First principles study of M2InC (M = Zr, Hf and Ta) MAX phases: The effect of M atomic species

Abstract

We have studied the physical properties of M2InC (M = Zr, Hf and Ta) MAX phases ternary carbides using density functional theory (DFT) methodology. The structural, elastic and electronic properties are revisited (and found to be in good agreement with recently reported results). The charge density distribution, Fermi surface features, Vickers hardness, dynamical stability, thermodynamics and optical properties have been investigated for the first time. The calculated single crystal elastic constants and phonon dispersion curves endorse the mechanical and dynamical stability of all the compounds under study. The calculated single crystal elastic constants Cij and polycrystalline elastic constants are found to increase with increasing atomic number of M species (M = Zr, Hf and Ta). The values of Pugh ratio and Poisson’s ratio revealed the brittleness of the compounds under study associated with strong directional covalent bond with a mixture of ionic contribution. Overlapping of conduction band and valence band at Fermi level notify the metallic nature of M2InC (M = Zr, Hf and Ta) MAX phases. Low values of Vicker hardness indicate the softness of the materials and easy machinability. The thermodynamic properties, such as the free energy, enthalpy, entropy, specific heat capacity and Debye temperature are evaluated using the phonon dispersion curves and a good correspondence is found with the characteristics of M atomic species. Major optical properties, e.g., dielectric functions, refractive index, photoconductivity, absorption coefficient, loss function and reflectivity are calculated and discussed in detail in this study. Keywords: MAX phase, M2InC (M = ZZr, Hf, Ta) compounds, Physical properties, First principles study, Phonon dispersion curve