We have performed a thermodynamical analysis of the phase diagrams for ${\mathrm{ZrO}}_2$-CaO and ${\mathrm{ZrO}}_2$-MgO solid solutions which has demonstrated that differential heats of mixing are important parameters determining the stabilization of the cubic phase of ${\mathrm{ZrO}}_2$ by impurities. It is shown that the differential heats of mixing in the cubic phase of these systems should be lower than in the tetragonal phase. To understand this effect we have studied the electronic and geometrical structures of the pure and doped ${\mathrm{ZrO}}_2$ crystals. Three computational techniques were employed: the ab initio Hartree-Fock pseudopotential method is used to study the atomic and electronic structures of the three phases of pure ${\mathrm{ZrO}}_2$ crystals; the defect energies and the differential heats of mixing values are calculated by means of the atomistic simulation technique using the shell model and the pair-potential approximation; the self-consistent semiempirical intermediate neglect of differential overlap method is used to study changes in the electronic structure imposed by the defects. From the results of various calculations, we are able to identify the key factors contributing to the mechanism of stabilization of cubic ${\mathrm{ZrO}}_2$ by impurities. These include the lattice distortion around vacancies, the lowering of the dielectric constant in the cubic phase, the impurity-stimulated increase of ionicity, and the removal of the Zr orbital degeneracy.

• Received 13 December 1993

DOI:https://doi.org/10.1103/PhysRevB.49.11560