'SIMPLE' BEHAVIOUR OF THE LOW TEMPERATURE ELECTRICAL RESISTIVITY OF SILVER ?

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’SIMPLE’ BEHAVIOUR OF THE LOW

TEMPERATURE ELECTRICAL RESISTIVITY OF

SILVER ?

Br. Barnard, A.D. Caplin

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C6, supple'ment au no 8 , Tome 39, aofit 1978, page

~6-1050

B R .

Barnard and A.D.Caplin

Physics Department, ImperiaZ CoZZege,

London

SW7

2 B Z ,

England

Rdsum6.- Pour l a premisre f o i s , l a r d s i s t a n c e d e monocristaux m d t a l l i q u e s a Q t d mesurde avec une r d s o l u t i o n e j r t r h e m e n t 61evBe ( j u s q u ' 8 l / l o 7 ) ; dans t o u s s e s a s p e c t s , l a r d s i s t i v i t d d e l ' a r g e n t e t d e s e s a l l i a g e s e s t en c o n t r a d i c t i o n avec l e s p r d d i c t i o n s t h d o r i q u e s couramment en vogue.

Abstract.- For t h e f i r s t time u l t r a high r e s o l u t i o n ( t o p a r t s lo7) r e s i s t a n c e measurements have been made on l a r g e m e t a l l i c s i n g l e c r y s t a l s ; i n every r e s p e c t , t h e r e s i s t i v i t y of s i l v e r and i t s a l l o y s c o n t r a d i c t s c u r r e n t t h e o r e t i c a l e x p e c t a t i o n s .

We have made d e t a i l e d measurements of t h e low temperature r e s i s t i v i t y of s i l v e r / I / , and s i l v e r a l l o y s , i n o r d e r t o study i n t e r f e r e n c e e f f e c t s / 2 / between phonon and impurity s c a t t e r i n g , and t o search f o r t h e a n t i c i p a t e d T2 dependence r e s u l t i n g from e l e c t r o n - e l e c t r o n s c a t t e r i n g . By u s i n g a novel r e - s i s t a n c e b r i d g e 131, we have been a b l e t o o b t a i n r e - s o l u t i o n (up t o 1 i n 107) on l a r g e s i n g l e c r y s t a l samples, and so avoid t h e complications a r i s i n g from s u r f a c e and g r a i n boundary s c a t t e r i n g . This i s t h e f i r s t time t h a t measurements of t h i s q u a l i t y have been performed on such well-defined samples of any metal.

Typical exoerimental r e s u l t s a r e shown i n f i g u r e 1; a s t r i k i n g f e a t u r e of a l l samples we have measured i s t h a t t h e temperature-dependent p a r t of

t h e r e s i s t i v i t y , (pT-p,), f o l l o w s a T' power law w i t h e x t r a o r d i n a r y f i d e l i t y ( a p a r t from t h e cold- worked sample, which d e v i a t e s s l i g h t l y below 1.8 K). o u r measurements extend up t o 9K i n temperature,and encompass over f i v e o r d e r s of magnitude i n r e s i s - t i v i t y change, so t h a t an o v e r a l l view of t h e d a t a i s b e s t obtained i n t h e condensed form of f i g u r e 2. The

T~

v a r i a t i o n extends t o higher temperatures f o r t h e a l l o y samples, and p a r t i c u l a r l y f o r t h e cold- worked sample, t h a n it does i n t h e ' p u r e ' samples. For t h e cold worked sample a power law f i t t o t h e d a t a from 1.8 t o 8.6 K g i v e s a n exponent of 4.00

+

0.005.

'Pure'

I

-*

;

Fig. 2 : Summary of a l l t h e d a t a . The v a l u e of o o i s t h a t o b t a i n e d by e x t r a p o l a t i o n a s i n f i g u r e I . For c l a r i t y i n d i v i d u a l d a t a p o i n t s a r e n o t shown,they have s c a t t e r of t y p i c a l l y 1% about t h e smooth cur- ves.Arrows on t h e top and bottom curves mark v a l u e s Fig. 1 : Typical d a t a below 3K f o r our s i l v e r samples. of (p -po)/po, and show how f a r t h e measurements The two upper s e t s of d a t a have been v e r t i c a l l y d i s - extenxed i n t o t h e ' d i r t y ' regime.

placed.Bars r e p r e s e n t t h e s t a t e d f r a c t i o n ofpo.Inset: sample shape.

Our low temperature d a t a show i n d i c a -

References t i o n (except p o s s i b l y i n t h e cold-worked sample) of

any T~ term, w i t h a n upper bound f o r t h e 'pure'

samples of between 5xl0-'%nd 2x10-l4 ohm cm K - ~ . / l / Barnard, B.R. and Caplin, A.D.,Comm.on Phys. _(1977).

2

This should be compared w i t h a r e c e n t c a l c u l a t i o n _{/ 2 / Cimberle, M.R., Babel, G. and Rizzuto, C.Adv.} by Lawrence / 4 / f o r e l e c t r o n - e l e c t r o n s c a t t e r i n g i n Phys.

3

(1974) 639.

s i l v e r of 1.4~10-13ohm cm K-2. /3/ Barnard, B.R. and C a p l i n , A.D. t h i s conference. / 4 / Lawrence, W.E. Phys.Rev.

B

((1976) 5316

Fig. 3 : Expected v a r i a t i o n of t h e r e s i s t i v i t y on an a n i s o t r o p y model. The t h r e e s o l i d l i n e s r e p r e s e n t t h e behaviour of samples of d i f f e r e n t p,. A t s u f f i - c i e n t l y h i g h temperatures a l l samples p a r a l l e l t h e ' c l e a n ' l i m i t , (p -p ) / p o _T >>, 1 , and a t low enough

0

temperatures t h e y converge on t h e ' d i r t y ' l i m i t

(p

-

p ) / p < c l . Tn i s a n asymptotic e m p i r i c a l

T o o

power law f i t t o t h e ' d i r t y ' l i m i t . C o n t r a s t f i g u r e 3b with f i g u r e 1 , f i g u r e 3c with f i g u r e 2, and n o t e p a r t i c u l a r l y t h e absence of convergence i n t h e mea- sured r e s i s t i v i t y of d i f f e r e n t samples a t t h e lowest temperatures.

F i g u r e 3 shows s c h e m a t i c a l l y t h e behaviour t o be expected f o r t h e r e s i s t i v i t y from any model /5,6/ t h a t invokes a n i s o t r o p y of s c a t t e r i n g r a t e s t o e x p l a i n i n t e r f e r e n c e e f f e c t s between phonon and impu- r i t y s c a t t e r i n g . Even a t t h e lowest temperatures o u r d a t a on d i f f e r e n t samples show no s i g n of convergence t o a common ' d i r t y ' l i m i t , d e s p i t e t h e f a c t t h a t t h e measurements go f a r i n t o t h e ' d i r t y ' r e g i m e ,

1 0 - ~ < ( p _{c T}

-

₀ p ) / p <10-' ( s e e f i g u r e 2). Within t h e

0%

a n i s o t r o p y model t h e r e i s r e a s o n t o expect a sus- t a i n e d simple'power law behaviour, l e t a l o n e one

/5/ Dosdale, T. and Morgan, G . J . J. Phys. F

4

(1974) 402.

161 Bergman, Y., Kaveh, M. and Wiser, N. Phys.Rev. L e t t .

32

(1974) 606.