The effect of grain boundaries on the recovery of electrical properties during annealing

The effect of grain boundaries on the recovery of electrical properties during annealing

Scripta METALLURGICA Vol. 4, pp. 575-580, 1970 Printed in the United States Pergamon Press, Inc. THE EFFECT OF GRAIN BOUNDARIES ON THE RECOVERY OF...

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Scripta METALLURGICA

Vol. 4, pp. 575-580, 1970 Printed in the United States

Pergamon Press,

Inc.

THE EFFECT OF GRAIN BOUNDARIES ON THE RECOVERY OF ELECTRICAL PROPERTIES DURING ANNEALING ~

M . B. Kasen Cryogenics Division, NBS-lnstitute for Basic Standards, Boulder, Colorado, 8030Z

(Received

June

3,

1970)

T h e r e c o v e r y of e l e c t r i c a l p r o p e r t i e s d u r i n g r e c r y s t a l l i z a t i o n of c o l d - w o r k e d m e t a l s p r e s u m a b l y r e f l e c t s a d e c r e a s e i n t h e d e n s i t y of r a n d o m l a t t i c e d e f e c t s ( v a c a n c i e s and d i s locations) which s e r v e as e l e c t r o n s c a t t e r i n g c e n t e r s . recovery,

the e l e c t r i c a l p r o p e r t i e s

If t h i s w e r e the only f a c t o r i n f l u e n c i n g

s h o u l d be c o m p l e t e l y r e c o v e r e d upon a t t a i n i n g a f u l l y r e -

c r y s t a l l i z e d s t r u c t u r e w h i c h r e d u c e s s u c h d e f e c t s to a m i n i m u m . Hargreaves

H o w e v e r , G r e g o r y and

(1, Z) h a v e n o t e d t h a t s m a l l but p r o b a b l y s i g n i f i c a n t c h a n g e s in e l e c t r i c a l p r o p -

e r t i e s m a y o c c u r i n v a r i o u s c o p p e r m a t e r i a l s when a n n e a l i n g at t e m p e r a t u r e s quired for p r i m a r y

above that r e -

r e c r y s t a l l i z a t i o n ; f o r e x a m p l e , the m a i n r e c o v e r y s t a g e in a n n e a l e d c o l d -

w o r k e d c o p p e r w a s found to be f o l l o w e d b y ' a f u r t h e r i n c r e a s e in c o n d u c t i v i t y by a p p r o x i m a t e ly 0 . 3 % IACS o v e r a t e m p e r a t u r e

i n t e r v a l of a p p r o x i m a t e l y 100°C.

T h e c o n t i n u e d r e c o v e r y of

m e c h a n i c a l p r o p e r t i e s was also noted. A r e v i e w of t h e l i t e r a t u r e r e v e a l s t h a t c o n t i n u e d r e c o v e r y of e l e c t r i c a l p r o p e r t i e s d u r i n g t h e g r a i n g r o w t h p o r t i o n of the a n n e a l i n g s p e c t r u m w as d o c u m e n t e d a s e a r l y a s 1913 by C r e d n e r (3) i n a l u m i n u m a n d i r o n and in t he s a m e y e a r by G e w e c k e (4) in a l u m i n u m and copper.

Furthermore,

t h e s e e a r l y s t u d i e s r e v e a l e d t h e p r e s e n c e of a r e s i s t i v i t y m i n i m u m

w i t h i n the g r a i n g r o w t h r e g i o n in c o l d - w o r k e d m a t e r i a l s increasing temperatures.

i s o c h r o n a l l y a n n e a l e d at a s e r i e s of

By 1953, W e y e r e r (5) w a s a b l e to c o m p i l e a l i s t of 14 p u b l i c a t i o n s

r e p o r t i n g the e x i s t e n c e of s u c h m i n i m a in AI, F e , Cu and a - b r a s s .

M o r e r e c e n t l y , the p h e -

n o m e n a h a v e b e e n o b s e r v e d by A n d r e w s (6) i n 1965 ( c o p p e r ) , by K o v a c s - C s e t e n y ,

et a l . ,

(7)

in 1966 ( a l u m i n u m ) a n d by M i s e k (8) in 1967 ( p l a t i n u m ) .

