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The optical properties of metals

Published online by Cambridge University Press:  24 October 2008

N. F. Mott  and
C. Zener
N. F. Mott
Affiliation:
Gonville and Caius College, Professor of Theoretical Physics, University of Bristol
C. Zener
Affiliation:
Wills Physical Laboratory, University of Bristol
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Extract

Three main stages may be marked in the development of the theory of the optical properties of metals. First, there is Drude's original theory, based on Maxwell's equations; in this theory the current density j at any point in a metal is supposed to be equal to the product of the electric vector of the light and of the conductivity of the metal. The theory yields the well-known Hagen-Rubens formula for the reflecting power, which appears to be in agreement with experiment for very long wave-lengths (λ > 10μ), but leads to completely incorrect results in the optical region. Various investigators ‡ have therefore modified the theory to take account of the finite mass of the electron; the formulae obtained pass over into the Drude formulae for sufficiently long wave-lengths. Finally a quantum theory of the phenomenon has been given by Kronig§, the electrons being treated as moving in a periodic field due to the crystal lattice in the manner originated by Bloch; this theory, in its turn, becomes identical with the modified classical theory if the periodic lattice is neglected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 30 , Issue 2 , 30 April 1934 , pp. 249 - 270
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

* Drude, , Physik des Äthers (1894), 574.Google Scholar

† Cf. for example, Schaeffer, and Massotti, , Das ultrarote Spektrum (Berlin, 1930).CrossRefGoogle Scholar

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* Cf. Born, , Lehrbuch d. Optik (Berlin, 1933), 260.Google Scholar

* Our reasons, mainly empirical, for equating the right-hand side of this equation to n2 − 1 rather than to 3 (n2 − 1)/(n2 + 2) are discussed in § 3.

* Phys. Rev. (1933), 353.Google Scholar

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‡ The method is apparently due in the first place to Drude, Ann. d. Phys. loc. cit.

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* An equivalent statement is that the effective mass is increased.

† This is not, of course, the usual photoelectric threshold, which is the energy required to throw an electron out of the metal.

‡ Loc. cit.

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‡ Bloch actually assumed E to be independent of t. However, in the proof of (11) we need not commute t and E; hence E may be an arbitrary function of time.

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‡ Handbuch der Physik, 2nd ed., 24/2. We are also greatly indebted to Dr R. Peierls, who sent us an alternative proof of this theorem, before Bethe's article appeared.

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For copper and λ = 0.577μ, Lowery, and Moore, (Phil. Mag. 13 (1932), 938CrossRefGoogle Scholar) have obtained, for a freshly polished copper plate, values of | n 2 (1 − k 2) | greater by 70% than those shown in Fig. 4. If the copper plate is left in the air for 24 hours, the value of | n 2 (1 − k 2)| decreases. It is therefore probable that the small value of N′ for Cu is not due to the tight binding of the electrons, but to copper oxide crystals in the surface layer. Thomson, G. P (Proc. Roy. Soc. 128 (1930), 649CrossRefGoogle Scholar) has shown that a freshly polished copper plate gives no rings by electron diffraction, but that after some hours the oxide rings appear.

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† The tail at the bottom of the sharp rise appears to become smaller at low temperatures, as shown by the work of Mohler (Bulletin of Bureau of Standards, 8 (1932), 363Google Scholar) on the transmission of light through thin films.

‡ Cf. Fröhlich, , Zeits. f. Phys. 81 (1933), 297CrossRefGoogle Scholar. n 2k is proportional to the transition probability, not n 2kv 2, as stated by Fröhlich.

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∥ Loc. cit.

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† Loc. cit.

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† Laue, and Martin, , Phys. Zeits. 8 (1907), 853Google Scholar, reflecting power of Pt at high temperatures; Hurst, , Proc. Roy. Soc. 142 (1933), 466CrossRefGoogle Scholar, emissivity of copper in the near infra-red.

‡ Bethe, , Handbuch d. Phys. 24, 2 (1933), 584Google Scholar, has stated that the high value of n 2k is due to the simultaneous excitation of a lattice vibration and of an electron. As he shows, however, such a process is not independent of temperature.

* Beilby, , Aggregation and flow in solids (London, 1921).Google Scholar

† Loc. cit.

‡ Proc. Roy. Soc. 140 (1933), 637.Google Scholar

§ Loc. cit.