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The thermal conductivity of metals

Published online by Cambridge University Press:  24 October 2008

R. E. B. Makinson
R. E. B. Makinson
Affiliation:
St John's College
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Extract

The methods used to measure separately the electronic and lattice heat conductivities κe and κg in a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κe and for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratio Le = κe/σT as a function of T, both for the monovalent metals and for a model metal with 1·8 × 10−2 conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κe and κg as functions of T are given in both cases, and these, together with a comparison of the observed Lorentz ratio and Le, show that in the monovalent metals κg is unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth.

Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls.

The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 3 , July 1938 , pp. 474 - 497
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

* E.g. Gruneisen, and Reddemann, , Ann. d. Physik (5), 20 (1934), 843.CrossRefGoogle Scholar

* Eucken, and Neumann, , Zeit. Phys. Chem. 111 (1924), 431.Google Scholar

† Reddemann, , Ann. d. Physik (5), 20 (1934), 441.CrossRefGoogle Scholar

‡ Wilson, A. H., The theory of metals (Cambridge 1936), referred to as IGoogle Scholar.

* Mott, and Jones, , Properties of metals and alloys (Oxford 1936), pp. 213, 317.Google Scholar

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

* Ann. d. Physik (5), 4 (1930), 121,Google Scholar also 5 (1930), 244 and 12 (1932), 154.

† Sommerfeld, and Bethe, , Handbuch der Physik, 2nd ed., vol. 24, pt 2, pp. 545 et seq.Google Scholar

* Inst. Physical and Chemical Research (Tokyo), 34 (1938), 194.Google Scholar

* Wilson II, equation (17).

* Thompson, N., Proc. Roy. Soc. A, 155 (1936), 111.CrossRefGoogle Scholar

* Kohler, , Ann. d. Physik (5), 31 (1938), 116.CrossRefGoogle Scholar

† Gruneisen, and Goens, , Zeit. f. Physik, 44 (1927), 615.CrossRefGoogle Scholar

‡ Physica (2), 1 (1933–1934), 929.Google Scholar

* Lees, , Proc. Roy. Soc. A, 80 (1907), 143CrossRefGoogle Scholar; Handbuch der Metallphysik, 1, 378.Google Scholar

† de, Haas and Biermasz, , Physica (2), 3 (1936), 672.Google Scholar

‡ Loc. cit. p. 871; Reddemann, loc. cit. p. 444.

* E.g. Wilson I, p. 202.

* Loc. cit. p. 547. In his equation (42·10) corresponding to (18) the term hνK 2/q 2E does not appear and the energy denoted by C is to be replaced by in the present notation.

† Ann. d. Physik (5), 3 (1929), 1055.Google Scholar

* Loc. cit. (1929); Ann. Inst. H. Poincaré, 5 (1935), 177.Google Scholar

† Phil. Mag. 19 (1935), 989.Google Scholar

* Bethe, loc. cit., obtains a limit of that given by (31), due to neglect of the transverse waves.

* Physica (2), 2 (1935), 673Google Scholar and 1 (1938), 47.

† Loc. cit. (1929).

‡ Physica (2), 4 (1938), 320.Google Scholar

* E.g. Wilson I, p. 202.

† Cf. Wilson II, equations (3), (8), (19), where the term in b(|z|) does not appear since b(z) is supposed to be zero.

* Loc. cit. II.

* Wilson, loc. cit. II, equation (11).