Based on Density Functional Theory (DFT), using first-principles pseudopotential plane wave method, elastic properties and electronic structure of TiB2 and ZrB2 were calculated. The elastic constants of these compounds were calculated by Voigt-Reuss-Hill method. The results show that the elastic modulus of TiB2 and ZrB2 are 594 and 520 GPa, and the shear modulus are 268 and 229 GPa, respectively. Pugh empirical criterion and Poisson's ratio show that the two compounds are very brittle, and the brittleness of TiB2 is higher than ZrB2. Finally, the differences in elastic properties between TiB2 and ZrB2 result form their electronic structures.
First-principles study of elastic modulus, shear modulus and some other elastic parameters of TiN and NbN are reported using the plane-wave pseudopotential density functional theory method in this paper. The calculated lattice and elastic constants are in good agreement with the experimental data and other theoretical results. The band structure and density of states of these two compounds were obtained, which show that the mainly contribution on pseudopotential calculations of the density of states of TiN is Ti-3d orbital and N-2p orbital, while TiN is the Nb-4d orbit and B-2p orbit, TiN with higher conductivity; Pugh empirical criterion shows that TiN and NbN are both brittle compounds, and NbN is more brittle than TiN.
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