T h i s w o r k w a s c a r r i e d out at t h e N a t i o n a l B u r e a u of S t a n d a r d s u n d e r the s p o n s o r s h i p of the U. S. A r m y M i s s i l e C o m m a n d , M I P R 3 1 6 8 2 - 3 7 - 7 0 0 5 . P a r t i a l s u p p o r t w a s a l s o r e c e i v e d f r o m the O f f i c e of S t a n d a r d R e f e r e n c e M a t e r i a l s of the N B S - I n s t i t u t e f o r M a t e r i a l s R e s e a r c h .

575

576

R E C O V E R YOF ELECTRICAL PROPERTIES DURING ANNEALING

S e v e r a l authors have suggested physical bases for the phenomena, of i m p u r i t i e s f r o m s u p e r s a t u r a t e d

e.g.,

4,

No.8

precipitation

s o l i d s o l u t i o n (1), g r a i n b o u n d a r y p o r o s i t y (6) and i n t e r -

a c t i o n b e t w e e n d i f f e r e n t s o l u t e s o r b e t w e e n s o l u t e s and d e f e c t s (7). e x p e r i m e n t a l data w e r e lacking.

Vol.

However, corroborative

R e c e n t l y , th e p r e s e n t a u t h o r c o m p l e t e d a s t u d y of t h e f a c -

t o r s i n f l u e n c i n g the r e s i s t i v i t y of g r a i n b o u n d a r i e s in u l t r a p u r i t y a l u m i n u m , the r e s u l t s of w h i c h h a v e b e e n p u b l i s h e d e l s e w h e r e (9).

In the c o u r s e of t h i s w o r k , d a t a w e r e o b t a i n e d

w h i c h s u g g e s t t h a t t h e c o n t i n u e d r e c o v e r y of e l e c t r i c a l p r o p e r t i e s w i t h i n the g r a i n g r o w t h s t a g e and t h e d e v e l o p m e n t of a r e s i s t i v i t y m i n i m u m a r e a d i r e c t c o n s e q u e n c e of s e g r e g a t i o n of s o l u t e to g r a i n b o u n d a r i e s c o n c o m i t a n t w i t h g r a i n g r o w t h d u r i n g s t e p - i s o c h r o n a l a n n e a l i n g of c o l d - w o r k e d and r e c r y s t a l l i z e d m a t e r i a l s . In r e f e r e n c e 9, the a u t h o r s h o w e d t h a t the s e g r e g a t i o n of s o l u t e to g r a i n b o u n d a r i e s d u r i n g s t e p - i s o c h r o n a l a n n e a l i n g r e m o v e s s o l u t e f r o m s o l i d s o l u t i o n , t h e r e b y d e c r e a s i n g the r e s i s t i v i t y of the m a t r i x m a t e r i a l b e l o w t h a t of the s a m e m a t e r i a l in the s i n g l e - c r y s t a l c o n dition.

Th e e f f e c t on r e s i s t i v i t y due to s e g r e g a t i o n to r a n d o m m a t r i x d i s l o c a t i o n s w as found

to be n e g l i g i b l e .

T h e a u t h o r a l s o d e t e r m i n e d that t h e p h y s i c a l p r e s e n c e of p u r e g r a i n b o u n d -

a r i e s c o n t r i b u t e s 1.35 ± 0 . 5 × 10 " 1 1 o h m - c m of r e s i s t i v i t y p e r unit a r e a of g r a i n b o u n d a r y ( r a m "1) in a l u m i n u m , t h e l a t t e r c o n t r i b u t i o n i n c r e a s i n g the r e s i s t i v i t y of the m a t e r i a l in c o m p a r i s o n to the s i n g l e c r y s t a l c o n d i t i o n . as a f u n c t i o n of a n n e a l i n g t e m p e r a t u r e

The o b s e r v e d v a r i a t i o n in r e s i d u a l r e s i s t i v i t y at 4 K is t h e r e f o r e d e t e r m i n e d b y the r e l a t i v e m a g n i t u d e of

t h e s e two f a c t o r s . T h i s i n t e r a c t i o n is s c h e m a t i c a l l y i l l u s t r a t e d in F i g .

