We present a rigorous calculation of the isobaric entropy, (S) change of the melting reaction for peridotite (partial derivative S/partial derivative F)(rxn)(P,) where F is the melt fraction. Calculations at 1 and 2 GPa for fertile and depleted peridotite show that (partial derivative S/partial derivative F)(rxn)(P) varies as a function of extent of melting temperature, and residual mineral assemblage. Changes in reaction stoichiometry cause discontinuous changes in (partial derivative S/partial derivative F)(rxn)(P). Although calculated (partial derivative S/partial derivative F)(rxn)(P) varies by about a factor of two (from similar to 0.25 to similar to 0.5 J/K per g), such variations have relatively little effect on the formation of melt during adiabatic upwelling and a characteristic value suitable for peridotite partial melting at least up to 3 GPa is 0.3 J/K per g. Calculated variations in isobaric melt productivity, (partial derivative F/partial derivative T)(p), are large and have a significant effect on calculated adiabatic productivity, (partial derivative F/partial derivative P)(s). For partial melting of fertile peridotite, MELTS calulations suggest that near-solidus productivities are greatly reduced relative to productivities at higher melt fraction, owing to the incompatible behavior Na2O and the effect of this component on the liquidus temperature of partial melts. This behavior can also be demonstrated in simple model systems. Calculated near-solidus productivity for fractional or incremental or incremental batch melting of peridotite is lower than for batch melting, but after a small amount of melting (similar to 2%), productivity for the fractional or incremental batch melting case is greater than that of batch melting. This too can be demonstrated both by MELTS calculations and by calculations in simple model systems. Productivities for systems enriched in incompatible components are systematically lower than those depleted in such components, though the total melt produced at any given temperature will be greater for an enriched system. Exhaustion of clinopyroxene from peridotite residua decreases calculated productivity by about a factor of four, and therefore extensive partial melting of harzburgitic residues is inhibited. Calculated isothermal addition of water to hot peridotite causes melting to increase roughly linearly with the abundance of water added to the system, in agreement with the trend recognized earlier for Mariana trough basalts. Melt production for calculated addition of a subduction fluid (45 wt % H2O, 45% Na2O, 10% K2O) is only slightly greater than for pure water. If water addition to peridotite is not forced to be isothermal by an externally imposed heat sink or by buffering from low variance chemical reactions, then it will approach isenthalpic conditions, which will reduce melt production per increment of water added by about a factor of two. For heating of peridotite containing minor amounts of H2O, calculations suggest that the extent of melting will remain small (<5%) until the temperature is sufficient to generate signficant melt for an equivalent dry peridotite. Small degrees of melting deep in mantle source regions caused by alkalis, CO2, and H2O probably result in several distinct melting regimes where melt productivities are very small and melt compositions are strongly influenced by high concentrations of alkalis and/or volatiles.Such regions are almost certainly in the garnet peridotite stability field, and owing to the small extents of melting and low productivities in these deep melting zones, they are likely regions for development of extreme U-series disequilibria.
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