The rise of 212 MAX phase borides, Ti$_2$PB$_2$, Zr$_2$PbB$_2$, and Nb$_2$AB$_2$ [A = P, S]: DFT insights into the physical properties for thermo-mechanical applications

An interesting class of ternary metallic borides, known as the 212 MAX phase borides, is the recent advancement of the MAX phase family. In this article, results from ab-initio calculations on unexplored Ti$_2$PB$_2$, Zr$_2$PbB$_2$, and Nb$_2$AB$_2$ [A = P, S] are reported wherein Ti$_2$PB$_2$ along with its 211 boride phase Ti$_2$PB are predicted for the first time. The stability was confirmed by calculating the formation energy, phonon dispersion curve, and elastic stiffness constants. The obtained elastic constants, elastic moduli, and Vickers hardness values of Ti$_2$PB$_2$, Zr$_2$PbB$_2$, and Nb$_2$AB$_2$ [A = P, S] were found to be significantly larger than those of their counterparts 211 borides and carbides, in a trend similar to other 212 borides. The studied compounds are brittle like most of the MAX and MAB phases. The electronic band structure and density of states revealed the metallic nature of the titled borides. Several thermal parameters were explored, certifying the suitability of Ti2PB2, Zr2PbB2, and Nb2AB2 [A = P, S] compared to their counterparts, and a similar trend was found for the other 212 borides. The obtained results predict that Ti2PB2, Zr2PbB2, and Nb2AB2 [A = P, S] have significant potential for use as efficient thermal barrier coating materials. The response of Ti$_2$PB$_2$, Zr$_2$PbB$_2$, and Nb$_2$AB$_2$ [A = P, S] to the incident photon was studied by computing the dielectric constant (real and imaginary part), refractive index, absorption coefficient, photoconductivity, reflectivity, and energy loss function. The ability to protect from solar heating was revealed from the studied reflectivity spectra. In this work, we have explored the physical basis of the improved thermo-mechanical properties of 212 MAX phase borides compared to their carbide and boride counterparts.