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The second order electrical effects in metals

Published online by Cambridge University Press:  24 October 2008

A. H. Wilson
A. H. Wilson
Affiliation:
Trinity College
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Extract

The theory of transport phenomena in metals depends upon the solution of an integral equation for the velocity distribution function f of the conduction electrons. This integral equation is formed by equating the rate of change in f due to external fields and temperature gradients to the rate of change in f due to the mechanism which produces the resistance. If this latter rate of change is denoted by [∂f/∂t]coll it happens with some mechanisms that

where f0 is the equilibrium distribution, and ℸ is the time of relaxation which does not depend on the external fields. When equation (1) is true, the problem is comparatively simple, but in general [∂/∂t]coll is an integral operator and it is not possible to define a time of relaxation and a free path. It is known that at high temperatures, such that (Θ/T)2 can be neglected, where Θ is the Debye temperature, a free path exists; but, in general, special methods have to be used to solve the integral equation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 3 , July 1937 , pp. 371 - 379
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

* Die Quantenstatistik (Springer, 1931), p. 357.Google Scholar

† Conductibilité. électrique et thermique des métaux (Hermann, 1934), p. 50.Google Scholar

‡ Zeit. f. Physik, 59 (1930), 208.Google Scholar

* Kroll, , Zeit. f. Physik, 80 (1933), 50,CrossRefGoogle Scholar and 81 (1933), 425.

† This and the other formulae required are given by Wilson, A. H., The theory of metals (Cambridge, 1936), pp. 215–18.Google Scholar

* Wilson, loc. cit. p. 208.

* Wilson, loc. cit. equation (250).

* Proc. Roy. Soc. A, 153 (1936), 699.Google Scholar

* Wilson, loc. cit. p. 223.

* Keesom, and Matthijs, , Physica, 2 (1935), 623.CrossRefGoogle Scholar