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

Abstract

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, blödite-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.