Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T18:48:23.647Z Has data issue: false hasContentIssue false
  • English
  • Français

Cellular Automaton Simulations of Surface Mass Transport Due to Curvature Gradients: Simulations of Sintering in 3-D.

Published online by Cambridge University Press:  25 February 2011

D.P. Bentz ,
P.J.P. Pimienta ,
E.J. Garboczi  and
W.C. Carter
D.P. Bentz
Affiliation:
Building Material Division and National Institute of Standards & Technology, Gaithersburg, MD 20899.
P.J.P. Pimienta
Affiliation:
Building Material Division and National Institute of Standards & Technology, Gaithersburg, MD 20899.
E.J. Garboczi
Affiliation:
Building Material Division and National Institute of Standards & Technology, Gaithersburg, MD 20899.
W.C. Carter
Affiliation:
Ceramics Division, National Institute of Standards & Technology, Gaithersburg, MD 20899.
Get access

Abstract

A cellular automaton algorithm is described that simulates the evolution of a surface driven by the reduction of chemical potential differences on the surface. When the surface tension is isotropic, the chemical potential is proportional to the curvature at the surface. This process is important in the development of microstructure during the sintering of powders. The algorithm is implemented in two and three dimensions in a digital image mode, using discrete pixels to represent continuum objects. The heart of the algorithm is a pixel-counting-based method for computing the potential at a pixel located in a digital surface. This method gives an approximate measure of the curvature at the given surface pixel. The continuum version of this method is analytically shown to give the true curvature at a point on a continuum surface. The digital version of the curvature computation method is shown to obey the scaling laws derived for the continuum version. The evolution of the surface of a three dimensional loosely packed powder, along with the percolation characteristics of its pore space, are computed as an example of the algorithm.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 249: Symposium Q – Synthesis and Processing of Ceramics: Scientific Issues , 1991 , 413
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Kingery, W.D., Bowen, H.K., and Uhlman, D.R., Introduction to Ceramics, 2nd Edition (John Wiley and Sons, New York, 1976).Google Scholar
[2] Herring, C., in Physics of Powder Metallurgy, Kingston, W.E. ed., pp. 143–179 (McGraw -Hill, New York, 1951).Google Scholar
[3] Scrivener, Karen L., in Materials Science of Concrete Vol. I, ed. by Skalny, Jan (American Ceramic Society, Westerville, 1989).Google Scholar
[4] Garboczi, E.J. and Bentz, D.P., in Materials Science of Concrete Vol, II, ed. by Skalny, J. and Mindess, S. (American Ceramic Society, Westerville, 1991).Google Scholar
[5] Garboczi, E.J. and Bentz, D.P., J. Mater. Res. 6, 196–201 (1991).CrossRefGoogle Scholar
[6] Bentz, D.P. and Garboczi, E.J., Cem. and Conc. Res. 21, 325–344 (1991).CrossRefGoogle Scholar
[7] Garboczi, E.J. and Bentz, D.P., “Computer simulation of the diffusivity of cement-based materials”, J. Mater. Sci, in press.Google Scholar
[8] Visscher, P.B. and Cates, J.E., J. Mater. Res. 5, 2184–2196 (1990).CrossRefGoogle Scholar
[9] Srolovitz, D.J. et al. , Scripta Metall. 17, 241–246 (1983).CrossRefGoogle Scholar
[10] Grest, G.S., Anderson, M.P., and Srolovitz, D.J., in Computer Simulation of Microstructural Evolution, edited by Srolovitz, D. J. (The Metallurgical Society, 1986).Google Scholar
[11] Ku, W., Gregory, O.J., and Jennings, H.M., J. Am. Ceram. Soc. 73, 286–296 (1990).CrossRefGoogle Scholar
[12] Madhavrao, L. R. and Rajagopalan, R., J. Mater. Res. 4, 1251–1256 (1989).CrossRefGoogle Scholar
[13] Hassold, G.N., Chen, I.W., and Srolovitz, D.J., J. Am. Ceram. Soc. 73, 2857–2864 (1990).CrossRefGoogle Scholar
[14] Chen, I.W., Hassold, G.N., and Srolovitz, D.J., J. Am. Ceram. Soc. 73, 2865–2872 (1990).CrossRefGoogle Scholar
[15] Pimienta, P.J.P., Garboczi, E.J., and Carter, W.C., “Cellular Automaton Simulations of Surface Mass Transport Due to Curvature Gradients: Simulations of Sintering”, preprint.Google Scholar
[16] Schwartz, L.M. and Banavar, J.R., Phys. Rev. B39, 11965 (1989).CrossRefGoogle Scholar
[17] Wolfram, S., Theory and Applications of Cellular Automata (World Sci., Singapore, 1986).Google Scholar
[18] Mullins, W.W., J. Appl. Phys. 28, 333–339 (1957); W.W. Mullins, in Metal Surfaces: Structure. Energetics. and Kinetics (American Society for Metals, Metals Park, Ohio, 1962).CrossRefGoogle Scholar
[19] Bross, P. and Exner, H.E., Acta Metall. 27, 1007–1012 (1979).CrossRefGoogle Scholar
[20] Visscher, W.M. and Bolsterli, M., Nature 239, 504 (1972).CrossRefGoogle Scholar
[21] xSelby, S.M., editor, CRC Standard Mathematical Tables, 15th edition (Chemical Rubber Co., Cleveland, 1967).Google Scholar
[22] Graham, R.A., M.S. Thesis, University of Florida (1973).Google Scholar
[23] Larson, R.G., Scriven, L.E., and Davis, H.T., Chem. Eng. Sci. 36, 57 (1981).CrossRefGoogle Scholar
[24] DeHoff, R.R., Aigeltinger, E.H., and Craig, K.R., J. of Microscopy 95, 69 (1972).CrossRefGoogle Scholar
[25] Zallen, R., The Physics of Amorphous Solids (Wiley, New York, 1983).CrossRefGoogle Scholar
[26] Martys, N. and Garboczi, E.J., “Length scales connecting fluid permeability and electrical conductivity in model 2-D porous media”, preprint.Google Scholar
[27] Day, A.R., Thorpe, M.F., Snyder, K.A., and Garboczi, E.J., in Mechanical Properties of Cellular and Porous Materials, Vol. 207, ed. by Sieradzki, K., Green, D., and Gibson, L.J. (Materials Research Society, Pittsburgh, 1991).Google Scholar
[28] Day, A.R., Snyder, K.A., Garboczi, E.J., and Thorpe, M.F., “The elastic moduli of a sheet containing circular holes”, J. Phys. and Mech. of Solids, in press.Google Scholar