Graphical analysis of enthalpy-composition relationships in mixed magmas

Enthalpy-composition diagrams (H^*-X) calculated from existing temperature-composition (T-X) phase diagrams and thermodynamic data provide a simple and effective means for evaluating the enthalpy-temperature effects of magma mixing. If athermal mixing is assumed, adiabatic mixing lines on H^*-X diagrams are straight lines because enthalpy, unlike temperature, is an extensive property of a system. Comparison of binary T-X diagrams with their derivative H^*-X diagrams shows that incorrect predictions can be obtained when T-X diagrams are used to analyze mixing problems.An H^*-X diagram calculated using experimentally determined phase equilibria for anhydrous basalt-rhyolite mixtures predicts that adiabatic mixing of basalt and rhyolite at their respective liquidus temperatures will result in small amounts of crystallization ( < 2 wt.% ). Because the phase equilibria of hydrous basalt-rhyolite mixtures have not yet been determined, an H^*-X diagram for such mixtures cannot be constructed. However, existing hydrous phase equilibria can be used to predict whether adiabatic mixtures of anhydrous basalt and hydrous rhyolite will be super- or subliquidus. Calculations at P_total = 200 MPa show that on an H^*-X diagram a mixing chord drawn between anhydrous basalt and water-saturated rhyolite at their respective liquidus temperatures lies below the enthalpy values calculated for a Paricutin andesite and Mt. St. Helens dacite at their estimated liquidus temperatures. This indicates that the liquidus for mixtures of anhydrous basalt and water-saturated rhyolite is noticeably convex upward, suggesting that larger amounts of crystallization will occur than in the anhydrous case.