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Elimination of an isolated pore: Effect of grain size

Published online by Cambridge University Press:  03 March 2011

Wan Y. Shih ,
Wei-Heng Shih  and
Ilhan A. Aksay
Wan Y. Shih
Affiliation:
Department of Chemical Engineering and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544–5263
Wei-Heng Shih
Affiliation:
Department of Materials Engineering, Drexel University, Philadelphia, Pennsylvania 19104
Ilhan A. Aksay
Affiliation:
Department of Chemical Engineering and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544–5263
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Abstract

The effect of grain size on the elimination of an isolated pore was investigated both by the Monte Carlo simulations and by a scaling analysis. The Monte Carlo statistical mechanics model for sintering was constructed by mapping microstructures onto domains of vectors of different orientations as grains and domains of vacancies as pores. The most distinctive feature of the simulations is that we allow the vacancies to move. By incorporating the outer surfaces of the sample in the simulations, sintering takes place via vacancy diffusion from the pores to the outer sample surfaces. The simulations were performed in two dimensions. The results showed that the model is capable of displaying various sintering phenomena such as evaporation and condensation, rounding of a sharp corner, pore coalescence, thermal etching, neck formation, grain growth, and growth of large pores. For the elimination of an isolated pore, the most salient result is that the scaling law of the pore elimination time tp with respect to the pore diameter dp changes as pore size changes from larger than the grains to smaller than the grains. For example, in sample-size-fixed simulations, tp ∼ d3p for dp < G and tp ∼ d2p for dp > G with the crossover pore diameter dc increasing linearly with G where G is the average grain diameter. For sample-size-scaled simulations, tp ∼ d4p for dp < G and tp ∼ d3p for dp > G. That tp has different scaling laws in different grain-size regimes is a result of grain boundaries serving as diffusion channels in a fine-grain microstructure such as those considered in the simulations. A scaling analysis is provided to explain the scaling relationships among tp, dp, and G obtained in the simulations. The scaling analysis also shows that these scaling relationships are independent of the dimensionality. Thus, the results of the two-dimensional simulations should also apply in three dimensions.

Type
Articles
Information
Journal of Materials Research , Volume 10 , Issue 4 , April 1995 , pp. 1000 - 1015
Copyright
Copyright © Materials Research Society 1995

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References

REFERENCES

1For example, see Aksay, I.A., Shih, W. Y., and Sarikaya, M., in Ultrastructure Processing of Advanced Ceramics, edited by Mackenzie, J. D. and Ulrich, D.R. (John Wiley & Sons, New York, 1988), p. 393.Google Scholar
2Slamovich, E. B. and Lange, F. F., J. Am. Ceram. Soc. 73, 3368–2 (1990).CrossRefGoogle Scholar
3Coble, R. L., J. Appl. Phys. 32, 787 (1961).CrossRefGoogle Scholar
4Kingery, W. D. and Francois, B., in Sintering and Related Phenomena, edited by Kuczynski, G. C., Hooton, N. A., and Gibbon, C. F. (Gordon and Breach, New York, 1967), pp. 471–496.Google Scholar
5Anderson, M. P., Srolovitz, D. J., Grest, G. S., and Sahni, P. S., ActaMetall. 32, 783 (1984).Google Scholar
6Burke, J. E., J. Am. Ceram. Soc. 40, 80 (1957).CrossRefGoogle Scholar
7Hassold, G. N., Chen, I-W., and Srolovitz, D. J., J. Am. Ceram. Soc. 73, 2857 (1990); Chen, I.W., Hassold, G. N., and Srolovitz, D. J., J. Am. Ceram. Soc. 73, 2865 (1990).CrossRefGoogle Scholar
8Herring, C., J. Appl. Phys. 21, 301 (1950).CrossRefGoogle Scholar
9Schick, M. and Shih, W-H., Phys. Rev. B 35, 5030 (1987).CrossRefGoogle Scholar
10Application of the Monte Carlo Method in Statistical Physics, edited by Binder, K. (Springer-Verlag, 1987).CrossRefGoogle Scholar
11Wu, F. Y., Review of Modern Physics 54, 235 (1982).CrossRefGoogle Scholar
12Zhao, J. and Harmer, M. P., J. Am. Ceram. Soc. 71, 530 (1988).CrossRefGoogle Scholar
13Slamovich, E. B. and Lange, F. F., J. Am. Ceram. Soc. 75, 2498–2508 (1992).CrossRefGoogle Scholar
14Rodel, J. and Glaeser, A. M., J. Am. Ceram. Soc. 73, 3302 (1990).CrossRefGoogle Scholar
15For example, see p. 219 in Vlack, L. H. Van, Elements of Materials Science and Engineering, 6th ed., Addison-Wesley, 1989.Google Scholar
16Liu, J., Sarikaya, M., Shih, W. Y., and Aksay, L. A., unpublished.Google Scholar
17Shih, W. Y., Shih, W-H., and Aksay, L. A., unpublished.Google Scholar