Modeling of prograde mineral δ¹⁸O changes in metamorphic systems

Abstract

A general model has been developed to calculate changes of δ¹⁸O of minerals in addition to their composition and modal abundance in metamorphic systems. A complete set of differential equations can be written to describe any chemical system in terms of the variables dP, dT, dX, dM, and dδ¹⁸O (X, M, and δ¹⁸O refer to the chemical composition, number of moles, and oxygen isotope composition of each phase respectively). This set is composed of the differentials of five subsets of equations: (1) conditions of heterogeneous equilibrium; (2) compositional stoichiometry for each mineral; (3) mass balance for each oxide component; (4) oxygen isotope partitioning between phases; (5) conservation of the oxygen isotope ratio of the system. The variance of the complete set of equations is 2, and changes of δ¹⁸O, composition, and modal abundance for each mineral can be calculated for arbitrary changes of P and T. Applications to a typical pelitic bulk composition at amphibolite and lower granulite facies conditions suggest that for systems dominated by continuous reactions such as: (a) chlorite + quartz = garnet+H₂O; (b) staurolite + biotite = garnet + muscovite + H₂O; or (c) garnet + muscovite = sillimanite + biotite, isopleths of mineral δ¹⁸O are nearly independent of pressure, and have a spacing of about 0.1‰ per 10–20°C. For nearly discontinuous reactions such as: (d) garnet + chlorite + muscovite = biotite + staurolite+H₂O; (e) staurolite + muscovite = biotite + aluminosilicate + garnet+H₂O; or (f) muscovite + quartz = sillimanite + K-feldspar+H₂O, isopleths of mineral δ¹⁸O have slopes more nearly parallel to endmember reaction boundaries and δ¹⁸O of phases can have a greater temperature dependence (e.g., 0.1‰ per 2°C for reaction d). This behavior results from relatively large amounts of reaction progress for small changes of P or T. However, the calculated exhaustion of a reactant within 0.1–5°C ensures that the predicted effects of such reactions on mineral δ¹⁸O will not exceed ∼0.25‰ for typical bulk compositions. Models that allow for fractional crystallization of garnet suggest that prograde garnet zoning in pelitic assemblages will be relatively smooth until staurolite becomes unstable. At higher temperatures, garnet may develop a step of as much as 0.6‰ in its core-rim zoning as a result of combined garnet resorption during the continuous reaction garnet + muscovite = sillimanite + biotite and repartitioning of the garnet rim composition to relatively heavy δ¹⁸O. The models are insensitive to the degree to which garnet fractionally crystallizes and to the isotope fractionation factors used; only extreme changes in modal abundance or bulk composition for a given mineral assemblage can produce significant changes in the predicted trends. In the absence of infiltration, isotopic shifts resulting from net transfer reactions for minerals in typical amphibolite, eclogite, and lower granulite facies metapelites and metabasites are inferred from the models to be ∼1‰ or less for ∼150°C of heating.