Abstract
We report in this paper a panoptic picture of the lattice dynamics for ${\mathrm{LiYF}}_{4},$ on the basis of a rigid ion model. The resulting analysis yields the dispersion of phonon branches in accord with the measured experimental phonon dispersion curves along some of the most important symmetry directions as measured by neutron inelastic scattering. The model is then extended for ${\mathrm{LiYbF}}_{4},$ using suitable parameters corresponding to ${\mathrm{Yb}}^{3+}$ ions. Our calculated results are found to comfortably match the experimental data on Raman as well as IR active phonons and also on various thermodynamic properties in both the crystals.
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