Perfect fractionation in multicomponent, multiphase systems

Perfect fractionation models help infer the conditions under which molten rock material travels from the planet’s interior to the Earth’s surface where it cools and crystallizes. Quantitative models of melt crystallization, perfect fractionation paths through P–T-composition space, return calculated values of predicted quantities that can be compared to glass, rock, and mineral compositions measured in lava flows. Perfect fractionation models are based on thermodynamics and material balance constraints. Linear combinations of chemical potentials define equilibrium positions. The composition of the melt follows a path directly away from the composition of the phases at saturation, a material balance criterion. The number of adjustable parameters in a perfect fraction model is limited to two by Duhem’s theorem. Perfect fractionation models with one or two phases at saturation require only one mole fraction and one adjustable parameter be specified to calculate the fractionation path. The temperature and compositions of the saturating phases are determined by the equilibrium equations for one- or two-phase saturation in a melt of known compositions. With three or more phases at saturation, the composition of the melt has to be adjusted in the general case. Fractionation paths can also be inferred from a sequence of thermodynamic states calculated by minimizing a thermodynamic potential. The minimization procedure produces a fraction path that is conceptually different from the perfect fractionation path. Perfect fractionation models can be constructed to conserve a particular thermodynamic potential or variable such as enthalpy or density.