Calculation of the thermal expansion of solids from the third-order elastic constants

Abstract

The thermal expansion of a solid is due to anharmonicity of the interatomic forces. It may therefore be calculated, on the basis of a continuum model, from the observed elastic anharmonicity, i.e. the third-order elastic constants. Using Lazarus' (1949) measurements on the pressure variation of the elastic moduli of several cubic crystals, the Grüneisen γ is calculated for the limiting cases of low and high temperatures. For KCl, NaCl the high temperature values agree with those obtained from thermal expansivities, and a decrease in γ at low temperatures is predicted. However, Lazarus' data on metals cannot be reconciled with the thermal expansions, which suggests that the continuum model is inapplicable to these cases.