The elastic and thermodynamic properties of Be₂SiO₄ are calculated. The calculated bulk modulus (B) values increase as pressure increases, while the shear modulus (G) and Young's modulus (E) values exhibit an initial increase followed by a subsequent decrease after reaching a certain point. According to the computed thermodynamic properties, phenakite exhibits a positive thermal expansion (α).

Abstract

Beryllium silicate, recognized as the mineral phenakite (Be₂SiO₄), is a prevalent constituent in Earth's upper mantle. This study employs density-functional theory (DFT) calculations to explore the structural, mechanical, dynamical, thermodynamic, and electronic characteristics of this compound under both ambient and high-pressure conditions. Under ideal conditions, the DFT calculations align closely with experimental findings, confirming the mechanical and dynamical stability of the crystalline structure. Phenakite is characterized as an indirect band gap insulator, possessing an estimated band gap of 7.83 eV. Remarkably, oxygen states make a substantial contribution to both the upper limit of the valence band and the lower limit of the conduction band. We delved into the thermodynamic properties of the compound, including coefficients of thermal expansion, free energy, entropy, heat capacity, and the Gruneisen parameter across different temperatures. Our findings suggest that Be₂SiO₄ displays an isotropic behavior based on estimated anisotropic factors. Interestingly, our investigation revealed that, under pressure, the compression of phenakite is not significantly affected by bond angle bending.