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Shape Evolution and Splitting of a Single Coherent Particle

Published online by Cambridge University Press:  10 February 2011

J. D. Zhang ,
D. Y. Li  and
L. Q. Chen
J. D. Zhang
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802.
D. Y. Li
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802.
L. Q. Chen
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802.
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Abstract

The morphology and its evolution of a single coherent precipitate was investigated using the Cahn-Hilliard equation and Khachaturyan's continuum elasticity theory for solid solutions. A cubic solid solution with negative elastic anisotropy and isotropic interfacial energy was considered. The lattice mismatch between the precipitate and the matrix was assumed to be purely dilatational and its compositional dependence obeys the Vegard's law. Both two- and three-dimensional systems were studied. The Cahn-Hilliard equation was numerically solved using a semi-implicit Fourier-spectral method. It was demonstrated that, with increasing elastic energy contribution, the equilibrium shape of a coherent particle gradually changes from a circle to a square in two dimensions, and from a sphere to a cube in three dimensions, and the composition profile becomes increasingly inhomogeneous within the precipitate with the minimum at the center of the particle, consistent with previous theoretical studies and experimental observations. It was also shown that, with sufficiently large elastic strain energy contribution, a coherent particle may split to four particles from a square, or eight particles from a sphere, during its evolution to equilibrium. For both two and three dimensions, the splitting starts by nucleating the matrix phase at the center of the particle.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 481: Symposium P – Science and Technology of Semiconductor Surface Preparation , 1997 , 243
Copyright
Copyright © Materials Research Society 1998

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References

REFERENCES

1. Khachaturyan, A. G., Theory of Structural Transformations in Solids, Wiley, New York, 1983.Google Scholar
2. Johnson, W. C. and Cahn, J. W., Acta Metall. 32, 1925 (1984).Google Scholar
3. Johnson, W. C. and Voorhees, P. W., J. Appl. Phys. 61, 1610 (1987)Google Scholar
4. Khachaturyan, A. G., Semenovskaya, S. V. and Morris, J. W., Acta metall. 36, 1563 (1988).Google Scholar
5. Miyazaki, T. and Doi, M., Matls. Sci. and Engr. A110, 175 (1989).Google Scholar
6. Wang, Y., Chen, L. Q., and Khachaturyan, A. G., Scripta Metall. et Mater. 25, 1387 (1991).Google Scholar
7. McCormack, M., Khachaturyan, A. G., and Morris, J. W. Jr, Acta Metall. Mater. 40, 325 (1992).Google Scholar
8. Voorhees, P. W., McFadden, G. B., and Johnson, W. C., Acta Metall. Mater. 40, 2979 (1992).Google Scholar
9. Nishimori, H. and Onuki, A., Phys. Lett. A 162, 323 (1992).Google Scholar
10. Thompson, M. E., Su, C. S., and Voorhees, P. W., J. Appl. Phys. 61, 1610 (1987).Google Scholar
11. Wang, Y., Wang, H. Y., Chen, L. Q., and Khachaturyan, A. G., J. Am. Ceram. Soc. 78, 657 (1995).Google Scholar
12. Lee, J., Scripta Metall. 32, 559 (1995).Google Scholar
13. Lee, J., Metall. Mater. Trans. 27A, 1449 (1996).Google Scholar
14. Thompson, M. E. and Voorhees, P. W., in Mathematics of Microstructure Evolution, edited by L. Q. Chen, et al, 125 (1996).Google Scholar
15. Jou, H. J., Leo, P. H., and Lowengrub, J. S., J. of Comp. Phys. 131, 109 (1997).Google Scholar
16. Li, D. Y. and Chen, L. Q., Acta mater. 45, 2435 (1997).Google Scholar
17. Westbrook, J. H., Z. Kristallogr. 110, 21 (1958).Google Scholar
18. Miyazaki, T., Imamura, H., and Kozakai, T., Mater. Sci. Eng. 54, 9 (1982).Google Scholar
19. Doi, M., Miyazaki, T., and Wakatsuki, T., Mater. Sci. Engr. 67, 247 (1984).Google Scholar
20. M. J.Kaufman, Voorhees, P.W., Johnson, W. C. and Biancaniello, F. S., Metall. Trans. 20A, 2171(1989)Google Scholar
21. Yoo, Y. S., Yoon, D. Y., and Henry, M. F., Met. and Mater. 1, 47 (1995).Google Scholar
22. Qu, Y. Y., Calderon, H. A. and Kostorz, G., in Solid → Solid Phase Transformations, edited by W. C. Johnson et al, 599 (1994)Google Scholar
23. Cahn, J. W., Acta Metall. 9, 795 (1961).Google Scholar
24. Chen, L. Q., and Jie, Shen, accepted in Comp. Phys. Comm., 1997 Google Scholar
25. Maheshuari, and Ardell, , Phys. Rev. Lett. 70, 2305(1990)Google Scholar
26. Wang, Y. Z. and Khachaturyan, A. G., Acta Metall. Mater., 43, 1837(1995)Google Scholar