Theoretical oxygen potential change of quaternary solid solution, A y2+B z3+U 1− y− zO 2+ x, by configurational entropy calculation

Abstract

The change of oxygen potential, Δ G ̄ O 2 , for the solid solutions of general formula A y 2+B z 3+U 1− y− z O 2+ 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 4 b 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, ( A 2+ U 5+), ( A 2+2 U 5+) and (B 3+U 5+) were assumed to be formed. For the first two complexes, an average composition (A 2+ αU 5+) was defined, and for (B 3+U 5+) a fraction, β, of B 3+ was considered to form the complex. The O/M ratio (M=A+B+U) which gave the steepest change of Δ G ̄ O 2 was calculated. Below this O/M ratio to 2− y−(1− β) z/2, the solid solution possibly satisfied the relation m= X/(2 y), where X=− x. In the region where this relation held, the solid solution was supposed to be oxygen stoichiometric.