Theoretical oxygen potential change of quaternary solid solution, Ay2+Bz3+U1−y−zO2+x, by configurational entropy calculation

The change of oxygen potential, ΔḠO2, for the solid solutions of general formula Ay2+Bz3+U1−y−zO2+x was studied by the method of configurational entropy calculation for cations and cation complexes. A part of Mg atoms (fraction m) were assumed to occupy the interstitial 4b sites of the solid solution, and the number of ways of arranging the free ions and intra-cation complexes was calculated followed by differentiation of the logarithm of this number with respect to oxygen non-stoichiometry to obtain partial molar entropy of oxygen. As the complexes, (A2+U5+), (A2+2U5+) and (B3+U5+) were assumed to be formed. For the first two complexes, an average composition (A2+αU5+) was defined, and for (B3+U5+) a fraction, β, of B3+ was considered to form the complex. The O/M ratio (M=A+B+U) which gave the steepest change of ΔḠO2 was calculated. Below this O/M ratio to 2−y−(1−β)z/2, the solid solution possibly satisfied the relation m=X/(2y), where X=−x. In the region where this relation held, the solid solution was supposed to be oxygen stoichiometric.