An algorithm of calculation of phase diagrams based on convex hulls approach and its implementation
Matematičeskoe modelirovanie, Tome 18 (2006) no. 1, pp. 67-78.

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A new algorithm for calculation of phase diagrams based on method of convex hulls is presented. The computer program and database for thermodynamic modeling of binary systems are described. The examples demonstrating the use of algorithm in education and in practical problems solving are presented.
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G. V. Belov; G. F. Voronin; V. I. Goriacheva; A. L. Emelina; I. A. Uspenskaya. An algorithm of calculation of phase diagrams based on convex hulls approach and its implementation. Matematičeskoe modelirovanie, Tome 18 (2006) no. 1, pp. 67-78. http://geodesic.mathdoc.fr/item/MM_2006_18_1_a6/

[1] Palatnik L. S., Landau A. I., Fazovye ravnovesiya v mnogokomponentnykh sistemakh, Izd. kharkovskogo gos. universiteta, Kharkov, 1961

[2] Pelton A. D., Thompson W. T., “Phase Diagrams”, part. 3, Progress in Solid State Chemistry, 10 (1976), 119 | DOI

[3] Kattner U. R., “Thermodynamic modeling of multicomponent phase equilibria”, Journal of Metals, 49:12 (1997), 14–19

[4] Chang Y. A. et al., “Phase diagram calculation: past, present and future”, Progress in materials science, 49 (2004), 313–345 | DOI

[5] Anosov V. Ya., Ozerova M. I., Fialkov Yu. Ya., Osnovy fiziko-khimicheskogo analiza, Nauka, M., 1976

[6] Voronin G. F., Fizicheskaya khimiya. Sovremennye problemy, Ezhegodnik, ed. Ya. M. Kolotyrkin, Khimiya, M., 1984

[7] Hildebrandt D., Glasser D., “Predicting phase and chemical equilibrium using the convex hull of the Gibbs free energy”, The Chemical Engineering Journal, 54 (1994), 187–197

[8] Voronin G. F., “Novye vozmozhnosti termodinamicheskogo rascheta i postroeniya diagramm fazovykh sostoyanii geterogennykh sistem”, Zhurnal fizicheskoi khimii, 77:10 (2003), 1874–1883

[9] Wightman A. S., Introduction to R. B. Israel “Convexity in the theory of lattice gases”, Princeton Univ. Press, Princeton, 1979, IX | MR

[10] Galgani L., Scotti A., “Remarks on convexity of thermodynamic functions”, Physica, 40 (1968), 150–152 | DOI

[11] Barber C. B., Dobkin D. P., Huhdanpaa H., “The Quihull Algorithm for Convex Hulls”, ACM Transactions on Mathematical Software, 22:4 (1996), 469–483 | DOI | MR | Zbl

[12] Karpov I. K., Fiziko-khimicheskoe modelirovanie na EVM v geokhimii, Nauka, Novosibirsk, 1981

[13] Smith W. R., Missen R. W., Chemical Reaction Equilibrium Analysis, J. Willey, NY, 1982

[14] Kormen T., Leizerson Ch., Rivest R., Algoritmy: postroenie i analiz, MTsNMO, M., 960 pp.