Biotite from pelitic hornfelses, northeastern Minnesota, shows a wide compositional range, from Mg/(Mg + Fe) = 0.35 to 0.95. Strong correlations among Mg, Fe, Ti, VIAl, and IVAl are observed, and the technique of principal components analyses is used to extract independent biotite components. The dependence of composition on assemblage is exemplified by biotite from the assemblage quartz + muscovite + biotite + cordierite + K-feldspar + ilmenite with compositions that contain more dioctahedral component and less Ti than biotite from a similar, but muscovite-free assemblage. Principal components analysis shows that 98% of the total variance in compositions of biotite from the muscovite-bearing assemblage can be ascribed to two substitutions with phlogopite: the substitution IVAl0.45 + Fe2.29 + VIAl0.21 + Ti0.31 + VI0.19 ⇌ Si0.45 + Mg3.0, and the substitution Ti1.5 + IV0.5VIAl2. The analysis indicates that although biotite is rigorously a six- or more-component mineral, three components are sufficient to describe the bulk of its compositional range. These three components are used to calculate the possible range in biotite compositions for the muscovite-bearing assemblage using ideal-mixing activity models. The calculated range is very similar to the observed range; however, the absolute value of KD (Mg/Fe, Cord/bio) is underestimated. In addition, the amounts of octahedral Al, Ti, and vacancies are poorly estimated, especially for Mg-rich biotite. These faults are probably the result of treating biotite as a three-component rather than a six-component phase. The observed cation correlations are believed to result from crystal chemical constraints on the volume of the biotite unit cell. It is proposed that biotite compositions from a particular assemblage might be sensitive indicators of the thermal gradient.

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