1 in w h i c h Po d e n o t e s t h e s i n g l e -

c r y s t a l r e s i s t i v i t y of the h o m o g e n e o u s m a t e r i a l w i t h a l l s o l u t e in s o l i d s o l u t i o n .

The r e s i s -

t i v i t y c o n t r i b u t i o n due to the p h y s i c a l p r e s e n c e of the p u r e b o u n d a r i e s , p gb(p), d e c l i n e s f r o m s o m e h i g h v a l u e at l o w a n n e a l t e m p e r a t u r e s z e r o at h i g h t e m p e r a t u r e s

( w h e r e the g r a i n s i z e is a s s u m e d to be s m a l l ) to

w h e r e the s i n g l e - c r y s t a l

c o n d i t i o n is a p p r o a c h e d .

The r e s i s t i v i t y

c o n t r i b u t i o n due to r e m o v a l of s o l u t e f r o m s o l i d s o l u t i o n by s e g r e g a t i o n to g r a i n b o u n d a r i e s , P gb(s), w i l l be n e g l i g i b l e b o t h at v e r y lo w t e m p e r a t u r e s very high temperatures mum.

w h e r e d i f f u s i o n r a t e s a r e l o w and at

w h e r e the g r a i n b o u n d a r y a r e a p e r unit v o l u m e t e n d s t o w a r d a m i n i -

As the s o l u t e e f f e c t a l w a y s c o n t r i b u t e s to a r e d u c t i o n in r e s i s t i v i t y as c o m p a r e d to t h a t

of a s i n g l e c r y s t a l ,

it is d e s i g n a t e d P o - Pgb(s) on F i g .

1.

Th e s o l u t e e x e r t s i t s g r e a t e s t i n -

f l u e n c e on the r e s i s t i v i t y at s o m e i n t e r m e d i a t e t e m p e r a t u r e

c o r r e s p o n d i n g to the a t t a i n m e n t

of a m a x i m u m in the t o t a l f r a c t i o n of s o l u t e r e m o v e d f r o m s o l i d s o l u t i o n .

Th e o b s e r v e d r e -

s i d u a l r e s i s t i v i t y , P o b s , is t h e r e f o r e g i v e n by the s u m : Pobs = Pgb(p) + [Po - Pgb(s) ]

Eqn. 1

Vol.

4,

No.

8

RECOVERY OF ELECTRICAL

Adding the base single-crystal erates

the dashed

curve

of F i g .

PROPERTIES

resistivity,

1 which represents

DURING ANNEALING

90, to the grain boundary the predicted

variation

577

contribution in residual

t i v i t y of t h e m a t e r i a l

resis-

if it contained

pure grain boundaries.

only

The difference

b e t w e e n t h e Po + Pgb(p) c u r v e curve therefore

gen-

and the Pobs

defines the Pgb(s) contri-

bution to residual

resistivity

at any tem-

perature. The application a determination

concepts

of the magnitude

P gb(s) contribution terials

of these

Z(b). T h e m a t e r i a l s the bulk residual

of t h e

in experimental

is illustrated

in Figs. are

characterized

resistivity

which the specimens 7 0 0 0 a n d 1900, impurity

FIG. 1 Schematic illustration of the summation of the p u r e b o u n d a r y e f f e c t , Pgb{p), a n d t h e s o l u t e e f f e c t , Oo - P g b ( s ) , t o p r o a u c e t h e e x p e r i m e n t ally observed curve, Pobs, with its attendant resistivity minimum. The curve shapes have been simplified for illustrative purposes.

by

ratios, from

were prepared,

corresponding

contents

ma-

2(a) a n d

Pe~ K/O4K, o f t h e i n g o t m a t e r i a l s ANNEAL TEMPERATURE

to

e.g.,

to total

of a p p r o x i m a t e l y

0.5

and 2 ppm atomic,

respectively.

