Computer Simulation of Atomic Structure and Hyperfine Interactions in Fe–C Austenite

A. M. Timoshevskii, S. O. Yablonovskii, V. I. Yeremin

Institute of Magnetism under NAS and MES of Ukraine, 36b Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

Received: 18.11.2011. Download: PDF

A new method based on the principles of self-organization is designed. For researcher, the method does not require to set up initial model of the spectrum. A criterion of correspondence between the experimental and model spectra is evaluation of empirical risk. Result of calculation is a set of optimal spectra models proposed to the researcher. Our tests for a number of experimental spectra showed a high efficiency of the method. The method is used for analysis of experimental Mössbauer spectra of Fe$_{10}$C austenite. As compared with already known expansions, we obtained a new accurate expansion of the measured spectrum into one singlet and two doublet lines. To interpret the results, we performed first-principle FLAPW calculations of electronic structure and hyperfine interactions in several ordered Fe$_{32}$C$_{2}$ structures, which model FeC$_{0.0625}$ austenite. There is a good agreement between the measured data and the theoretical calculations.

Keywords: self-organization of mathematical models, minimization of empiric risk, carbonaceous austenite, Mossbauer spectrums, first-principle calculations.

PACS: 07.05.Kf, 61.05.Qr, 71.15.Ap, 71.15.Mb, 71.15.Nc, 76.80.+y, 82.80.Ej

DOI: https://doi.org/10.15407/ufm.12.04.451

Citation: A. M. Timoshevskii, S. O. Yablonovskii, and V. I. Yeremin, Computer Simulation of Atomic Structure and Hyperfine Interactions in Fe–C Austenite, Usp. Fiz. Met., 12, No. 4: 451—470 (2011) (in Russian), doi: 10.15407/ufm.12.04.451


References (23)  
  1. V. B. Zlokazov, Fiz. elementar. chastits i atom. yadra, 16, No. 5: 1126 (1985).
  2. V. B. Zlokazov, VIII shkola po neytronnoy fizike: Sb. lektsiy (Dubna: OIYaI: 1998), s. 223.
  3. A. H. Tikhonov, B. Ya. Apsenin, Metody resheniya nekorrektnykh zadach (Moskva: Hayka: 1974).
  4. S. A. Bruggemann, Y. A. Artzybashev, and S. V. Orlov, (UNIVEM) Version 4.5 (1990–1993).
  5. V. S. Rusakov, Messbauerovskaya spektroskopiya lokal'no neodnorodnykh sistem (Almaty: OPNI IYaF NYaTs RK: 2000).
  6. K. Lagarec and D. G. Rancourt, Nucl. Instrum. Methods Phys. Res. B, 129, No. 2: 266 (1997). Crossref
  7. Z. Klencsár, E. Kuzmann, and A. Vértes, J. Radioanal. Nucl. Chem., 210, No. 1: 105 (1996). Crossref
  8. H. Ahonen, P. A. de Souza Júnior, and V. K. Garg, Nucl. Instrum. Methods Phys. Res. B, 124, No. 4: 633 (1997). Crossref
  9. A. G. Ivakhnenko, Dolgosrochnoe prognozirovanie i upravlenie slozhnymi sistemami (Kyiv: Tekhnіka: 1975).
  10. V. N. Vapnik, Vosstanovlenie zavisimostey po empiricheskim dannym (Moskva: Nauka: 1979).
  11. A. Timoshevskii and V. Yeremin, Hyperfine Interact., 159, Nos. 1–4: 395 (2004). Crossref
  12. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Englewood Cliffs, New Jersey: Prentice-Hall: 1974). Crossref
  13. R. H. Byrd, Peihuang Lu, J.Nocedal, and Ciyou Zhu, SIAM J. Sci. Comput., 16, No. 5: 1190 (1995). Crossref
  14. V. G. Gavriljuk and H. Berns, High Nitrogen Steels (Berlin: Springer-Verlag: 1999). Crossref
  15. N. DeCristofaro and R. Kaplow, Metall. Mater. Trans. A, 8: 35 (1977). Crossref
  16. D. L. Williamson, K. Nakazawa, and G. Krauss, Metall. Mater. Trans. A, 10: 1351 (1979). Crossref
  17. V. N. Bugaev, V. G. Gavriljuk, V. M. Nadutov, and V. A. Tatarenko, Acta Metall., 31, No. 3: 407 (1983). Crossref
  18. K. Oda, H. Fujimura, and H. Ino, J. Phys.: Condens. Matter, 6: 679 (1994). Crossref
  19. O. N. C. Uwakweh, J. P. Bauer, and J. M. Génin, Metall. Mater. Trans. A, 21: 589 (1990). Crossref
  20. K. Laneri, J. Desimoni, G. J. Zarragoicoechea, and A. Fernández Guillermet, Phys. Rev. B, 66: 134201 (2002). Crossref
  21. D. Singh, Planewaves, Pseudopotential and the LAPW Method (Boston–Dordrecht–London: Kluwer Academic: 1994).
  22. P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k: An Augmented Plane Wave plus Local Orbitals Program for Calculating Crystal Properties (Wien, Austria: Tech. Universität: 2001).
  23. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett., 77, No. 18: 3865 (1996). Crossref