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

In terms of first-principles calculations, elastic stiffness constants Cij’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.