Linear free energy relationship applied to trivalent cations with lanthanum and actinium oxide and hydroxide structure

Linear free energy relationships for trivalent cations with crystalline M₂O₃ and, M(OH)₃ phases of lanthanides and actinides were developed from known thermodynamic properties of the aqueous trivalent cations, modifying the Sverjensky and Molling equation. The linear free energy relationship for trivalent cations is as , where the coefficients a_MvX, b_MvX, and β_MvX characterize a particular structural family of MvX, r_M³⁺ is the ionic radius of M³⁺ cation, is the standard Gibbs free energy of formation of MvX and is the standard non-solvation free energy of the cation. The coefficients for the oxide family are: a_MvX = 0.2705, b_MvX = −1984.75 (kJ/mol), and β_MvX = 197.24 (kJ/mol nm). The coefficients for the hydroxide family are: a_MvX = 0.1587, b_MvX = −1474.09 (kJ/mol), and β_MvX = 791.70 (kJ/mol nm).