Calculating Mineral—Melt Equilibria with Stoichiometry, Mass Balance, and Single-Component Distribution Coefficients
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Application of phase equilibria is essential to understanding igneous processes. Usually the phase equilibria in systems of interest to petrologists are presented graphically in the form of phase diagrams. Such diagrams are compact representations of data from which the proportions and compositions of phases as functions of temperature and bulk composition can be determined [e.g., Morse (1976)]. These diagrams are strictly applicable, however, only to systems consisting of a small number of components and can be fully presented in two or at most three dimensions. In systems of more components, projections can be used, but the quantitative calculations can no longer be carried out graphically. Since almost all liquids of interest to petrologists have many components, there is a need for methods of numerical calculation which are applicable to both simple and complex systems. One approach to such calculations uses thermodynamic data and is exemplified by the work of Weill et al. (1979) and Burnham (1979). At present, thermodynamic data and models are insufficient to allow calculation of phase diagrams for many simple systems of geological interest, much less the complex multicomponent systems in which rocks melt and crystallize. An alternative approach is to use the large and growing body of equilibrium temperature, pressure, and composition data which are available for simple systems as well as rock compositions. One way of processing those data is regression analysis, which supplies lengthy equations to minimize the errors in reproducing the data base [e.g., Weill et al. (1979) and Hostetler and Drake (1978)]. A similar method of estimating liquidus temperatures using linear equations is that of Roeder (1975), based on the suggestion of French (1971).
KeywordsFractional Crystallization Liquid Line Liquid Composition Invariant Point Compositional Dependence
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