Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.chem.msu.ru/rus/vmgu/131/3.pdf Äàòà èçìåíåíèÿ: Wed Nov 28 18:39:31 2012 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 04:58:40 2016 Êîäèðîâêà:

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- 2002 . , « » . , [1]. , . , [2­7]. , - , [8­10]. , -, , , .

. . , . , 40 [11], . . , , , .., , « ».


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XX . , «» , 60­70- . , . , . , , S (U, V, N) , . . , 1- , U, , . , , S (U, V, N) , U (S, V, N) ­ [12, 13]. : () S(U, V, N) = S(U, V, N) 0; S(U,V, N) S(U,V, N) U U; S(U+U, V+V, N+N) S(U, V, N) + + S(U, V, N); U(S + S, V + V, N + N) U(S, V, N) + + U(S, V, N).

S(U+(1­)U, V+(1­)V, N + (1­)N) S(U, V, N) + + (1­)S(U, V, N) 1 0; , ­ . . 1 , , , [13]. , , . [14, 15]. , , , , ­ . , , , , . , . , , , -

S(U, V, N) S(U, V, N) S(U, V, N)





S(U, V, N)



U(S, V, N) U(S, V, N)







S(U, V, N)



U(S, V, N)



. 1. S(U, V, N) U(S, V, N)


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[16]. , , . , , . , . , , . , , . . , , S(U, V, N) , . ­ « » , , .. . , , , ( , ). , . . , , , . , . , , . , , .

, , , . , , , , , . , . , , , V, N , , . , , 1- , , . , , , . , : GTP(), GTP() GTPx(), FTx(V), FT(V, ), FTV(), FT(V, ), FTV(), FTx(V, ). (, ), ­ . , . . , , ( ) . [8]. ,


6

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. . . , , , (, ) , . . , (. ). [8]. , , , ( ). . , , (. . 7 [1]). , (, , ) , [17, 18]. . . [19, . 369] , , , . , . , , ­

. . , , , . , . . . (n ­ 1)- xi (i = 1,..., n), , n xi(k) (k = 1,..., n)

z(k) xi 1. , i- , k , xi(k) ­ , z(k) ­ . . , , , , ­ . , , ( ). [9, 20]. PhDi [10].


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, . , .. [21, 22]. , ­ . . . ­ . ­ , . . . . 2 Al1,5O­CaO­MgO­SiO2 473,15 .

49 FactSage 6.0. . 2 , . 23 , . 2 , 36 . , . , , , . -, . , , . , Y­Ba­Cu­O 800 , 20 (123, 247 124) [1]. Cd­Zn­Te, Cd­Hg­Te, Hg­Zn­Te [2]. , , , [23]. -

. 2. AlO1,5­CaO­MgO­SiO 473,15

2


8

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, , QuickHull, , , [24]. - , . , , , , . , 1, , 0, . 1 0 0 1 . , . , . , . . 3 ­ , A­B. , ­ . , , . . 3, PhDi (http://td.chem.msu.ru). - . , . 3, . , , - . ,

. 3. , ­ . PhDi

, , , . [9]. TernAPI MATLAB [9, 20]. (x2, x3). , , .


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9

, . . 4. TernAPI (, , ). . . 5 (P, T)- Al­Mg­Zn T = 673 K -

[25]. Al­Mg­Zn : -Al3Mg2, -Al0,56Mg0,44, -AlMg, Mg7Zn3, MgZn, Mg2Zn3, Mg2Zn11, Al2Mg5Zn2 (-), , ( ), T, fcc, hcp . -Al3Mg2, -AlMg, Mg7Zn3 MgZn , [25, 26]. fcc

. 4. Ga­In­Sb T = 800 K TernAPI ( [27]): a ­ , ­ , ­ (L ­ , ­ (Ga, In)Sb)

. 5. Al­Mg­Zn T = 673 K


10

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hcp ­, . , T ­ . ­ , . - , , - ~0,001 . . . , , ­ ( - . , , ), , - . . , , , , , , - , . , , - . , . -, ­ . . , . , - , , ­ , , . - , - . , - , , . . , , ­, : - ­. , , , , . - . , , , , - - ­ ­, . - , , , , . , , - ­ . . ­ - , , . - , -, - . , - , . , , , . ( 11-03-00499-a 12-03-31069-_a).


