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THERMAL AND ELECTRICAL CONDUCTIVITY OF
PURE VANADIUM AT LOW TEMPERATURES
H. Weinstock, C. Tsai, F. Schmidt
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, suppliment au no 8, Tome 39, aozit 1978, page
C6-1026
THERMAL AND ELECTRICAL CONDUCTIVITY OF PURE VANADIUM A T LOW TEMPERATURES
X H. Weinstock, C.L. T s a i and F.A. Schmidt'
Department of Physics IZZinois I n s t i t u t e of TechnoZogy, Chicago, IL
60616 USAR6sumd.- L ' a n a l y s e des mesures des c o n d u c t i v i t d s thermique e t d l e c t r i q u e de vanadium de h a u t e p u r e t d a rdv616 une n o t a b l e d i f f u s i o n Q l e c t r o n - d l e c t r o n 1 b a s s e s temp6ratures.
Abstract.- Measurements of b o t h t h e thermal and e l e c t r i c a l c o n d u c t i v i t y of h i g h p u r i t y vanadium have been analyzed t o show s i g n i f i c a n t 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 t low temperatures.
INTRODUCTION.- E a r l i e r measurements by Jung e t a l , / l / on t h e thermal and e l e c t r i c a l c o n d u c t i v i t y of high p u r i t y vanadium have been extended t o below T f o r a sample w i t h p 3 001p4. 2 = 1760. This work i s aimed a t o b t a i n i n g a b e t t e r understanding of e l e c - t r o n s c a t t e r i n g mechanisms and t h e e l e c t r o n i c s t r u c - t u r e of vanadium. There a r e s e v e r a l important e l e c t r o n s c a t t e - r i n g mechanisms t o be considered / 2 / : electron-de- f e c t ; e l e c t r o n - e l e c t r o n ; electron-phonon i n t e r b a n d ; and electron-phonon i n t r a b a n d s c a t t e r i n g . For e l e c t r i c a l r e s i s t i v i t y , i f M a t t h i e s s e n ' s r u l e i s v a l i d , one may w r i t e 131 J (e/T) J S ( BIT) p = p,
+
p e e ~ 2 ,+ psdT3 7.212'
'ssTSm
'
(1)e
where =)'
dx i s t h e Debye i n t e - ( e % 1 2 0 g r a l . RESULTS.- E l e c t r i c a l r e s i s t i v i t y from 2 K t o 300 K shows a r e s i d u a l r e s i s t i v i t y of 10.9 &.cm and Tc= 5.43 (f 0.02) K. F i g u r e 1 e x h i b i t s t h e thermal c o n d u c t i v i t y v s . temperature. The maximum v a l u e of thermal c o n d u c t i v i t y , 11.2 W/K.cm, o c c u r s a t about 8 . 0 K. Below T t h e thermal c o n d u c t i v i t y , i n t h e superconducting s t a t e , Ks, i s l e s s t h a n t h a t i n t h e normal s t a t e , Kn, w i t h (Kn
-
K ) i n c r e a s i n g a s T +0, i n d i c a t i n g t h a t e l e c t r o n s a r e t h e dominant h e a t c a r r i e r s a t low temperature. Thus, i n t h e f o l l o w i n g
-
Ken, i . e . , a l l nor- a n a l y s i s , i t i s assumed t h a t K -mal s t a t e thermal conduction i s due t o e l e c t r o n s . The measurements of b o t h thermal and e l e c t r i c a l con- d u c t i v i t y above 15 K a r e i n good agreement w i t h t h o s e of Jung, e t a 1 / l / , and show t h a t i n t r i n s i c e l e c t r o n i c t r a n s p o r t i s dominant i n t h i s range a l s o .
The b e s t f i t of eq. ( I ) t o t h e p(T) d a t a , f o r
The f i r s t term on t h e r i g h t hand s i d e of eq. ( l ) i s 0 = 380 K 171, i s
due t c e l e c t r o n - d e f e c t s c a t t e r i n g . The second term, p = (1.09 X 10-' + 1.30 X 10-'l T 2
+
2.75 x 10-l2J J
P e e ~ 2 , was p r e d i c t e d by Appel / 4 / and observed f o r T3
3
+
9.50 x 10-16 T5 5 7.212 124.43) Q.cm. ( 3 )s e v e r a l t r a n s i t i o n m e t a l s . The t h i r d term, suggested The b e s t f i t of t h e thermal d a t a , a p p l i e d t o by Mott 151 was v e r i f i e d e a r l i e r by White and Woods e a .
