STATISTICAL ANALYSIS OF THE STEREOCHEMISTRY OF (BO3)3- IN THE TOURMALINE-GROUP MINERALS

The tourmaline group minerals are boron-rich cyclosilicates with the general formula: X Y₃ Z₆ T₆ O₁₈ (BO₃)₃ V₃ W.  The most common occupants of these sites are X = Na, Ca, vacancy, K; Y = Mg, Al, Fe²⁺, Fe³⁺, Li; Z = Al, Mg; T = Si, Al; B=B; V = O, (OH); and W = (OH), O, F.  Due to the numerous chemical variations in tourmaline and currently limited abilities in measuring Li, B, H and Fe²⁺/Fe³⁺ without bulk samples, a number of normalization schemes have been utilized to determine the formula of tourmaline species.  However, even the best of these normalization schemes involve the use of assumptions and chemical gerrymandering.  Clark and Hawthorne (in press; Clark, Hawthorne, and Henry, 2003; Clark-McCracken, PhD. Thesis, 2002) proposed using the lengths of the bonds in the triangularly-coordinated (BO₃)^3- group as a way to more definitively determine the chemical formula.  They observed that the mean boron-oxygen bond length was static, while the ratio of the individual B-O2 and B-O8 bonds varied with chemistry at the cation sites.  Preliminary results suggest that the Z'-O8 bond has the greatest effect on the stereochemistry of the B-site.  In order to verify this relationship, electron microprobe analysis and single crystal X-ray diffraction data were collected from previously published literature.  The data were condensed using stepwise linear regression in order to find a function that models the relationship between bond-length ratio and chemistry.  The statistical relationship between the B-O2/B-O8 ratio and cation-site chemistry provides a test for validity of assumptions in tourmaline normalization when complete chemistry cannot be obtained.