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The Electrical Resistance of Dilute Solid Solutions

Published online by Cambridge University Press:  24 October 2008

N. F. Mott
N. F. Mott
Affiliation:
Professor of Theoretical Physics, University of Bristol
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Extract

1. As is well known, the electrical resistance of a metal is very greatly in-creased by the addition of a second metal with which it forms a solid solution. The increase Δρ in the resistivity due to the addition of a small percentage of the second metal is in general independent of the temperature (Matthiessen's rule), though there are oertain exceptions (e.g. Cr in Au). The quaritum-mechanical explanation of both these facts was first given by Nordheim, and may be expressed as follows: the electrical conductivity of any metal may be written in the form

where τ is the “time of relaxation”, equal to half the time between collisions, and N is the effective number of free electrons per unit volume: hence, for the resistivity, we have

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 32 , Issue 2 , May 1936 , pp. 281 - 290
Copyright
Copyright © Cambridge Philosophical Society 1936

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References

† Ann. d. Phya. (5), 9 (1931), 607.Google Scholar

† Zeits. f. Phys. 45 (1927), 307. Cf. also Mott and Massey, The theory of atomic collisions, Ch. II.CrossRefGoogle Scholar

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‡ Loc. cit. Ch. VII.

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§ Unpublished; I wish to thank Miss Littleton for carrying out the calculations, and Prof. Hartree for providing us with the field before publication.

‖ Loc. cit.

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† Loc. cit.

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