2016-Sustainable Industrial Processing Summit
SIPS 2016 Volume 5: Starkey Intl. Symp. / Mineral Processing
| Editors: | Kongoli F, Kumar P, Senchenko A, Klein B, Silva A.C., Sun C, Mingan W |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2016 |
| Pages: | 270 pages |
| ISBN: | 978-1-987820-44-7 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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Concentration Complexes Polyhedration for the Quinary Reciprocal Systems
Vasily Lutsyk1; Vera Vorob'eva1; Maria Parfenova2;1INSTITUTE OF PHYSICAL MATERIALS SCIENCE SB RAS, Ulan-Ude, Russian Federation; 2TOMSK STATE UNIVERSITY OF CONTROL SYSTEMS AND RADIO-ELECTRONICS, Tomsk, Russian Federation;
Type of Paper: Regular
Id Paper: 148
Topic: 5
Abstract:
The algorithm for topological correction of lists of simplexes of different dimensions (TCLSDD) has been used to analyze the published methods for determining the internal diagonals in polyhedration of reciprocal systems. The errors were found in the polyhedration of the quinary system Li,K,Ca,Ba||F,WO4 with the five binary compounds. Advantages of the algorithm have been demonstrated in cases of a competition of internal secants, when all the possible (allowed) combinations of 1D, 2D, 3D and 4D simplexes are checking. The end result of polyhedration should satisfy the formulas relating the numbers of graph vertices and links between them with the numbers of 1D (internal diagonals), 2D (secant planes), 3D (tetrahedra) and 4D (pentatops) simplexes. TCLSDD gives a table that enumerates all the possible internal secant planes and tetrahedra. After analyzing the table, an unambiguous answer is given by the combinations of 2D, 3D and 4D simplexes that satisfy the resulting formulas. The algorithm allows one to determine all the variants of polyhedration and reveal the participation of competing internal diagonals in it. Of 15 pentatopes, into which the Li,K,Ca,Ba||F,WO4 system is partitioned, eight pentatopes were missed in the earlier study.
This work has been performed under the program of fundamental research SB RAS (project 0336-2014-0003) and was partially supported by the Russian Foundation for Basic Research (projects 14-08-00453, 15-43-04304).
References:
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[3] V.I. Lutsyk, V.P. Vorob’eva and O.G. Sumkina: Triangulation of Salt Systems with Barium Borate, Crystallography Reports, 57 (2012), 115-125.
[4] P.A. Akhmedova, B.Yu. Gamataeva and A.M. Gasanaliev: Topology and Chemical Interactions in the Li,K,Ca,Ba||F,WO4 Quinary Reciprocal System and the Phase Complex of Its LiF-LiKWO4-Li2WO4-CaWO4-BaWO4 Pentatope, Russian Journal of Inorganic Chemistry, 54 (2009), 779-791.
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[6] A.V. Chuvakov, A.S. Trunin and O.E Morgunova, The Theory and the Methodology of the Differentiation of the Multicomponent Systems, 2007. Samara State Technology University.
[7] A.M. Gasanaliev, P.A. Akhmedova and B.Yu. Gamataeva: Differentiation of Multinary Systems with Inner (Latent) Secants, Russian Journal of Inorganic Chemistry, 55 (2010), 1970-1982.
[8] A.M. Gasanaliev, P.A. Akhmedova and B.Yu. Gamataeva: Metodology for Determing Hidden Partitioning Elements in Mutual Multicomponent Systems and Physicochemical Interactions in the LiF-K2WO4-CaF2-BaF2 System, Russian Journal of Inorganic Chemistry, 57 (2012), 274-283.
[9] P.A. Akhmedova, A.M. Gasanaliev and B.Yu. Gamataeva, Physical and Chemical Analysis: State, Problems, Prospects for the Development, Proceedings of IV All-Russian with international participation scientific Bergman conference, Makhachkala, 2012, 129.
[10] V.I. Lutsyk and V.P. Vorobeva: Search for Internal Diagonals in Poly-hydration of Reciprocal Systems by the Algorithm for Topological Correction of Lists of Simplexes of Different Dimensions, Russian Journal of Inorganic Chemistry, 59 (2014), 1123-1137.
[11] V.I. Lutsyk, V.P. Vorob'eva, O.G. Sumkina and M.V. Lamueva: Poly-hydration of Multicomponent Mineral Systems, IFAC Proceedings Volumes (IFAC-PapersOnline), 15 (2013), 288-293.
[12] V.I. Lutsyk, V.P. Vorob'eva and M.D. Parfenova: Quaternary Reciprocal Systems with the Inner Diagonals: Variants of Poly-hydration, Advanced Materials Research, 704 (2013), 55-60.