On the Theory of Thermal Conductivity of Monovalent Metals

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Abstract
Sondheimer's theory of thermal conductivity contradicts in two points with experimental results. i) The theoretical values of the conductivity at low temperatures are too small compared with experimental values. ii) At intermediate temperatures, the theory predicts the existence of a minimum of the conductivity which is not observed. We criticize Sondheimer's theory in several points, and confining ourselves only to the problem of thermal conductivity, we obtain on a new basis satisfactory results. The main results are as follows: i) Bloch's hypothesis that the phonon system is in thermal equilibrium in all temperature regions is applicable in the case of thermal conductivity. ii) Sondheimer solved Bloch equation by expanding C(ε) in a power series of ε, but this type of function does not give a correct solution in the case of the second order phenomena. By using a more reasonable variational function, we obtain a more correct lower limit of thermal conductivity which is about 20% larger than Klemens' result. Further, we obtain an upper bound by a certain method and thus determine the bounds of the correct solution. iii) By considering exchange field and correlation field, it is shown that the method of self-consistent field gives fairly large resistivity at high temperatures. The ratio C/ζ becomes 1.22. By this effect, the theoretical values of thermal conductivity becomes more consistent with experimental values, and the minimum of the conductivity at intermediate temperatures disappears. iv) Debye temperature determined by comparing with experimental values agrees very well with the Debye temperature of longitudinal sound waves calculated by Toya.

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