The volume dependence of the Grüneisen parameter and crystal stability

Utilizing only the general features of the lattice structure and potential, the explicit volume dependence of the entire frequency spectrum is derived in terms of its zero pressure values. It is shown that even though the frequencies and the mode Grüneisen parameters depend on the various details of the interactions and lattice structure, their variation with volume can be relatively simple functions of the volume. A criterion for mode instability with pressure is established involving only the measured value of γ(kλ). The volume dependence of the high temperature Grüneisen parameter is derived utilizing the characteristics of the full frequency spectrum through the first two moments of the mode gammas and the results are applied to the alkali-halides.