Anisotropic elasticity, sound velocity and thermal conductivity of TiO ₂ polymorphs from first principles calculations

We have investigated the anisotropies in mechanical properties, sound velocity and thermal conductivity of seven TiO₂ polymorphs using the computed elastic constants by PBEsol functional. The computed equilibrium lattice constants in this work are in agreement with those experimental values. We plot the planar contours of Young's moduli and sound velocities of TiO ₂ structures at several crystallographic planes to reveal their anisotropic properties. The minimum thermal conductivities of them are calculated using either Cahill-Pohl model or Cahill model. Our results imply that TiO₂ polymorphs have strong anisotropic elasticity, but they exhibit weak anisotropies in sound velocities. Otherwise, Cahill-Pohl model gives reasonable estimations for the minimum thermal conductivities for amorphous TiO₂ structures. The anisotropy in sound velocity revealed by Christoffel equation can be considered as a good starting point for investigating the anisotropy of lattice thermal conductivity in a crystalline material.