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Physics of Metals
Название Regularities of phase equilibria based on the Bjerrum-Guggenheim concept for the Fe-Al binary system
DOI 10.17580/cisisr.2022.02.12
Автор V. V. Tolokonnikova, S. O. Baisanov, G. I. Narikbayeva, G. S. Yerekeyeva
Информация об авторе

Zh. Abishev Chemical and Metallurgical Institute (Karaganda, Kazakhstan):

V. V. Tolokonnikova, Cand. Chem., Chief Researcher, "Metallurgical melts" laboratory
S. O. Baisanov, Dr. Eng., Prof., Director, Head of the "Metallurgical melts" laboratory
G. I. Narikbayeva, Scientific Researcher, "Metallurgical melts" laboratory
G. S. Yerekeyeva, Postgraduate Student, "Metallurgical melts" laboratory, e-mail: yerekeyeva.g@mail.ru


A theoretically justified method of mathematical description of phase equilibrium lines based on the regularity of the behavior of components along the phase crystallization line has been developed. When analyzing the state diagrams of various systems, a regularity was found in the formation of crystallization fields of phases in the form of a correlation dependence between the osmotic coefficient of the crystallizing component and the ratio of its activity in the liquid and solid phases. The Bjerrum-Guggenheim osmotic coefficient can serve as a measure of the deviation of the energy properties of a real system from the ideal one described by the Schroeder-Le Chatelier equation. Two types of generalized mathematical expression in the form of a modified Schroeder-Le Chatelier equation are proposed for the analytical description of the liquidus and solidus lines of state diagrams of a whole class of systems. These types make it possible to calculate the dependence between the composition and the temperature. Mathematical expressions describing the lines of monovariant phase equilibria are presented on a single analytical basis. Mathematical expressions represent the liquidus and solidus lines of the Fe-Al system for the corresponding elements and compounds using the Schroeder-Le Chatelier equation and the Bjerrum-Guggenheim coefficient (Фi). The linear nature of the change in the osmotic coefficient of crystallizing phases (Фi) on the ratio of the activity of the components in the ideal liquid and solid phases under the boundary conditions of the formation of crystallization fields of the phases was revealed. The type of change in the Bjerrum-Guggenheim osmotic coefficient depends on the intermolecular interaction of the components in the melt. If only van der Waals forces of interaction between the structural units of the considered component with the second prevail, then a linear relationship is observed. When the formation of various groups from the initial components or the dissociation of a chemical compound takes place in the melt, the osmotic coefficient has a curved dependence.

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08855453).

Ключевые слова Iron, aluminum, Bjerrum-Guggenheim coefficient, state diagram, phases, mathematical model
Библиографический список

