通过基于密度泛函理论的第一性原理计算方法, 对Mg₂Sn, Mg₂Ca和MgZn₂的结构稳定性、电子结构和弹性性质进行了计算, 计算所得晶格参数与实验值和文献计算值吻合.合金形成热和结合能的计算结果表明, Mg₂Sn具有最强的合金形成能力和结构稳定性.通过对Mg₂Sn, Mg₂Ca和MgZn₂的电子态密度(DOS)和差分电荷密度进行计算,分析了其结构稳定性和弹性性质的机制. 计算了Mg₂Sn, Mg₂Ca和MgZn₂的弹性常数,推导了体模量B_u, 剪切模量G, Young's模量E和Poisson比ν的数值, 结果表明, Mg₂Sn为脆性相,Mg₂Ca和MgZn₂为延性相, Mg₂Sn的刚度最大, MgZn₂的塑性最好.

Electronic structure and elastic properties of Mg₂Sn, Mg₂Ca and MgZn₂ phases were investigated by means of first-principles calculations from CASTEP program based on density functional theory (DFT). The calculated lattice parameters were in good agreement with the experimental and literature values. The calculated heats of formation and cohesive energies show that Mg₂Sn has the strongest alloying ability and structural stability. The density of states (DOS) of Mg₂Sn, Mg₂Ca and MgZn₂ phases were calculated to analyze the mechanism of structural stability and mechanical properties. The calculated band structures show that Mg₂Sn phase has the widest bandgap. The electron density difference indicate that bonding characteristics of Mg₂Sn, Mg₂Ca and MgZn₂ phases were all covalent bond, ionic bond and metallic bond. The elastic constants of Mg₂Sn, Mg₂Ca and MgZn₂ phases are calculated, the bulk moduli, shear moduli, Young's moduli and Poisson's ratio are then derived. Bulk moduli is assumed to be the ability of material resistance to volume change by applied stress, the larger bulk modulus of MgZn₂ phase shows that it has stronger ability to resist deformation. Shear moduli is a measure of resistance to shear strain deformation under the deformation condition of shear stress, the larger shear moduli value of Mg₂Sn phase indicates that it has the stronger ability to resist shear strain deformation. The calculated Poisson's ration shows that MgZn₂ has the largest value, and then followed by Mg₂Ca and Mg₂Sn. Hence, the plasticity of MgZn₂ phase is the best. The calculated Young's moduli of Mg₂Sn phase has the largest value and MgZn₂ phase has the smallest value. Hence, among the three phases Mg₂Sn phase has the strongest stiffness. The ratio of the shear moduli to bulk moduli of phase can be used to demonstrate the brittle and ductile of materials. The critical value, which separates ductility from brittleness, is about 0.57. A higher G/B_u value is associated withbrittleness, otherwise is ductility. The calculated values of Mg₂Sn, Mg₂Ca and MgZn₂ phases are 0.66, 0.53 and 0.18, respectively. The results show that Mg₂Sn is brittle, Mg₂Ca and MgZn₂ are both ductile.