. . -. . 2. . 2013. . 54. 1 1. . . // . 2003. 77. 10. . 1874. 2. . ., . . // . 2005. 79. 10. . 1771. 3. Lee D. D., Choy J. H., Lee J. K. // J. Phase Equilib. 1992. 13. N 4. P. 365. 4. Hildebrandt D., Glasser D. // Chem. Eng. J. 1994. 54. N 3. P. 187. 5. Chen S.-L., Zhang J.-Y., Lu X.-G., Chou K.-C., Chang Y.A. // J. Phase Equlib. Diffus. 2006. 27. N 2. P. 121. 6. Cool T., Batrol A., Kasenga M., Modi K., Garcia R. A. // CALPHAD. 2010. 34. N. 4. P. 393. 7. Perevoshchikova N., Appolaire B., Teixeira J., Aeby-Gautier E., Denis S. // Computational Materials Science. 2012. 61. P. 54. 8. .. // . 2005. 79. 12. . 2126. 9. .., . . // . 2010. 84. 4. . 605. 10. .., . ., . ., . ., . . // . . 2006. 18. 1. . 67. 11. Wightman A.S. Introduction to: Israel R. B. Convexity in the theory of lattice gases. Princeton, New Jersey, 1979. 12. Galgani L., Scotti A. // Physica. 1968. 40. P. 150. 13. Landsberg P. T. // Pure and Appl. Chem. 1970. 22. P. 215. 14. Galgani L., Scotti A. // Physica. 1969. 42. P. 242. 15. Galgani L., Scotti A. // Pure Appl. Chem. 1970. 22. Iss. 34. P. 229.

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16. ter Horst H. J. // Annals of Physics. 1987. 176. P. 183. 17. .. // . . , . 1988. 33. . 157. 18. . // . 2003. 37. 3. . 1. 19. .., .. // M., 1964. 20. . . , . . , . . , .., .. // . . 2010. 1. . 110. 21. Smirnova N. A., Victorov A. I. // Fluid Phase Equilibria. 1987. 34. Iss. 23. P. 235. 22. .., .., .. . ­ / . .. . ., 1989. 23. ., . : . ., 1989. 24. Barber C. F., Dobkin D. P., Huhdanpaa H. // ACM Trans. Math. Software. 1996. 22. N 4. P. 469. 25. Liang H., Chen S.L., Chang Y.A. // Metall. Mater. Trans. A. 1997. 28a. N 9. P. 1725. 26. Liang P., Tarfa T., Robinson J. A., Wagner S., Ochin P., Harmelin P., Seifert H. J., Lukas H.L., Aldinger F. // Thermochim. Acta. 1998. 314. N 12. P. 87. 27. Jianrong Y., Watson A. // CALPHAD. 1994. 18. N 2. P. 165.
20.10.12

The CalCulaTion of Phase equilibria and ConsTruCTion of diagrams by Convex hull meThod
g.f. voronin, a.l. voskov
The work is devoted to the review and analysis of the few past years' results of the new method developed for the phase equilibria calculation. The method is based on the construction of convex hulls of characteristic functions in heterogeneous systems. Theoretical basis of the method, its possibilities and features of its practical application in scientific research and teaching chemical thermodynamics have been considered. software complexes developed on the department of Chemistry of lomonosov moscow state university have been briefly presented.

Key words: Chemical thermodynamics, calculation of phase equilibria, convex hull, phase diagrams.
: ­ , . . (gf.voronin@gmail.com); ­ . . , . . (alvoskov@gmail.com).