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

Abstract

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 $\sim$1100 K and within a narrow pressure range that broadens with increasing temperature. On the contrary, HfB₂ is identified as a thermodynamically stable phase in the Hf$-$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.