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Back-Diffusion In Crystal Growth. Eutectics

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Warianty tytułu
PL
Dyfuzja wsteczna we wzroście kryształu. Eutektyki
Języki publikacji
EN
Abstrakty
EN
Solute segregation/redistribution model for some eutectic alloys is presented. The differential equation for the solute micro-segregation during solidification accompanied by the back-diffusion is formulated. The solution to this equation results in the definitions of: solidification path, solid/liquid (s/l) interface path and redistribution path. An equation for the estimation of the amount of equilibrium and non-equilibrium precipitates is also delivered. It is proved that the current model is universal one. Thus, the model reduces perfectly, mathematically to both description of diffusion-less solidification and model of equilibrium solidification.
PL
Przedstawiono model segregacji/redystrybucji składnika dla stopów eutektycznych. Sformułowano równanie różniczkowe dla mikrosegregacji składnika podczas krystalizacji, której towarzyszy dyfuzja wsteczna. Rozwiązanie tego równania pozwoliło na zdefiniowanie ścieżek: krystalizacji, frontów krystalizacji i redystrybucji. Sformułowano równanie dla oceny ilości wydzieleń równowagowych i nierównowagowych. Pokazano, że model jest uniwersalny. Dlatego, redukuje się perfekcyjnie, matematycznie do opisu krystalizacji bez dyfuzji a także do modelu krystalizacji równowagowej.
Twórcy
  • Institute of Metallurgy and Materials, Polish Academy of Sciences, 25 Reymonta Str., 30-059 Kraków, Poland
Bibliografia
  • [1] E. Scheil, Über die Eutektische Kristallization. Zeitschrift für Metallkunde 34, 70-76 (1942).
  • [2] A. Krupkowski, General Solution of the Equation Characterizing the Crystallization Process in Binary Alloys of Dendritic Type, Bulletin of the Polish Academy of Sciences, Technical Sciences 13, 61-66 (1965).
  • [3] W. Krajewski, A. L. Greer, T. E. Quested, W. Wołczyński, Identification of the Substrate of Heterogeneous Nucleation in Zn-Al Alloy Inoculated with Zn-Ti Based Master Alloy, Chapter 16 in: Solidification and Crystallization, p. 137-147, ed. Wiley-VCH, Weinheim, Germany, 2004, eds. D.M. Herlach.
  • [4] T. Lipiński, Modification of Al-Si Alloys with the Use of a Homogenous Modifiers. Archives of Metallurgy and Materials 53, 193-197 (2008).
  • [5] T. Lipiński, P. Szabracki, Modification of the Hypo-eutectic Al-Si Alloys with an Exothermic Modifier. Archives of Metallurgy and Materials, 58, 453-458 (2013).
  • [6] H. Nguyen-Thi, B. Drevet, W. Wołczyński, Influence of Microgravity on the Back-diffusion Phenomenon in the Al-3.5Li Alloy Solidified Directionally, Archives of Metallurgy and Materials 44, 365-371 (1999).
  • [7] J. Kloch, B. Billia, T. Okane, T. Umeda, W. Wołczyński, Experimental Verification of the Solute Redistribution in Cellular/Dendritic Solidification of the Al-3.5Li and Fe-4.34Ni Alloys, Materials Science Forum 329/330, 31-36 (2000).
  • [8] W. Wołczyński, J. Kloch, Mass Conservation for Micro-segregation and Solute Redistribution in Cellular/Dendritic Solidification with Back-Diffusion, Materials Science Forum 329/330, 345-351 (2000).
  • [9] H. D. Brody, M. C. Flemings, Solute Redistribution in Dendritic Solidification, Transactions of the Metallurgical Society of AIME, 236, 615-624 (1966).
  • [10] M. Solari, H. Biloni, Micro-segregation in Cellular and Cellular-Dendritic Growth, Journal of Crystal Growth 49, 451-457 (1980).
  • [11] T. Clyne, W. Kurz, Solute Redistribution during Solidification with Rapid Solid State Diffusion, Metallurgical Transactions 12A, 965-971 (1981).
