Determination of interatomic interactions in ${\mathrm{Ca}}_{10}$${\left(\mathrm{P}{\mathrm{O}}_4\right)}_6$${\mathrm{F}}_2$ (fluorapatite) from structural and lattice-dynamical data

In this paper we illustrate a method for determining interatomic interactions in complex ionic crystals by considering specifically a rigid-ion model for fluorapatite. Structural data are the primary input to the model while Raman scattering measurements (reported here) are used to determine seven additional parameters. While point charges are assumed, the values within the P${\mathrm{O}}_4^{-3\mathrm{}}$ group are adjusted to account for covalency and compensate for neglecting dipole terms in the oxygen-ion charge distribution. The computed phonon frequencies are in remarkably good agreement with values obtained from both Raman and infrared measurements.