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

We have carried out a first-principles investigation of mechanical, electronic, thermodynamic and optical properties of the recently predicted thermodynamically stable MAX phase boride Hf 3 PB 4 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 C 44 , B (bulk modulus), G (shear modulus), Y (Young's modulus), H macro (macro-hardness) and H micro (micro-hardness) of Hf 3 PB 4 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 Hf 3 PB 4 nanolaminate. Calculations of stiffness constants (C ij) indicate that Hf 3 PB 4 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 Hf 3 PB 4 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-5 d states around the Fermi level. The technologically important thermal parameters such Debye temperature, minimum thermal conductivity, Grüneisen parameter and melting temperature of Hf 3 PB 4 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 Hf 3 PB 4 has the potential to be the hardest known MAX phase based on the values of C 44 , H macro and H micro. ga1 • The physical properties of Hf 3 PB 4 have been studied using first-principles technique. • Hf 3 PB 4 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 Hf 3 PB 4. • Hf 3 PB 4 has the highest melting temperature and might be an efficient candidate as thermal barrier coating material. • Hf 3 PB 4 has the potential to be used as reflecting coating to diminish solar heating. [ABSTRACT FROM AUTHOR]