Electronic structure, elasticity and hardness of diborides of zirconium and hafnium: First principles calculations

The explanations for the bonding nature for ZrB₂ and HfB₂ from electronic structure calculations based on different approaches are inconsistent and even contradictory with each other. First principles pseudopotential calculations have been performed to investigate the bonding nature, elastic property and hardness for the two compounds. The nature of chemical bonding for ZrB₂ and HfB₂ can be recognized as a combination of covalent, ionic and metallic bonds from their electronic structures. Density of state, valence charge density and Mulliken population have also been explored to assess the origins of "pseudogap" and charge transfer. The calculated independent elastic constants using finite strain technique generate accurately elastic, bulk and shear modulus for polycrystalline aggregate compared with extrapolated experimental data. The calculated anisotropy factors indicate that ZrB₂ and HfB₂ are largely compression and shear isotropic. While the different bond strengths of boron-boron and boron-metal produces the significant XZ in-plane elastic anisotropy. The model for hardness calculation using Mulliken population is also proved to be effective in hardness prediction for the metal diborides.