立方Mg_(3)P_(2)弹性性质的理论计算研究

Theoretical calculation of elastic properties of cubic Mg_(3)P_(2)

在密度泛函理论(DFT)的基础上,通过第一性原理计算方法在理论上研究了磷化镁(Mg_(3)P_(2))立方Ia3相的弹性性质。运用应变能-应变(E-S)和应力-应变(S-S)两种计算方法获得了立方Ia3 Mg_(3)P_(2)的单晶独立弹性常数和弹性柔顺常数。S-S方法与文献值吻合更好,在此方法的基础上获得了其多晶弹性模量,如弹性模量E、剪切模量G等,还获得了B/G、泊松比、各向异性因子等一系列物理参数。表明立方Ia3 Mg_(3)P_(2)是处于力学稳定状态,同时反映出其具有韧性的特点。表示弹性性质对晶体方向依赖性的杨氏模量及线性压缩系数等的三维曲面图像直观反映出立方I a3 Mg_(3)P_(2)的各向异性程度较弱与各向异性因子反映出的信息一致。此外,计算了Ia3 Mg_(3)P_(2)的德拜温度及不同方向上的声速,结果给出Ia3 Mg_(3)P_(2)原子间作用力弱,且在零温零压下,纵波沿[111]方向传播最快,横波沿[110]方向最慢。

In this paper,on the basis of density functional theory(DFT),the elastic properties of cubic Ia3 phase of magnesium phosphide(Mg_(3)P_(2))were studied theoretically by first principles calculation and elastic theory.The independent elastic constants and elastic compliance constants of Mg_(3)P_(2)in cubic Ia3 phase are obtained by using two methods of calculating elastic constants,namely energy-strain(E-S)and stress-strain(S-S).By comparing the elastic constants of single crystals calculated by the two methods,it is shown that the S-S method is in better agreement with the literature values of previous researchers.Therefore,the polycrystalline elastic modulus of cubic Ia3 Mg_(3)P_(2),such as elastic modulus E and shear modulus G,are obtained on the basis of the S-S method,as well as a series of physical parameters such as B/G,Poisson s ratio and anisotropy factor.It is shown that cubic Ia3 Mg_(3)P_(2)satisfies the mechanical stability condition of cubic phase,which proves that it is a structure in mechanical stability state.At the same time,the calculated physical parameters show that cubic Ia3 Mg_(3)P_(2)has the characteristics of toughness.In order to further analyze and verify the characteristics of the materials,we calculated the Vickers hardness.By analyzing the calculated anisotropy factors and the 3D surface images of elastic modulus,linear compression coefficient and shear modulus,which represents the dependence of the elastic properties on the crystal direction,both show that the degree of anisotropy of cubic Ia3 Mg_(3)P_(2)is weak,and the latter is more intuitive.In addition,Debye temperature of Ia3 Mg_(3)P_(2)and sound velocity in different directions are also calculated in this paper.The results show that the interatomic force of Ia3 Mg_(3)P_(2)is weak,and the longitudinal wave propagates the fastest along the direction[111]and the shear wave propagates the slowest along the direction[110]under the condition of zero temperature and zero pressure.