 1

FIG. 2

Stereographic plots of the axes of minimum angle of rotation. Half-filled circles represent grains which did not grow beyond the width of the crystal.

Crystallographic directions of grains para llel to specimen axis. The d o t t e d a r c i s the locus of points 5 ° from [i12].

III

//r:,~x~. DIR~ECTIONS OF I ~ / l'["~k I FASTEST

~

iW

GROWTH

/i "4%3 1 %%%

DEFORMED MATRIX

OI ..... 8

/ 001

FIG. 3 Schematic representation of cusp formation due to directions of fast growth in twinned hicrystal, stage I; subsequent cusp elimination to minimize grain boundary energy, stage 2; repeat formation of cusp, stage 3.

,, ~ 4 ~ T4~/"Te TT9

011

FIG. 4 Stereographic plots of the rotation axes near <012> for all grains which grew along the specimen axis. The dotted arc is the locus of points 5 ° from [012].

1012

PREFERENTIAL GROWTH OF ANNEALING TWINS IN Cu

parallel

t o t h e sample a x i s .

In two c a s e s

(A3 and A8), s e v e r a l p a r a l l e l

w i t h t h e t h i r d g r a i n p o s s e s s i n g t h e same o r i e n t a t i o n

as t h e f i r s t

twin.

t i o n p r o c e d u r e o f Aust and R u t t e r ( 1 ) , minimum a n g l e s o f r o t a t i o n pondence between t h e new g r a i n s and t h e deformed [001] c r y s t a l s symbols T9 i n d i c a t e

it

o f minimum r o t a t i o n the r e c r y s t a l l i z e d several grains,

plotted

in Pig.

g r a i n s a lo n g t h e specimen a x i s ,

1.

Fig.

4,

No.

12

twins were o b s e r v e d Following the s e l e c -

necessary for exact corres-

are l i s t e d

i s a twin t o g r a i n 9 and TT9 a twin t o T9.

are s t e r e o g r a p h i c a l l y

Vol.

f o r each g r a i n .

The o r i e n t a t i o n s

o f t h e axes

2 shows t h e o r i e n t a t i o n s

t h e growth d i r e c t i o n .

The

of

In t h e above diagrams

which r e a c h e d t h e dimension comparable t o t h e specimen w i d t h , were a l s o

included (half-filled

circles)

and t h e i r

s i g n i f i c a n c e w i l l be d i s c u s s e d . Discussion

Preferential growth of twin related bicrystals in the direction parallel to the twin plane has been observed by Becker and Hobstetter (9) during annealing of deformed copper crystals and by Kronberg and Wilson (i0) during secondary recrystallization of cube textured copper.

The

former did not find a simple relationship between the new grain and the matrix, whereas the latter found the well-known 22 ° and 38 ° rotations about the axis.

The present results

will be considered according to three possible criteria: i)

the orientations of the twinned bicrystals are compatible with the Kronberg-Wilson coincidence site model using minimum angle of rotation,

2)

the preferential growth direction according to Gleiter (ii) is one which forms a maximum angle with

3)

the poles of both the new grain and the original matrix,

there is a rotation axis other than minimum (i.e. any one of the other 23 axes (4,12)) which all the long twins have in common. If the first criterion of minimum angle of rotation about low index axes [001], [011]

and Jill] is invoked, then the data tend to cluster about 47 ° (Table i) which could be related to the coincident lattice of 46.8 ° about .

(All axes of rotation and their minimum angles

of rotation are quoted for Brandon et al (13).)

The density of coincident points in this case

is 1 in 19.

Except for an axis with a 40 ° rotation, higher density coincidence of 1 in 7 (38.2 °)

and 1 in 13 (27.8 °) are not evident.

Moreover close study of grain 9 which was the parent twin

to T9 showed that one of its poles was within S ° of that of the matrix with a rotation axis within 3 °.

Considering experimental errors as pointed out by Liu (4) this particular grain

can be considered to have 29 ° rotation angle with a common .

Nevertheless this grain did

not grow but twinned to produce a grain with an apparently lower density of coincident points. Specimen B1 can also be considered similarly.

The poles were 7 ° apart but a grain with

axis of minimum rotation 22 ° away from outgrew it.

The large deviation between the

!

rotation axes of T3 and T3

(Fig. l) arises from the same cause.

Although the <001> poles are

only 6 ° apart with three rotation axes within 6 ° of them, the axes for minimum rotation diverge as shown. It can be argued that due to the geometry of the twin as schematically shown in Pig. 3, the additional driving force of the boundary due to the cusp as described by Nielsen (14) would enhance growth even with low density coincident points.

However, the orientations of the mini-

mum axes of rotations for twin pairs were such that in some bicrystals the condition necessary

Vol.

4, No.

12

PREFERENTIAL

GROWTH

OF A N N E A L I N G

TWINS

IN Cu

1013

for cusp formation was fulfilled by twist boundaries and not by tilt boundary orientations (poles 90 ° from axis of rotation) and in others, the reverse was true.

Since tilt boundaries

are expected to have higher migration rates (15), this inconsistency indicates cusps are not essential for preferred growth.

The growth of grain 7 as a single crystal instead of a twinned

bicrystal seems to confirm this notion.

Thus the criterion of minimum angle of rotation does

not satisfactorily rationalize the present results. If the second criterion holds, one would expect that twist boundaries with (001) planes would manifest fastest growth.

Although this condition seems to be fulfilled in lightly

deformed [001] oriented aluminum crystals (16), the present result does not confirm it for !

copper.

Grains T3, T3

and i0 which possessed orientations nearest to a (001) twist boundary

(Fig. i) in fact did not grow.