The

details

preparation,

of t h e

of s p e c i m e n

determination

of grain boundary

and other aspects procedure

areas

of the experimental

have been described

in refer-

e n c e 9. The curves served

containing

change in residual

isochronal

annealing

data points on Figs.

resistivity,

run concomitantly.

flect a significant

increase

fined.

The vertical

bars indicate

The dashed portion

in scatter,

T h e Po v a l u e f o r e a c h m a t e r i a l

the terminal

leaving this portion

of the curves

was taken as the mean

during

the range of scatter

of the curves

obstepin the

beyond the minima relatively

of the residual

re-

poorly de-

resistivity

after

anneal at 600°C.

The average neal was multiplied

grain boundary

area

per unit volume

b y 1 . 3 5 x 1 0 - z± o h m - c m

perature

for each material.

predicted

curve

sidering

Pobs' at 4 K as a function of temperature

of the materials.

5 or 6 specimens

2(a) a n d 2(b) s h o w t h e e x p e r i m e n t a l l y

of the residual

to determine

corresponding

to t h e r e s p e c t i v e

t h e Pgb(p) c o n t r i b u t i o n

at each tem-

T h i s v a l u e w a s t h e n a d d e d t o t h e b a s e Po v a l u e t o e s t a b l i s h resistivity

only the effect of pure grain

for each material

boundaries.

an-

as a function of temperature,

the con-

Vol.

RECOVERY OF ELECTRICAL PROPERTIES DURING ANNEALING

578

4, No.8

0.02 -

400

200

ANNEAL

360

600

600

l60

400

ANNEAL

TEMPERATURE,C

6oQ

660

TEMPERATURE,

(a)

600

C

(b)

FIG. 2 Experimentally

observed

ing of aluminum effect

is equal

having

change bulk

in residual

residual

to the vertical

resistivity

resistivity

separation

at 4K

ratios

of the cobs

of

during

7000(a)

and the co t

step-ieochronal annealThe solute

and 1900 (b).

~gb(p) curves

at any tem-

perature.

As provides accord was

discussed,

an estimate with Eqn.

When

1.

2. 3 X 10-llohm-cm

tribution 0.6

from

solid

ohm-cm, solution

* The studies solute

atoms

tribution

the appropriate

effect

leading at pmi,.,~

of Arkharov, may

to resistivity

would

resistivity

(11)

to-

inserted

resistivity

of the 7000

from

X

into Eqn.

The average

the data of Arp, of solute

101’ impurity

in each figure

segregation

data were

that - 0.04ppm 2.4

the two curves

due to solute

minimum.

can be estimated

corresponding

et al.,

resistivity

the residual

to the conclusion

not be completely

between

experimental

had reduced

of impurity

separation

to residual

at the observed

per ppm atomic

X lo-’

the vertical

of the contribution

found that the solute

about

-

previously

per

1,

material resistivity

et al.,

had been

atoms

in

(10)

it by conto be

removed

cm3 of metal.

indicate

relieved

be retained.

that the screened state of certain species of in which case some positive conby adsorption, However, the reduction in lattice strain accom-

panying adsorption should contribute to an overall decrease in the scattering probability of a The assumption has therefore been made in the present study segregated grain boundary. that a solute atom adsorbed at a grain boundary has a negligible effect on residual resistivity as compared to the same atom in random solid solution.

*

Vol.

4, No.

8

R E C O V E R Y OF E L E C T R I C A L

PROPERTIES

DURING ANNEALING

579

T h e g r a i n b o u n d a r y a r e a p e r u n i t v o l u m e at the m i n i m u m was e x p e r i m e n t a l l y known to be 7 . 5 c m -1 (9); c o n s e q u e n t l y , t h e s e d a t a i n d i c a t e t h a t the g r a i n b o u n d a r i e s e x i s t i n g i n the 7000 m a t e r i a l a t the r e s i s t i v i t y m i n i m u m c o n t a i n e d at l e a s t 3 × 1014 i m p u r i t y a t o m s p e r c m 2 of boundary.

