Selected mode for rapidly growing needle-like dendrite controlled by heat and mass transport / Alexandrov D.V., Galenko P.K. // Acta Materialia. - 2017. - V. 137, l. . - P. 64-70.

ISSN:
13596454
Type:
Article
Abstract:
The boundary integral method is developed for fast anisotropic interfaces. A general integro-differential equation for curved interfaces controlled by heat and mass transport is derived and applied to the problem of rapid dendritic growth. A selection criterion for the steady-state mode of growing parabolic interfaces is obtained and, in common solution with the undercooling balance, it is compared with experimental data on rapid dendritic solidification of deeply supercooled liquid droplets. In this comparison, transitions from solute diffusion-limited to thermo-solutal regime and, finally, to pure thermally controlled regime of the anisotropic dendrite are discussed and revealed. Limiting cases of known selection criteria for anisotropic dendrites growing at small and high growth Péclet numbers are provided. © 2017 Acta Materialia Inc.
Author keywords:
Local non-equilibrium; Phase interface; Solute diffusion
Index keywords:
Anisotropy; Differential equations; Diffusion in solids; Integrodifferential equations; Phase interfaces; Supercooling; Undercooling; Anisotropic interfaces; Boundary integral methods; Dendritic solid
DOI:
10.1016/j.actamat.2017.07.022
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85025087130&doi=10.1016%2fj.actamat.2017.07.022&partnerID=40&md5=529ce55beb24fb307f972a810fb2d196
Соавторы в МНС:
Другие поля
Поле Значение
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-85025087130&doi=10.1016%2fj.actamat.2017.07.022&partnerID=40&md5=529ce55beb24fb307f972a810fb2d196
Affiliations Ural Federal University, Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ekaterinburg, Russian Federation; Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät, Jena, Germany
Author Keywords Local non-equilibrium; Phase interface; Solute diffusion
Funding Details 16-11-10095, RSF, Russian Science Foundation
Funding Text This work was supported by the Russian Science Foundation (project 16-11-10095) and by the German Space Center Space Management under contract number 50WM1541.
References Cross, M., Greenside, H., Pattern Formation and Dynamics in Nonequilibrium Systems (2009), Cambridge University Press; Herlach, D.M., Galenko, P.K., Holland-Moritz, M., Metastable Solids from Undercooled Melts (2007), Elsevier Amsterdam; Herlach, D., Non-equilibrium solidification of undercooled metallic melts (1994) Mater. Sci. Eng. R, 12, pp. 177-272; Langer, J.S., Turski, L.A., Studies in the theory of interfacial stability – I. Stationary symmetric model (1977) Acta Metall., 25, pp. 1113-1119; Langer, J.S., Studies in the theory of interfacial stability – II. Moving symmetric model (1977) Acta Metall., 25, pp. 1121-1137; Barber, M.N., Barbieri, A., Langer, J.S., Dynamics of dendritic sidebranching in the two-dimensional symmetric model of solidification (1987) Phys. Rev. A, 36, pp. 3340-3349; Brener, E.A., Mel'nikov, V.A., Pattern selection in two-dimensional dendritic growth (1991) Adv. Phys., 40, pp. 53-97; Kessler, D.A., Koplik, J., Levine, H., Pattern selection in fingered growth phenomena (1988) Adv. Phys., 37, pp. 255-339; Willnecker, R., Herlach, D.M., Feuerbacher, B., Evidence of nonequilibrium processes in rapid solidification of undercooled metals (1989) Phys. Rev. Lett., 62, pp. 2707-2710; Eckler, K., Cochrane, R.F., Herlach, D.M., Feuerbacher, B., Jurisch, M., Evidence for a transition from diffusion-controlled to thermally controlled solidification in metallic alloys (1992) Phys. Rev. B, 45, pp. 5019-5022; Galenko, P.K., Danilov, D.A., Local nonequilibrium effect on rapid dendritic growth in a binary alloy melt (1997) Phys. Lett. A, 235, pp. 271-280; Galenko, P.K., Herlach, D.M., Diffusionless crystal growth