Modulated structures fluorite-related

The parent structure of the anion-deficient fluorite structure phases is the cubic fluorite structure (Fig. 4.7). As in the case of the anion-excess fluorite-related phases, diffraction patterns from typical samples reveals that the defect structure is complex, and the true defect structure is still far from resolved for even the most studied materials. For example, in one of the best known of these, yttria-stabilized zirconia, early studies were interpreted as suggesting that the anions around vacancies were displaced along < 111 > to form local clusters, rather as in the Willis 2 2 2 cluster described in the previous section, Recently, the structure has been described in terms of anion modulation (Section 4.10). In addition, simulations indicate that oxygen vacancies prefer to be located as second nearest neighbors to Y3+ dopant ions, to form triangular clusters (Fig. 4.11). Note that these suggestions are not... 

Some of the earliest examples of modulated structures to be unraveled were the fluorite-related vernier structures. These structures occur in a number of anion-excess fluorite-related phases and use a modulation to accommodate composition variation. They can be illustrated by the orthorhombic phases formed when the oxyfluoride YOF reacts with small amounts of YF3 to give composition YOxF3 with x in the range 0.78-0.87, but similar phases occur in the Zr(N, O, F) system with x taking values of 2.12-2.25 and other systems in which the Zr is replaced by a variety of lanthanides. 

The lanthanide higher oxides have not only peculiar thermodynamic properties, but also unique physical and chemical properties. The physical and chemical properties are presented as a macroscopic parameter, such as the electrical conductivity, the coefficient of expansion, and the conversion rate of a catalysis process. Due to the lack of knowledge of the wide range of non-stoichiometry of the oxygen-deficient fluorite-related homologous series of the lanthanide higher oxides, the macroscopically measured data of the physical and chemical properties are scattered, and therefore, based on the structural principle of the module ideas a deep understanding the relationship between the properties and structures is needed. 

---