Bond-valence theory is used to explore the local arrangements involving vacancies at the Y and Z sites in the tourmaline structure. The local bond-valence requirements of all possible local arrangements around the O8, O7, O6, O3 and O1 anion-sites have been determined for Y- and Z-site vacancies locally associated with Li1+, Mg2+, Al3+, Fe2+, Fe3+, B3+ and Si4+. The results show that arrangements involving tetrahedrally coordinated TR3+-cations and octahedrally coordinated YR2+- and ZR2+-cations around O8, 07 and O6 can be ruled out, together with arrangements involving vacancies and YLi1+. As the occurrence of a Y-site vacancy (Y☐) is more in accord with the valence-sum rule than the occurrence of a Z-site vacancy (Z☐), Y☐ is more likely to occur than Z☐ in tourmaline. Local arrangements involving vacancies around O1- and O3-sites can be stable for OH−, but not for O2−. Of particular interest in this regard are the arrangements [YR3+YR3+Y☐]−O1(OH−) and [ZR3+ZR3+Y☐]−O3(OH−), which yield the smallest deviations from the valence-sum rule. Coupling these stable arrangements with 2 × [TSi4+ZR3+Y☐]−O6(O2−) forms larger vacancy clusters: [Y(R3+)2−O1(OH−)−y(☐)− O3(OH−)−O6(O2−)2−(ZR3+TSi4+)2]. In tourmaline, vacancies are more favoured to occur at Y rather than at Z, in tandem with OH− at O3 and O1, R3+ at Y and Z and Si4+ at T.

The stabilities of possible Y(R3+ + R2+ + Li+) clusters around the W anion (O1 site) of the tourmaline structure were checked using the bond-valence approach. Arrangements involving R3+ = Al3+ or Fe3+ and R2+ = (Fe, Mn, Mg)2+ were all found to be stable. Structural data show a strong linear correlation between the mean formal valence (MFV) of the Y cations and the long-range average bond valence sum (BVS) at the O1 site, as estimated from bond-valence parameters. This correlation is observed for all chemical compositions of tourmaline, except for fluor-buergerite where the O3 site is dominated by oxygen anions. Results show that the long-range site populations of the Y and O1 sites are related to each other by valence constraints described by the empirical and theoretical equations: BVS(O1) = [0.99 MFV(Y) − 1.20] and MFV(O1) = [1.00 MFV(Y) − 1.00], respectively. The systematic deviation of the empirical equation from the ideal one is ascribed to the occurrence of bond strain involving the O1 site. An important implication of the correlation between MFV(Y) and BVS(O1) is that the (OH) content at the O1 site may be estimated by the equation W(OH) = 2 − [1.01 BVS(O1)] − 0.21 − F.