Investigation of the Physical Properties of 211 MAX Phase Material Cr 2 TlN ${\rm Cr}_2{\rm TlN}$ with DFT and DFT+U Methods

This study utilizes Perdew-Burke-Ernzerhof (PBE) and PBE+U exchange-correlation functionals to investigate the electronic, magnetic, and structural properties of ${\mathrm{Cr}}_2\mathrm{TlN}$. The spin polarization calculations indicate that the predicted material exhibits ferromagnetic properties in bulk when U = 0 eV. As the U parameter increases from 0 to 1 eV, it demonstrates antiferromagnetic behavior with the spin magnetic moment per Cr atom of 2.17 ${\mu }_B$. The supercell method reveals that the in-plane antiferromagnetic 1 (in-AFM1) state is more stable than the ferromagnetic state, in-AFM2, and in-AFM3 when U equals 0 eV and 1 eV, respectively. The analysis of the electron band structures and density of states suggests that ${\mathrm{Cr}}_2\mathrm{TlN}$ displays metallic characteristics due to the hybridization of Cr-d with N-p and Cr-d with Tl-p states. The predicted compound is found to be mechanically stable as per the Born–Huang criteria. The elastic moduli are successfully assessed using the Voigt–Reuss–Hill approximation. Poisson's and Pugh's ratios show that ${\mathrm{Cr}}_2\mathrm{TlN}$ is ductile in nature. The low Young's modulus value and minimum thermal conductivity suggest that ${\mathrm{Cr}}_2\mathrm{TlN}$ could be an excellent candidate for thermal barrier coating applications. Further, the projected material undergoes confirmation of its dynamic stability via phonon spectra analysis, showing no negative or imaginary frequencies.