Another way to view solid solutions and nonstoichio­metry is as a function of defects in the ideal lattice.

This has been of particular interest for oxide fuels as they are seen to govern dissolution of cations and nonstoichiometry in oxygen behavior and as a result, transport properties. Defect concentrations are inherent in the CEF, as vacancies and interstitials on the oxygen lattice for fluorite-structure actinide systems are treated as constituents linked to cations (see Section 1.17.4.3). A more explicit treatment of oxide systems with point defects has been applied to a wide range of materials such as high-temperature oxide superconductors, TiO2, and ionic conducting membranes, among others. For oxide fuels, point defects have been described thermochemically by a number of investigators starting as early as 1965 with more recent treatments in fuels by Nakamura and Fujino,36 Stan eta/.,37 and Nerikar eta/.38 Oxygen site defects, which dominate in the fluorite-structure fuels, are of course driven by the multiple possible valence states of the actinides, most notably uranium, which can exhibit U+3, U+4, U+5, and U+6.

A simple example of the point defect treatment can be seen in Stan et a/.37 They optimized defect concentrations from the defect reactions described in the Kroger-Vinck notation

oo = + Vo

VO2 + 2U U = Ot + 2U’V

A dilute defect concentration was assumed such that there were no interactions between defects and thus no excess energy terms. The results of the fit to literature data are seen in Figure 7(a), where the stoichiometry of the fluorite-structure hyperstoi­chiometric urania is plotted as a function of defect concentration xa. The relationships were also used to compute oxygen potentials as a function of stoichi­ometry and are plotted in Figure 7(b) illustrating relatively good agreement with values computed by Nakamura and Fujino.36