Abstract
Some general results for thermoelastic quantities are derived by considering a solid in different states of strained reference frames. It is shown that simple relationships hold between the nth order and the volume derivatives of (n-1)th order elastic constants. Explicit expressions for these results are obtained for a cubic solid. The contribution to thermoelastic properties of the inert gas solids Ne, A, Kr and Xe for long-range three-body forces of the form given by Axilrod and Teller are calculated. The second order elastic constants C[ij] and the third order elastic constants C[ijk] are calculated at the absolute zero assuming only two-body forces. The approach employed here was not the standard lattice dynamical methods. Instead, an Einstein model modified for anisotropic effects and including correlation as a perturbation was used. This model was found to be more flexible than the standard lattice dynamical approach. Where possible comparision with standard lattice dynamical methods was made. It is shown that although both, the three-body forces and the two-body zero-point effects violate the Cauchy relations they do so in opposite sense. In the case of some of the it is found that contributions due to three-body forces and two-body zero-point effects are often larger than the classical two-body contributions and differing in sign. The calculations of the C[ijk] have further shown that in a certain instance it is possible to distinguish between the contributions of the 3-body forces and the two-body zero-point effect, which is not possible in the case of the C[ij] A method is presented to calculate in a simple manner the contribution of the zero-point energy and the free-energy at finite teperatures to the elastic constants. In the case of the C[ij] where comparision with refined lattice dynamical method are available, good agreement is found. The method also enabled us to assess the many particle correlation effects.