Phase Diagrams Of Quaternary Systems Research Articles

Topological transformations of phase diagrams of quaternary systems through the boundary tangential azeotrope stage

The specific features of quaternary system phase diagram transformations induced by formation ofboundary tangential azeotrope were investigated. The characteristics of bifurcation states corresponding to the transition from one structure of the diagram to another were determined. The principal possible transformations of diagrams with varying pressure were illustrated by the systems acetone-chloroform-ethanol-water and chloroform-ethanol-cyclohexane-water. The obtained results expand the understanding of thermodynamics of heterogeneous equilibria of multicomponent systems and make it possible to solve the practical problem of maintaining favorable phase equilibrium conditions for rectification in certain pressure ranges.

Optimizing Experimental Determination of the Tetrahedration of Isobaric–Isothermal Phase Diagrams of Four-Component Systems

An algorithm and programs are developed for optimizing the experimental study of isobaric–isothermal phase diagrams of quaternary systems with constant-composition phases or phases with narrow homogeneity range. These include (a) a program for enumerating phase diagrams with phases of specified composition and (b) an algorithm and a program software for the iterative analysis of phase diagrams. At each iteration, the researcher enters experimental data into the program to obtain a list of compositions for further study. Data are presented from modeling the plotting of phase diagrams with one binary, three ternary, and one quaternary compounds. It is found that among ten given examples, the number of iterations sufficient for charting the diagram is 1 (one example), 2 (four examples), 3 (two examples), 4 (one example), and 5 (two examples).

Thermodynamic and Topological Analysis of Phase Diagrams of Quaternary Systems with Internal Singular Points

A review of the literature published in Russia and abroad on the experimental studies of phase equilibria, methods for analyzing and predicting phase diagram structures, and simulating problems of the vapor–liquid equilibrium (VLE) of quaternary systems containing internal singular points is presented. A complete set of parameters that adequately describe the liquid–vapor and liquid–liquid equilibrium is obtained for the following four systems: acetone–chloroform–ethanol–water, acetone–chloroform–propanol-2–water, chloroform–ethanol–cyclohexane–water, and ethyl acetate–methyl ethyl ketone–cyclohexane–propanol-2. The methodology for determining the structure of the VLE diagram and predicting the presence of an internal azeotrope in the systems under study and in a model system that contains binary azeotropes and a quaternary azeotrope is illustrated. Possible ways for evolutionary changes in the structure of the VLE diagram with a variation in the pressure are shown, and the Poincare indices of boundary single azeotropes and a double tangential azeotrope are determined.

Topology of the liquidus hypersurface of the phase diagrams of quaternary systems

Consideration was made of structural features of the liquidus and solidus hypersurfaces of the isobaric melting diagrams of quaternary systems with a single liquid phase and solid phases of constant compositions which undergo neither phase transitions nor decomposition into other phases while cooling. An intimate relationship between the topologies of such hypersurfaces was noted. The oriented graph of the liquidus hypersurface can be obtained from the graph of the solidus hypersurface by drawing arrows on its edges in the direction of decreasing temperature along the corresponding monovariant lines or by labeling its vertices with symbols of types of invariant reactions. An example was given for constructing different variants of the melting diagram of a system that correspond to the same topology of the solidus hypersurface.

Partition of the composition tetrahedron during construction of subsolidus isobaric-isothermal sections of the phase diagrams of quaternary systems

A problem of constructing subsolidus isobaric-isothermal sections of phase diagrams with constant-composition compounds and limited solid solutions was considered. Relations between the topological characteristics of such sections were derived. Their topological classification was proposed. An algorithm for constructing sections using the theory of finite graphs was developed. A problem of enumerating sections for diagrams with a given set of classification characteristics was solved.

The construction of isothermal quaternary phase diagrams of the Na-M-O-S type for hot corrosion applications

This paper presents a computer program for the calculation of the isothermal phase diagrams of quaternary systems involving sodium, a pure metal, oxygen and sulfur, which are useful for examining the experimental results concerning the hot corrosion of metallic materials. The procedures adopted to calculate the location of the points where four condensed phases are simultaneously present (quadruple points) and to draw the regions of stability of each phase containing the metal are presented by means of examples concerning a practical system. The nature of these quaternary phase diagrams is examined with reference to the various types of quadruple points and to their interconnections with lines of equilibrium involving the participation of three different phases. Examples of phase diagrams of some quaternary systems calculated by means of the present program are given.