MODAL-SPACE THEORY: A STUDY OF THE MINERALOGICAL EXPRESSION OF THOLEIITIC COMPOSITIONS AT T > 850 degrees C IN THE LITHOSPHERE AND MANTLE

摘要

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 = M(1/4)A(1/6)Si(1/4)O, 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 cm(3) /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 an(1/3)ab(2/3) = csk(1/2) jd(1/2) (an = 1/8CaAl(2)Si(2)O(8), ab = 1/8NaAlSi(3)O(8), csk = 1/6Ca(1/2)square 1/2AlSi2O6, jd = 1/6NaAlSi(2)O(6)) is subtracted from the bulk composition. This works because the composition of any plagioclase can be expressed as a linear combination of an(1/3)ab(2/3) and an. The residual bulk-rock chemistry (after subtracting an(1/3)ab(2/3) = csk(1/2) jd(1/2)) is in the CMAS system (M = Fe2+ + Mg + Mn, A = Al + Fe3+). Two CMAS exchange components are included, tk = A(2)M(-1)Si(-1) (tschermak) and cm = CaM-1. The modal space is then defined by three independent vectors in CMAS: