Anion polarizabilities are a function of anion volume, Van, according to where α− = anion polarizability, , and Van = anion molar volume. Cation polarizabilities depend on cation coordination according to a light-scattering (LS) model with the polarizability given by where CN = number of nearest neighbor ions (cation-anion interactions), and a1, a2, and a3 are refinable parameters. This expression allowed fitting polarizability values for Li+, Na+, K+, Rb+, Cs+, Mg2+, Ca2+, Sr2+, Ba2+, Mn2+, Fe2+, Y3+, (Lu3+-La3+), Zr4+, and Th4+. Compounds with: (1) structures containing lone-pair and uranyl ions; (2) sterically strained (SS) structures [e.g., Na4.4Ca3.8Si6O18 (combeite), Δ = 6% and Ca3Mg2Si2O8 (merwinite), Δ = 4%]; (3) corner-shared octahedral (CSO) network and chain structures such as perovskites, tungsten bronzes, and titanite-related structures [e.g., MTiO3 (M = Ca, Sr, Ba), Δ = 9–12% and KNbO3, Δ = 10%]; (4) edge-shared Fe3+ and Mn3+ structures (ESO) such as goethite (FeOOH, Δ = 6%); and (5) compounds exhibiting fast-ion conductivity, showed systematic deviations between observed and calculated polarizabilities and thus were excluded from the regression analysis. The refinement for ~2600 polarizability values using 76 cation polarizabilities with values for Li+ → Cs+, Ag+, Be2+ → Ba2+, Mn2+/3+, Fe2+/3+, Co2+, Cu+/2+, Zn2+, B3+ → In3+, Fe3+, Cr3+, Sc3+, Y3+, Lu3+ → La3+, C4+ → Sn4+, Ti3+/4+, Zr4+, Hf4+, Th4+, V5+, Mo6+, and W6+ in varying CN’s, yields a standard deviation of the least-squares fit of 0.27 (corresponding to an R2 value of 0.9997) and no discrepancies between observed and calculated polarizabilities, Δ > 3%.
In a comparison of polarizability analysis with 68 Gladstone-Dale compatibility index (CI) (Mandarino 1979, 1981) values rated as fair or poor, we find agreement in 32 instances. However, the remaining 36 examples show polarizability Δ values <3%. Thus, polarizability analysis may be a more reliable measure of the compatibility of a mineral’s refractive index, composition, and crystal structure.