Short Notes K95

phys. stat. sol. (b) 5 l , K95 (1972)

Subject classification: 8; 2 1 . 3

Laboratoire de Physique du Solide, E.N.S. M, I. M., Laboratoire associ6 au C.N.R.S., Nancy

Electronic Thermal Resistivity of Cadmium

BY

G. TOUSSAINT and P. PECHEUR

Using the Ziman-Baym theory (1) , we calculated the thermal resistivity of

cadmium parallel and perpendicular to the c-axis. In this method, the Fermi surface

is taken to be spherical; in which case the anisotropy comes only from the phonon

spectrum and the geometry of the umklapp processes. Such a calculation has already

been made for the electrical resistivity (2 , 3) with reasonable success in the case

of cadmium, magnesium, and zinc.

We used the simplest trial function O ( ? ) = (EK - EF)E ' d (1) and a s in the

case of the electrical resistivity, the calculation is reduced to a single integration

over the phonon wave vector.

We obtain for the thermal resistivity along the direction of unit vector d

The notation a re the same as those of (2 to 4). A s in (2) we used the pseudopo-

tential form factor of Allen and Cohen (5) , and the same phonon spectrum (6). 2

can be neglected and 'we

recover the Wiedemann-Franz law. Terms in (%w/kT) which appear in the calculation

have been neglected.

At high temperature all terms which contain (%o/kT) 5

K96 physica status solidi (b) 51

A A A /------------- I 1

Y I * * c

Fig. 1 Fig. 2

Fig. 1. Thermal resistivity of Cd parallel and perpendicular to the c-axis ,

Fig. 2 . Contribution of N and U processes to the resistivity

experimental points from (7)

The results of numerical calculations a re given in the figures. One notes that:

i) The theoretical values a re lower than the experimental ones, a s in the case

of electrical resistivity, which could be explained, at least in part, by the uncer-

tainties of the pseudopotential form factor (2).

ii) The deviation from the Wiedemann-Franz law occurs in the right temperature

rallge.

iii) The N processes contribution is always weaker than that of the U processes

(at most l/lOth) , so that their strong variation with T is not observed experimentally.

iiii) At low temperature, the anisotropy of the U processes has been shown to have

a great importance in transport phenomena (8), so the use of higher hexagonal har-

monics in the trial function is required to get a valuable estimate of the anisotropy

ratio in this model. This work i s in progress,

Short Notes K97

References

(1) J.M. ZIMAN, Electrons and Phonons, Clarendon P r e s s , Oxford 1960.

G. BAYM, Phys. Rev. 135, 1691 (1964). (2) G. TOUSSAINT and P. PECHEUR, phys. stat. sol. (b) 48, K109 (1971). (3) P. PECHEUR and G. TOUSSAINT, to be published.

(4) E. BORCHI, S. DE GENNARO, and P.L. TASSELLI, phys. stat. sol. (b) 9, 489 (1971).

(5) P .B. ALLEN and M.C. COHEN, Phys. Rev. 187, 525 (1969).

(6) G. TOUSSAINT, Thesis, to be published.

(7) R. BOGAARD and A.N. GERRITSEN, Phys. Rev. B3, 1808 (1971). (8) Y. KAGAN and A.P. ZHERNOV, Soviet Phys. - J. exper. theor. Phys. 33, 990

(1971).

(Received March 23, 1972)