The enthalpies of formation of cubic urania - thoria (c-ThxU(1) O-x(2+y)) and urania - zirconia (c-ZrxU(1) O-x(2), x < 0.3) solid solutions at 25 degrees C from end-member binary oxides (c-UO2, and c-ThO2 or m-ZrO2) have been measured by high temperature oxide melt solution calorimetry. The enthalpies of mixing for both systems are zero within experimental error. The interaction parameters for binary solid solutions MO2 - M'O-2 (M, M' = U, Th, Ce, Zr, and Hf), fitted by regular and subregular thermodynamic models using both calorimetric and computational data, increase linearly with the corresponding volume mismatch. Cubic UO2 - ZrO2 appears to be an exception to this correlation and shows a zero heat of mixing despite large size mismatch, suggestive of some short-range ordering and/or incipient phase separation to mitigate the strain. The incorporation of ZrO2 into UO2 stabilizes the system and makes it a potential candidate for immobilization and disposal of nuclear waste. (C) 2017 Elsevier Ltd.