Phonon dispersion relations, phase transitions, and thermodynamic properties of ZrSiO4:: Inelastic neutron scattering experiments, shell model, and first-principles calculations

Zircon, ZrSiO4, is a geophysically important mineral for which a knowledge of the phonon spectra and interatomic potentials would be very useful for modeling the thermodynamic properties at high temperatures and high pressures. We have carried out extensive inelastic neutron scattering experiments on zircon which extend previous phonon measurements to several branches not yet studied, in particular at high energy transfer up to 85 meV. First principles density functional perturbation theory calculations of the phonon dispersion relations have been completed and found to be in agreement with the measurements. The experimental data of the phonon frequencies and the crystal structure have been used to refine an interatomic potential with a lattice dynamical shell model. The shell model calculations produce a very good description of the available data on the phonon density of states measured on a polycrystalline sample. The model is used further to calculate the structure, dynamics, and the Gibb's free energy as a function of pressure, in the zircon and scheelite phases. The free energy calculation reproduces the stability of the scheelite phases above 10 GPa as compared to the zircon phase.