Crystal Structures of the Tetragonal Ceria−Zirconia Solid Solutions Ce_xZr_1−xO₂ through First Principles Calculations (0 ≤ x ≤ 1)

Crystal structures of metastable tetragonal Ce_xZr_1−xO₂ have been studied through first principles calculations (0 ≤ x ≤ 1). Unit-cell parameters a, c, and atomic coordinates of 24 atoms were optimized for all the occupational configurations of Ce and Zr atoms by using the constraints for cell parameters: a = b and α = β = γ = 90°. Axial ratio and oxygen displacement from the regular position of the optimized structures of ground states decrease with increasing CeO₂ content, which is consistent with diffraction experiments in the literature. The tetragonal (t”) form with axial ratio of unity is strongly suggested to be stable in Ce_0.875Zr_0.125O₂, compared with the tetragonal (t’) form with axial ratio larger than unity and the cubic phase. This work also demonstrates that the ground state of Ce_xZr_1−xO₂ (x ≤ 0.75) is the t’ form. The phase stability of the t’ and t” forms are discussed by comparing the ground states with experimental data in the literature.