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Germany; Russia Jena; Yekaterinburg
Section Mathematics
Title Influence of convective flow on the growth of pure and alloyed dendrite
Author(-s) Kazak O.V.a, Galenko P.K.b, Alexandrov D.V.a
Affiliations Ural Federal Universitya, University of Jenab
Abstract The paper presents the model of anisotropic growth of dendritic crystallization of chemically pure and binary liquid (solution or melt) based on forced convection of the liquid phase. The dependencies of the growth rate and the radius of the top of a dendrite from under-cooling fluid in cases of a chemically pure material and alloys are presented. A comparative analysis of the influence of forced convection on the dendrite growth kinetics is carried out. Evaluation of growth rate and morphology of dendrite by high-speed crystal growth model was done. The contribution of convective flow and the anisotropic properties of the liquid-crystal boundary were taking into account. The model is also used hyperbolic diffusion equation to describe the non-equilibrium impurity capture by crystal surface, which occurs under the rapid crystals growth.
Keywords crystallization, dendrite growth, numerical simulation, convection
UDC 51-72
MSC 76D07, 76M45
DOI 10.20537/vm160301
Received 15 May 2016
Language Russian
Citation Kazak O.V., Galenko P.K., Alexandrov D.V. Influence of convective flow on the growth of pure and alloyed dendrite, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 299-311.
  1. Flemings M.C. Solidification processing, New York: McGraw-Hill, 1974.
  2. Chernov A.A. Modern crystallography III. Crystal growth, Berlin-Heidelberg: Springer, 1984. DOI: 10.1007/978-3-642-81835-6
  3. Kurz W., Fisher D.J. Dendrite growth at the limit of stability: tip radius and spacing, Acta Metallurgica, 1981, vol. 29, issue 1, pp. 11-20. DOI: 10.1016/0001-6160(81)90082-1
  4. Lipton J., Glicksman M.E., Kurz W. Dendritic growth into undercooled alloy metals, Materials Science and Engineering, 1984, vol. 65, issue 1, pp. 57-63. DOI: 10.1016/0025-5416(84)90199-X
  5. Boettinger W.J., Coriell S.R. Microstructure formation in rapidly solidified alloys, Science and Technology of the Undercooled Melt, Eds.: Sahm P.R., Jones H., Adam C.M. Springer, 1986, pp. 81-109. DOI: 10.1007/978-94-009-4456-5_5
  6. Lipton J., Kurz W., Trivedi R. Rapid dendrite growth in undercooled alloys, Acta Metallurgica, 1987, vol. 35, issue 4, pp. 957-964. DOI: 10.1016/0001-6160(87)90174-X
  7. Trivedi R., Lipton J., Kurz W. Effect of growth rate dependent partition coefficient on the dendritic growth in undercooled melts, Acta Metallurgica, 1987, vol. 35, issue 4, pp. 965-970. DOI: 10.1016/0001-6160(87)90175-1
  8. Boettinger W.J., Coriell S.R., Trivedi R. Application of dendritic growth theory to the interpretation of rapid solidification microstructures, Rapid Solidification Processing: Principles and Technologies IV, Eds.: Mehrabian R., Parrish P.A. Claitor, 1988.
  9. Herlach D.M., Matson D.M. (Eds.) Solidification of containerless undercooled melts, Wiley, 2012. DOI: 10.1002/9783527647903
  10. Hoyt J.J., Asta M., Karma A. Atomistic and continuum modeling of dendritic solidification, Materials Science and Engineering: R: Reports, 2003, vol. 41, issue 6, pp. 121-163. DOI: 10.1016/S0927-796X(03)00036-6
  11. Funke O., Phanikumar G., Galenko P.K., Chernova L., Reutzel S., Kolbe M., Herlach D.M. Dendrite growth velocity in levitated undercooled nickel melts, Journal of Crystal Growth, 2006, vol. 297, issue 1, pp. 211-222. DOI: 10.1016/j.jcrysgro.2006.08.045
  12. Binder S., Galenko P.K., Herlach D.M. Faceting of a rough solid-liquid interface of a metal induced by forced convection, Philosophical Magazine Letters, 2013, vol. 93, issue 10, pp. 608-617. DOI: 10.1080/09500839.2013.830201
  13. Langer J.S., Hong D.C. Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy, Physical Review A, 1986, vol. 34, issue 2, pp. 1462-1471. DOI: 10.1103/PhysRevA.34.1462
  14. Pelcé P., Bensimon D. Theory of dendrite dynamics, Nuclear Physics B - Proceedings Supplements, 1987, vol. 2, pp. 259-270. DOI: 10.1016/0920-5632(87)90022-3
