The Softness Parameters of Ions. Prediction of the Occurrence of Miscibility Gaps in Molten Salt Mixtures

Softness parameters σ_M for cations and σ_X for anions, have been calculated as dimensionless quantities for approx. 90 cations and 18 anions. They are given by σ_M = σ_A (M^m+) - σ_A(H⁺)]/σ_A(H⁺) and σ_X = σ_B(X^a?) - σ_B(OH^?)]/σ_A(H⁺) where σ_A = σI_i(M) + ΔH⁰_h(M^m+)]/m and σ_B = -E_a(X) + ΔH⁰_h(X^a?)]/a are Ahrland's parameters. The new normalized and comparative (to the test ions H⁺ and OH^?) softness parameters are positive for soft ions and negative for hard ones. These parameters, obtained independently, are used with a four-coefficient equation to calculate coordinate bond energies for metal halides with acceptable accuracy. Considerations of the average coordination in reciprocal molten salt mixture lead to an expression for the metathesis energy change as proportional to the product of the differences in softness parameters of the two cations and the two anions. An empirical one-coefficient equation involving the softness parameters is proposed to deal with next-nearest-neighbor interactions in binary common-ion molten salt mixtures. These relationships are then used with Blander and Topol's equation to predict the occurrence of irascibility gaps in uni-univalent reciprocal salt mixtures. The gaps found in other systems are also discussed in terms of the softness of the constituent ions.