Stable and hard hafnium borides: A first-principles study

Congwei Xie, Qi Zhang, Hayk A. Zakaryan, Hao Wan, Ning Liu, Alexander G. Kvashnin, Artem R. Oganov

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 F m 3 ̄ m - Hf B 12) 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 F m 3 ̄ m - Hf B 12).

Original languageEnglish
Article number205109
JournalJournal of Applied Physics
Issue number20
Publication statusPublished - 28 May 2019


Dive into the research topics of 'Stable and hard hafnium borides: A first-principles study'. Together they form a unique fingerprint.

Cite this