The chemical compositions of solid-solution minerals in metamorphic rocks are controlled by equilibria not only of exchange reactions but also of net-transfer reactions among coexisting minerals. In rocks with a variance of 2, the compositions of solid-solution minerals are functions of temperature and pressure alone as is illustrated in Figs. 2 and 3, and so can be used as a measure of the P-T condition under which the rocks were recrystallized. In rocks with a variance of 3 or greater, on the other hand, the compositions of solid-solution minerals vary not only with temperature and pressure but also with the bulk-rock composition (Fig. 4). The growth of zoned crystals causes fractional crystallization, resulting in a change of composition of the reacting system. If the variance of the system is 3 or greater, the change of the composition of the reacting system causes a change in the composition of the crystallizing mineral.
Pelitic metamorphic rocks are commonly simplified as belonging to the 6-component system : Al
2O
3-FeO-MgO-K
2O-SiO
2-H
2O. In this case the mineral assemblages may be shown on the THOMPSON AFM diagram. Any 3-AFM phase assemblage in the diagram has a variance of 2, whereas any 2-AFM phase assemblage has a variance of 3.
In the paragenetic relations of garnet, MnO commonly plays an essential role, and so garnet-bearing metapelites are commonly treated as belonging to the 7-component system : Al
2O
3-FeO-MgO-MnO-K
2O-SiO
2-H
2O. Most metapelites with MnO-rich garnet have a variance of 3 or greater. Garnets in low- and middle-grade metamorphic rocks are usually strongly zoned. Hence, the composition (or the MnO content) of garnet is strongly influenced by the initial bulk-rock composition and fractional crystallization. SPEAR (1988) has calculated the progressive compositional change of garnet that grows not only under complete equilibrium condition but also with fractional crystallization for garnet-bearing 3-AFM phase assemblages that are observed in the Barrovian sequence.
In the Sanbagawa high P/T ratio metamorphic belt, progressive metamorphism is represented by a sequence of the chlorite zone, garnet zone (with no biotite), and biotite zone (with garnet) for metapelites. In other words, garnet begins to occur at a considerably lower temperature than biotite. In the garnet zone, garnet probably forms by reaction involving Tschermak exchange component like (4), whereas in the biotite zone, garnet forms by the same reactions as in the garnet zone of the Barrovian sequence. Such a change in the garnet-producing reactions between the two zones may cause a break in the MnO and FeO curves in the composition profile of zoned garnets. Some of the observed features of the compositional trends of garnets could be ascribed to the effect of a variation in bulk-rock composition.
The average composition of zoned garnets in metapelite shows a progressive decrease of the MnO content with increasing metamorphic grade. This is probably related mainly to a progressive increase of the amount of garnet. Higher pressure tends to increase the amount of garnet, and to decrease its MnO content.
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