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

• Published in: Computational materials science 2008-12, Vol.44 (2), p.411-421
• Main Authors: Zhang, Xinghong, Luo, Xiaoguang, Han, Jiecai, Li, Jinping, Han, Wenbo
• Format: Article
• Language: English
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Condensed matter: structure, mechanical and thermal properties; Diborides; Elastic constants; Elasticity, elastic constants; Electron density of states and band structure of crystalline solids; Electron states; Electronic structure; Exact sciences and technology; First principles calculations; Hardness; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Methods of electronic structure calculations; Other inorganic compounds; Physics
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2008.04.002

The explanations for the bonding nature for ZrB 2 and HfB 2 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 ZrB 2 and HfB 2 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 ZrB 2 and HfB 2 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.