Structural and anisotropic elastic properties of hexagonal MP (M = Ti, Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M=Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young's modulus E and Poisson's ratio were calculated by Voigt-Reuss-Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP>HfP>TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke's model and Cahill's model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.