  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.
