Ternary boride Hf3PB4: Insights into the physical properties of the hardest possible boride MAX phase

Highlights: • The physical properties of Hf₃PB₄ have been studied using first-principles technique. • Hf₃PB₄ exhibits the highest values of hardness parameters among the MAX phases. • The charge density mapping and bond population analysis disclose the existence of very strong B–B covalent bonds in Hf₃PB₄. • Hf₃PB₄ has the highest melting temperature and might be an efficient candidate as thermal barrier coating material. • Hf₃PB₄ has the potential to be used as reflecting coating to diminish solar heating. -- Abstract: We have carried out a first-principles investigation of mechanical, electronic, thermodynamic and optical properties of the recently predicted thermodynamically stable MAX phase boride Hf₃PB₄ for the first time. The calculated lattice constants of the optimized cell volume are consistent with those found earlier. Mechanical properties characterized by parameters such as C₄₄, B (bulk modulus), G (shear modulus), Y (Young's modulus), H_macro (macro-hardness) and H_micro (micro-hardness) of Hf₃PB₄ boride are compared with those of existing 211, 312 and 413 MAX phases. None of the MAX compounds synthesized so far has higher H_macro and/or H_micro than that of the predicted Hf₃PB₄ nanolaminate. Calculations of stiffness constants (C_ij) indicate that Hf₃PB₄ is mechanically stable. The extraordinarily high values of elastic moduli and hardness parameters are explained with the use of density of states (DOS) and charge density mapping (CDM). The high stiffness of Hf₃PB₄ arises because of the additional B atoms which results in the strong B–B covalent bonds in the crystal. The band structure and DOS calculations are used to confirm the metallic properties with dominant contribution from the Hf-5d states around the Fermi level. The technologically important thermal parameters such Debye temperature, minimum thermal conductivity, Grüneisen parameter and melting temperature of Hf₃PB₄ are calculated. The important optical constants are calculated and analyzed in detail and their relevance to possible applications in the optoelectronic sectors is discussed. Our study reveals that Hf₃PB₄ has the potential to be the hardest known MAX phase based on the values of C₄₄, H_macro and H_micro.