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Crystal Growth and Solute Trapping

Published online by Cambridge University Press:  22 February 2011

Michael J. Aziz
Michael J. Aziz*
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, MA 02138
*
* Present address: Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831.
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Abstract

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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 23 , 1983 , 369
Copyright
Copyright © Materials Research Society 1984

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References

REFERENCES

[1]Baker, J.C. and Cahn, J.W., in Solidification (ASM, Metals Park, Ohio, 1970).Google Scholar
[2]White, C.W., Wilson, S.R., Appleton, B.R., and Young, F.W. Jr., J. Appl. Phys. 51, 738 (1980).Google Scholar
[3]Brice, J.C., The Growth of Crystals From the Melt (North-Holland, Amsterdam, 1965), pp. 63–7.Google Scholar
[4]Hall, R.N., J. Phys. Chem. 57, 836 (1953).Google Scholar
[5]Hillert, M. and Sundman, B., Acta Metall. 25, 11 (1977).Google Scholar
[6]Baker, J.C., reported by Cahn, J.W., Coriell, S.R. and Boettinger, W.J., in Laser and Electron Beam Processing of Materials, ed. White, C.W. and Peercy, P.S. (Academic, New York, 1980), pp. 89–103.Google Scholar
[7]Jackson, K.A., Gilmer, G.H. and Leamy, H.J., pp. 104–110 of [6].Google Scholar
[8]Gilmer, G.H., Mat. Res. Soc. Symp. Proc. 13, 249 (1983).Google Scholar
[9]Wood, R.F., Appl. Phys. Lett. 37, 302 (1980).Google Scholar
[10]Coriell, S.R. and Turnbull, D., Acta Metall. 30, 2135 (1982). See also references in [15].Google Scholar
[11]Broughton, J.Q., Gilmer, G.H., and Jackson, K.A., Phys. Rev. Lett. 49, 1496 (1982).Google Scholar
[12]Jackson, K.A., these proceedings.Google Scholar
[13]Aziz, M.J., “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).Google Scholar
[14]Aziz, M.J., J. Appl. Phys. 53, 1158 (1982).Google Scholar
[15]Aziz, M.J., Appl. Phys. Lett. 43, 552 (1983).Google Scholar
[16]Aziz, M.J., in Rapid Solidification Processing Principles and Technologies III, ed. Mehrabian, R. (Nat. Bur. Standards, Gaithersburg MD, 1982), pp. 113–7.Google Scholar
[17]Baeri, P., Foti, G., Poate, J.M., Campisano, S.U., and Cullis, A.G., Appl. Phys. Lett. 38, 800 (1981).Google Scholar
[18]White, C.W., Appleton, B.R., Stritzker, B., Zehner, D.M., and Wilson, S.R., in Mat. Res. Soc. Symp. Proc. 1, 59 (1981).Google Scholar
[19]Baeri, P., reported by White, C.W., Zehner, D.M., Campisano, S.U. and Cullis, A.G., in Surface Modification and Alloying By Laser, Ion, and Electron Beams, ed. Poate, J.M., Foti, G. and Jacobson, D.C. (Plenum, New York, 1983), pp. 93–6.Google Scholar
[20] Ref. [13], pp. 76–82.Google Scholar
[21]Cahn, J.W., Acta Metall. 10, 789 (1962).Google Scholar
[22]Hillert, M. and Sundman, B., Acta Metall. 24, 731 (1976).Google Scholar
[23] Ref. [13], chapter 5.Google Scholar
[24]Wood, R.F. and Giles, G.E., Phys. Rev. B 22, 2923 (1981).Google Scholar
[25]Baeri, P., Campisano, S.U., Foti, G. and Rimini, E., J. Appl. Phys. 50 788 (1979).Google Scholar
[26]Galvin, G.J., Mayer, J.W. and Peercy, P.S., these proceedings.Google Scholar