New insight into the structural, elastic, dynamics and thermodynamic properties of Fe₃P under high pressures

Many efforts have been devoted to developing the linkage between atomic characteristics and the mechanical properties. Equilibrium lattice parameters, elastic constants, dynamics and thermodynamic properties of Fe₃P are systematically explored by density functional theory (DFT) calculations with a generalized gradient approximation (GGA) from Perdew-Wang's 1991 (GGA-PW91), Perdew-Burke- Erzenhof (GGA-PBE), local density approximation (LDA), GGA-PW91+U, GGA-PBE + U and (LDA) + U method (U is the Hubbard correction), respectively. It concluded that the lattice parameters and bulk modulus B from GGA-PBE + U results tend to be more compatible with experimental results than others. The elastic moduli of Fe₃P is reported based on the Voigt-Reuss-Hill model. Meanwhile, the anisotropy index and the three dimensional (3D) surface profile of Young's modulus determine the anisotropy. The obtained results indicate that Fe₃P exhibits strong elastic anisotropy under high pressure. In addition, the dynamical and mechanical stabilities of Fe₃P are confirmed by calculating the phonon and elastic constants up to 40 GPa. Finally, we studied the thermodynamic properties of Fe₃P under pressures based on quasi-harmonic approximation.