ALBERT

Notes: Abstract A combined analytical and numerical evaluation of the uncertainties in P-T paths is made for three assemblages that propagates errors in the parameters: initial pressure, initial temperature, initial composition, change of composition of monitor parameters, endmember entropy, and endmember volume. Propagated errors along an isobaric heating path (ΔT=77°C) for assemblage 1 (Grt-Bt-Pl-Qtz-Ms-Chl-H2O), using as monitor parameters the mole fractions of almandine, spessartine, grossular, and anorthite, and ignoring uncertainties in thermodynamic properties, are approximately ±320 bars (1σ) and ±8.3°C (1σ) if rim compositional uncertainties of 5% in major cations are assumed, or ±2.5°C (1σ) and ±50 bars (1σ) if electron microprobe analytical uncertainties are assumed for compositions. The largest source of uncertainty is from the errors in the monitor parameters, and P-T path uncertainties can depend critically on which monitor parameters are used. If the mole fraction of annite is used as a monitor parameter in place of the anorthite content of plagioclase, then propagated uncertainties are worse than ±29°C (1σ) and ±5800 bars (1σ). P-T path uncertainties also depend on assemblage. 1σ precisions in assemblages 2 (Grt−Bt−Pl−Qtz−Ms−Sil−H2O) and 3 (Grt−Bt−Qtz−Kfs−Sil−H2O) using as monitor parameters the mole fractions of almandine, spessartine, grossular, and anorthite are calculated to be ±267 bars and ±43.4°C and ±372 bars and ±8.2°C respectively. Estimates of the accuracies in P-T paths that include potential errors in endmember entropy of ±1 J/mol·K and in endmember volume of ±1 cm3/mol are: ±324 bars and ±8.5°C (assemblage 1), ±341 bars and ±48.6°C (assemblage 2), and ±388 bars and ±9.7°C (assemblage 3). Use of different garnet, plagioclase, and muscovite activity models can change the length of a P-T path by as much as 15%, but does not typically change directions in P-T space significantly. Models that incorporate changes of fluid composition shorten P-T paths in assemblages 1 and 3 but do not change trajectories significantly. Assemblage 2 is virtually unaffected by fluid phase models. For the mineral assemblages considered here and using appropriate monitor parameters, propagated errors are small compared to the total path length, suggesting that the differential thermodynamic approach is a precise and accurate method for determining amounts of heating or thickening during metamorphism, and hence for interpreting orogenic processes.

Notes: 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.