Introduction

In recent years, much insight has been gained into the nature of magmatic crystallization and assimilation phenomena through the use of equilibrium thermodynamic models of multicomponent silicate melts (Ghiorso et al., 1983, Ghiorso & Carmichael, 1985, Ghiorso & Kelemen, 1987). As a consequence of these studies, it has become apparent that theoretical simulation of chemical reactions in magmas requires the incorporation of numerical techniques that allow the boundaries of the system to be open to oxygen transfer (Ghiorso, 1985, Ghioso & Carmichael, 1985, Carmichael & Ghiorso, 1986). These techniques rely upon the definition of a thermodynamic potential which is minimal, at thermodynamic equilibrium, in systems subject to boundary conditions including fixed temperature, pressure, and bulk composition of all components save oxygen, which is constrained by specification of fixed chemical potential. The creation of a thermodynamic potential which satisfies these requirements was first described by Korzhinskii (1949,1956,1959) and later introduced to the western scientific community by Thompson (1970). Ghiorso & Kelemen (1987) have recently extended the Korzhinskii approach to allow the specification of arbitrary thermodynamic potentials, minimal at equilibrium in thermodynamic systems subject to very general boundary constraints. In particular, Ghiorso & Kelemen (1987) have derived a potential function which allows for the modeling of chemical equilibrium in magmatic systems as a function of pressure, the heat content of the system (specified as the enthalpy), the system bulk composition and the chemical potential of oxygen.