A comprehensive exploration of the physical properties of M2GaB (M = Ti, Zr, Mo, Hf) through DFT method

Abstract

The M2GaB (M = Ti, Zr, Mo, Hf) MAX phase borides were investigated in the present study. We have calculated the fracture toughness, brittleness index, acoustic behavior, Mulliken bond-overlap population, theoretical Vickers hardness, f-index, phonon, charge density mapping, and thermodynamic and optical properties via the density functional theory (DFT). To assess the correctness of our calculations, we revisit the lattice constants, band structure, density of states, elastic constants, mechanical stabilities, and dynamic stabilities. We studied these compounds' formation energies, elastic constants Cij, and phonon dispersion curves to evaluate their chemical, mechanical, and dynamical stability. The fracture toughness and brittleness index were calculated to determine the crack extension and damage tolerance resistance. The acoustic behavior was also studied. The Mulliken bond population was used to investigate the distribution of electrons between the atomic bonds and to determine the compounds' Vickers hardness. Calculating the f-index, we analyzed the bonding strength along the a- and c-directions. The essential thermodynamic properties of M2GaB (M = Ti, Zr, Mo, Hf) compounds were calculated to understand their thermal response at different temperatures and possible applications. Finally, we computed the optical properties to assess their electronic response to the incident photon and predict the possibility of their use.