Estimating Free Energies of Formation of Titanate () and Zirconate () Pyrochlore Phases of Trivalent Lanthanides and Actinides
Table 4
Ionic radii and thermodynamic data for aqueous cations and estimated standard Gibbs free energies of formation for perovskite and pyrochlore families of solids.
(nm)
Ξ (kJ/mol)
(kJ/mol)
(kJ/mol)
Perovskite
Pyrochlore
Pyrochlore
(M2(ZrO3) 3) (Calc.)
(M2(ZrO3)3) (Estim.)
(M2Ti2O7) (Calc.)
(M2Ti2O7) (Estim.)
(M2Zr2O7) (Calc.)
(M2Zr2O7) (Estim.)
(M2Ti2O7) (Estim.)
La3+
0.1061
757.70
β4835.98
β4920.94
β3583.89
β3567.62
β3842.30
β3848.29
β63.77
Sm3+
0.0964
781.88
β4857.71
β4914.34
β3530.10
β3566.39
β3829.52
β3847.09
β51.40
Gd3+
0.0938
789.21
β4855.00
β4912.34
β3544.03
β3565.99
β3817.44
β3846.69
β42.78
Tb3+
0.0923
799.51
β
β4909.52
β
β3565.24
β
β3845.96
β30.89
Dy3+
0.0908
787.21
β4894.71
β4912.89
β3570.15
β3566.40
β3850.86
β3847.11
β33.71
Ho3+
0.0894
779.85
β4912.01
β4914.91
β3569.08
β3567.13
β3860.59
β3847.84
β23.59
Er3+
0.0881
785.41
β4930.46
β4913.39
β3576.73
β3566.78
β3872.94
β3847.48
β15.20
Tm3+
0.0870
793.33
β4919.59
β4911.23
β3625.85
β3566.21
β3857.27
β3846.93
β22.84
Yb3+
0.0930
806.96
β4945.84
β4907.49
β3500.50
β3565.15
β3790.61
β3845.89
β57.56
Lu3+
0.0850
829.12
β4924.03
β4901.42
β3555.91
β3563.36
β3853.82
β3844.11
β27.61
Y3+
0.1080
746.28
β4953.24
β4924.07
β3612.56
β3568.42
β3891.27
β3849.08
β35.70
Nd3+
0.0995
774.61
β4841.48
β4916.32
β3535.94
β3566.74
β3825.21
β3847.43
β57.67
Ce3+
0.1034
771.37
β
β4917.20
β
β3566.70
β
β3847.38
β64.51
Pr3+
0.1013
765.77
β
β4918.74
β
β3567.34
β
β3848.01
β57.68
Am3+
0.1070
841.66
β4733.58
β4897.92
β
β3560.49
β
β3841.24
β53.65
Np3+
0.1100
921.57
β
β4876.00
β
β3553.54
β
β3834.36
β68.75
U3+
0.1165
957.85
β4502.28
β4866.03
β
β3549.95
β
β3830.81
β75.70
Pu3+
0.1080
862.05
β4758.69
β4892.32
β
β3558.70
β
β3839.47
β57.51
Eu3+
0.0950
875.42
β4690.74
β4888.69
β3360.55
β3558.65
β3657.06
β3839.44
β59.79
Cationic radii are from [41]. Values of of the cations were calculated using values obtained from [42, 43] as described in [30]. The calculated of the perovskite and pyrochlore solid crystals are from (4) by the thermochemical cycles shown in Table 2. The estimated values of the perovskite and pyrochlore solid crystals are from (1). Calculated values of the solid titanate pyrochlore solid crystals are from (8) using the estimated of the solids. All calculations are at 25Β°C and 1βbar.