Abstract

Extension of the local bond-valence approach from Mg–Al to Fe2+–Fe3+ short-range arrangements is explored in the structure of tourmaline. Stable local arrangements involving trivalent (R3+) cations (Al, Fe3+) and divalent (R2+) cations (Mg, Fe2+) around the W and V anion sites in Li-free tourmaline result from short-range bond-valence requirements. The coupling of these stable local arrangements determines the formation of larger clusters of octahedra of general form [WY3VZ2], which can have either ordered or disordered distributions of R3+ and R2+ cations. These clusters are related through four different expressions: 1) 2 YR2+ + ZR3+ + W(OH)1− ⇌ 2 YR3+ + ZR2+ + WO2−, 2) 2 YR2+ + 2 ZR3+ + W(OH)1− ⇌ 2 YR3+ + 2 ZR2+ + WO2−, 3) YR2+ + 2 ZR3+YR3+ + 2 ZR2+, and 4) YR2+ + ZR3+YR3+ + ZR2+. Such relations describe the occurrence of both R3+ cations at the octahedrally coordinated Y site and R2+ cations at the octahedrally coordinated Z site of tourmaline, and lead to long-range ordered or disordered arrangements. In nature, disordered structural formulae are the rule owing to long-range requirements of geometrical fit and the minimization of strain.

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