Use of linear free energy relationship to predict Gibbs free energies of formation of zirconolite phases (MZrTi_2O_7 and MHfTi_2O_7)

摘要

In this letter, the Sverjensky-Molling equation derived from a linear free energy relationship is used to calculate the Gibbs free energies of formation of zirconolite crystalline phases (MZrTi_2O_7 and MHfTi_2O_7) from the known thermodynamic properties of the corresponding aqueous divalent cations (M~(2+)). Sverjensky-Molling equation is expressed as #DELTA#G_(f.M_v)X~0=a_(M_vX)#DELTA#G_(n.M~2+)~0 + b_(M_vX) + #beta#_(M_vX)r_(M~(2+)), where the coefficients a_(M_vX), b_(M_vX), and #beta#_(M_vX) characterize a particular structural family of M_vX, r_(M~(2+)) is the ionic radius of M~(2+) cation, #DELTA#G_((f.M_vX)~0) is the standard Gibbs free energy of formation of M_vX, and #DELTA#G_((n.M~(2+))~0) is the standard non-solvation energy of cation M~(2+). This relationship can be used to predict the Gibbs free energies of formation of various fictive phases (such as BaZrTi_2O_7, SrZrTi_2O_7, PbZrTi_2O_7, etc.) that may form solid solution with CaZrTi_2O_7 in actual Synroc-based nuclear waste forms. Based on obatained linear free energy relationships, it is predicted that large cations (e.g., Ba and Ra) prefer to be in perovskite structure, and small cations (e.g., Ca and Cd) prefer to be in zirconolite structure.