Magnesium-europium solid solutions of uranium dioxide, MgyEuzU1-y-zO2+x, with y = 0.05, 0.1 and z = 0.05, 0.1 were prepared, and their oxygen potential, Delta(G) over bar (O2), was measured as a function of O/M ratio (M = Mg + Eu + U) at temperatures of 1000 degreesC, 1100 degreesC and 1200 degreesC. The O/M ratio which gave the steepest change of Delta(G) over bar (O2) (referred to as GOM) was 1.955 for y = 0.05, z = 0.1 (and y = 0.05, z = 0.05), but it decreased to 1.908 at higher Mg2+ concentrations of y = 0.1, z = 0.05. The GOM did not change with temperature in the range 1000-1200 degreesC. The solid solutions showed distinct Delta(S) over bar (O2) peaks of near 0 J mol(-1) K-1 at GOM, which was the same for Delta(H) over bar (O2) though the peaks were much smaller. The rates partial derivativea/partial derivativey and partial derivativea/partial derivativez for the lattice parameter change were -0.162 and -0.154 Angstrom, respectively. At GOM, the Mg2+ ions of a fraction of 0.473 of total Mg2+ ions occupy the interstitial position of the fluorite lattice. The averaged numbers of U5+ ions bonded to one Mg2+ ion, alpha, were very small, i.e. 0.1-0.4. The large leftward shift in the curves of Delta(G) over bar (O2) vs. O/M ratio for this quarternary solid solution was considered to be caused by these small alpha values. (C) 2001 Elsevier Science B.V. All rights reserved.