Don State Technical University (Rostov-na-Donu, Russia):

Yu. V. Dolgachev, Cand. Eng., Associate Prof., Dept. of Physical and Applied Materials Science, e-mail: yuridol@mail.ru
V. N. Pustovoit, Dr. Eng., Prof., Dept. of Physical and Applied Materials Science

The results of magnetic state simulation of carbon steel austenite are presented in this work. Quantitative parameters of the areas of short-range magnetic order, which are presented in paramagnetic austenite matrix and are observed as potential places of α-phase nucleation, are examined. This austenite heterogeneity in steels and clean iron is confirmed by the experimental data; however, detailed quantitative study meets technical complication of such experiments. It is suggested to use the Ising model for realization of the calculation experiment. The obtained spin configurations were analyzed for determination of geometric parameters of magnetic inhomogeneities and period of their sustainable existence. Calculations were conducted within the temperature range of austenite phase existence in steel, as well as without and with taking into account presence of external magnetic field, which strengthens existing austenite heterogeneity and has the effect on conduction of phase transformations in steel. The results of simulation confirm presence of the areas of short-range magnetic order in austenite, their size is close to the existing theoretical assessments and experimental data. It is shown that temperature rise leads to decrease of dimensions, number and life period of clusters, but these parameters are still important at the temperature of martensite transformation in steel. Overlapping of external magnetic field creates the conditions for existence of large-size ferromagnetic clusters also at more high temperatures, as well as increases time of their sustainable existence. The external magnetic field provides the conditions for more intensive and multiplicative nucleation of ferromagnetic phase, similar to short-range magnetic order fluctuations in location of atoms during liquid metal cooling. 

1. Sedov V. L. Antiferromagnetism of γ-iron: a problem of invar. Moscow : Nauka. 1987. 288 p.
2. Lee D. K., Hong S. C. Correlation between Structures and Magnetism in Iron: Ferromagnetism and Antiferromagnetism. Journal of Magnetics. 2007. Vol. 12 (2). pp. 68-71.
3. Steinle-Neumann G., Cohen R. E., Stixrude L. Magnetism in iron as a function of pressure. Journal of Physics: Condensed Matter. 2004. Vol. 16 (14). p. 1109.
4. Spooner S., Averbach B. L. Spin correlations in iron. Physical Review. 1966. Vol. 142 (2). pp. 291-299.
5. Romashev L. N., Voronchikhin L. D., Fakirov I. G. Variation of steel magnetic properties near martensite point. Fizika metallov i metallovedenie. 1973. Vol. 36 (2). p. 291.
6. Sort J., Concustell A., Menéndez E., Suriñach S., Baró M. D., Farran J., Nogués J. Selective generation of local ferromagnetism in austenitic stainless steel using nanoindentation. Applied physics letters. 2006. Vol. 89 (3). p. 032509.
7. Brink B. K., Ståhl K., Christiansen T. L. Composition-dependent variation of magnetic properties and interstitial ordering in homogeneous expanded austenite. Acta Materialia. 2016. Vol. 106. pp. 32-39.
8. Shima M., Nasu S. Ferromagnetic gamma-Fe Nanoparticles Trapped in Carbon Nanotubes. American Physical Society: March Meeting Abstracts. 2005. p. D42-009.
9. Witte R., Feng T., Fang J. X., Fischer A., Ghafari M., Kruk R., Brand R. A., Wang D., Hahn H., Gleiter H. Evidence for enhanced ferromagnetism in an iron-based nanoglass. Applied Physics Letters. 2013. Vol. 103 (7). p. 073106.
10. Glushkov V. V., Voskoboinikov I. B., Demishev S. V., Krivitskii I. V., Menovsky A., Moshchalkov V. V., Samarin N. A., Sluchanko N. E. Spin-polaron transport and magnetic phase diagram of iron monosilicide. Journal of experimental and theoretical physics. 2004. Vol. 99 (2). pp. 394-414.
11. Razumov I. K., Gornostyrev Yu. N., Katsnelson M. I. On theory of phase transformations in iron and steel on the base of primary principle approaches. Fizika metallov i metallovedenie. 2017. Vol. 118. No. 4. pp. 380–408.
12. Ignatenko A. N., Katanin A. A., Irkhin V. Yu. Strong short-range magnetic order in frustrating FCC lattice and its possible role in iron structure transformation. Pisma v zhurnal eksperimentalnoy i teoreticheskoy fiziki. 2008. Vol. 87 (10). pp. 642–646.
13. Razumov I. K., Gornostyrev Yu. N., Katsnelson M. I. Effect of magnetism on kinetics of γ–α transformation and pattern formation in iron. Journal of Physics: Condensed Matter. 2013. Vol. 25 (13). p. 135401.
14. Razumov I. K., Boukhvalov D. V., Petrik M. V., Urtsev V. N., Shmakov A. V., Katsnelson M. I., Gornostyrev Yu. N. Role of magnetic degrees of freedom in a scenario of phase transformations in steel. Physical Review B. 2014. Vol. 90 (094101). p. 8.
15. Okatov S. V., Kuznetsov A. R., Gornostyrev Yu. N., Urtsev V. N., Katsnelson M. I. Effect of magnetic state on the γ-α transition in iron: First-principles calculations of the Bain transformation path. Physical Review B. 2009. Vol. 79. p. 094111.
16. Zolotarevskiy I. V. Influence of volumetric magnetostriction on martensite transformation in ferrous alloys. Magnetic phase transition of the first order. Metallofizika i noveishie tekhnologii. 2015. Vol. 37. No. 5. pp. 625-636.
17. Pustovoit V. N., Dolgachev Y. V., Arefyeva L. P. Martensite Nucleation under Conditions of Austenite Superplasticity and External Magnetic Field. IOP Conference Series: Materials Science and Engineering. 2020. Vol. 969 (1). p. 012009.
18. Pustovoit V. N., Dolgachev Y. V. Revisiting the nature of sites of martensite nucleation during steel hardening. Izvestiya Ferrous Metallurgy. 2019. Vol. 62 (2). pp. 109–114.
19. Pustovoit V. N., Dolgachev Y. V. Ferromagnetically ordered clusters in austenite as the areas of martensite formation. Emerging Materials Research. 2017. Vol. 6 (2). pp. 249–253.
20. McCoy B. M., Wu T. T. The two-dimensional Ising model. Cambridge: Harvard University Press. 2013. 438 p.
21. Landau L. D., Lifshitz E. M. Statistical Physics. Volume 5. Oxford: Elsevier, 2013. 544 p.
22. Sandler S. I. An introduction to applied statistical thermodynamics. N.Y.: John Wiley & Sons. 2010. 368 p.
23. Pustovoit V. N., Dolgachev Y. V. Magnetic austenite heterogeneity and transformations in steels. Rostov-na-Donu : DGTU. 2021. 198 p.
24. Dolgachev Y. V., Pustovoit V. N., Filonenko I. O., Ivankov I. V. On the problem of simulation of martensite nucleation process of in clusters of ferromagnetic nature. Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta. 2020. Vol. 20. No. 1. pp. 51-60.
25. Suzdalev I. P. Magnetic phase transitions in nano-clusters and nano-structures. Rossiyskie nanotekhnologii. 2006. Vol. 1. No. 1. pp. 46-57.