Abstract
A linear morphological stability of the solid-liquid interface is analyzed for a binary alloy in the limit of low and high crystal growth velocities. Using the result of this analysis, a diagram of morphologies is derived for a whole range of solidification rates with indicating critical growth velocities for the transitions planar front ⇔ cellular/dendritic structure. It is specially noted that the speed of solute diffusion in the bulk liquid limits the absolute chemical stability velocity from the high-rate transition cells/dendrites ⇒ planar front.
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References
V.T. Borisov, Theory of two-phase mushy zone of metallic ingot, (Metallurgia, Moscow, 1987)
V.A. Zhuravlev, Solidification and crystallization of alloys with hetero-trasformations, (Regular and Chaotic Dynamics, Izhevsk, 2006)
V.T. Borisov, YuE Matveev, Fizika Metallov i Metallovedenie 13, 465 (1962)
R. Trivedi, W. Kurz, Int. Mater. Rev. 39, 49 (1994)
W. Kurz, D.J. Fisher, R. Trivedi, Int. Mater. Rev. 64, 311 (2019)
P.K. Galenko, D.V. Alexandrov, Philos. Trans. R. Soc. A 376, 20170210 (2018)
W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 34, 323 (1963)
W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35, 444 (1964)
R.F. Sekerka, J. Appl. Phys. 36, 264 (1965)
S.R. Coriell, R.F. Sekerka, in Rapid solidification processing II, edited byR. Mehrabian, B.H. Kear, M. Cohen, (Claitor’s, Baton Rouge, Louisiana, 1980), p. 35
S.R. Coriell, G.B. McFadden, R.F. Sekerka, Annu. Rev. Mater. Sci. 15, 119 (1985)
S.R. Coriell, G.B. McFadden, inHandbook of crystal growth, edited by D.T.J. Hurl (Amsterdam, Elsevier, 1993), 1a, p.785
S.H. Davis, Theory of solidification, (Cambridge University Press, Cambridge, UK, 2001)
R. Trivedi, W. Kurz, Acta Metall. 34, 1663 (1986)
W. Kurz, B. Giovanola, R. Trivedi, Acta Metall. 34, 823 (1986)
W. Kurz, D.J. Fisher, Fundamentals of solidification, 3rd edn (Trans Tech Publications, Aedermannsdorf, 1992)
P.K. Galenko, D.A. Danilov, Phys. Rev. E 69, 051608 (2004)
D.M. Herlach, P.K. Galenko, D. Holland-Moritz, Metastable solids from undercooled melts, (Elsevier, Amsterdam, 2007)
P.K. Galenko, D.A. Danilov, J. Cryst. Growth 216, 512 (2000)
W.J. Boettinger, S.R. Coriell, R.F. Sekerka, Mater. Sci. Eng. A 65, 27 (1984)
P. Galenko, Phys. Rev. B 65, 144103 (2002)
P.K. Galenko, Mater. Sci. Eng. A 375–377, 493 (2004).
G.P. Ivantsov, Dokl. Akad. Nauk SSSR 81, 179 (1951)
W.A. Tiller, K.A. Jackson, J.W. Rutter, B. Chalmers, Acta Metall. 428, 1 (1953)
J.S. Langer, H. Müller-Krumbhaar, Acta Metall. 26, 1681 (1978)
P.K. Galenko, D.A. Danilov, Phys. Lett. A 235, 271 (1997)
P. Galenko, Phys. Rev. E 76, 031606 (2007)
M.J. Aziz, T. Kaplan, Acta Metall. 36, 2335 (1988)
M.J. Aziz, J. Appl. Phys. 53, 1158 (1982)
D.E. Hoglund, M.O. Thompson, M.J. Aziz, Phys. Rev. B 58, 189 (1998)
D.E. Hoglund, M.J. Aziz, Mater. Res. Soc. Symp. Proc. 205, 325 (1992)
D.E. Hoglund, M.J. Aziz, S.R. Stiffler, M.O. Thompson, J.Y. Tsao, P.S. Peercy, J. Cryst. Growth 109, 107 (1991)
H. Biloni, W.J. Boettinger, Solidification, in Physical metallurgy, edited by R.W. Cahn, P. Haasen, (Elsevier Science Publishers, Amsterdam, 1996), Vol. I, Chap. 8, pp.669842
K. Reuther, P.K. Galenko, M. Rettenmayr, J. Cryst. Growth 506, 55 (2019)
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Galenko, P.K., Danilov, D.A. Morphological stability diagram for slowly and rapidly solidifying binary systems. Eur. Phys. J. Spec. Top. 229, 353–364 (2020). https://doi.org/10.1140/epjst/e2019-900104-6
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DOI: https://doi.org/10.1140/epjst/e2019-900104-6