Lattice vibrations in high-pressure phases of LiYF$_{4}$
  Possible variations in the dynamical behaviour of LiYF$_{4}$ due to its several structural changes under pressure are examined by making use of the complementary techniques of quasi-harmonic lattice dynamics and molecular dynamics simulations. The phonon spectra in the entire Brillouin zone together with the respective Gibbs free energies are calculated for the three high-pressure polymorphs of LiYF$_{4}$ (that are stable at T = 0) with a view to better understand their relative stabilities as functions of pressure and temperature. The present work predicts anomalous thermal expansion at low temperatures in phases I and IIa while irreversibilty of phase II $\to$ phase III transition on subsequent pressure release. Molecular dynamics simulations provide qualitative impressions about a temperature-driven second-order transition and also of kinetic effects in the subsequent pressure-driven first-order phase transformation. 
A. Sen, S. L. Chaplot and R. Mittal