Application of an Ion‐Packing Model Based on Defect Clusters to Zirconia Solid Solutions: I, Modeling and Local Structure of Solid Solutions

Oxygen vacancies can be introduced into zirconia solid solution ZrO 2 –MO u ( u = 1 and 1.5) to maintain electroneutrality. Recently, the local structures around Zr 4+ and M 2 u + ions in ZrO 2 –MO u solid solutions have been studied through EXAFS spectroscopy, diffuse scattering analysis, and single‐crystal structure analysis. The present study constructs an ion‐packing model for zirconia solid solutions based on some defect cluster models. The decrease of cell volume with the occurrence of vacancies is assumed to be expressed by decreasing the coordination number (CN) of cations around the vacancy. The distribution of CNs in a solid solution was calculated from a certain defect cluster model. The average interatomic distances, the average CN, and the short‐range order parameters were calculated using this distribution of CNs. The local structures calculated from the model were compared with experimental data in the systems ZrO 2 –MO 1.5 (M = Y, Gd, Yb, and Ca). In the ZrO 2 –YO 1.5 system, the r (s–O) interatomic distance, where s represents Zr 4+ or Y 3+ and O represents O 2− , decreased with Y content and therefore vacancy content. The probability of finding Y 3+ around a vacancy increases with increasing yttria content from a comparison of the calculated results with the ones from recent EXAFS studies. The present model can qualitatively explain compositional and size dependences of the dopant on various local structures.