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Finite Elenent Analysis of The Effect of a Non-Planar Solid-Liquid Interface on The Lateral Solute Segregation During Unidirectional Solidification.

Published online by Cambridge University Press:  15 February 2011

F. M. Carlson ,
L-Y Chin ,
A. L. Fripp  and
R. K. Crouch
F. M. Carlson
Affiliation:
KRAR Incorporated, Bagdad Road, Potsdam, New York 13676
L-Y Chin
Affiliation:
Phillips Petroleum Company, Bartlesville, Oklahoma 74003
A. L. Fripp
Affiliation:
NASA Langley Research Center, Hampton, Virginia 23665
R. K. Crouch
Affiliation:
NASA Langley Research Center, Hampton, Virginia 23665
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Abstract

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly non-planar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 9 , 1981 , 629
Copyright
Copyright © Materials Research Society 1982

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References

REFERENCES

1.Coriell, S.R. and Sekerka, R.F., J. Crystal Growth 46, 479 (1979).Google Scholar
2.Carlson, F.M. and Chin, L-Y., Semiannual Progress Report, Sept. 10, 1979, NASA Grant NSG–1572.Google Scholar
3.Coriell, S.R., Boisvert, R.F., Rehm, R.G., Sekerka, R.F., J. Crystal Growth 54, 167 (1981).Google Scholar
4.Zienkiewicz, O.C., The Finite Element Method in Engineering Science, (McGraw-Hill, London 1971).Google Scholar