Electrical and thermal resistivities of ruthenium from 2 to 20 K

Volume 33A. number8

PHYSICS L E T T E R S

ELECTRICAL AND THERMAL OF RUTHENIUM FROM

28 December 1970

RESISTIVITIES 2 T O 20 K

J. T. SCHRIEMPF and W. M. MACINNES Naval Research Laboratory, Washington, D.C. 20390, USA Received 10 November 1970

Electron-electron scattering contributions to the electrical and thermal resistivities varying as T 2 and T respectively have been observed in a high purity single crystal sample of Ru. The electron scattering Lorenz number is 1.8 + 0.8 ×10 -8 V2/K2.

P r e v i o u s m e a s u r e m e n t s [1,2] of the e l e c t r i c a l and t h e r m a l r e s i s t i v i t i e s of r u t h e n i u m have been made on s a m p l e s of insufficient p u r i t y to p e r m i t r e l i a b l e d e t e r m i n a t i o n s of the ideal t h e r m a l r e s i s t i v i t y much below 20 K. As a consequence, no t e m p e r a t u r e v a r i a t i o n of the t h e r m a l r e s i s t i v i t y that could be a s s o c i a t e d with 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 was found. We r e p o r t h e r e m e a s u r e m e n t s of ideal r e s i s t i v i t i e s of r u t h e n i u m below 20 K which show good evidence of 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 c o n t r i b u t i o n s to both the e l e c t r i cal and t h e r m a l r e s i s t i v i t i e s . The equipment u s e d for these m e a s u r e m e n t s h a s been d e s c r i b e d in detail before [3], and was u s e d unmodified in making the p r e s e n t m e a s u r e m e n t s . The r e p r o d u c i b i l i t y of the m e a s u r e m e n t s u s i n g this equipment ,is of the o r d e r of 0.5%. The single c r y s t a l s a m p l e of r u t h e n i u m on which the m e a s u r e m e n t s were made was p r e p a r e d f r o m 99.999% p u r e r u t h e n i u m powder and complete d e t a i l s of the s a m p l e p r e p a r a t i o n were given e l s e w h e r e [4]. The section of the rod on which the e l e c t r i c a l and t h e r m a l r e s i s t i v i t y m e a s u r e m e n t s were made had a r e s i d u a l r e s i s t a n c e r a t i o (p(297 K)/p(4.2 K)) of 1220 and was d e t e r m i n e d by X - r a y m e a s u r e m e n t s to be a single c r y s t a l with the c - a x i s making an angle of 85 ° with the rod axis. The shape of the rod was quite i r r e g u l a r . The value of the shape factor ( F ) u s e d to d e t e r m i n e the r e s i s t i v i t i e s was obtained by m e a s u r i n g the d i a m e t e r s at 0.010 in. i n t e r v a l s along the rod, c a l c u l a t i n g the c r o s s sectional a r e a s (A), and n u m e r i c a l l y evaluating f d l / A . T h e value of F obtained in this way l i m i t s the absolute a c c u r a c y of the e l e c t r i c a l and t h e r m a l r e s i s t i v i t i e s to 2.3%. The l o w - t e m p e r a t u r e v a r i a t i o n of the e l e c t r i cal and t h e r m a l r e s i s t i v i t i e s for t r a n s i t i o n m e t -

alS that can exhibit 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 effects is expected on t h e o r e t i c a l grounds to be

[5-7]: P

= PO +

AT2

+

BT5

(la)

for the e l e c t r i c a l r e s i s t i v i t y , and

W = C/T + aT + ~T 2

(lb)

for the t h e r m a l r e s i s t i v i t y . In w r i t i n g down these equations, it is a s s u m e d that the r e s i s t i v i t i e s due to different s c a t t e r i n g p r o c e s s e s a r e additive, and that the heat t r a n s p o r t e d by the lattice is n e gligible. The t e r m s in each of these equations c o r r e s p o n d r e s p e c t i v e l y to s c a t t e r i n g of elec ~ t r o n s by i m p u r i t i e s , by other e l e c t r o n s , and by phonons. A least s q u a r e s fit of the data was made to the above equations, and the c o n s t a n t s A, B, C, a and ~ where t h e r e b y d e t e r m i n e d . The e l e c t r i c a l and t h e r m a l r e s i s t i v i t y data a r e plotted in fig. 1 in such a m a n n e r as to e m phasize the 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 c o n t r i butions to the r e s i s t i v i t i e s . The u n c e r t a i n t i e s of +0.5% in the e l e c t r i c a l , and +0.6% in the t h e r m a l r e s i s t a n c e s give r i s e to the e r r o r b a r s shown in the f i g u r e s . The solid l i n e s a r e the l e a s t s q u a r e s fit to the data of eqs. (la) and (lb), and the v a l u e s of the c o n s t a n t s a r e l i s t e d in the figure. The i m p u r i t y s c a t t e r i n g L o r e n z n u m b e r , L o , a g r e e s v e r y well with the S o m m e r f i e l d value of 2.44× 10 -8 V 2 / K 2. The value of the 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 L o r e n z n u m b e r . L e, (=A/a = 1 . 8 - 0 . 8 × 10 -8 V2/K 2) obtained from the l e a s t s q u a r e s fit of the data to eqs. (la) and (lb) i s l a r ger than the t h e o r e t i c a l l y expected value for Bab e r (Coulomb) s c a t t e r i n g of e l e c t r o n s . We have u s e d the theory developed by Schriempf et al. [8] 511

33A, number S

Volume

0

I

2

8 ~43)1(83}

PHYSICS

103 x ; : ' 4

5

(K) 5

6

7

b

i(1631

{123)

(20.~) i

(505) (A )

7

6 ~' '

ELECTRICAL RESISTIVITY

oE

5 "7~ / 4

!

