Anharmonic contributions to the helmholtz free energy of a simple crystal model: High-temperature limit and zero-point energy

The leading anharmonic contributions to the Helmholtz free energy of face-centred cubic crystals have been considered on the basis of the nearest-neighbour central-force model. Results of computer calculations of these contributions at T = 0 °K and at the high-temperature limit are presented for six values of a 1 , essentially the ratio of the first to second radial derivative of an arbitrary interatomic potential energy. Our work depends on the potential parameters a 1 , ϕ", a 3 and a 4 , which are related to the first up to fourth potential derivatives. For a specified form of the interatomic potential energy our results yield the volume dependence of anharmonic effects. Chiefly for illustrative purposes, results are given for the m -6 Mie-Lennard-Jones potentials and some of the inert gas solids. The high-temperature anharmonic effect is found to vary considerably over the range of volumes studied. It is pointed out that, perhaps for the inert gas solids, anharmonic effects to a higher order than the first are appreciable We have examined the work of Ludwig, Lloyd, Barron and Wallace and compared their results with ours. The leading-term approximation of Maradudin et al . is quite unreliable except for the calculation of the total groundstate energy and C p , where we show that it is very good owing to an unexpected cancellation in the coefficients of the neglected terms when the force constants are defined with respect to the volume for which the static lattice energy is a minimum.