However, these observations do not refute Gleiter's basic

mechanism for boundary migration, that of adding atoms on kinked steps of {iii} planes.

It does

suggest that the orientation dependence of the activation energy for grain boundary migration (ll) is more important than that of step density. If the third statement were true, the selection of a common rotation axis should simply rationalize the observation that is almost parallel to the specimen axis.

Close

scrutiny of all the 24 possible rotation axes showed that all the twinned bicrystals have a rotation axis very near <012> as shown in Fig. 4. from the 1 in 5 (Table i).

The angles of rotation and their deviations

(131.8 °) and 1 in 19 (96.4 °) density of coincident points are tabulated

It is apparent that the [i12] direction which is on the (021) trace is not normal

to an "incoherent coincidence twist boundary".

The boundary of preferred growth can be

described as a tilt boundary of nearly 114 ° rotation about [031] such that [i12] grain [001]matri x relationship is developed.

This observation agrees well with those of Rath and

Hu (15) who found that migration rates of tilt boundaries were the fastest and that similar as yet inexplicable crystallographic relationships between the new grain and the matrix manifest themselves.

The Bishop and Chalmers (17) description of grain boundaries or its modification

(18) using [021] tilt axis may elucidate this phenomenon. graphic pair seems to be applicable to silver.

The present grain-matrix crystallo-

Ahlborn and Wassermann (19) found twin related

crystals growing with <112> parallel to the wire axis at the expense of the <001> component of highly drawn silver. Although Aust and Rutter (1) have shown that annealing twins replace high angle boundaries with coincidence site boundaries whose axes of rotation are near , <011> <001>, the above discussion indicates that the orientation for preferred growth of twins into [001] matrix is related by a [021] rotation axis.

A possible cause for this discrepancy could

be that the earlier work used striation boundary as a driving force and the present study employed almost homogeneously distributed dislocation network.

As recently pointed out by Liu

(20), it is important to differentiate between "selective growth" and "oriented growth".

Most

"selective growth" experiments have been performed on rod-like (one-dimensional) samples. Hence, geometry restricts growth to only those directions along the sample axis.

It follows that

in a two or three dimensional environment, other boundaries with faster migration rates may predominate.

This situation seems to hold in the study of Rath and Hu (15) where they found

the grain boundary of [ll2]g - [001]m to move slower than those of I l l 2 ] g

[ll0]m and

1014

PREFERENTIAL GROWTH OF ANNEALING TWINS IN Cu

[ l 1 2 ] g - [112]m.

It is interesting

Vol.

4,

No.

12

t o n o t e t h a t even f o r a randomly o r i e n t e d m a t r i x a x i s , twin

related bicrystals

seems t o have favoured growth ( 4 , 5 ) .

are many d i f f e r e n t

sets of p r e f e r r e d c r y s t a l l o g r a p h i c a l l y

Such o b s e r v a t i o n s i n d i c a t e t h a t t h e r e r e l a t e d p a i r s between t h e r e c r y s t a l l -

i z e d g r a i n and t h e deformed m a t r i x . Acknowledgements This s t u d y was s u p p o r t e d by a g r a n t from the N a t i o n a l Research C o u n c i l (Canada). a u t h o r s thank Dr. Z. S. B a s i n s k i o f N.R.C f o r use of f a c i l i t i e s

to determine r e s i s t i v i t y

The

ratios~

References 1.

K. Aust, T e x t u r e s i n Research and P r a c t i c e , S p r i n g e r - V e r l a g , B e r l i n (1969).

eds. J . Grewen and G. Wassermann, p. 160,

2.

B. Liebmann, K. Lficke and G. Masing, Z. M e t a l l k 47, 57, (1956).

3.

H. Yoshida, B. Liebmann and K. L~cke, Acta Met. ~, 51, (1959).

4.

Y.C. Liu, T r a n s . AIME 250 , 1513, (1964).

5.

G. Ibe and K. Lucke, R e c r y s t . , G r a i n Growth and T e x t u r e s , p. 434 ASM, Metals Park,

6.

Z. S. B a s i n s k i , D i s c u s s i o n s o f the Faraday S o c . , No. 38, p. 93, (1964).

7.

G. Van Drunen and S. Saimoto, Acta Met. a c c e p t e d f o r p u b l i c a t i o n (1970).

8.

A. Wolfenden, Acta Met. 1S, 971, (1967).

9.

J.J.

(1966).

Becker and J.N. H o b s t e t t e r , T r a n s . AIME 197, 1235, (1955).

10.

M.L. Kronberg and F.H. Wilson, T r a n s . AIME 185, 501, (1949).

ii.

H. g l e i t e r , Acta Met. 17, 853, (1969).

12.

C. Goux, Mem. Sci. Rev. Met. 58, 661, (1961).

13.

D.G. Brandon, B. Ralph, S. Ranganathan and M.S. Wald, Acta Met. 12, 813, (1964).

14.

J.P. Nielsen, Recryst., Grain Growth and Textures, p. 141, ASM, Metals Park, (1966).

15.

B.B. Rath and H. Hu, Trans. AIME 236, 1193, (1966); Trans. AIME 245, 1243, (1969).

16.

D.C. Larson and B. Chalmers, Trans. A I ~ 230, 908 (1964).

17.

G.H. Bishop and B. Chalmers, Scripta Met. ~, 133, (1968).

18.

M. Weins, B. Chalmers, H. Gleiter and M. Ashby, Scripa Met. 3, 602, (1969).

19.

H. Ahlborn and G. Wassermann, Z. Metallk. 55, 167, (1964).

20.

Y.C. Liu, Met. Trans. ~, 2342, (1970).