Atomistic calculations of the thermodynamic properties of mixing for tetravalent metal dioxide solid solutions: (Zr, Th, Ce)O2

The thermodynamic mixing properties for isometric ThxCe1−xO2, CexZr1−xO2, and ThxZr1−xO2 were determined using quantum-mechanical calculations and subsequent Monte-Carlo simulations. Although the ThxCe1−xO2 binary indicates exsolution below 600 K, the energy gain due to exsolution is small (Eexsoln=1.5 kJ/(mol cations) at 200 K). The energy gain for exsolution is significant for the binaries containing Zr; at 1000 K, Eexsoln=6 kJ/(mol cations) for the CexZr1−xO2 binary, and Eexsoln=17 kJ/(mol cations) for the ThxZr1−xO2 binary. The binaries containing Zr have limited miscibility and cation ordering (at 200 K for x=0.5). At 1673 K, only 4.0 and 0.25 mol% ZrO2 can be incorporated into CeO2 and ThO2, respectively. Solid-solution calculations for the tetragonal ThxZr1−xO2 binary show decreased mixing enthalpy due to the increased end-member stability of tetragonal ZrO2. Inclusion of the monoclinic ZrO2 is predicted to further reduce the mixing enthalpy for binaries containing Zr.

Temperature-composition phase diagram showing miscibility gaps for the isometric ThxCe1−xO2, isometric CexZr1−xO2, isometric ThxZr1−xO2, and tetragonal ThxZr1−xO2 binaries at low composition (0► ΔHmix, ΔGmix, and ΔSmix of ThxCe1–xO2, ThxZr1–xO2, and CexZr1–xO2 binaries are calculated.
► Cation ordering is identified at low T for binaries containing ZrO2.
► Phase diagrams are estimated based on DFT and Monte-Carlo calculations.
► DFT and Monte-Carlo calculations are in agreement with experimental (and previous computational) results, where available.
► Increased thermodynamic stability of monoclinic and tetragonal ZrO2 end-member affects solid solution binaries.