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 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), Hmacro (macro-hardness) and Hmicro (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 Hmacro and/or Hmicro than that of the predicted Hf3PB4 nanolaminate. Calculations of stiffness constants (Cij) 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, Hmacro and Hmicro.