Table 1 Adopted thermodynamic parameters for the solid solution phases.

Fluorite solid solution (cubic)

Endmember

i

\(\Delta G_{i}^{0}\)(kJ/mol)

\(\Delta S_{i}^{0}\)(J/K/mol)

\(\Delta {Cp}_{i}^{0}\)(J/K/mol)

\({\mathrm{UO}}_{2}\)

1

0.0

0.0

0.0

\({Ln\mathrm{O}}_{1.5}\)

2

0.0

0.0

0.0

\({\mathrm{UO}}_{2.5}\)

3

−81.025

7.0

8.5

\({Ln}_{1/2}^{3}{{\mathrm{U}}_{1/2}^{5}\mathrm{O}}_{2}\)

4

−76.0

0.0

4.25

\({Ln}_{2/3}^{3}{{\mathrm{U}}_{1/3}^{6}\mathrm{O}}_{2}\)

5

−72.0

3.5

6.0

Margules parameter

i,j

\({W}_{ij}^{h}\)(kJ/mol)

\({W}_{ij}^{s}\)(J/K/mol)

1,2

28.0

0.0

1,3

28.3

27.75

U₄O₉ solid solutions (cubic, β or γ)

Endmember

i

\({\Delta G}_{i}^{0}\)(kJ/mol)

\({\Delta S}_{i}^{0}\)(J/K/mol)

\({\Delta Cp}_{i}^{0}\)(J/K/mol)

\({\mathrm{U}}_{1/2}^{4}{{\mathrm{U}}_{1/2}^{5}\mathrm{O}}_{9/4}\)

1

−37.75

8.7

6.0

\(\{{{Ln}_{1/4}^{3}\mathrm{U}}_{1/4}^{5}{{\}\mathrm{U}}_{1/2}^{5}\mathrm{O}}_{9/4}\)

2

−80.3

6.37

3.0

Margules parameter

i,j

\({W}_{ij}^{h}\)(kJ/mol)

\({W}_{ij}^{s}\)(J/K/mol)

1,2

0.0

0.0

α-U₃O₈ solid solution (orthorhombic)

Endmember

i

\({\Delta G}_{i}^{0}\)(kJ/mol)

\({\Delta S}_{i}^{0}\)(J/K/mol)

\({\Delta Cp}_{i}^{0}\)(J/K/mol)

\({\mathrm{U}}_{2/3}^{5}{{\mathrm{U}}_{1/3}^{6}\mathrm{O}}_{8/3}\)

1

−95.3

11.21

15.7

\(\{{{Ln}_{2/9}^{3}\mathrm{U}}_{4/9}^{6}{{\}\mathrm{U}}_{1/3}^{6}\mathrm{O}}_{8/3}\)

2

−97.7

14.84

14.05

Margules parameter

i,j

\({W}_{ij}^{h}\)(kJ/mol)

\({W}_{ij}^{s}\)(J/K/mol)

1,2

5.0

0.0

α’-U₃O₈ solid solution (hexagonal)

Endmember

i

\({\Delta G}_{i}^{0}\)(kJ/mol)

\({\Delta S}_{i}^{0}\)(J/K/mol)

\({\Delta Cp}_{i}^{0}\)(J/K/mol)

\({\{\mathrm{U}}_{2/3}^{5}{{\mathrm{U}}_{1/3}^{6}\}\mathrm{O}}_{8/3}\)

1

−92.0

11.21

15.7

\(\{{{Ln}_{2/9}^{3}\mathrm{U}}_{7/9}^{6}{\}\mathrm{O}}_{8/3}\)

2

−97.7

14.84

14.05

Margules parameter

i,j

\({W}_{ij}^{h}\)(kJ/mol)

\({W}_{ij}^{s}\)(J/K/mol)

1,2

5.0

0.0

A-Ln₂O₃ (hexagonal)

\({Ln\mathrm{O}}_{1.5}\)

1

3.3

7.5

0.0