Multi-stage pseudomorphic replacement of garnet during polymetamorphism: 2. Algebraic analysis of mineral assemblages

Chemical relationships among four metapelites have been studied by investigation of mineral and bulk chemistry data and by singular value decomposition analysis of single and composite assemblage matrices. Bulk rock compositions cluster close together in an AFM diagram, all within the intersection space defined by the four sample assemblages. The similarity of bulk compositions normalized on a silica-free, anhydrous basis indicates that sample chemistries differ mainly as a result of inhomogeneous distribution of quartz layers. The existence of mass balance relationships among samples indicates that assemblages also overlap in the Si–Ti–Al–Fe–Mg–Mn–Ca–Na–K multisystem. Analysis of single and composite matrices helps in defining possible mass balances linking sample mineral facies to one another during progressive contact metamorphism. The assemblage in sample A can form as the result of the model reaction 5.000  Ky+0.269 Grt+0.965 Bt+0.314 Pl=0.049 Ilm+1.115 Ms+0.849 Chl+0.306 St and react to assemblage B via reaction 0.97 Chl+0.52 Grt+0.66 Ms+0.14 Ilm+1.26  Ky=0.42 St+0.63 Bt+0.22 Pl coupled with the Ky→And transition. Assemblage B can transform into C by initial progress of Ky+Ilm+Chl+Grt+Ms=And+St+Bt+Pl followed by 0.142 Ilm+0.175 St+1.089 Chl+1.533 Ms+0.003 Grt=5.000 And+1.266 Bt+0.551 Pl Matrix analysis cannot satisfactorily model the C–D transition, because it predicts a net production of staurolite, which is in disagreement with petrographic evidence. All mass balances in the C–D composite matrix indicate net consumption of muscovite; this is integrated with the contrasting evidence of prograde pseudomorphs of muscovite after staurolite, observed in the nodules of sample D, within a model involving the progress of ionic reaction cycles.