Issues »  Volume 36, Issue 12

Analysis of Spatial Structures Arising During Eutectic Crystallization and Cellular Decomposition of Solid Solutions

M. O. Ivanov, A. Yu. Naumuk

G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03680 Kyiv-142, Ukraine

Received: 18.11.2014. Download: PDF

The conditions for occurrence of different structures during stationary processes of eutectic crystallization and cellular decomposition of supersaturated solid solutions are analysed. This discussion is based on a previously proposed approach, which is composed of a comparison of the rates of change of free energy calculated by two different methods and a certain variational principle to choose between different ways of implementing such processes. It turns out that the most advantageous under given external conditions is such a structure, for which the minimum value is achieved for product of the total value of surface energy related to the formed phases on the structure factor of the process, which arises under this approach. Besides, the form of the structure factor depends essentially on the mechanism for the implementation of the separation (bulk or surface) diffusion. Based on such considerations, comparison of the lamellar and rod structures arising during eutectic crystallization and cellular decomposition of solid solutions is carried out. For a rod structure, various types of rods’ arrangements over a two-dimensional lattice are considered, namely, with the regular triangular or rectangular cells, and certain rod cross-section facetings different from circular one, for instance, in the form of regular hexagon, are also considered.

Key words: stationary non-equilibrium processes, eutectic crystallization, cellular decomposition of supersaturated solid solutions, lamellar structure, rod structure, diffusion, the rate of change of free energy.

URL: http://mfint.imp.kiev.ua/en/abstract/v36/i12/1571.html

DOI: https://doi.org/10.15407/mfint.36.12.1571

PACS: 64.60.A-, 64.60.My, 64.70.dg, 65.40.gd, 65.40.gp, 66.30.Fq, 81.30.-t

Citation: M. O. Ivanov and A. Yu. Naumuk, Analysis of Spatial Structures Arising During Eutectic Crystallization and Cellular Decomposition of Solid Solutions, Metallofiz. Noveishie Tekhnol., 36, No. 12: 1571—1596 (2014) (in Russian)

REFERENCES
  1. S. R. de Groot, Introduction to Thermodynamics of Irreversible Processes (New York: Interscience Publishers, Inc.: 1951).
  2. I. Prigogine, Non-Equilibrium Statistical Mechanics (New York: John Wiley: 1961).
  3. S. R. de Groot and P. Masur, Nonequilibrium Thermodynamics (Amsterdam: North-Holland: 1962).
  4. I. Gyarmati, Non-Equilibrium Thermodynamics. Field Theory and Variational Principles (Berlin: Springer: 1970). Crossref
  5. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (New York: John Wiley: 1971).
  6. D. N. Zubarev, Neravnovesnaya Statisticheskaya Termodinamika (Moscow: Nauka: 1971) (in Russian).
  7. H. C. H. Carpenter and J. M. Robertson, J. Iron Steel Inst., 125, No. 1: 309 (1932).
  8. D. Turnbull and H. N. Treaftis, Acta. Met., 3, No. 1: 43 (1955). Crossref
  9. W. de Sorbo and D. Turnbull, Acta. Met., 4, No. 5: 495 (1956). Crossref
  10. R. G. Rose, Acta. Met., 5, No. 7: 404 (1957). Crossref
  11. N. N. Buynov and R. R. Zakharova, Raspad Metallicheskikh Peresyshchennykh Tverdykh Rastvorov (Moscow: Metallurgiya: 1964) (in Russian).
  12. K. N. Tu and D. Turnbull, Acta Met., 15, Iss. 2: 369; ibidem, Iss. 8: 1317 (1967). Crossref
  13. K. P. Bunin, Ya. N. Malinochka, and Yu. N. Taran, Osnovy Metallografii Chuguna (Moscow: Metallurgiya: 1969) (in Russian).
  14. L. N. Larikov and O. A. Shmatko, Fiz. Met. Metalloved., 30, No. 6: 1173 (1970) (in Russian).
  15. L. N. Larikov and O. A. Shmatko, Yacheistyy Raspad Peresyshchennykh Tverdykh Rastvorov (Kiev: Naukova Dumka: 1976) (in Russian).
  16. O. A. Shmatko, Metallofizika, 2, No. 2: 97 (1980) (in Russian).
  17. M. V. Itkin, V. S. Krasil'nikov, and O. A. Shmatko, Metallofizika, 7, No. 6: 27 (1985) (in Russian).
  18. W. H. Brandt, J. Appl. Phys., 16, No. 1: 139 (1945). Crossref
  19. C. Zener, Trans. AIME, 167, No. 1: 550 (1945).
  20. D. Turnbull, Acta. Met., 3, No. 1: 55 (1955). Crossref
  21. M. Hillert, Jernkont. Ann., 141, No. 1: 757 (1957).
  22. J. W. Cahn, Acta. Met., 7, No. 1: 18 (1959). Crossref
  23. K. A. Jackson and J. D. Hunt, Trans. AIME, 236, No. 1: 1129 (1966).
  24. J. M. Shapiro and J. S. Kirkaldy, Acta. Met., 16, No. 1: 579 (1968). Crossref
  25. B. E. Sundquist, Acta. Met., 16, No. 1: 1413 (1968). Crossref
  26. F. M. A. Carpay and J. Boomgard, Acta. Met., 19, No. 1: 1279 (1971). Crossref
  27. S. Milenkovic and R. Caram, J. Crystal Growth, 237–239, No. 1: 95 (2002). Crossref
  28. H. Deng, E. C. Dickey, Y. Paderno, V. Paderno, V. Filippov, and A. Sayir, J. Mater. Sci., 39, No. 1: 5987 (2004). Crossref
  29. M. A. Ivanov, V. I. Glushchenko, and A. Yu. Naumuk, Fiz. Met. Metalloved., 113, No. 1: 3 (2012) (in Russian).
  30. M. A. Ivanov and A. Yu. Naumuk, Fiz. Met. Metalloved., 115, No. 5: 502 (2014) (in Russian). Crossref
  31. M. A. Ivanov and A. Yu. Naumuk, Fiz. Met. Metalloved., 115, No. 9: 941 (2014) (in Russian). Crossref
  32. M. A. Ivanov, A. Yu. Naumuk, and O. A. Shmatko, Metallofiz. Noveishie Tekhnol., 36, No. 8: 1059 (2014) (in Russian). Crossref

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