Insight into phase stability and mechanical behavior of HfB2 and HfB12 under high pressures and high temperatures: A first-principles investigation

Previous attempts to synthesize pure crystalline hafnium dodecaboride (HfB12) have been unsuccessful, raising doubts about its existence as one of the thermodynamically stable phases in the binary Hf-B system. In this work, we employ first-principles calculations based on density functional theory and quasi-harmonic approximation to evaluate the phase stability of HfB12 with respect to its competing phases, in particular HfB2, across a range of pressures of 0-20 GPa and of temperatures of 0-1200 K to determine the conditions under which HfB12 is stable from the thermodynamic aspect. Our results suggest that HfB12 could be thermodynamically stabilized only at temperatures higher than similar to 1100 K and within a narrow pressure range that broadens with increasing temperature. On the contrary, HfB2 is identified as a thermodynamically stable phase in the Hf-B system for all considered temperatures and pressures. By investigating the mechanical behaviors and phonon dispersion curves of HfB2 and HfB12, we confirm that the two compounds are mechanically and dynamically stable. Also, we demonstrate that HfB2 exhibits superhard behavior with a Vickers hardness exceeding the superhard threshold of 40 GPa, while the values for Vickers hardness of HfB12 are predicted to fall slightly below the threshold. This comprehensive study of HfB2 and HfB12 sheds light on their phase stability and mechanical behavior, offering a valuable insight into future synthesis of the materials and their potential uses as hard-coating materials for cutting tools.