Sodic, calcic and subcalcic amphiboles are expressed by the combination of tremolite, edenite, tschermakite, glaucophane, magesioriebeckite and Fetremolite. Because such complex compositions of amphiboles provide enough chemical variables to constrain equilibrium conditions of the metabasic syste, amphibole composition makes it possible for Gibbs' method to be applied to this system. We made a framework for estimating quantitative P-T paths from compositions of a zoned amphibole in metabasite consisting of amphibole, chlorite, epidote, plagioclase, quartz and water in the system derivatives simply, mole fractions of cations in each site were introduced as the variables of amphibole composition. In obtaining non-ideality terms of amphibole activity, we used the regular solution models with 15 Margules parameters derived from published data. Application of the differential thermodynamics to a natural basic schist from the Sanbagawa metamorphic belt in central Shikoku provides both prograde and retrograde paths. The ranges of calculated P-T conditions are in good agreement with the previous study, and calculated compositions of co-existing minerals are consistent with the values from analyses of minerals in the sample. Activity models for amphiboles, especially non-ideality of tremolite-tschermakite (tr-ts) and tremolite-edenite (tr-ed) joins, provide significant effects on the calculated P-T paths. The initial P-T conditions given at the amphibole rim affect the calculated P-T paths slightly, but the shapes and lengths of the paths almost do not change. If compositional changes in each step of the amphibole zoning are small enough, Gibbs' method is able to transform the change of amphibole chemistry into changes of P-T conditions that are independent of the histories of the compositional changes of amphibole. This implies that all amphibole chemistry can be translated into the specific P-T condition, considering the relative compositional change from the reference amphibole, as long as the same mineral assemblage is preserved.
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