•

2•

/9 = P0 + A T 2

_

+ BT5

Po = 6 . 0 4 5

=•

.

. 2.66 *-0.55

x I0 - m OHM cm K -2

B

= 2.12z0.56

x i0-16 O H M c m K -5

2b Decem/)er 197(I

v a l u e s r a n g i n g f r o m 1.02 to 1.11 ~ 10-8 V 2 / K 2, d e p e n d i n g on t h e s p e c i f i c v a l u e s of t h e p a r a m e t e r s chosen. This t h e o r e t i c a l e s t i m a t e does lie w i t h i n the r a t h e r l a r g e u n c e r t a i n t y a s s o c i a t e d with the o b s e r v e d Le v a l u e . It s h o u l d b e p o i n t e d out t h a t t h e o b s e r v e d tow t e m p e r a t u r e b e h a v i o r of t h e e l e c t r i c a l r e s i s t i v i t y w o u l d 7also a g r e e w i t h t h e p r e d i c t i o n s of E h r l i e h [10]. He h a s s h o w n t h a t d e v i a t i o n s f r o m M a t t h i e s s e n ' s r u l e c a u s e d by low t e m p e r a t u r e p h o n o n - i n d u c e d U m k l a p p p r o c e s s e s c a n g i v e r i s e to an a p p a r e n t 7`2 c o n t r i b u t i o n to t h e e l e c t r i c a l resistivity. T h e r o o m t e m p e r a t u r e r e s i s t i v i t y of t h i s s i n g l e c r y s t a l s a m p l e of r u t h e n i u m i s h i g h e r t h a n t h a t m e a s u r e d by W h i t e a n d c o - w o r k e r s [ 1 , 2 ] on p o l y c r y s t a l l i n e s a m p l e s . T h e v a l u e o b t a i n e d in

this work, is in good et el. [ii] the same lar to the

I 0 . 0 4 4 x 10-7 OHM cm

A

L E T T E RS

p(297 K) 7.45 ± 0.17 x 10-6 ohm-cm, agreement with that obtained by Powell for a single crygstal sample with nearly orientation as ours (c axis perpendicurod axis).

o t {-r8.o) (B) 6

THERMAL

RESISTIVITY

T h e a u t h o r s w o u l d l i k e to t h a n k R. W. S c o t t a n d R. R i g h t e r f o r e l e c t r o n b e a m w e l d i n g a n d z o n e r e f i n i n g t h e r u t h e n i u m , C. L. V o l d f o r h i s X - r a y d e t e r m i n a t i o n s of t h e o r i e n t a t i o n of t h e s p e c i m e n , a n d J. B a t t e r s o n f o r d e t a i l e d m e a s u r e m e n t s of t h e s p e c i m e n d i a m e t e r s . W e a r e g r a t e f u l to D r . A. I. S c h i n d l e r for his continued e n c o u r a g e m e n t and s u p p o r t t h r o u g h o u t t h e c o u r s e of t h i s s t u d y . One of t h e a u t h o r s (W. M. M. ) i s h a p p y to a c k n o w l e d g e t h e a w a r d of a N a t i o n a l R e s e a r c h C o u n c i l R e s i d e n t R e s e a r c h A s s o c i a t e s h i p at t h e N a v a l Research Laboratory.

•

°)7 T

2 C = 02498 : 00058cmW -~ K 2 a = 150 t 0 6 4 x I0 -4 crnW -I

I

B = 188 *- 0 3 7

x 10-ScmW-~K -I

[iejerences

(-16.6) I

O0

2

4

6

S

12

I0

14

16

18

20

T(K)

Fig.1. Electrical

resistivity

(A),

and t h e r m a l

resisti

vity (B) of ruthenium. The straight lines through the data are the least s q u a r e s fit to the indicated equations with the constants taking on the values listed. The e r r o r b a r s r e p r e s e n t uncertainties of =~0.5% and =k0.6% in the e l e c t r i c a l and t h e r m a l r e s i s t i v i t i e s respectively. The Lorenz number for impurity s c a t t e r i n g (Po/C) and 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 (A~a) are r e s p e c t i v e l y 2.42 =k 0.04 and 1.8 =~ 0.8 x 10-8 V2/K 2. a n d a p p r o p r i a t e p a r a m e t e r s f o r a two b a n d a p p r o x i m a t i o n to t h e b a n d s t r u c t u r e a n d F e r m i s u r f a c e of r u t h e n i u m [9], a n d h a v e o b t a i n e d L e

512

[1] G.K. White and S. B. Woods, Can. J. Phys. 36 (1958) 875. [2] R. J. Tainsh and (i.. K. White, Can. J. Phys. 42 (]964) 208. [3] J . T . Schriempf, J. Phys. Chem,Solids 28 (1967) 2581. [4] J . T . Schriempf, J . L e s s - C o m m o n Metals 9 (1965) 35. [5] L. Colquitt, J r . , J. Appl. Phys. 36 (1965) 2454. [6] C . H e r r i n g , Phys. Rev. L e t t e r s 19 (1967) 167, 684. [7] M.J. Rice, Phys. Rev. L e t t e r s 20 (1968) 1439: 21 (1968) 871. [8] J. T. Schriempf, A. I. Sehindler and D. L. Mills, Phys. Rev. 187 (1969) 959. [91 P . T . Coleridge, Low-Temp. Phys. 1 (1969) 577. []0l A . C . E h r l i c h , Phys. Rev. B1 (1970) 4537. [11] R. W. Powell, R . P . Tye and M. J. Woodman, J. L e s s - C o m m o n Metals 12 (1967) 1.