Structural stability, electronic, mechanical, phonon, and thermodynamic properties of the M2 GaC (M = Zr, Hf) max phase: An AB initio calculation

Abstract

The novel ternary carbides and nitrides, known as MAX phase materials with remarkable combined metallic and ceramic properties, offer various engineering and technological applications. Using ab initio calculations based on generalized gradient approximation (GGA), local density approximation (LDA), and the quasiharmonic Debye model; the electronic, structural, elastic, mechanical, and thermodynamic properties of the M2 GaC (M = Zr, Hf) MAX phase were investigated. The optimized lattice parameters give the first reference to the upcoming theocratical and experimental studies, while the calculated elastic constants are in excellent agreement with the available data. Moreover, obtained elastic constants revealed that both the Zr2 GaC and Hf2 GaC MAX phases are brittle. The band structure and density of states analysis showed that these MAX phases are electrical conductors, having strong directional bonding between M-C (M = Zr, Hf) atoms due to M-d and C-p hybridization. Formation and cohesive energies, and phonon calculations showed that Zr2 GaC and Hf2 GaC MAX phases’ compounds are thermodynamically and dynamically stable and can be synthesized experimentally. Finally, the effect of temperature and pressure on volume, heat capacity, Debye temperature, Grüneisen parameter, and thermal expansion coefficient of M2 GaC (M = Zr, Hf) are evaluated using the quasiharmonic Debye model from the nonequilibrium Gibbs function in the temperature and pressure range 0–1600 K and 0–50 GPa respectively.