Abstract
The sphericalisation approximation in the cell model of a crystal is investigated for the three cubic lattices and various inverse power potential functions. It is shown that for most purposes the approximation is a good one. The contributions to various properties of the inert gas solids Ne, A, kr and Xe of a long-range three-body force of the form given by Axilrod and Teller are calculated. It is shown that the three-body lattice energy is not negligible in these solids and that the three-body force contribution to the harmonic zero point vibrational energy is of the same order of magnitude as, but opposite in sign to, the two-body anharmonic energy. The elastic constants C[11], C[12] and related elastic properties are calcu- lated at the absolute zero assuming only two-body forces. A second calculation is then presented in which the three-body force is included. It is shown that the quantity B = (C[44]-C[12])C[12][-1] which is always positive when calculated with only two-body forces is reduced when the three-body interaction is included. In the cases of A, kr and Xe B in fact becomes negative. It should be possible to test this experimentally and if B were found negative this would provide strong evidence for the existence of three-body forces. The zero point vibrational and free energy at finite temperatures are calculated using the Bethe approximation. The harmonic and quartic anharmonic energies are in good agreement with the results of standard lattice dynamical methods. However the cubic and some of the non-leading anharmonic terms appear to he less accurately determined. The zero point energy results are applied to the inert gas solids to investigate various crystal models. The hulk moduli are also determined at 0 K. All the investigations indicate that three-body forces play an important role in determining the theoretical properties of the inert gas solids, especially anisotropic properties.