  • [12] A. Roosz, Z. Gacsi, G. Fuchs, Solute Redistribution during Solidification and Homogeneisation of Binary Solid Solution, Acta Metallurgica 32, 1745-1754 (1984).
  • [13] D. H. Kirkwood, Micro-segregation, Materials Science and Engineering 65, 101-109 (1984).
  • [14] I. Ohnaka, Mathematical Analysis of the Solute Redistribution during Solidification with Diffusion in the Solid Phase, Transactions of the ISIJ 26, 1045-1051 (1986).
  • [15] S. Kobayashi, A Mathematical Model for Solute Redistribution during Dendritic Solidification, Transactions of the ISIJ 28, 535-542 (1988).
  • [16] S. Kobayashi, Mathematical Analysis of Solute Redistribution during Solidification Based on a Columnar Dendrite Model, Transactions of the ISIJ 28, 728-735 (1988).
  • [17] S. Kobayashi, Solute Redistribution during Solidification with Diffusion in the Solid Phase, Journal of Crystal Growth, 88, 87-96 (1988).
  • [18] S. W. Chen, Y. A. Chang, Micro-segregation in Solidification for Ternary Alloys, Metallurgical Transactions, 23A, 1038-1043 (1992).
  • [19] L. Nastac, D. M. Stefanescu, An Analytical Model for Solute Redistribution during Solidification of Planar, Columnar, or Equiaxed Morphology, Metallurgical Transactions 24A, 2107-2118 (1993
  • [20] N. F. Dean, A. Mortensen, M. C. Flemings, Micro-segregation in Cellular Solidification, Metallurgical Transactions 25A, 2295-2301 (1994).
  • [21] T. Himemiya, T. Umeda, Solute Redistribution Model of Dendritic Solidification Considering Diffusion in both the Liquid and Solid Phases. ISIJ International 38, 730-738 (1998).
  • [22] W. Wołczyński, J. Kloch, R. Ebner, W. Krajewski, The Use of Equilibrium Phase Diagram for the Calculation of Non-Equilibrium Precipitates in Dendritic Solidification. Validation, Calphad 25, 391-400 (2002).
  • [23] W. Wołczyński, W. Krajewski, R. Ebner, J. Kloch, The Use of Equilibrium Phase Diagram for the Calculation of Non-Equilibrium Precipitates in Dendritic Solidification. Theory, Calphad 25, 401-408 (2002).
  • [24] W. Wołczyński, Back-Diffusion Phenomenon during the Crystal Growth by the Bridgman Method, Chapter 2. in the book: Modelling of Transport Phenomena in Crystal Growth, p. 19-59, WIT Press, Southampton (UK) – Boston (USA), 2000, eds. J.Szmyd & K.Suzuki.
  • [25] W. Wołczyński, W. Gąsior, Z. Moser, Interpretation and Meaning of the Diffusion Coefficient in Solid Al-3.5Li Alloy by Measurement of the Li-Solute Redistribution, Archives of Metallurgy and Materials 47, 231-238 (2002).
  • [26] T. Himemiya, W. Wołczyński, Prediction of Solidification Path and Solute Redistribution of an Iron-Based Multi-Component Alloy Considering Solute Diffusion in the Solid, Materials Transactions of the Japan Institute of Metals 43, 2890-2896 (2002).
  • [27] C. Senderowski, Z. Bojar, W. Wołczyński, A. Pawłowski, Microstructure Characterization of D-Gun Sprayed Fe-Al Intermetallic Coatings, Intermetallics 18, 1405-1409 (2010).
  • [28] M. J. Aziz, Model for Solute Redistribution during Rapid Solidification, Journal of Applied Physics 53, 1158-1168 (1982).
  • [29] A. W. Bydałek, S. Biernat, A. Bydałek, P. Schlafka, The Innovative Analysis of the Refinement Ability Extractive Slag, International Journal of Engineering and Innovative Technology 4, 186-197 (2014).
  • [30] A. W. Bydałek, A. Bydałek, W. Wołczyński, S. Biernat, The Concept of Slag Decopperisation in the Flash Furnace Process by Use of Complex Reagents, Archives of Metallurgy and Materials 60, 319-322 (2015).
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-65cf8f00-a5c7-4f25-9cce-fc850ca6b95e
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