Vibrational and thermodynamic properties of high-pressure phases in   LiYF_4
  Possible variations in the dynamical behaviour of LiYF$_{4}$ due to its structural changes following several pressure-induced phase transitions are examined by making use of the complementary techniques of quasi-harmonic lattice dynamics and molecular dynamics simulation. The phonon spectra in the entire Brillouin zone and the respective Gibbs free energies are calculated for the three high-pressure polymorphs of LiYF$_{4}$ that are stable at T = 0, with an aim to understand their relative stabilities as functions of pressure and temperature in terms of volume compression and vibrational entropy. Molecular dynamics simulations provide qualitative impressions about a temperature-driven second-order transformation and also of kinetic effects in the subsequent pressure-driven first-order phase transition. In addition, the calculations predict anomalous thermal expansion at low temperature in phases I and IIa while irreversibilty of phase II $\to$ phase III transition on subsequent pressure release. 
A. Sen, S. L. Chaplot and R. Mittal