Betpakdalite Unmasked, and a Comment on Bond Valences

Abstract

A new representation of the crystal structure of complex betpakdalite reported in 1984 (R ≈ 0.08) reveals a remarkable case of . hccchhccch 10-layer anion (O^2-)/void ( ) close-packing. The transformation matrix from earlier C12/m 1 cell to new F 2/m 11 cell is [010/100/102], new a = 11.10, b = 19.44, c = 22. 93 Å, α)/10 = 2.29 Ǻ. The packing efficiency is V_e = 15.45 Å α³ for 10 layers of 32(O₂^-+ ) per layer. For Pauling r(O²-) = 1.40 Å, V_e = 15.52 ų. Oxide anions populate only 46.25% of the close-packed slots; the rest are voids. The difference, Δ, between real structure and ideal (perfect) structure is (0.13 Å) for O^2-, (0.20 Å) for cations and (0.15 A) for all atoms in the close-packed frame, range 0.00-0.43 Å. The cell formula for x = 2 is H₈ [K(H₂O)₆]₄ [Ca(H₂0)₆]₈ [MO⁶⁺₃₂ As⁵⁺₈O₁₄₈]^28-.8H₂O. It is suggested that H₈ bonds with 8O(10) in the cell, the only anion bonded to only one Mo₆₊. The cell formula gives D(calc) = 2.90 g cm^-3, close to reported D( obs ) = 2.98, 3.05; and 2.92 g cm^-3.

Bond strength/bond valence calculations for assorted M^p+₆ ø ^q- (M = octahedral cation linked to generalized anion ø) often show extreme deviations. This is shown to be a consequence of Pauling's third rule of cation-cation repulsions across shared polyhedral edges and faces.