.
( 2 ) .. .,
is/3/ f o r vanadium. L a s t i s t h e
loch-Griineisen
term-
=a r i s i n g form i n t r a b a n d phonon s c a t t e r i n g of e l e c s Ken (0.446 + 1.30 X 1 0 - ~ T2
+
3.09 X 10-h T3)t r o n s . c ~ . K ~ / w (4)
For thermal r e s i s t i v i t y , b o t h electron-pho-
ANALYSIS.- The Sommerfeld-Lorenz number e x t r a c t e d non i n t e r b a n d and i n t r a b a n d s c a t t e r i n g g i v e r i s e t o
from t h e s e measurements i s ' 2 . 4 4 X I 0-B (v/K)
',
q u i t e a q u a d r a t i c temperature dependence / 6 / . E l e c t r o n -elwtron scattering yields a linear Thus, the c l o s e t o t h e accepted t h e o r e t i c a l v a l u e . The Lorenz t o t a l thermal r e s i s t i v i t y , m u l t i p l i e d by T, i s r a t i o o b t a i n e d 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 ,
pee/B, i s 1.0 X ~ o - ' ( v / K ) ~ , c o n s i s t e n t w i t h e a r l i e r
- .
= A + B T ~ + c T ~
W T = - (2) experimental /8/ and t h e o r e t i c a l r e s u l t s / g / . The
en Ken v a l u e found f o r t h e 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
'
Supported by t h e U. S. Department of Energy term i n e l e c t r i c a l r e s i s t i v i t y i s about 50 % h i g h e rt
Address: Ames Laboratory- DOE, Ames, Iowa,
USA than t h a t measured f o r niobium /2/. This can be a t -t r s b u t e d t o t h e h i g h e r d e n s i t y of s t a t e s i n t h e d-
band of vanadium. The thermal resistivity due to
range reported here. Although electron-electron
electron-phonon interband scattering can be estima-
scattering appears unimportant for both thermal and
ted by
/3/
electrical resistivity at higher temperatures, such
- =
wsd(T)
2(:)2~3(~/~)
for T f 0.
scattering seems significant in determining both of
Wsd(">
these properties in the liquid helium temperature
with Wsd(m)
=L ~ - ~ P ~ ~ T ~
J3(8/T)/J,(m)
=1.24 cm.K/W.
range.
Thus, W T
=1.12
XC ~ . K ~ / W
and W
T = SS1.97
X::-*T3cm.K2/W.
Fig.
high
References
/I/ Jung, W.D., Schmidt, F.A. and Danielson, G.C.,
Phys. Rev.
B15
(1977) 650.
/2/ Webb, G.W., Phys. Rev.
181
(1969) 1127.
/3/ White, G.K. and Woods, S.B., Phil. Trans. Roy.
Soc.
(1959), 273.
/ 4 /
Appel, J., Phil. Mag.
8
(1963) 1071.
/5/ Mott, N.F., Proc. Roy. Soc. (London)
A153
(1935)
699.
161
Kemp, W.R.G., Klemens, P.G., Sreedhar, A.K. and
White, G.K., Proc. Phys. Soc.
A67
(1954) 728.
/ 7 /
Leupold, H.A., Iafrate, G.J., Rothwarf, F.
Breslin,
J.T., Edmiston, D. and Aucoin, T.R.,
J.
Low. Temp. Phys.
2
(1977) 241.
/S/ White, G.K. and Tanish, R.J., Phys. Rev. Lett.
19 (1967) 165.
/g/ Herring, C., Phys. Rev. Lett.
2
(1967) 167.
/10/ Parker, R.D. and Halloran, M.H., Phys. Rev.
(1974) 4130.
1 :
Thermal conductivity vs. temperature
purity vanadium.
for
W T can be estimated assuming a spherical Fermi
S S
