An analysis of variations in isentropic melt productivity

The amount of melt generated per unit pressure drop during adiabatic upwelling, the isentropic melt productivity, cannot be determined directly from experiments and is commonly assumed to be constant or to decrease as melting progresses. From analysis of one- and two-component systems and from calculations based on a thermodynamic model of peridotite partial melting, we show that productivity for reversible adiabatic (i.e. isentropic) depressurization melting is never constant; rather, productivity tends to increase as melting proceeds. Even in a one-component system with a univariant solid-liquid boundary, the 1/T dependence of (∂S/∂T)_P and the downward curvature of the solidus (due to greater compressibility of liquids relative to minerals) lead to increased productivity with increasing melt fraction during batch fusion (and even for fractional fusion in some cases). Similarly, for multicomponent systems, downward curvature of contours of equal melt fraction between the solidus and the liquidus contributes to an increase in productivity as melting proceeds. In multicomponent systems, there is also a lever-rule relationship between productivity and the compositions of coexisting liquid and residue such that productivity is inversely related to the compositional distance between coexisting bulk solid and liquid. For most geologically relevant cases, this quantity decreases during progressive melting, again contributing to an increase in productivity with increasing melting. These results all suggest that the increases in productivity with increasing melt fraction (punctuated by drops in productivity upon exhaustion of each phase from the residue) predicted by thermodynamic modelling of melting of typical mantle peridotites using MELTS are neither artifacts nor unique properties of the model, but rather general consequences of adiabatic melting of upwelling mantle.