in rapidly solidifying eutectic systems (2006) Phys. Rev. Lett., 96, p. 150602; 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 (2011) Phys. Rev. Lett., 107, p. 025505; Jou, D.J., Galenko, P.K., Coarse graining for the phase-field model of fast phase transitions (2013) Phys. Rev. E, 88, p. 042151; Galenko, P., Extended thermodynamical analysis of a motion of the solid-liquid interface in a rapidly solidifying alloy (2002) Phys. Rev. B, 65, p. 144103; Galenko, P., Solute trapping and diffusionless solidification in a binary system (2007) Phys. Rev. E, 76. , 031606-1-8; Morse, P.M., Feshbach, H., Methods of Theoretical Physics (1953), McGraw-Hill New York; Nash, G.E., Capillary-limited, Steady State Dendritic Growth, Part I - Theoretical Development (1974), NRL Report 7679, May 1974; Nash, G.E., Glicksman, M.E., Capillary-limited steady-state dendritic growth – I. Theoretical development (1974) Acta Metall., 22, pp. 1283-1290; Saville, D.A., Beaghton, P.J., Growth of needle-shaped crystals in the presence of convection (1988) Phys. Rev. A, 37, pp. 3423-3430; Alexandrov, D.V., Galenko, P.K., Boundary integral approach for propagating interfaces in a binary non-isothermal mixture (2017) Phys. A, 469, pp. 420-428; Gradshteyn, I.S., Ryzhik, I.M., Tables of Integrals, Series, and Products (2007), Academic Press New York; Galenko, P.K., Danilov, D.A., Steady-state shapes of growing crystals in the field of local nonequilibrium diffusion (2000) Phys. Lett. A, 272, pp. 207-217; Galenko, P.K., Danilov, D.A., Alexandrov, D.V., Solute redistribution around crystal shapes growing under hyperbolic mass transport (2015) Int. J. Heat. Mass Trans., 89, pp. 1054-1060; Galenko, P.K., Local-nonequilibrium phase transition model with relaxation of the diffusion flux (1994) Phys. Lett. A, 190, pp. 292-294; Alexandrov, D.V., Galenko, P.K., Thermo-solutal and kinetic regimes of an anisotropic dendrite growing under forced convective flow (2015) Phys. Chem. Chem. Phys., 17, pp. 19149-19161; Langer, J.S., Hong, D.C., Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy (1986) Phys. Rev. A, 34, pp. 1462-1471; Ben Amar, M., Pelcé, P., Impurity effect on dendritic growth (1989) Phys. Rev. A, 39, pp. 4263-4269; Eckler, K., Herlach, D.M., Aziz, M.J., Search for a solute-drag effect in dendritic solidification (1994) Acta Metall. Mater, 42, pp. 975-979; Pelce, P., Bensimon, D., Theory of dendrite dynamics (1987) Nucl. Phys. B, 2, pp. 259-270; Bouissou, P., Pelcé, P., Effect of a forced flow on dendritic growth (1989) Phys. Rev. A, 40, pp. 6673-6680; Alexandrov, D.V., Galenko, P.K., Dendrite growth under forced convection: analysis methods and experimental tests (2014) Phys.–Usp, 57, pp. 771-786; Müller-Krumbhaar, H., Abel, T., Brener, E., Hartmann, M., Eissfeldt, N., Temkin, D., Growth-morphologies in solidification and hydrodynamics (2002) JSME Int. J. Ser. B, 45, pp. 129-132; Alexandrov, D.V., Galenko, P.K., Selection criterion of stable dendritic growth at arbitrary Péclet numbers with convection (2013) Phys. Rev. E, 87. , 062403-1-7; Brener, E.A., Effects of surface energy and kinetics on the growth of needle-like dendrites (1990) J. Cryst. Growth, 99, pp. 165-170; Kantorovich, L., Akilov, G., Functional Analysis in Normed Spaces (1964), Macmillan New York; Rudin, W., Functional Analysis (1973), McGraw Hill New York; Tanveer, S., Analytic theory for the selection of a two-dimensional needle crystal at arbitrary Péclet number (1989) Phys. Rev. A, 40, pp. 4756-4769; Kruskal, M.D., Segur, H., Asymptotics beyond all orders in a model of crystal growth (1991) Stud. Appl. Math., 85, pp. 129-181. , (1991)
Correspondence Address Galenko, P.K.; Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische FakultätGermany; email: peter.galenko@uni-jena.de
Publisher Acta Materialia Inc
Language of Original Document English
Abbreviated Source Title Acta Mater
Source Scopus