First principle insights into the physical properties of Ti-based 211-MAX phase nitrides Ti₂AN (A = Tl and Pb)

Abstract

We have used the theoretical ab initio approach to scrutinize the electronic and other physical properties of Ti2AN (A = Tl and Pb). Geometrical optimization has been carried out to obtain accurate lattice constants and internal coordinates. The formation energies of Ti2TlN and Ti2PbN are found to be negative, which confirms their stability. The aforementioned compounds are found to be metallic because of their zero-band gaps. The metallicity fm (x 10−3) of Ti2TlN and Ti2PbN phases were determined to be 1.77 and 2.11, respectively. In addition, we evaluate the elastic constant Cij , which obeys the Born-Huang mechanical stability criterion. We used the Voigt-Reuss-Hill approximation for the analysis of Young’s modulus, shear modulus, and bulk modulus successfully. Furthermore, Ti2TlN is found to be brittle, but Ti2PbN is close to the brittle-ductile boundary line according to Pugh’s and Poisson’s ratios. The Debye temperature, melting temperature, and minimum thermal conductivity have all been rigorously studied to examine the potential scenarios of genuine high-temperature applications. Lower Young’s modulus, the minimum thermal conductivity (Ti2TlN and Ti2PbN), and Debye temperature values reveal that Ti2PbN might be used as a thermal barrier coating application. A study of elastic anisotropy
demonstrates that Ti2PbN has a higher degree of anisotropy than Ti2TlN, according to the universal anisotropy index. We confirmed the dynamic stability (i.e., no negative frequencies at the gamma point) of predicted compounds by performing phonon DOS
and phonon band structures. Finally, the temperature-dependent thermodynamic properties of Ti2TlN and Ti2PbN have been thoroughly analyzed, where the entropy (S), free energy, and internal energy (E) vary with respect to temperature. Moreover, the convergence of specific heat capacity is observed at constant volume to the DulongPetit limit at higher temperatures.