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THE ELECTRICAL RESISTIVITY OF ULTRA PURE
ALUMINUM AT LOW TEMPERATURE
H. van Kempen, J. Ribot, P. Wyder
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplkment au no 8 , Tome 39, aotit 1978, page C6-1048
THE E L E C T R I C A L R E S I S T I V I T Y OF ULTRA PURE ALUMINUM A T LOW TEMPERATURE
H. Van Kempen, J.H.J.M. Ribot and P. Wyder
Physics Laboratory and Research I n s t i t u t e for Materials,
U n i v e r s i t y o f Nijmegen, Toernooiveld, Nijmegen, The Netherlands
RQsumd. Nous prdsentons des mesures d'une haute ~rscision, de la partie p(T) ddpendante de la tempdrature de la r6sistivitL Qlectrique de quatre dchantillons d'aluminium dont les rapports de rgsistivitd rdsiduelle s'stendent de 9000 1 41000. Elles dsmontrent bien l'existence d 'un terme en
AT^,
oii A =2,8 ~GIIIK-~. Le couplage Glectron-phonon fournit un autre terme dans p(T) dont le comportement approche T~ pour T < 2 K.Abstract.- High precision measurements of the temperature dependent part of the electrical resistivity p(T) of four aluminum samples, with residual resistivity ratios ranging from
9000 to 41000, are presented. They show that the presence of a
AT^
term with A 1 2 . 8 f ~ - ~ , can clearly be established. Electron-phonon interaction gives a term in p(T) which approa- ches T~ for temperatures below 2 K.Recently there has been a greatly renewed interest in the low temperature limit of the tempe- rature dependence of the electrical resistivity of simple metals. This has been especially true for aluminum. As an example of a simple polyvalent metal, it has been studied very thoroughly both theoretically and experimentally. Nevertheless no consensus has emerged; both experimentally 11-31 and theoretically 14-61 very different temperature dependences are determined. The presence of an
AT^
term (p ) in simple metals, due to electron-el-el
electron scattering is predicted theoretically al- ready by Landau and Pomerantschuk 171 in 1936. Theo- retical calculations of Lawrence and Wilkins /5/ give for aluminum p
el-el =
AT^
with A =O. 12 ~ G I I I K - ~ but these calculations are quite subtle and could easilj. be off by an order of magnitude. Experiments of Garland and Bowers 121 suggested a T~ dependence with A ~ 4 . 4 fGmK-2 as do the recent experiments of Garland and van Harlingen / 31. However, experiments of Senoussi and Oampbell /l/ showed a T~ dependence. By subtracting the theoretically calculated resis- tivity pel-ph' due to electron-phonon scattering, from the measured p(T) of reference Ili Kaveh and Wiser 161 found an
AT^
term with A 7 2 ..F26$ite small deviations of the calculated p el-ph should make this analysis invalid. So more precise knowledge of the experimentally determined p(T) is essential, in order to verify if a T~ term is indeed present, and to determine more precisely the tempe- rature dependence of p
el-ph '
In this paper new measurements are presen-
ted of the temperature dependent part of the resistivity p(T) of aluminum, for the first time of a precision sufficient to determine the tempe- rature dependence in the low temperature limir
.
The measurements were taken on four wires. All wires were annealed at 550 K for an hour. Two wires were made from the same bulk material with a bulk RRR of about 80.000 (sample 1 and 2). Sample 3 had a RRR of 21.000 and sample 4 of 9.000. All wires had a diameter of 3 mm except for sample 1, which had a diameter of 1.4 mm. The resistance measurements had an accuracy varying for the four samples from 2 to 10ppm. The temperature determination was within 1 mK below T A and 5 mK above TA.Figure la and Ib show bp/(T.dT) versus T3. The AT'S are taken from data points. 1 K apart below TA and .2 K apart above TA. The spreading of the points in the two figures is solely due to un- certainties in the temperature determination. Pre- senting the data this way eliminates the extrapo- lated resistivity at T = 0 K, po, as an extra pa- rameter. At the lowest temperatures A~/(T.AT) approaches a constant value which corresponds to an AT= term in p (T) with A
--
2.B
A F5T5 term should giveasloping line in these plots which seems to be the case below T = 2 K. This is as expected by Lawrence and Wilkins 141. For B we find B=0.05 f ~ m K - ~ with B slightly size dependent.The magnitude of p el-ph = p(T)
-
AT^
cannot be directly compared to theoretical calculationsas there exists no such results for the temperatu- re- and purity-regime of our measurements. While
we a r e c l e a r l y i n t h e d i r t y l i m i t ( p / p
o el-ph > l o 3 ) To summarize : t h e t e m p e r a t u r e dependence f o r t h e l o w e s t t e m p e r a t u r e s , t h i s i s n o t t h e c a s e of t h e r e s i s t i v i t y of aluminum c a n n o t b e d e s c r i b e d a t 4 K. T h i s makes t h a t d e v i a t i o n s from Matthie- by a s i n g l e power of T. below T = 2 K, p(T) can be s e n ' s r u l e become a p p a r e n t a t t h e h i g h e r tempera- e x p r e s s e d by a sum of a q u a d r a t i c term and a term t u r e s ( F i g u r e l a ) . a p p r o a c h i n g T ~ : p(T) = A T ~ + B T ~ T < 2 K The q u a d r a t i c t e r m d o e s n o t depend on t h e i m p u r i t y c o n t e n t o r s i z e of t h e samples. P a r t o f t h i s work h a s b e e n s u p p o r t e d by t h e " S t i c h t i n g v o o r Fundamenteel Onderzoek d e r M a t e r i e " (FOM) w i t h f i n a n c i a l s u p p o r t from t h e "Nederlandse O r g a n i s a t i e v o o r Z u i v e r W e t e n s c h a p p e l i j k Onderzoek" (ZWO)
.
R e f e r e n c e s 20 40 60 T 3 IK'I / l / S e n o u s s i , S. and Campbell, I . A . , J - P h y s . F : Metal Phys.3
(1973) L19. F i g . l a5
( f ~ r n / ~ ' ) TAT F i g . IbF i g . I , a and b : Ap/T.AT v e r s u s T~ f o r f o u r alumi- num samples :
/ 2 / G a r l a n d , J . C . and Bowers, R . , Phys. Kondens. M a t e r i e
2
-(1969) 36.1 3 1 Garland, J . C . and Van H a r l i n g e n , D . J . , J.Phys. F : Metal Phys.
5
(1978) 117.1 4 1 Lawrence, W.E. and W i l k i n s , J.W., Phys. Rev.
3
(1972) 4466.151 Lawrence, W.E. and W i l k i n s , J.W., Phys. Rev. B7 (1973) 2317.
/ 6 / Kaveh, M. and Wiser, N . , Phys. L e t t e r s
2
(1975) 89.1 7 1 Landau, L. and Pomerantschuk, I., Phys. Z. Sowjet
10
(1936) 649.0 sample 1 RRR: 29000; d i a m e t e r : 1.4 mm sample 2 . RRR: 41000; d i a m e t e r : 3.0 m
+ sample 3 RRR: 21000; d i a m e t e r : 3.0 mm
