A First Principle Study of Antifluorite $Be_2X$ (X = C, Si) Polymorph

The crystal structure, electronic, and mechanical properties of antifluorite $Be_2X$ (X = C, Si) are calculated using the first-principles method based on density functional theory. Our calculated lattice parameters at equilibrium volume are in good agreement with the experimental data and other theoretical calculations. In order to obtain further information, the mechanical properties including bulk modulus, shear modulus, Young's modulus, and Poisson's ratio are deduced from calculated elastic constants. Meanwhile, the sound velocity and Debye temperature are also predicted. The bonding nature in $Be_2X$ (X = C, Si) is a complex mixture of covalent and ionic characters.