Anisotropic elastic properties and ideal uniaxial compressive strength of TiB₂ from first principles calculations

The structural, anisotropic elastic properties and the ideal compressive and tensile strengths of titanium diboride (TiB₂) were investigated using first-principles calculations based on density functional theory. The stress-strain relationships of TiB₂ under <1010>, <1210>, and <0001> compressive loads were calculated. Our results showed that the ideal uniaxial compressive strengths are |σ_<1210>|=142.96 GPa,|σ_<0001>|=188.75 GPa, and |σ_<1010>|=245.33 GPa, at strains-0.16,-0.32, and-0.24, respectively. The variational trend is just the opposite to that of the ideal tensile strength with σ_<1010>=44.13 GPa, σ_<0001>=47.03 GPa, and σ_<1210>=56.09 GPa, at strains 0.14, 0.28, and 0.22, respectively. Furthermore, it was found that TiB₂ is much stronger under compression than in tension. The ratios of the ideal compressive to tensile strengths are 5.56, 2.55, and 4.01 for crystallographic directions <1010>, <1210>, and <0001>, respectively. The present results are in excellent agreement with the most recent experimental data and should be helpful to the understanding of the compressive property of TiB₂.