Atomistic simulations of mixing properties and the local structure of the (Ca, Sr)10[PO4]6F2 solid solution

Abstract

The thermodynamics of mixing is computed for eight different distributions of Sr and Ca over the M1 and M2 cation sites in the fluorapatite solid solution. Calculations are carried out for a 4×4×4 supercell via the semi-empirical approach using the GULP package. In the solid solution with the most energetically favorable distribution, Sr tends to occupy the M2 site rather than the M1 site and the x (Sr1): x (Sr2) ratio varies as a function of the Sr content. These structures are used for further investigation of the effect of mixing on the lattice parameters, local structure and elasticity of the Ca-Sr fluorapatite solid solution. Changes in the Sr2-F bond lengths as the Sr content increases turn out not to comply with Vegard’s rule. However, this deviation occurs in order to keep the linear dependence of the polyhedral volumes with the solid-solution composition. The obtained data allow us to estimate the structural relaxation parameters for both independent cation positions. Analysis of the bond sums also backs up the preference of Sr cations for the M2 site.