download PDF


The aim of the study is mathematical modeling of the process of nucleation of crystallites in liquid iron. To solve the problem, the authors used the stationarity principle and put forward a hypothesis that short-range order regions are formed in the volume of a liquid (metal melt) due to temperature fluctuations and the temperature of the short-range region is during the crystallization time the fluctuation of temperature near zero on the Kelvin scale. Studies were carried out for the substance in the liquid state, in particular for pig iron in the paramagnetic state at the melting temperature. In constructing a mathematical model of the process, analytical expressions are obtained for determining the average number of atoms in the short-range order region for crystallized cast iron. To obtain a regularity, the method of statistical physics, probability theory and mathematical statistics were used. The results of the computational experiment showed that the short-range order regions contain a sufficiently large number of atoms in order for the interaction with the pulsed magnetic field to lead to an increasing the number of crystal nuclei and a decrease in their dimensions. The results obtained are applicable for making decisions on the conduct of technological measures aimed at obtaining a homogeneous structure of metals, in particular when designing installations for the action of a pulsed magnetic field on melts, particularly for ferrous and non-ferrous metallurgy.


Mathematical model of fluctuations, crystallization of metallic melts, pulsed magnetic field, short-range order, the energy of thermal motion.

Mikhail B. Arkulis

Ph.D., Assistant Professor, Nosov Magnitogorsk State Technical University, Magnitogorsk, Russia.

Lev M. Velus

Ph.D. (Eng.), Assistant Professor, Magnitogorsk, Russia.

Michail N. Tseitlin

D.Sc. (Eng.), Department of Physics, Ariel University, Ariel, Israel.

Oksana S. Logunova

D.Sc. (Eng.), Professor, Head of the Computer Science and Programming Department, Nosov Magnitogorsk State Technical University, Magnitogorsk, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..

1. Yajchikov I.M., Devyatov D.Kh., Logunova O.S., Portnova I.V. Investigating the macrokinetics of the process of metal reduction from its oxides with the use of the pulsing plasma jets // Izvestiya Vysshikh Uchebnykh Zavedenij. Chernaya Metallurgiya. 2002. № 7. P. 17-19.

2. Kolokoltsev V.M., Vdovin K.N., Mayorova T.V., Ponomareva O.S. Ecological indicators in the system of non-financial reporting at industrial enterprises. CIS Iron and Steel Review. 2017. doi: 10.17580/cisisr.2017.01.01

3. Vdovin K.N., Pivovarova K.G., Lisovskaya M.A. The Use of Thermal Analysis to Study the Structure and Properties of Roll Steels. Metal Science and Heat Treatment. 2014, no. 6, pp. 22-25.

4. Chukin M., Polyakova M., Gulin A., Nikitenko O. The possibility of manufacturing long-length metal products with ultra-fine grain structure by combination of strain effects. Key Engineering Materials. 2016, vol. 685, pp. 487-491. doi: 10,4028 / / KEM.685.487.

5. Arkulis M.B., Velyus L.M., Savchenko Yu.I. Control of cast iron crystallization process by pulsed magnetic field. Elektrotehnicheskie sistemyi i kompleksy. [Electrotechical systems and complexes] 2016, no. 3, pp. 66-68. (In Russian)

6. Petrik M.V., Gorbatov O.I., Gornostyrev Yu.N. Role of Magnetism in the Formation of a Short Range Order in an Fe–Ga Alloy. JETP Letters. 2013, vol. 98, no. 12, pp. 809-812.

7. Petrik M.V., Gorbatov O.I. and Gornostyrev Yu.N. Effect of Magnetism on the Solution Energy of 3p(Al, Si) and 4p(Ga, Ge) Elements in Iron. The Physics of Metals and Metallography. 2013, vol. 114, no. 11, pp. 885-892.

8. Levich V.G. Kurs teoreticheskoy fiziki [The course of theoretical physics]. Moscow: Nauka, 1969, vol. 1, pp. 582-588. (In Russian)

9. Landau L.D., Lifshits E.M. Statisticheskaya fizika [Statistical physics]. Moscow: Gostehizdat, 1951, 372 p. (In Russian)

10. Yavorskiy B.M., Detlaf A.A. Spravochnik po fizike [Reference book on physics]. Moscow: Science, 1985. 512 p. (In Russian)

11. Chernikov D.G. Development of physical method of modifying cast aluminum alloys by pulsed magnetic processing. Izvestiya OrelGTU. Seriya «Fundamentalnyie i prikladnyie problemyi tehniki i tehnologii» [Series «Fundamental and practical problems of engineering and production»]. 2009. vol. 2-3/274(560), pp. 87-92. (In Russian)

12. Chernikov D.G., Gluschenkov V.A., Grechnikov F.V., Igolkin A.Yu., Nikitin V.I., Nikitin K.V. Pulsed magnetic processing of silumin AK9T. Liteynoe proizvodstvo [Foundry]. 2011, no. 9, pp. 8-11. (In Russian)

13. Levin M.N., Postnikov V.V., Matveev N.N. Influence of pulsed magnetic processing on crystallization of flexible polymers. Vyisokomolekulyarnoe soedinenie A [High-molecular compounds]. 2003, vol. 45, no. 2, pp. 217-223. (In Russian)

14. Postnikov V.V., Levin M.N., Matveev N.N., Skoridanov R.V., Kamalova N.S., Shamaev V.A. Influence of weak magnetic fields on modified wood. Pisma v zhurnal tehnicheskoy fiziki [Proceedings of technical physics]. 2005, vol. 31, iss. 9, pp. 14-19. (In Russian)

15. Alekseenko V.I. Influence of pulsed magnetic field on the structural states in oxide glass. Zhurnal tehnicheskoy fiziki [Proceedings of technical glass]. 1998, vol. 68, no. 10, pp. 50-54. (In Russian)

16. Gmurman V.E. Teoriya veroyatnostey i matematicheskaya statistika [Mathematical probability and mathematical statistics]. Moscow: High school, 1972. 360 p. (In Russian)