First-principles calculations of the structural, electronic, mechanical and thermodynamic properties of MAX phase Mon+1GeCn (n = 1–3) compounds

Abstract

A novel class of nitrides and carbides called MAX phase materials offers an exceptional blend of metal and ceramic properties together with new guidelines to structure modifications for a variety of technological and engineering applications. In this study, we predict the structural, electronic, elastic, mechanical, and thermodynamic properties of the Mon+1GeCn (n = 1, 2, and 3) MAX phase materials via first-principles (density functional theory (DFT)) calculations. The lattice parameters and formation energies are calculated for the simulated MAX phases under consideration. Five independent elastic constants (C11, C12, C13, C33, and C44 = C55) are determined and we have used them to calculate the bulk modulus (B), Young’s modulus (E), shear modulus (G), Poisson’s ratio (υ) and anisotropy index (A). From our calculations, the predicted electronic band structure and density of states plots show that for the investigated MAX phases, a major contribution in the electronic density of states around the Fermi energy originates from the Mo-4d states. The investigated compounds are metallic with electrical conductivity arising primarily due to the Mo-4d electrons. Thermal effects on some macroscopic properties (lattice constants, Debye temperature, heat capacity, and thermal expansion coefficient) of Mon+1GeCn (n = 1, 2, and 3) are investigated by employing the quasi-harmonic Debye model in a temperature range from 0 K to 1000 K and in the pressure range from 0 GPa to 40 GPa as well.