Systematic study on the anisotropic elastic properties of tetragonal XYSb (X = Ti, Zr, Hf; Y = Si, Ge) compounds

• The obtained elastic constants have showed that all compounds are mechanically stable.
• The calculated hardness has suggested that these compounds are hard materials.
• The anisotropy of HfGeSb is higher than the other compounds.

The anisotropic elastic properties of XYSb (X = Ti, Zr, Hf; Y = Si, Ge) compounds have been investigated by using first-principles calculations based on density functional theory. The calculated lattice parameters are in excellent agreement with the available experimental data. The computed elastic constants indicate that all compounds are mechanically stable according to the elastic stability criteria under pressure. We have calculated the bulk modulus, shear modulus, Young's modulus, Poisson's ratio, Debye temperature, and anisotropy value from the obtained elastic constants according to the Voigt–Reuss–Hill approximation. Additionally, the ductility and brittleness are characterized with the estimation from Pugh's rule (B/G) and Poisson's ratio. Furthermore, the elastic anisotropy have been visualized in detail by plotting the directional dependence of compressibility, Young's and shear moduli.

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