Elastic properties of cubic, tetragonal and monoclinic ZrO₂ from first-principles calculations

In terms of first-principles calculations, elastic stiffness constants C_ij's as well as the polycrystalline aggregates including the bulk, shear, Young's moduli, Possion's ratio, and anisotropy factors have been predicted for three technologically important polymorphs of ZrO₂, i.e., monoclinic m-ZrO₂, tetragonal t-ZrO₂, and cubic c-ZrO₂. Here, both the strain vs. stress (S-S) and the strain vs. strain energy (S-E) methods are adopted. In the first-principles calculations, both the local density approximation (LDA) and the generalized gradient approximation (GGA) are utilized. It is found that the more accurate structural and elastic properties are determined by LDA in comparison with experimental results and the S-S method is more effective than the S-E method although the two methods predict the similar results. The predicted negative values for C₁₆, C₃₆, and C₄₅ of m-ZrO₂ suggest that the certain normal or shear stress corresponds to an opposite shear strain for reducing the total energy. Small differences of shear and Young's modulus between m-ZrO₂ and t-ZrO₂ suggest that their mechanical properties are comparable.