Estimating Free Energies of Formation of Titanate () and Zirconate () Pyrochlore Phases of Trivalent Lanthanides and Actinides

Abstract

A linear free energy relationship was developed to predict the Gibbs free energies of formation (, in kJ/mol) of crystalline titanate (M2Ti2O7) and zirconate (M2Zr2O2) pyrochlore families of trivalent lanthanides and actinides (M3+) from the Shannon-Prewitt radius of M3+ in a given coordination state (, in nm) and the nonsolvation contribution to the Gibbs free energy of formation of the aqueous M3+ (). The linear free energy relationship for M2Ti2O7 is expressed as . The linear free energy relationship for M2Zr2O7 is expressed as . Estimated free energies were within 0.73 percent of those calculated from the first principles for M2Ti2O7 and within 0.50 percent for M2Zr2O7. Entropies of formation were estimated from constituent oxides (J/mol), based on an empirical parameter defined as the difference between the measured entropies of formation of the oxides and the measured entropies of formation of the aqueous cation.