Abstract
The kinetic coefficient, μ, is the constant of proportionality between the velocity of a solid-liquid interface and the interface undercooling. The value of μ and its anisotropy are critical parameters in phase field modeling of dendritic solidification. In this paper we review several different molecular dynamics simulation methods which have been proposed to compute the kinetic coefficient. Techniques based on forced velocity simulations, free solidification simulations and fluctuation analyses are discussed and compared. In addition, a model of crystalline growth kinetics due to Broughton, Gilmer and Jackson will be compared with available atomistic simulation data.
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References
J.S. Langer, in Directions in Condensed Matter, edited by G. Grinstein and G. Mazenko (World Scientific, Singapore, 1986), p. 164.
A. Karma and W.-J. Rappel, Phys. Rev. E 57, 4323 (1998).
M. Plapp and A. Karma, Phys. Rev. Lett. 84, 1740 (2000).
N. Provatas, N. Goldenfeld, and J. Dantzig, Phys. Rev. Lett. 80, 3308 (1998).
J.S. Langer, in Chance and Matter, Lectures on the Theory of Pattern Formation, Les Houches, session XLVI, edited by J. Souletie, J. Vannimenus, and R. Stora (North Holland, Amsterdam, 1987), p. 629.
D. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37, 255 (1988).
J.S. Langer, Phys. Rev. A 37, 434 (1986).
E.A. Brener, Sov. Phys. JETP 69, 133 (1989).
E.A. Brener and V.I. Mel'nikov, Adv. Physics 40, 53 (1991).
J. Bragard, A. Karma,Y.H. Lee, andM. Plapp, Interface Science, this volume.
J.J. Hoyt, M. Asta, and A. Karma, Phys. Rev. Lett. 86, 5530 (2001).
A.A. Wheeler, W.J. Boettinger, and G.B. MacFadden, Phys. Rev.A 45, 7424 (1992).
A.A. Wheeler, W.J. Boettinger, and G.B. MacFadden, Phys. Rev.E 47, 1893 (1993).
A.M. Mullis and R.F. Cochrane, Acta Mater. 49, 2205 (2001).
S.R. Coriell and D. Turnbull, Acta Metall. 30, 2135 (1982).
J.Q. Broughton, G.H. Gilmer, and K.A. Jackson, Phys. Rev Lett. 49, 1496 (1982).
E. Burke, J.Q. Broughton, and G.H. Gilmer, J. Chem. Phys. 89, 1030 (1988).
H.A. Wilson, Philos. Mag. 50, 238 (1900).
J. Frenkel, Phys. Z. Sowjetunion 1, 498 (1932).
F.C. Celestini and J.-M. Debierre, Phys. Rev.B 62, 14006 (2000).
M.J. Aziz, J. Appl. Phys. 53, 1158 (1981).
F.C. Celestini, private communication.
J.J. Hoyt, B. Sadigh, M. Asta, and S.M. Foiles, Acta Mater. 47, 3181 (1999).
J.J. Hoyt and M. Asta, Phys. Rev. B, to be published.
M.S. Daw and M.I. Baskes, Phys. Rev. Lett. 50, 1285 (1983).
M.S. Daw and M.I. Baskes, Phys. Rev. B 29, 6443 (1984).
M.S. Daw, S.M. Foiles, and M.I. Baskes, Mater. Sci. Rep. 9, 251 (1993).
W.J. Briels and H.L. Tepper, Phys. Rev. Lett. 79, 5074 (1997).
C.J. Tymczak and J.R. Ray, Phys Rev. Lett. 64, 1278 (1990).
K.A. Jackson, in Treatise on Solid State Chemistry, edited by N.B. Hannay (Plenum Press, NY, 1975), Vol. 5, p. 233.
K.A. Jackson, Interface Science, this volume.
H.E.A. Huitema, M.J. Vlot, and J.P. van der Eerden, J. Chem.Phys. 111, 4714 (1999).
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Hoyt, J., Asta, M. & Karma, A. Atomistic Simulation Methods for Computing the Kinetic Coefficient in Solid-Liquid Systems. Interface Science 10, 181–189 (2002). https://doi.org/10.1023/A:1015828330917
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DOI: https://doi.org/10.1023/A:1015828330917