A potential model for fluorapatite

For the mineral fluorapatite, Ca₁₀(PO₄)₆F₂, a potential model of the polarizable ion type has been developed in order to reproduce the following physical constants: the vibrational frequencies (transverse and longitudinal), the elastic constants and the static and high frequency dielectric constants. The parameters of the model are short range force constants, ionic charges and ionic polarizabilities. The polarizable ion model was built up in three stages in order to facilitate comparison with simpler models. In the first stage a short range valence type model was set up, assuming interaction up to a distance of 3.5 Å. In the second stage this model was extended to a rigid ion model by the addition of long range Coulomb forces. In the third stage, which resulted in the polarizable ion model, the polarizabilities of the ions were also taken into account. There was good agreement between calculated and observed data. This demonstrates that even for a crystal structure as complicated as that of fluorapatite with 42 atoms per unit cell a potential model can be constructed which reproduces in a satisfactory way the above-mentioned physical constants.