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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

‡ Phys. Rev. 43 (1933), 804.CrossRefGoogle Scholar

† Cf., for instance, Sommerfeld, and Bethe, , Handb. d. Phys. 24/2 (1933), 548et seq.Google Scholar

‡ Cf. Mott, and Massey, , loc. cit. p. 230.Google Scholar

† Cf. Mott, and Massey, loc. cit. Ch. II.Google Scholar

‡ Loc. cit. Ch. VII.

† Cf. Sommerfeld, and Bethe, , loc. cit., and Zener, Nature, 132 (1933), 968.Google Scholar

‡ Ann. d. Phys. 15 (1932), 219.Google Scholar

§ Meier, , Ann. d. Phys. 31 (1910), 1017.CrossRefGoogle Scholar

║ Forsterling, and Freederichsz, Ann. d. Phys. 40 (1913), 201.CrossRefGoogle Scholar

Hagen, and Rubens, , Ann. d. Phys. 40 (1913), 201.Google Scholar

** Mott, and Zener, , Proc. Camb. Phil. Soc. 30 (1934), 249. Cf. the table on p. 262.CrossRefGoogle Scholar

‡‡ Proc. Roy. Soc. A, 151 (1935), 585.CrossRefGoogle Scholar

† Cf. Mott, , Proc. Phys. Soc. 46 (1934), 680, for other examples of the same kind.CrossRefGoogle Scholar

‡ Fuchs, , Proc. Roy. Soc. A, 151 (1935), 585.CrossRefGoogle Scholar

§ 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.

† Proc. Roy. Soc. A, 141 (1930), 225.Google Scholar

† Loc. cit.

‡ Proc. Camb. Phil. Soc. 23 (1927), 542.CrossRefGoogle Scholar

§ Zeits. f. Phys. 48 (1928), 73.CrossRefGoogle Scholar

† Cf. Wentzel, , Zeits. J. Phys. 40 (1927), 590.CrossRefGoogle Scholar