Composites and methods useful for oxygen sorption and other uses are presented, the composites comprising:(A) one or more crystalline ceramic oxides selected from compounds within general formula (1):AxA′x′ByB′y′O3-δ and (1)(B) one or more crystalline ceramic oxides selected from compounds within general formulas (2), (3), (4), (5), (6), (7), and (8):A2BO4-δ (2)A2B2O5-δ (3)AO(ABO3-δ)n (4)AM2Cu3O7-δ (5)Bi4V2(1-x)Me2xO11-3x, (6)A″B″O3 (7)A2B2O7-δ. (8)