Empirical electronic polarizabilities: deviations from the additivity rule. I. M2+SO4·nH2O, blödite Na2M2+(SO4)2·4H2O, and kieserite-related minerals with sterically strained structures

Empirical electronic polarizabilities allow the prediction of total mineral polarizabilities and mean refractive indices of the vast majority of minerals and synthetic oxides. However, deviations from the valence-sum rule at cations in some minerals are associated with large deviations of observed from calculated total polarizabilities. We have identified several groups of minerals and compounds where deviations from the valence-sum rule at cations lead to polarizability deviations of 2–5%: M(SO4)·nH2O, n = 1–6, blodite-group minerals [Na2M2+(SO4)2·4H2O], and the kieserite-related minerals: isokite, panasqueiraite and tilasite. In these minerals, the environment of the M ions contains both O and H2O: Mg[O4(H2O)2] in kieserite, szmikite, and szomolnokite; Mg[O2(H2O)4] in starkeyite, ilesite, and rozenite, and Mg[(H2O)6] in hexahydrite. In compounds where the ligands are only H2O, deviations from the valence-sum rule at the M(H2O)6 groups are not accompanied by significant polarizability deviations. This is the case for epsomite, MgSO4·7H2O; bieberite, CoSO4·7H2O; goslarite, ZnSO4·7H2O, six silicofluorides, MSiF6·6H2O; eighteen Tutton’s salts, M2M′(SO4)2·6H2O, where M = K, Rb, Cs and M′ = Mg, Mn, Fe, Co, Ni, Cu, and Zn; and eleven MM′(SO4)2·12H2O alums, where M = Na, K, Rb and Cs, and M′ = Al, Cr, Ga and In. This is also the case for the sulfates alunogen, Al2(SO4)3·17H2O and halotrichite, FeAl2(SO4)4·22H2O; three hydrated nitrates; one phosphate; three antimonates and two hydrated perchlorates. A possible explanation for this different behavior is that the bond-valence model treats O and H separately, whereas polarizability calculations treat the polarizability of the entire H2O molecule.