Construction of pressure-temperature diagrams for multicomponent systems after the method of Schreinemakers - a geometric approach
E‐an Zen · 1966
p--T DIAGRAMS.MULTICOM.PONENT SYSTEMS An n-component system is degenerate if one or more of the associated univariant curves can be described by fewer than n components.Chemographically, this corresponds to the coincidence of phases (n=2,3,4, . . .), colinearity of pha~es (n=3,4,5, . . .), coplanarity of phases (n=4,5,6, . . . ) and so on.The phases participating in degenerate univariant reactions are the singular phases; those which do not participate are the indifferent phases.In a degenerate system, two or more univariant lines assume the same value of slope at the invariant point.If the indifferent phases are chemographically on opposite sides of the singular phases, the degenerate curves coincide stable to stable (so that fewer than n+ 2 univariant lines obtain); if t}le indifferent phases are on the same side of the singular phases, the degenerate curves coincide stable to metastable.All the possible cases of degeneracy for binary and ternary systems are described in this paper.The method of Schreinemakcrs is useful in analyzing petrologic problems.Thus, for a given mineralogical system, if only some of the n+2 univariant curves about an invariant point have been determined experimentally or by calculation from available thermodynamic data, the application of the method enables one to compute approximately the remaining curves.Because the chemographic relations of the phases determine the sequence of univariant curves about the invariant point, the method is useful in evaluating the consistency of existing thermochemical data on minerals of known compositions.Even when no experimental or thermochemical data are available, knowledge of the chemical compositions of the phases alone often allows one to calculate and predict the relative p-T dispositions of mineral assemblages in specified chemical and mineralogical systems; such knowledge is frequentlylhelpful in the study of mineral paragenesis.Examples of the application of the Schreinemakers method to mineralogical systems are given.' Although these values refer to 26° C and 1 bar pressure, for reactions involving only condensed phases the error caused by this approxbnation is likely negligible.