2015-Sustainable Industrial Processing Summit
SIPS 2015 Volume 10: Mineral & Secondary Battery

Editors:Kongoli F, Silva AC, Arol AI, Kumar V, Aifantis K
Publisher:Flogen Star OUTREACH
Publication Year:2015
Pages:340 pages
ISSN:2291-1227 (Metals and Materials Processing in a Clean Environment Series)
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    Transformation of Concentration Coordinates and Polyhedration of Concentration Complexes in Multicomponent Systems

    Vasily Lutsyk1; Vera Vorob'eva1; Maria Parfenova2;
    Type of Paper: Regular
    Id Paper: 124
    Topic: 5


    The investigation of n-component systems gives answers to many practical questions concerned with different methods to represent their concentrations:
    1) preparation of a binary, ternary, quaternary or any n-component mixture from several mixtures of different compositions; 2) dilution of an initial mixture by adding one or several liquids; 3) determination of relative weight proportions of equilibrium phases or individual structure elements in binary, ternary, quaternary, ..., n-component mixtures at different temperatures; 4) analysis of phase equilibrium in mixtures containing two, three, four, ..., n phases. An algorithm which allows to define relations between concentration coordinates of subsystems formed in the initial system consisting of simple elements is proposed. It gives also a possibility to determine the conditions under which the point belongs to the given concentration simplex or complex. All different methods to express the n-component mixture concentrations can be represented by only one system of coordinates which corresponds to the input of its simple elements to the mixture composition.
    This coordinate system allows: 1) to correlate concentration coordinates of various subsystems (both simplexes and complexes); 2) to compare experimental data represented in the literature by different concentration coordinates; 3) to analyze some phase reaction possibility by verifying if the concentration point, which corresponds to the given chemical interaction, belongs to some elementary concentration simplex (or complex).
    One more new algorithm for polyhedration of quaternary and quaternary reciprocal systems is based on checking all the links between vertices of a graph describing the composition diagram and selecting the polyhedration variants that correspond to the relations between the numbers of geometric elements of the complex undergoing polyhedration (graph vertices, links between them, and two- and three-dimensional complexes). It can control the entire polyhedration process, accelerates the search for internal diagonals in the polyhedron, and takes into account their possible competition. The work was partially supported by the Russian Foundation for Basic Research (projects 14-08-00453 and 14-08-31468).


    Materials; Mineral; Modeling; Ore; Simulation;


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    Lutsyk V, Vorob'eva V, Parfenova M. Transformation of Concentration Coordinates and Polyhedration of Concentration Complexes in Multicomponent Systems. In: Kongoli F, Silva AC, Arol AI, Kumar V, Aifantis K, editors. Sustainable Industrial Processing Summit SIPS 2015 Volume 10: Mineral & Secondary Battery. Volume 10. Montreal(Canada): FLOGEN Star Outreach. 2015. p. 145-154.