1. Kazakov A. I., Mokritskiy V. I., Romanenko V. I., Khitova L. Calculation of phase equilibria in multi-component systems. Moscow : Metalurgiya. 1987. p. 136.
2. Ageev N. V. Calculations and experimental methods of building the state diagrams. Moscow : Nauka. 1985. 184 p.
3. Zakharov M. A. Calculation of the main types of state diagrams for binary solutions within the framework of generalized lattice model. Vestnik Novgorodskogo gosudarstvennogo universiteta. 2016. No. 7 (98). pp. 22-26.
4. Shakhnazarov K. Yu. Attributes of intermediate phases in Al-Si, Fe-C and Al-Cu systems. Vestnik Magnitogorskogo gosudarstvennogo tekhnicheskogo universiteta im. G. I. Nosova. 2016. Vol. 14. No. 3. pp. 71-77.
5. Voronin G. F. New opportunities of thermodynamic calculation and building the diagrams of phase states of heterogeneous systems. Zhurnal fizicheskoy khimii. 2003. Vol. 77. No. 10. pp. 1874-1883.
6. Moshchenskaya E. Yu., Slepushkin V. V. The method of building liquidus curves in binary eutectic systems. Zhurnal neorganicheskoy khimii. 2015. Vol. 60. No. 1. pp. 78-84.
7. Samoilova O. V., Makrovets L. A., Mikhailov G. G., Trofimov E. A. Thermodynamic simulation of the liquidus line in Ni-Si system. Vestnik YUrGU. 2012. No. 24. pp. 69-73.
8. Sryvalin I. T., Korpachev V. G. Assessment of applicability of different models for theory of solutions to liquid metallic alloys. In book: Physical and chemical investigations of metallurgical processes. Sverdlovsk. 1977. Iss. 5. pp. 48-54.
9. Voronin G. F., Voskov A. L. Calculations of phase equilibria and building the diagrams via the method of convex shells. Vestnik Moskovskogo universiteta, Series 2. Khimiya. 2013. Vol. 54. No. 1. pp. 3-11.
10. Panish M. Liquidus Isotherms in the Ga-system. Journal of the electrochemical society. 1970. Vol. 117. No. 9. pp. 1202-1203.
11. Shim Jae-Hycok, Lee Dong Nyung. Mn absorption characteristics of Ti2O3 inclusions in low carbon steels. Scripta Materialia (Z. Metallk.). 2000. Vol. 91. No. 2. pp. 114-120.
12. COST 507. Thermochemical data base for light metal alloys. Under edition of Ansara I., Dinsdale A. T., Rand M. H. Brussels. 1998. Vol. 2. p. 420.
13. Abe F. Alloy Design of Creep and oxidation Resistant 9Cr steels for Thick Section Boiler Components Operating at 650 °C. 4th ERPI International Technology for Fossil Power Plants. USA, SC. 2004, October 25-28. pp. 273-283.
14. Glazov V. M., Pavlova L. M. Chemical thermodynamics and phase equilibria. Moscow : Metallurgiya. 1981. 336 p.
15. Baisanov S. O., Tolokonnikova V. V., Narikbaeva G. I. Mathematical models of phase equilibriums lines on the base of modified Schroeder-Le Chatelier equation. Proceedings of International scientific conference “XX Mendeleev meeting on general and applied chemistry”. Ekaterinburg. 2016. p. 137.
16. Baisanov S., Tolokonnikova V., Narikbayeva G., Korsukova I., Mukhambetgaliyev E. Estimation of dissociation degree of congruently melting compounds through osmotic coefficient of Bjerrum-Guggenheim. Metalurgija. 2020. Vol. 59. Iss. 3. pp. 343-346.
17. Baisanov S., Tolokonnikova V., Narikbayeva G., Korsukova I., Mukhambetgaliyev E. Mathematical method of phase equilibrium of binary system Cr-Si based on Bjerrum-Guggenheim concept. Metalurgija. 2020. Vol. 59. Iss. 1. pp. 97-100.
18. Baisanov S. O., Tolokonnikova V. V., Narikbayeva G. I., Korsukova I. Ya., Zhuchkov V. I. Thermodynamic assessment of smelting of manganese and chromium ferroalloys based on the analysis of their state diagrams. Izvestiya NAN RK, series “Khimiya i technologii”. 2018. No. 5. pp. 47-57.
19. Philips H. W. L. Annotated equilibrium phase diagrams of some aluminum alloy systems. London : Inst. Met. Monograph. 1959. Vol. 25. p. 86.
20. Vol. D. E. Structure and properties of binary metallic systems, in 4 volumes. Moscow : Fizmatgiz. 1962. 230 p.
21. Shank F. A. Structures of binary alloys. Moscow : Metallurgiya. 1973. 760 p.
22. Hansen M., Anderko K. Structure of binary alloys, in 2 volumes. Moscow : Metallurgiya. 1962. 1488 p.
23. Kubashevski O. State diagrams of Fe-based binary systems. Directory. Moscow : Metallurgiya. 1985. 184 p.
24. Mejer Hansen T. M., Skou Cordua K., Mosegaard K. Inverse problems with non-trivial priors: efficient solution through sequential Gibbs sampling. Comput Geosci. 2012. Vol. 16. pp. 593-611. DOI: 10.1007/s10596-011-9271-1.
25. Lucena J., Costa Laranjeiras C., Novaes Chiappin J. R. Gibbs' rational reconstruction of thermodynamics according to the heuristic tradition of Descartes' analytical method - History of Physics and Related Sciences. Revista Brasileira de Ensino de Fisica. 2019. Vol. 41 (1). р. 41. DOI: 10.1590/1806-9126-RBEF-2018-0012.
26. Nikolaidis I. K., Poursaeidesfahani A., Csaszar Z., Ramdin M., Vlugt Thijs J. H., Economou I. G., Moultos O. A. Modeling the phase equilibria of asymmetric hydrocarbon mixtures using molecular simulation and equations of state. AIChE Journal. 2019. Vol. 65. No. 2. pp. 792-803.
27. Gomez H., Bures M., Moure A. A review on computational modelling of phase-transition problems. The Royal Society publishing. Mathematical, physical and engineering scinces. 2019. March. p. 377. DOI: 10.1098/rsta.2018.0203.

Полный текст статьи Regularities of phase equilibria based on the Bjerrum-Guggenheim concept for the Fe-Al binary system