Quantitative P-T paths from zoned minerals: Theory and tectonic applications |
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| Authors: | Frank S Spear Jane Selverstone |
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| Institution: | (1) Department of Earth and Planetary Science, Massachusetts Institute of Technology, 02139 Cambridge, Massachusetts, USA |
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| Abstract: | An analytical approach to the analysis of zoning profiles in minerals is presented that simultaneously accounts for all of the possible continuous reactions that may be operative in a given assemblage. The method involves deriving a system of simultaneous linear differential equations consisting of a Gibbs-Duhem equation for each phase, a set of linearly independent stoichiometric relations among the chemical potentials of phase components in the assemblage, and a set of equations describing the total differential of the slope of the tangent plane to the Gibbs free energy surface of solid solution phases. The variables are the differentials of T, P, chemical potentials of all phase components, and independent compositional terms of solid solution phases. The required input data are entropies, volumes, the compositions of coexisting phases at a reference P and T, and an expression for the curvature of the Gibbs functions for solid solution phases. Results derived are slopes of isopleths (dP/dT, dX/dT or dX/dP) which can be used to contour P-T diagrams with mineral composition.To interpret mineral zoning, T and P can be expressed as functions of n independent composition parameters, where n is the variance of the mineral assemblage. The total differentials of P and T are differential equations that can be solved by finite difference techniques using the derivatives obtained from the analytical formulation of phase equilibria.Results calculated from Zone I and Zone IV garnets of Tracy et al. (1976) indicate that Zone I garnets grew while T increased ( T +72° C) and P decreased sharply (P–3 kb). Zone IV garnets zoned in response to decreasing T (T–17° C) and P (P–1 kb). A P-T path calculated for a zoned garnet from the Greinerschiefer series, western Tauern Window, Austria, also indicates growth during decompression ( –3kb) and heating (T+15° C). A P-T path calculated for the Wissahickon schist (Crawford and Mark 1982) indicates growth during cooling and compression (T–25 C, P+2.2 kb). The calculated P-T paths differ according to structural environment and can be used to relate mineral growth to tectonic processes. |
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