Revealing the elastic properties and anisotropies of Mg2X(X = Si, Ge and Sn) with different structures from a first-principles calculation

The elastic constants and modulus, elastic anisotropy, Debye temperature, and sound velocity properties of hP6- and cF24-Mg2X (X = Si, Ge, and Sn) compounds were investigated by first-principles calculations, and a comparison with cF12-Mg2X was performed. By employing the stress-strain method and Voigt-Reuss-Hill approximation, we calculated the elastic properties of single and polycrystalline crystals, respectively. The calculated Poisson's ratio v, G(H) / B-H and Cauchy pressure PCauchy values indicate that cF12-Mg2X is brittle, while hP6- and cF24-Mg2X are ductile. The elastic anisotropy of Mg2X (X = Si, Ge and Sn) is estimated by several elastic anisotropy indices, three-dimensional surface constructions and projections of Young's, shear and bulk modulus. The elastic anisotropy of Mg2X (X = Si, Ge and Sn) is in a sequence of cF24 > hP6 > cF12. Finally, Debye temperature and the directional sound velocity were obtained from the elastic constant and the modulus conversion, respectively.