Estimating Free Energies of Formation of Titanate (M_𝟐Ti_𝟐O_𝟕) and Zirconate (M_𝟐Zr_𝟐O_𝟕) 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.

M^3+	𝑟M^3+ (nm)	Δ𝐺^0𝑛 (kJ/mol)	Δ𝐺^0𝑓,MvX (kJ/mol)						Δ𝐺^0𝑟,OX (kJ/mol)
		M^(3+aq)	Perovskite		Pyrochlore				Pyrochlore
			(M2(ZrO3) 3) (Calc.)	(M2(ZrO3)3) (Estim.)	(M2Ti2O7) (Calc.)	(M2Ti2O7) (Estim.)	(M2Zr2O7) (Calc.)	(M2Zr2O7) (Estim.)	(M2Ti2O7) (Estim.)
La^3+	0.1061	757.70	−4835.98	−4920.94	−3583.89	−3567.62	−3842.30	−3848.29	−63.77
Sm^3+	0.0964	781.88	−4857.71	−4914.34	−3530.10	−3566.39	−3829.52	−3847.09	−51.40
Gd^3+	0.0938	789.21	−4855.00	−4912.34	−3544.03	−3565.99	−3817.44	−3846.69	−42.78
Tb^3+	0.0923	799.51	—	−4909.52	—	−3565.24	—	−3845.96	−30.89
Dy^3+	0.0908	787.21	−4894.71	−4912.89	−3570.15	−3566.40	−3850.86	−3847.11	−33.71
Ho^3+	0.0894	779.85	−4912.01	−4914.91	−3569.08	−3567.13	−3860.59	−3847.84	−23.59
Er^3+	0.0881	785.41	−4930.46	−4913.39	−3576.73	−3566.78	−3872.94	−3847.48	−15.20
Tm^3+	0.0870	793.33	−4919.59	−4911.23	−3625.85	−3566.21	−3857.27	−3846.93	−22.84
Yb^3+	0.0930	806.96	−4945.84	−4907.49	−3500.50	−3565.15	−3790.61	−3845.89	−57.56
Lu^3+	0.0850	829.12	−4924.03	−4901.42	−3555.91	−3563.36	−3853.82	−3844.11	−27.61
Y^3+	0.1080	746.28	−4953.24	−4924.07	−3612.56	−3568.42	−3891.27	−3849.08	−35.70
Nd^3+	0.0995	774.61	−4841.48	−4916.32	−3535.94	−3566.74	−3825.21	−3847.43	−57.67
Ce^3+	0.1034	771.37	—	−4917.20	—	−3566.70	—	−3847.38	−64.51
Pr^3+	0.1013	765.77	—	−4918.74	—	−3567.34	—	−3848.01	−57.68
Am^3+	0.1070	841.66	−4733.58	−4897.92	—	−3560.49	—	−3841.24	−53.65
Np^3+	0.1100	921.57	—	−4876.00	—	−3553.54	—	−3834.36	−68.75
U^3+	0.1165	957.85	−4502.28	−4866.03	—	−3549.95	—	−3830.81	−75.70
Pu^3+	0.1080	862.05	−4758.69	−4892.32	—	−3558.70	—	−3839.47	−57.51
Eu^3+	0.0950	875.42	−4690.74	−4888.69	−3360.55	−3558.65	−3657.06	−3839.44	−59.79

Cationic radii are from [41]. Values ofΔ𝐺^0𝑛 of the cations were calculated using Δ𝐺^0𝑓values obtained from [42, 43] as described in [30]. The calculatedΔ𝐺^0𝑓,_MvX of the perovskite and pyrochlore solid crystals are from (4) by the thermochemical cycles shown in Table 2. The estimated Δ𝐺^0𝑓,_MvX values of the perovskite and pyrochlore solid crystals are from (1). Calculated Δ𝐺^0𝑟,_OX values of the solid titanate pyrochlore solid crystals are from (8) using the estimated Δ𝐺^0𝑓,_MvX of the solids. All calculations are at 25°C and 1 bar.