  15. Ben Amar M., Pelcé P. Impurity effect on dendritic growth, Physical Review A, 1989, vol. 39, issue 8, pp. 4263-4269. DOI: 10.1103/PhysRevA.39.4263
  16. Brener E.A. Effects of surface energy and kinetics on the growth of needle-like dendrites, Journal of Crystal Growth, 1990, vol. 99, issues 1-4, pp. 165-170. DOI: 10.1016/0022-0248(90)90505-F
  17. Galenko P.K., Danilov D.A. Local nonequilibrium effect on rapid dendritic growth in a binary alloy melt, Physics Letters A, 1997, vol. 235, issue 3, pp. 271-280. DOI: 10.1016/S0375-9601(97)00562-8
  18. Galenko P.K., Danilov D.A. Model for free dendritic alloy growth under interfacial and bulk phase nonequilibrium conditions, Journal of Crystal Growth, 1999, vol. 197, issue 4, pp. 992-1002. DOI: 10.1016/S0022-0248(98)00977-4
  19. Yang Y., Humadi H., Buta D., Laird B.B., Sun D., Hoyt J.J., Asta M. Atomistic simulations of nonequilibrium crystal-growth kinetics from alloy melts, Physical Review Letters, 2011, vol. 107, issue 2, 025505, 4 p. DOI: 10.1103/PhysRevLett.107.025505
  20. Jou D., Galenko P. Coarse graining for the phase-field model of fast phase transitions, Physical Review E, 2013, vol. 88, issue 4, 042151, 8 p. DOI: 10.1103/PhysRevE.88.042151
  21. Herlach D.M. Non-equilibrium solidification of undercooled metallic metls, Materials Science and Engineering: R: Reports, 1994, vol. 12, issues 4-5, pp. 177-272. DOI: 10.1016/0927-796X(94)90011-6
  22. Herlach D., Galenko P., Holland-Moritz D. Metastable solids from undercooled melts, Amsterdam: Elsevier, 2007.
  23. Alexandrov D.V., Danilov D.A., Galenko P.K. Selection criterion of a stable dendrite growth in rapid solidification, International Journal of Heat and Mass Transfer, 2016, vol. 101, pp. 789-799. DOI: 10.1016/j.ijheatmasstransfer.2016.05.085
  24. Galenko P.K., Danilov D.A., Reuther K., Alexandrov D.V., Rettenmayr M., Herlach D.M. Effect of convective flow on stable dendritic growth in rapid solidification of a binary alloy, Journal of Crystal Growth, 2016. DOI: 10.1016/j.jcrysgro.2016.07.042
  25. Barbieri A., Langer J.S. Predictions of dendritic growth rates in the linearized solvability theory, Physical Review A, 1989, vol. 39, issue 10, pp. 5314-5325. DOI: 10.1103/PhysRevA.39.5314
  26. Alexandrov D.V., Galenko P.K. Selection criterion of stable dendritic growth at arbitrary Peclét numbers with convection, Physical Review E, 2013, vol. 87, 062403, 5 p. DOI: 10.1103/PhysRevE.87.062403
  27. Alexandrov D.V., Galenko P.K. Dendrite growth under forced convection: analysis methods and experimental tests, Physics-Uspekhi, 2014, vol. 57, issue 8, pp. 771-786. DOI: 10.3367/UFNe.0184.201408b.0833
  28. Galenko P. Solute trapping and diffusionless solidification in a binary system, Physical Review E, 2007, vol. 76, issue 3, 031606, 9 p. DOI: 10.1103/PhysRevE.76.031606
  29. Galenko P. Extended thermodynamical analysis of a motion of the solid-liquid interface in a rapidly solidifying alloy, Physical Review B, 2002, vol. 65, issue 14, 144103, 11 p. DOI: 10.1103/PhysRevB.65.144103
  30. Hartmann H., Galenko P.K., Holland-Moritz D., Kolbe M., Herlach D.M., Shuleshova O. Nonequilibrium solidification in undercooled $Ti_{45}Al_{55}$ melts, Journal of Applied Physics, 2008, vol. 103, issue 7, 073509. DOI: 10.1063/1.2903920
  31. Alexandrov D.V., Galenko P.K. Thermo-solutal and kinetic regimes of an anisotropic dendrite growing under forced convective flow, Physical Chemistry Chemical Physics, 2015, vol. 17, pp. 19149-19161. DOI: 10.1039/C5CP03018H
  32. Ben Amar M. Theory of needle-crystal, Physica D: Nonlinear Phenomena, 1988, vol. 31, issue 3, pp. 409-423. DOI: 10.1016/0167-2789(88)90006-1
  33. Brener E., Melnikov V.I. Velocity selection and instability spectrum in 3D dendritic growth, Journal of Experimental and Theoretical Physics, 1995, vol. 80, no. 2, pp. 341-345.
  34. Bouissou P., Pelcé P. Effect of a forced flow on dendritic growth, Physical Review A, 1989, vol. 40, issue 11, pp. 6673-6680. DOI: 10.1103/PhysRevA.40.6673
  35. Müller-Krumbhaar H., Abel T., Brener E., Hartmann M., Eissfeldt N., Temkin D. Growth-morphologies in solidification and hydrodynamics, JSME International Journal Series B, 2002, vol. 45, no. 1, pp. 129-132. DOI: 10.1299/jsmeb.45.129
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