Elastic and mechanical properties of hydroxyapatite under pressure: A first-principles investigation

The structural, elastic, and mechanical properties of hydroxyapatite (HAp) were investigated by generalized gradient approximation (GGA) in the functional form by Perdew, Bruke, and Ernzerhof (PBE) exchange-correlation functional using density-functional theory. Our calculated equilibrium lattice parameters at ambient pressure are in good agreement with the experimental and previous theoretical results. The details of the structural, mechanical, and electrical properties such as elastic constants, bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratioν, Cauchy pressure, shear anisotropic factor A, and total density of states under pressure ranging 0 GPa to 10 GPa are studied. The lattice parameters a and c are found to be decreased with increasing pressure. Moreover, the lattice parameter a is more sensitive to external pressure than c. The calculated elastic constants of hexagonal HAp increase with increasing pressure. The elastic constants C11 and C33, which represent the elasticity in length are larger than the elasticity in shape, which represent by the elastic constants C12, C13, C44, and C66. The deformation resistances along the axial direction are stronger than the deformation resistances in shape. The calculated B/G, Poisson’s ratio ν, and Cauchy pressure show that the hexagonal HAp behaves as a ductility material at ambient pressure and has more ductile under pressure. While the calculated shear anisotropic factor A indicate that the HAp shows elastic anisotropy under pressure. Moreover, calculated total density of states (DOS) show that HAp becomes more insulator property with increasing pressure.