Equation of state of hexagonal hydroxylapatite (P63) as obtained from density functional theory simulations

Hydroxylapatite is an important calcium phosphate phase whose knowledge is useful in different fields, for instance in bone biology, development of biomaterials and even cultural heritage. In this work, the equation of state of this mineral was calculated by using the quasi‐harmonic approximation, also including for the first time the temperature effect. In athermal conditions (0 K), we found that the pressure dependence of the hydroxylapatite unit cell volume is well described by a third‐order Birch–Murnaghan formulation, with parameters K₀ = 115.9(1), K' = 4.47(6), and V₀ = 524.323(27). The inclusion of temperature led to a lower bulk modulus, for example, KT₀ = 109.55 GPa at 300 K. The thermal expansion coefficient between 0 and 1000 K was also reported. The results are in good agreement with the few available experimental data reported in literature and further extend the knowledge of the mechanical and thermal behavior of this important mineral.