A quantum theory of thermal dilatation in solids

A new approach to the theory of thermal dilatation for a solid is presented. Because of the presence of anharmonic terms in the crystal Hamiltonian, it is shown that every atom becomes a centre of expansion, applying to its neighbours a distribution of radial forces that, in principle, can be evaluated when the interatomic potential is known. The corresponding change in volume is obtained using a result given by Eshelby. The theory is specialized to a Debye model, by which a very simple formula for the high temperature limit of the Gruneisen constant can be obtained. The result is applied to a crystal of solid argon and a fair agreement between theory and experiment is achieved.