Prediction of HfB₃ from first-principles calculations: crystal structures, stabilities, electronic properties and hardnesses

ABSTRACT

First-principles calculations combined with particle swarm optimisation technique are employed to provide an in-depth understanding of the structures, stabilities, electronic properties, and hardnesses for hafnium triboride. Three novel structures of HfB₃ with C2/m, Cmmm, and Pmma phases are predicted under the ambient pressure. The new phases are energetically much superior to the previously proposed m-AlB₂-, and TMB₃-type (TM = W, Mo) structures. The mechanical and thermodynamic stabilities of the new structures are confirmed by the elastic constants and formation enthalpies. The phonon dispersion curves reveal that they are dynamic stable. The large bulk, shear modulus, and small Poisson’s ratio of the C2/m and Pmma phases, make them the promising high incompressible materials. It is worth mentioning that the considerable hardness of 40.8 GPa testifies the most stable C2/m-HfB₃ to be considered as a potential superhard material. On the basis of the electronic density of states and chemical bonding analysis, one can find that the strong B–B and Hf–B covalent bonds are present in HfB₃ compounds. Particularly, higher incompressible and hardness of the C2/m-HfB₃ may also relate to its stacking of ‘sandwiches’ structure.

GRAPHICAL ABSTRACT

KEYWORDS:

• Structure prediction
• HfB₃
• superhard materials
• electronic properties

Additional information

Funding

This work was supported by the Natural Science Foundation of China [grant number 11404008], the China Postdoctoral Science Foundation funded project [grant number 2017M623310XB], the Natural Science Basic Research Plan in Shaanxi Province of China [grant numbers 2016JM1012, 2013JQ1007], the Education Department of Sichuan Province [grant numbers 17ZA0278, 18ZA0340], and the research fund of Sichuan University of Science and Engineering [grant numbers 2015RC44 and 2013RC10].