Stable and hard hafnium borides: A first-principles study

We investigate the stability of hafnium borides at zero pressure via the evolutionary crystal structure prediction and first-principles calculations. Our results indicate that the well-known P6/mmm-HfB2 is the only thermodynamically stable phase at zero temperature and pressure, and two more phases (Pnma-HfB and Fm3¯m-HfB12) become thermodynamically stable at higher temperatures. We compute the mechanical properties including bulk, shear and Young’s moduli, Vickers hardness, and fracture toughness for all stable and metastable hafnium borides (∼30 phases) and then study in detail the effect of boron concentration and topology of B-sublattice on their mechanical properties. We show that not only the concentration of boron, but also the topology of the boron sublattice is important for the mechanical properties of hafnium borides. Among the predicted stable and low-energy metastable hafnium borides, the highest possible hardness is exhibited by P6/mmm-HfB2 with graphenelike boron sheets and by phases with 3D boron networks and high B/Hf ratios (e.g., Pnnm-HfB5 and Fm3¯m-HfB12).