Crystal structure and elastic properties of ZrB compared with ZrB ₂: A first-principles study

The existences of potential crystal structures of ZrB and ZrB₂ are studied by means of first-principles molecular dynamics calculations. The face-centered cubic ZrB (space group Fm-3 m, No. 225) with lattice constant a = 4.900 and hexagonal ZrB₂ (space group P6/mmm, No. 191) with a = 3.170 and c = 3.544 have been proved to be both mechanically and dynamically stable. The optimized lattice parameters for both ZrB and ZrB₂ agree with both the experimental data and previous theoretical calculations. Basic elastic properties of ZrB compared with ZrB₂ using the first-principles calculations are investigated. The bulk moduli 160.6 and 229.1 GPa, shear moduli 102.7 and 210.5 GPa, Young's moduli 253.9 and 483.5 GPa, and Poisson ratios 0.2365 and 0.1483, are obtained for ZrB and ZrB₂, respectively. Density of state has been explored to discuss the difference of electronic structure between ZrB and ZrB₂. The reasons of lower Young's moduli of ZrB compared with that of ZrB₂ are discussed as well.