On the Statistical Mechanics of the Ideal Inert Gas Solids

Results are reported of machine calculations of specific heat and Gruneisen's γ and their variation with temperature for a face-centred cubic solid. Estimates are also made for the elastic constants of a polycrystal at 0 °K. The harmonic approximation is employed and Houston's method, as developed by Horton and Schiff in 1959, is applied to a model assuming central forces derivable from a Mie-Lennard-Jones m-6 potential. Dispersion curves are obtained for six different lattice directions. A systematic investigation is made of the effects of varying the value of m and of the number of interacting neighbours for each of the inert gas solids Ne, Ar, Kr and Xe. The potential parameters are in each case determined from experimental values of lattice constant and sublimation energy and the often neglected importance of this part of the calculation is demonstrated. The result of neglecting zero point energy in expanding the lattice is also investigated and is found to lead to appreciable error. A limited assessment of the effect of anharmonicity, made by using the potential parameters suggested by Domb and Zucker in 1956, indicates that this may be small at low temperatures. A comparison is made with experimental specific heat data in the case of Ar and Kr and best agreement found using a model involving only limited neighbour interactions. The implications of the results for the validity of the model are discussed.

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