Empirical electronic polarizabilities of ions for the prediction and interpretation of refractive indices: Oxides and oxysalts

An extensive set of refractive indices determined at lambda = 589.3 nm (n(D)) from similar to 2600 measurements on 1200 minerals, 675 synthetic compounds, similar to 200 F-containing compounds, 65 Cl-containing compounds, 500 non-hydrogen-bonded hydroxyl-containing compounds, and similar to 175 moderately strong hydrogen-bonded hydroxyl-containing compounds and 35 minerals with very strong H-bonded hydroxides was used to obtain mean total polarizabilities. These data, using the Anderson-Eggleton relationship alpha(r) = (n(D)(2) - 1)V-m/4 pi+(4 pi/3 - c) (n(D)(2) - 1) where alpha(T) = the total polarizability of a mineral or compound, n(D) = the refractive index at lambda = 589.3 nm, V-m = molar volume in angstrom(3), and c = 2.26, in conjunction with the polarizability additivity rule and a least -squares procedure, were used to obtain 270 electronic polarizabilities for 76 cations in various coordinations, H2O, 5 HxOy species [(H3O)(+), (H3O2)(-), (H3O2)(-), (H4O4)(4-)], NH4+ and 4 anions (F-, Cl-, OH-, O2-. Anion polarizabilities are a function of anion volume, V-an, according to alpha_ = alpha(0)_.10(-NoV1.20) where alpha_ = anion polarizability, alpha_(o) = free -ion polarizability, and V-an = anion molar volume. Cation polarizabilities depend on cation coordination according to a light -scattering (LS) model with the polarizability given by alpha((CN)) = (alpha(1) + alpha 2CNe-alpha 3CN)(-1) where CN = number of nearest neighbor ions (cation -anion interactions), and a(1), a(2), and a(3) are refillable parameters. This expression allowed fitting polarizability values for Li+, Na+, Rb+, Cs+, Mg2+, Ca+, Sr+, Ba+, Mn+, Fe+, 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), Delta = 6% and Ca3Mg2Si2O8 (merwinite), Delta = 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), Delta = 9-12% and KNbO3, A = 10%]; (4) edge -shared Fe3+ and Mn3+ structures (ESO) such as goethite (FeOOH, Delta = 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 similar to 2600 polarizability values using 76 cation polarizabilities with values for Li+ -> Cs+, Ag+, Be2+ > Ba2+, Me2+3+, Fe2+3+, Co2+, Cu+/2+ Zn2+, B2+ -> In3+, Fe3+, Cr3+, Sc3+, Y3+, Lu3+ -> La3+, -> Cs+, Ag+, Be2+ -> Ba-2+,Ba- Mn2+/3+ ,Fe2+/3+, Co2+,Cu+/2+, B3+ -> In3+ Fe3+, Cr3+, '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, Delta > 3%. Using n(D) = root 4 pi alpha/(2.26 - 4 pi/3) alpha+V-m the mean refractive index can be calculated from the chemical composition and the polarizabilities of ions determined here. The calculated mean values of for 54 common minerals and 650 minerals and synthetic compounds differ by <2% from the observed values. In a comparison of polarizability analysis with 68 Gladstone-Dale compatibility index (CI) (Mandarin 1979, 1981) values rated as fair or poor, we find agreement in 32 instances. However, the remaining 36 examples show polarizability Delta values <3%. Thus, polarizability analysis may be a more reliable measure of the compatibility of a mineral's refractive index, composition, and crystal structure.