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The electrical resistance of a metal at low temperatures and Matthiessen's rule

Published online by Cambridge University Press:  24 October 2008

G. P. Dube
G. P. Dube
Affiliation:
Fitzwilliam House
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Extract

By solving the fundamental integral equation an expression is obtained for the electrical resistance which takes into account, to the first approximation, the mutual influence of the impurities and the lattice vibrations. It is found that deviations from Matthiessen's rule are to be expected and that these deviations are surprisingly large. The formulae derived only indicate the trend of the resistance curve, but this trend is not confirmed by experiment. Whereas the theory indicates that the mutual influence of the impurities and the lattice vibrations should decrease the electrical resistance, the experimental results of Grüneisen on copper show that, when deviations from Matthiesen's rule occur, the resistance is increased.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 4 , October 1938 , pp. 559 - 567
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

* Wilson, A. H., The theory of metals (Cambridge, 1936), pp. 159, 219Google Scholar, referred to as I.

* Wilson, I, pp. 215–18.

† Wilson, , Proc. Cambridge Phil. Soc. 33 (1937), 371CrossRefGoogle Scholar, referred to as II.

* This is a particular case of a more general result given by Wilson, II, equation (11).

* Haas, de, Boer, de and Berg, Van den, Physica (2), 1 (1934), 1115.CrossRefGoogle Scholar

† Ann. d. Physik (5), 16 (1933), 530.Google Scholar

* Wilson, II, equation (11).