Thermodynamic model for partial melting of peridotite by system energy minimization

Abstract We present a new straightforward algorithm that calculates the energy minimization of a melt‐present system and incorporates newly calibrated silicate melt thermodynamic parameters. This algorithm searches for equilibrium phase assemblages, fractions, and compositions that lead to the system having a global minimum of total Gibbs free energy ( G ). It calculates changes in G with respect to minimal amounts of dissolution or solidification of melt and solid end‐member components using a constant bulk composition constraint. In addition, we have formulated a set of solid‐melt end‐member components and dissolution‐precipitation stoichiometry that enables the modeling of a melt‐present system. Melt thermodynamic properties are calibrated based on an ideal mixing model using Δ Cp and Δ V (the differences in molar specific heat and volume between the corresponding melt and solid end‐member components, respectively), based on solid properties established during previous studies. We also describe the application of the energy minimization algorithm and thermodynamic melt parameters to melting of spinel lherzolite at 1 GPa, in a SiO 2 –Al 2 O 3 –FeO–Fe 3 O 4 –MgO–CaO system, including olivine, clinopyroxene, orthopyroxene, and spinel. Our calculations agree well with experimentally determined melting phase relations, and temperature and phase fraction relationships, including solidus temperatures, indicating that direct calibration of thermodynamic melt parameters at pressures and temperatures corresponding to melting conditions is a useful approach. The energy minimization algorithm and thermodynamic configuration presented here will allow the modeling of mantle melting in a variety of geodynamic settings.