Electronic structure, elastic anisotropy, thermal conductivity and optical properties of calcium apatite Ca₅(PO₄)₃X (X = F, Cl or Br)

Highlights: • The degree of elastic anisotropy is ordered as follows BrA > ClA > FA. • The thermal conductivity in (112^¯0) plane is smaller than in (0 0 0 1) plane. • The refractive indexes for FA, ClA and BrA are 1.17, 1.19 and 1.21, respectively. - Abstract: The density-functional theory with the generalized gradient approximation was performed to investigate the structural properties, phase stability, electronic structure, elastic properties, and optical properties of selected Ca₅(PO₃)₄F (FA), Ca₅(PO₃)₄Cl (ClA) and Ca₅(PO₃)₄Br (BrA). Results of formation enthalpies show that FA is regarded as the most stable one in these apatites. The electronic structures including band structure, density of states and Mulliken analysis have been discussed. The predicted elastic moduli results indicate that the degree of elastic anisotropy is ordered as follows BrA > ClA > FA. By using the Clarke's model and Cahill's model, the thermal conductivities and the anisotropy in thermal conductivity have also been analyzed. Optic properties results indicate that the refractive indexes n for FA, ClA and BrA are 1.17, 1.19 and 1.21, respectively