Theoretical predictions of elastic anisotropies and thermal properties of TMRe2 (TM=Sc, Y, Zr and Hf)

Elastic anisotropy and thermal properties of hexagonal TMRe2 (TM = Sc, Y, Zr and Hf) were predicted by first-principles calculations. Elastic moduli were calculated from the single-crystal elastic constant (Cij) by Voigt-Reuss-Hill approximations. The theoretical Vickers hardness was calculated from elastic modulus. By calculating the anisotropic indexes, 3D surface constructions and projections of elastic modulus, the sequence of anisotropy in elastic modulus is YRe2 > ScRe2 > ZrRe2 > HfRe2. Moreover, Debye temperature is in a sequence of ScRe2 > HfRe2 > ZrRe2 > YRe2, indicating that ScRe2 has the strongest chemical bonds and the greatest thermal conductivity. By calculating the sound velocities in different directions, it is concluded that these TMRe2 compounds are anisotropic in sound velocities.