Abstract

Modal-space illustrates changes in the volumes and compositions of minerals in a rock (Thompson 1991), for example, in response to P-T-sensitive, high-variance reactions. The method is applied to retrograded eclogite (Pl + Cpx + Grt + Qz + Hbl + Ep) in the Cuaba Unit of the Rio San Juan Complex in the Dominican Republic (Abbott & Draper 2007), where the issue is characterizing the highest-grade mineral assemblage (Omp + Grt + Coe ± Ky). For the purpose of comparing volumes, additive mineral components are normalized to one oxygen atom, such that grt = M1/4A1/6Si1/4O, px = M1/3Si1/3O, where M = Fe2+ + Mg + Mn, A = Al + Fe3+; an = Ca1/8Al1/4Si1/4O(anorthite), qz(quartz) = coe(coesite) = Si1/2O, and ky(kyanite) = Al2/5Si1/5O. A mole of each has approximately the same volume for all phases (10.6 ± 1.1 cm3/mole “O”). The error in the approximation is acceptable, given the error in estimating modal proportions, and especially given normal heterogeneity in a rock. Sodium in the form of an1/3ab2/3 = csk1/2jd1/2 (an = 1/8CaAl2Si2O8, ab = 1/8NaAlSi3O8, csk = 1/6Ca1/21/2AlSi2O6, jd = 1/6NaAlSi2O6) is subtracted from the bulk composition. This works because the composition of any plagioclase can be expressed as a linear combination of an1/3ab2/3 and an. The residual bulk-rock chemistry (after subtracting an1/3ab2/3 = csk1/2jd1/2) is in the CMAS system (M = Fe2+ + Mg + Mn, A = Al + Fe3+). Two CMAS exchange components are included, tk = A2M–1Si–1 (tschermak) and cm = CaM–1. The modal space is then defined by three independent vectors in CMAS:  
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For a particular bulk composition, accessible parts of the modal space define a polyhedron. A point within the polyhedron is defined by a linear combination of V1, V2, and V3, and in CMAS relates to the modal proportions of the minerals and their compositions. The composition and total volume of plagioclase or pyroxene are easily corrected for the amounts of non-CMAS an1/3ab2/3 or csk1/2jd1/2, respectively. For mafic compositions, different parts of the polyhedron correspond to basalt/gabbro, pyroxene granulite, garnet granulite, eclogite, and extremely high-P assemblages with majoritic garnet. The modal polyhedron can be calculated in two ways: (1) from the bulk composition, or (2) from mineral chemistry and observed modal proportions. When the description of the system is internally consistent, the two approaches converge on the same polyhedron.
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