Abstract:
We present a method for calculating quantitative melting reactions in systems with multiple solid solutions that accounts for changes in the mass proportions of phases between two points at different temperatures along a melting curve. This method can be applied to any data set that defines the phase proportions along a melting curve. The method yields the net change in mass proportion of all phases for the chosen melting interval, and gives an average reaction for the melting path. Instantaneous melting reactions can be approximated closely by choosing sufficiently small melting intervals. As an application of the method, reactions for melting of model upper mantle peridotite are calculated using data from the system CaO-MgO-Al2O3-SiO2-Na2O (CMASN) over the pressure interval 0.7-3.5 GPa. Throughout almost this entire pressure range, melting of model lherzolite involves the crystallization of one or more solid phases, and is analogous to melting at a peritectic invariant point. In addition, we show that melting reactionsfor small melting intervals (< 5%) along the solidus of mantle peridotite are significantly different from those calculated for large melting intervals. For large melting intervals (> 10%), reaction stoichiometries calculated in CMASN are usually in good agreement with those available for melting of natural peridotite. The coefficients of melting reactions calculated from this method can be used in equations that describe the behavior of trace elements during melting. We compare results from near-fractional melting models using (1) melting reactions and rock modes from CMASN, and (2) constant reactions representative of those used in the literature. In modeling trace element abundances in melt, significant differences arise for some elements at low degrees of melting (< 10%). In modeling element abundances in the residue, differences increase with increase in degree of melting. Reactions calculated along the model lherzolite solidus in CMASN are the only ones available at present for small degrees of melting so we recommend them for accurate trace element modeling of natural lherzolite.