We have studied the delta-phase to defect fluorite F* (order-disorder) transition in the R4M3O12 (R = Sc, Tm, Lu; M = Zr, Hf) compounds. The temperature of the delta-F* phase transition in Tm4Zr3O12 is similar to 1600 degrees C. The rate of this transition in R4Zr3O12 (R = Sc, Tm, Lu) decreases markedly with decreasing difference in ionic radius between the R3+ and Zr4+, leading to stabilization of the delta-phases R4Zr3O12 with R = Sc and Lu at high temperatures (similar to 1600 degrees C). During slow cooling (5 degrees C/h), the high-temperature defect fluorites PR2Hf2O7(R = Tm, Lu) decompose reversibly to form the delta-phases R4Hf3O12. Some of the materials studied exhibit microdomains formation effects, typical of the fluorite-related oxide compounds in the R2O3-MO2 (M = Ti, Zr, Hr) systems of the heavy rare earths. The high-temperature defect fluorites F*-R4M3O12 (R = Tm, Lu; M = Zr, HO as a rule contain antiphase microdomains of S-R4Zr3O12. After slow cooling (5 degrees C/h), such microdomains are large enough for the delta-phase to be detected by X-ray diffraction. The conductivity data for R4M3O12 (R = Sc, Tm, Lu; M = Zr, HO and Ln(2)Hf(2)O(7) (Ln = Dy, Lu) prepared by different procedures show that the rhombohedral phases delta-R4M3O12 (R = Sc, Tm, Lu; M = Zr, HO are poorer conductors than the defect fluorites, with 740 degrees C conductivity from 10(-6) to 10(-5) S/cm. The conductivity drops with decreasing rare-earth ionic radius and, judging from the Ea values obtained (1.04-1.37 eV), is dominated by oxygen ion transport. The highest conductivity, similar to 6 x 10(-4) S/cm at 740 degrees C, is offered by the rapidly cooled F*-Dy2Hf2O7. In the fluorite homologous series, oxygen ion conductivity decreases in the order defect pyrochlore > defect fluorite > delta-phase. (C) 2011 Elsevier Ltd. All rights reserved.