Finding and characterization of an energetically favorable cubic Ce0.75Zr0.25O2 solid solution using genetic algorithm and density functional theory

We studied an energetically favorable cubic Ce0.75Zr0.25O2 solid solution using a genetic algorithm and density functional theory. The 2 x 2 x 2 Ce1-xZrxO2 supercell that we used for this study contained 32 metal atoms and 64 O atoms; the 2 x 2 x 2 Ce0.75Zr0.25O2 supercell with x = 0.25 contained 24 Ce, 8 Zr, and 64 O atoms. The genetic algorithm parameters were tested for their optimum values using another 2 x 2 x 2 Ce0.875Zr0.125O2 supercell that contained 28 Ce, 4 Zr, and 64 O atoms; and the parameters were population, crossover rate, mutation rate, and temperature. We applied these values to the Ce0.75Zr0.25O2 supercell to find an energetically favorable solid solution. The favorable Ce0.75Zr0.25O2 solid solution contained monoclinic ZrO2-like polyhedrons, and its volume expanded compared with that of the Ce0.75Zr0.25O2 compound