Classification of planar quadrangular diagrams

Abstract

Analysis of classifications of planar quadrangular diagrams published in the literature was carried out. These classifications deal with projections of chemical equilibrium surfaces in a quarternary system, with ternary intermutual systems containing liquid and solid solutions between constituent salts and also with graphical representation of response surfaces. The synthesis of the complete set of topological types of planar quadrangular diagrams was carried out. The complete set includes 98 types, which differ in boundary and inner simple singular points (elliptic and hyperbolic); the total amount of subtypes is 120. The subtypes of the diagrams may differ in the mutual arrangement of either boundary or both boundary and inner singular points. In previously published classifications, repeating diagram structures and unstable structures were revealed. The most accurate results are achieved by a formalized procedure of synthesis of a topologically possible set of planar quadrangular diagrams. By “formalized procedure” we mean the use of a specific program for variants enumeration of possible mutual arrangement of singular points in planar quadrangular diagrams. This procedure in the most correct way allows to take into account diagrams differing in the mutual arrangement of not only boundary, but also inner singular points.

Keywords

• classification, planar quadrangular diagram, scalar property, contour line, singular points, node, saddle, elliptic point, the hyperbolic point, type, subtype, boundary points.