  We report a lattice dynamics study of relative stability of various phases of
natural silicates MSiO4 (M=Zr, Hf, Th, U) as a function of pressure (P) and
temperature (T), which is important in the context of their use in nuclear
waste storage media. Extending our previous work on ZrSiO4, the Gibbs free
energy has been calculated using a transferable interatomic potential in
various phases over a range of P and T. Due to an interesting interplay between
the vibrational entropy and atomic packing, the zircon (body centered
tetragonal, I41/amd), scheelite (body centered tetragonal, I41/a) and huttonite
(monoclinic, P21/n) phases occur at different P and T. It is shown that for
ThSiO4 at high P, the huttonite and scheelite phases are favored at high and
low T respectively. However, for both USiO4 and HfSiO4 the huttonite phase is
dynamically unstable and the scheelite phase is stable as the high pressure
phase. In fact, the calculations reveal that the stability of the huttonite
phase is determined by the ionic size of the M-atom; this phase is unstable for
the silicate with the smaller Hf and U ions and stable with the larger Th ion.
The calculated phase diagrams are in fair agreement with the reported
experimental observations. The calculated structures, phonon spectra, and
various thermodynamic properties also fairly well reproduce the available
experimental data. The low-energy phonons in the huttonite phase that
contribute to its large vibrational entropy are found to involve librational
motion of the silicate tetrahedral units.