T h e s e d a t a a r e s u m m a r i z e d i n T a b l e I a l o n g with data f r o m a s i m i l a r a n a l y s i s

p e r f o r m e d on m a t e r i a l 1900.

T h e s e d a t a i n d i c a t e t h a t the c o n c e n t r a t i o n of i m p u r i t y a t o m s

p e r u n i t a r e a of g r a i n b o u n d a r y is e s s e n t i a l l y the s a m e i n b o t h m a t e r i a l s ,

despite large dif-

f e r e n c e s i n the r e s p e c t i v e b o u n d a r y d e n s i t i e s at the r e s i s t i v i t y m i n i m u m .

The c a l c u l a t e d i m -

p u r i t y c o n c e n t r a t i o n is 10~ to 105 t i m e s h i g h e r t h a n would b e p r e d i c t e d on the b a s i s of a n e q u i l i b r i u m s e g r e g a t i o n p r o c e s s (l Z) and is the a p p r o x i m a t e e q u i v a l e n t of a d s o r b i n g 1/3 of a m o n o l a y e r of s o l u t e on the e x i s t i n g b o u n d a r i e s .

The s i g n i f i c a n c e of the l a t t e r o b s e r v a t i o n is the

s u b j e c t of c o n t i n u i n g s t u d y . TABLE

I

E s t i m a t i o n of the S p e c i f i c B o u n d a r y Solute C o n t e n t E x i s t i n g at the R e s i d u a l R e s i s t i v i t y M i n i m a Material

7000

Pgb(s) at P m i n ( o h m - c m )

.

E q u i v a l e n t Solute R e m o v e d (ppm)

2.3xI0

1900 -n

0.04

I m p u r i t y A t o m s R e m o v e d p e r c m 3 of M e t a l

2 . 4 X l O Is

B o u n d a r y D e n s i t y a t p m i n (c m - l )

7.5

I m p u r i t y A t o m s p e r c m ~ of G r a i n B o u n d a r y at p r n i n

3X1014

_

1 . 1 × 1 0 -1o 0.17

I X l O le 30

3X101~

The a u t h o r w i s h e s to t h a n k D r . R. P . Reed for h e l p f u l d i s c u s s i o n s and for r e v i e w of the m a n u s c r i p t . References 1.

P . G r e g o r y a n d J. E. H a r g r e a v e s ,

J. I n s t . M e t a l s , 93, 165 (1964-65).

2.

P . G r e g o r y a n d 2. E. H a r g r e a v e s ,

J. A u s t . I n s t . M e t a l s , 11, 23 (1966).

3.

F. Credner,

4.

H. G e w e c k e , Z. P h y s . C h e m . , 8Z, 457 (1913).

5.

H. W e y e r e r ,

6.

P . V. A n d r e w s , P h y s . L e t t e r s ,

7.

E. K o v a c s - C s e t e n y i and C. R. V a s s e l , A c t a . P h y s . A c a d . Sci. H u n g . , 71, 195 (1966).

8.

K. M i s e k , C z e c h . J. P h y s . ,

Z. P h y s . C h e m . ,

82, 457 (1913).

Z. M e t a l l k u n d e , 44, 51 (1953). 19, 558 (1965).

B17, 647 (1967).

580

RECOVERY

OF E L E C T R I C A L

PROPERTIES

DURING

ANNEALING

Vol.

9,

M. K a s e n , P h i l . M a g . ,

10.

V. D. A r p , M. B. K a s e n a n d R. P . R e e d , T e c h . R e p t . A F A P L - T R - 6 8 - 8 7 , PattersonAFB, Ohio, ( F e b . 1969).

11.

V. I. Arkharov, S. D. Vangengeyrn, Metalloved., 24, 289 (1967).

12.

D. M c Lean, Grain Boundaries in Metals, p. 118.

4, No.8

Z l , 599 (1970). Wright-

I. B. Klyuyeva and V. P. Serikova, Fiz. Metal.

Clarendon Press, Oxford (1957).