Theory of the Anharmonic Properties of Solids

Abstract

A theory is presented with which one can calculate the anharmonic properties of solids such as thermal expansion, temperature dependence of elastic constants, dependence of elastic constants under stresses, and the deviation of the specific heat from the Dulong-Petit law at high temperatures. The theory is applied to sodium under the assumption of a special force interaction between nearest neighbors only. In the approximation used, three parameters enter. The three parameters are obtained from experimental measurements of the elastic constants near 0\ifmmode^\circ\else\textdegree\fi{}K, the temperature dependence of the compressibility, and the thermal expansion. Then the variation of the volume with pressure and the deviation of the specific heat from the Dulong-Petit law at high temperatures are calculated. A satisfactory agreement with experiment is obtained. Another prediction of the theory, that the temperature derivative of the compressibility is proportional to the specific heat, also shows satisfactory agreement with the experimental measurements for sodium.