First-principles study of mechanical and electronic properties of Lu₂SnC under pressure

In this work, the structure, elastic, and electronic properties of the recently synthesized MAX phase Lu$2$SnC under pressure were studied by the first-principle calculation. The effect of high pressures, up to 20 GPa, on the structure shows that the compressibility along the $a$-axis was higher than that along the $c$-axis, which indicates that the Lu–C bonds are more resistant than Lu–Sn bonds. Meanwhile, we derived the elastic modulus (B, G, Y), Pugh’s ratio (⁠$G/B$⁠), Poisson’s ratio (⁠$ν$⁠), and averaged compressibility (⁠$β$⁠). The value of bulk moduli, Young’s moduli, and shear moduli increases under pressure, which means that the pressure can enhance the ability of resisting to shape change and improve the stiffness and hardness of Lu$2$SnC. Poisson’s ratio change from 0.184 to 0.246 in the 0–20 Gpa pressure range, which means that Lu$2$SnC is brittle in nature, this result is consistent with that obtained from the Cauchy pressure and Pugh’s ratio. In addition, we calculated the shear anisotropy factor (⁠$A$⁠), $Ai$ (i = 1,2,3), $AB$⁠, and $AG$⁠. We found that the elastic anisotropy increases with increasing pressure. Finally, the electronic properties of Lu$2$SnC were calculated. As the pressure increases, a pseudo-gap appears in the energy range of $−2eV$ to $−3eV$⁠. The total density of state at the Fermi level remains virtually unchanged with the increasing pressure. We hope that our study can complement the future experimental and theoretical work, which can lead to further insights.