Schreinemakers Rule as Applied to Non-Degenerate Ternary Systems

Author:  Liow Yuh Han John
Institution:  California Institute of Technology (SURF Fellow)
Date:  May 2009


In experimental studies of phase relations in chemical, ceramic, metallurgical, and mineralogical systems, it is fairly rare for pressure-temperature (P-T) diagrams to be fully mapped, i.e. with all the univariant lines directly determined. This typically requires an extraordinarily large number of experiments; in many cases this is impractical or, due to extreme temperature or pressure conditions, sluggish kinetics, or other considerations, effectively impossible. Even if the availability of thermodynamic data allows the slopes of such univariant curves to be calculated, there remains a possibility that such data are not always mutually consistent. Fortunately, in a series of classic monographs published in Dutch between 1915 and 1925, F.A.H Schreinemakers derived and demonstrated the usefulness of a set of rules which is aptly suited to overcoming this problem. When some subset of the n+2 univariant lines that meet at an invariant point in an n-component system are known, this set of topologically-governed principles, which later came to be known as Schreinemakers rules, not only allows the determination of the location of remaining univariant lines, it also provides insights into the stability of divariant assemblages around the invariant point at various temperatures and pressures. In this paper, we review the 180° rule, overlap rule and half-plane rule, all of which make up Schreinemakers rules, and show how they can be applied to a ternary non-degenerate system where five phases coexist at an invariant point.