Elastic properties and thermal conductivities of fluor-, chlor- and brom-barium apatites predicted by first-principles simulations

Abstract

First-principles calculations based on density functional theory were employed to investigate the anisotropic elastic properties and thermal conductivities of barium apatite Ba₁₀(PO₄)₆X₂ (X = F, Cl and Br). The bulk, Young’s and shear moduli were predicted. The results of anisotropic indexes and 3-D figures of bulk modulus and Young’s modulus show that the order of degree of elastic anisotropy is Ba₁₀(PO₄)₆F₂ < Ba₁₀(PO₄)₆Cl₂ < Ba₁₀(PO₄)₆Br₂. The thermal conductivities obtained from the Clarke’s model and Cahill’s model reveal that Ba₁₀(PO₄)₆F₂ has the largest thermal conductivity, and Ba₁₀(PO₄)₆Br₂ possesses the smallest one. The anisotropy of thermal conductivity indicates that the thermal conductivity in the (0 0 0 1) plane is larger than that in the plane.

Keywords:

• First-principles calculations
• barium apatite
• elastic anisotropy
• thermal conductivity