STUDY OF PHYSICAL PROPERTIES OF MAX PHASES M2TlC (M = Ti, Zr, Hf): A DFT CALCULATION

Abstract

The projected ternary carbide MAX phases M2TlC (M = Ti, Zr, and Hf) have been investigated for their phonon dispersion and optical properties, including Mulliken population analysis, optical and theoretical Vickers hardness. We reviewed the compound's structural and electrical characteristics to evaluate the accuracy of our calculations. The examined MAX phases are mechanically and dynamically stable, according to the examination of the formation energies, elastic constants, phonon dispersion, and phonon density of states. Ti-3d, Zr-4d, Hf-5p, 5d, and Tl-6p electronic orbitals, which have a substantial impact on the phases' physical characteristics and heavily contribute to electronic conduction, are the main causes of the sub-band crossing the EF. For the phases, the values of total density of states (TDOS) at EF are determined to be 3.0, 2.55, and 2.09 states/eV. In the compounds under investigation, the bond Hf-C has the highest covalency of all the bonds. The hardness of the examined compounds may be compared in such a way that Ti2TlC for both Hmicro (24 GPa) and Hmacro (17 GPa) is harder than that of Hf2TlC (17 and 13 GPa) and Zr2TlC (20 and 16 GPa). The Vickers hardness are discovered to be 2.18, 1.61, and 2.60 GPa, respectively for the phases. The reported hardness values are in the range of 2 to 8 GPa that is comparable with the well-known MAX phase nanolaminates, such as Hf2InC (3.45 GPa) and Ta2InC (4.12 GPa). The values of the longitudinal optical (LO) and transverse optical (TO) components at  are 19.74 and 21.63 THz (Ti2TlC), 16.62 and 17.18 THz (Zr2TlC), and 18.66 and 19.94 THz (Hf2TlC), respectively. The phonon dispersion curves (across the entire BZ) do not exhibit imaginary (negative on the frequency scale) phonon frequency, suggesting the dynamic stability of the phases. The value of reflectivity rises to high as 92%, 82%, and 86% for the compounds Ti2TlC, Zr2TlC, and Hf2TlC, respectively, at energy 8.76 eV, 9.6 eV, and 10.7 eV. It is an intriguing observation that the reflectivity is always greater than 44% for the phases Ti2TlC (11.67 eV), Zr2TlC (12.44 eV), and Hf2TlC (13.8 eV). According to reflectivity's findings, the visible (1.7 eV–3.3 eV) and IR (1.24 eV–1.7 eV) sectors account for more than 44% of the energy up to 12.0 eV. Therefore, the investigated compounds might be a good contender for use as a covering material to reduce solar heating.