Elasticity of Mg₃Bi_2-xSb_x

Mg₃Bi_2-xSb_x is a promising thermoelectric material working around room temperatures. Compared to electronic and thermoelectric properties, its mechanical properties are of great importance in practical applications but much less understood. Herein, we have systematically studied the elasticity of Mg₃Bi_2-xSb_x by means of first-principles calculations with a large supercell of 40 atoms. We demonstrated that the 10-atom-unitcell is undersized with improper electronic structures. With the elastic constants, we have explored the comprehensive elastic features and the three-dimensional distribution of fundamental characteristics of Young's modulus and Poisson's ratio and their variation with respect to the Sb content x. We interpolate the variation in terms of the valence electron concentration. We have further examined the hardness, ductility, anisotropicity, and Debye temperatures. The elasticity exhibits strong anisotropy where the maxima are approximately three times larger than the minima for modules. A nearly linear dependence is also observed on the Sb content except x in the vicinity of 0.5. Our atomistic insights on elasticity might be helpful in the material design of thermoelectrics with desirable mechanical properties. Our work could serve as a map for tuning the mechanical properties of Mg₃Bi_2-xSb_x and guide the possible synthesizing of novel thermoelectric material.