A simple model for solute trapping during rapid solidification is presented in terms of a single unknown parameter, the interfacial diffusivity Di. A transition from equilibrium segregation to complete solute trapping occurs over roughly an order of magnitude in growth speed, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal. This diffusive speed is given by Di/λ, where λ is the interatomic spacing, and is typically of the order 10 meters per second. Comparison is made with experiment. The steady-state speed of a planar interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. A solute drag term and an intrinsic interfacial mobility term are included in the dissipation calculations. Steady-state solutions are presented for Bi-doped Si during pulsed laser annealing.
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J.C. Baker and J.W. Cahn, in Solidification (ASM, Metals Park, Ohio, 1970).
C.W. White, S.R. Wilson, B.R. Appleton, and F.W. Young Jr., J. Appl. Phys. 51, 738 (1980).
J.C. Brice, The Growth of Crystals From the Melt (North-Holland, Amsterdam, 1965), pp. 63–7.
R.N. Hall, J. Phys. Chem. 57, 836 (1953).
M. Hillert and B. Sundman, Acta Metall. 25, 11 (1977).
J.C. Baker, reported by J.W. Cahn, S.R. Coriell and W.J. Boettinger, in Laser and Electron Beam Processing of Materials, ed. C.W. White and P.S. Peercy (Academic, New York, 1980), pp. 89–103.
K.A. Jackson, G.H. Gilmer and H.J. Leamy, pp. 104–110 of .
G.H. Gilmer, Mat. Res. Soc. Symp. Proc. 13, 249 (1983).
R.F. Wood, Appl. Phys. Lett. 37, 302 (1980).
S.R. Coriell and D. Turnbull, Acta Metall. 30, 2135 (1982). See also references in .
J.Q. Broughton, G.H. Gilmer, and K.A. Jackson, Phys. Rev. Lett. 49, 1496 (1982).
K.A. Jackson, these proceedings.
M.J. Aziz, “Kinetics of Crystallization of B2O3 Under Pressure and Theory of Motion of the Crystal-Melt Interface at Wide Departures from Equilibrium”, Ph.D. thesis, Harvard University (University Microfilms International, Ann Arbor, Michigan, 1984).
M.J. Aziz, J. Appl. Phys. 53, 1158 (1982).
M.J. Aziz, Appl. Phys. Lett. 43, 552 (1983).
M.J. Aziz, in Rapid Solidification Processing Principles and Technologies III, ed. R. Mehrabian (Nat. Bur. Standards, Gaithersburg MD, 1982), pp. 113–7.
P. Baeri, G. Foti, J.M. Poate, S.U. Campisano, and A.G. Cullis, Appl. Phys. Lett. 38, 800 (1981).
C.W. White, B.R. Appleton, B. Stritzker, D.M. Zehner, and S.R. Wilson, in Mat. Res. Soc. Symp. Proc. 1, 59 (1981).
P. Baeri, reported by C.W. White, D.M. Zehner, S.U. Campisano and A.G. Cullis, in Surface Modification and Alloying By Laser, Ion, and Electron Beams, ed. J.M. Poate, G. Foti and D.C. Jacobson (Plenum, New York, 1983), pp. 93–6.
Ref. , pp. 76–82.
J.W. Cahn, Acta Metall. 10, 789 (1962).
M. Hillert and B. Sundman, Acta Metall. 24, 731 (1976).
Ref. , chapter 5.
R.F. Wood and G.E. Giles, Phys. Rev. B 22, 2923 (1981).
P. Baeri, S.U. Campisano, G. Foti and E. Rimini, J. Appl. Phys. 50 788 (1979).
G.J. Galvin, J.W. Mayer and P.S. Peercy, these proceedings.
I am indebted to E. Nygren for assistance with the computer calculations; to J.L. Murray, J.W. Cahn, S.R. Coriell, W.J. Boettinger, and F. Spaepen for much helpful discussion; and to D. Turnbull for guidance. This work was supported in part by an Allied Corp. Fellowship Grant and by National Science Foundation Grant DMR-79-2 3597.
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Aziz, M.J. Crystal Growth and Solute Trapping. MRS Online Proceedings Library 23, 369–374 (1983). https://doi.org/10.1557/PROC-23-369