Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-11T05:28:41.493Z Has data issue: false hasContentIssue false
  • English
  • Français

Percolative composite model for prediction of the properties of nanocrystalline materials

Published online by Cambridge University Press:  31 January 2011

Rachman Chaim
Rachman Chaim
Affiliation:
Department of Materials Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel
Get access

Abstract

A physical percolating composite model is presented for description of the changes in the transport-type properties with grain size in nanocrystalline materials. The model is based on hierarchial percolation through the different microstructural components such as grain boundaries, triple lines, and quadruple nodes at grain sizes when their respective percolation thresholds are reached. The model yields critical grain sizes at which the properties may change significantly. These grain sizes depend on the grain boundary thickness. Master curves were calculated for the elastic modulus and compared to the experimental data from the literature. Better fit was found with the experimental data in comparison to Hill's approximation model. The critical grain size at grain boundary percolation threshold is suggested as a criterion for definition of materials to exhibit nanocrystalline properties.

Type
Articles
Information
Journal of Materials Research , Volume 12 , Issue 7 , July 1997 , pp. 1828 - 1836
Copyright
Copyright © Materials Research Society 1997

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.Gleiter, H., Prog. Mater. Sci. 33, 223 (1989).CrossRefGoogle Scholar
2.Gleiter, H., J. Appl. Crystallogr. 24, 79 (1991).CrossRefGoogle Scholar
3.Siegel, R. W., Nanostructured Mater. 4, 121 (1994).CrossRefGoogle Scholar
4.Suryanarayana, C., Int. Mater. Rev. 40, 41 (1995).CrossRefGoogle Scholar
5.Gryaznov, V. G., Solov'ev, V. A., and Trusov, L. I., Scripta Metall. Mater. 24, 1529 (1990).CrossRefGoogle Scholar
6.Nieh, T. and Wadsworth, J., Scripta Metall. Mater. 25, 955 (1991).CrossRefGoogle Scholar
7.Scattergood, R. O. and Koch, C. C., Scripta Metall. Mater. 27, 1195 (1992).CrossRefGoogle Scholar
8.Pande, C. S., Masumura, R. A., and Armstrong, R. W., Nanostructured Mater. 2, 323 (1993).CrossRefGoogle Scholar
9.Lian, J., Baudelet, B., and Nazarov, A. A., Mater. Sci. Eng. A 172, 23 (1993).CrossRefGoogle Scholar
10.Bush, M. B., Mater. Sci. Eng. A 161, 127 (1993).CrossRefGoogle Scholar
11.El-Sherik, A. M., Erb, U., Palumbo, G., and Aust, K. T., Scripta Metall. Mater. 27, 1185 (1992).CrossRefGoogle Scholar
12.Kobelev, N. P., Ya. Soifer, M., Andrievski, R. A., and Gunther, B., Nanostructured Mater., 2 (1993).CrossRefGoogle Scholar
13.Chokshi, A. H., Rosen, A., Karch, J., and Gleiter, H., Scripta Metall. 23, 1679 (1989).CrossRefGoogle Scholar
14.Shen, T. D., Kock, C. C., Tsui, T. Y., and Pharr, G. M., J. Mater. Res. 10, 2892 (1995).CrossRefGoogle Scholar
15.Fougere, G. E., Riester, L., Farber, M., Weertman, J. R., and Siegel, R. W., Mater. Sci. Eng. A 204, 1 (1995).CrossRefGoogle Scholar
16.Hashin, Z. and Shtrikman, S., J. Mech. Phys. Solids 11, 123 (1963).CrossRefGoogle Scholar
17.Hill, R., Proc. Phys. Soc. London, Sect. A 65, 439 (1952).Google Scholar
18.Palumbo, G., Thorpe, S. J., and Aust, K. T., Scripta Metall. Mater. 24, 1347 (1990).CrossRefGoogle Scholar
19.Wang, N., Palumbo, G., Wang, Z., Erb, U., and Aust, K. T., Scripta Metall. Mater. 28, 253 (1993).CrossRefGoogle Scholar
20.Hilliard, J. E., in Stereology, edited by Elias, H. (Springer-Verlag, Berlin, 1967), p. 211.CrossRefGoogle Scholar
21.Zallen, R., The Physics of Amorphous Solids (John Wiley & Sons, New York, 1983), Chap. 4.CrossRefGoogle Scholar
22.Sahimi, M., Applications of the Percolation Theory (Taylor & Francis Ltd., United Kingdom, 1994).CrossRefGoogle Scholar
23.Bergman, D. J. and Kantor, Y., Phys. Rev. Lett. 53, 511 (1984).CrossRefGoogle Scholar
24.Deptuck, D., Harrison, J. P., and Zawadzki, P., Phys. Rev. Lett. 54, 913 (1985).CrossRefGoogle Scholar
25.Scher, H. and Zallen, R., J. Chem. Phys. 53, 3759 (1970).CrossRefGoogle Scholar
26.Wray, P. J., Acta Metall. 24, 125 (1976).CrossRefGoogle Scholar
27.Feng, S. and Sen, P. N., Phys. Rev. Lett. 52, 216 (1984).CrossRefGoogle Scholar
28.Deptuck, D., Harrison, J. P., and Zawadzki, P., Phys. Rev. Lett. 54, 913 (1985).CrossRefGoogle Scholar
29.Masumoto, T. and Maddin, R., Mater. Sci. Eng. 19, 1 (1975).CrossRefGoogle Scholar
30.Chou, T. C., Adamson, D., Mardinly, J., and Nieh, T. G., Thin Solid Films 205, 131 (1991).CrossRefGoogle Scholar
31.Kluge, D. M., Wolf, D., Lutsko, J. F., and Phillpot, S. R., J. Appl. Phys. 67, 2370 (1990).CrossRefGoogle Scholar
32.Fougere, G. E., Riester, L., Ferber, M., Weertman, J. R., and Siegel, R. W., Mater. Sci. Eng. A 204, 1 (1995).CrossRefGoogle Scholar
33.Adams, J. B., Wolf, W. G., and Foiles, S. M., Phys. Rev. B 40, 9479 (1989).CrossRefGoogle Scholar
34.Phillpot, S. R., Wolf, D., and Gleiter, H., Scripta Metall. Mater. 33, 1245 (1995).CrossRefGoogle Scholar
35.Wang, J., Wolf, D., Phillpot, S. R., and Gleiter, H., Philos. Mag. A 73, 517 (1996).CrossRefGoogle Scholar
36.Thomas, G. J., Siegel, R. W., and Eastman, J. A., Scripta Metall. Mater. 24, 201 (1990).CrossRefGoogle Scholar
37.Wen, S., and Yan, D., Ceramics Int. 21, 109 (1995).CrossRefGoogle Scholar
38.Ping, D. H., Li, D. X., and Ye, Q., J. Mater. Sci. Lett. 14, 1536 (1995).CrossRefGoogle Scholar
39.Kobelev, N. P., Ya.Soifer, M., Andrievski, R. A., and Gunther, B., Nanostruct. Mater. 2, 537 (1993).CrossRefGoogle Scholar
40.Nieman, G. W., Weertman, J. R., and Siegel, R. W., J. Mater. Res. 6, 1012 (1991).CrossRefGoogle Scholar
41.Bonetti, E., Campari, E. G., Bianco, L. Del, and Scipione, G., Nanostruc. Mater. 6, 639 (1995).CrossRefGoogle Scholar
42.Korn, D., Morsch, A., Birringer, R., Arnold, W., and Gleiter, H., J. Phys. (Paris) 49, 769 (1988).CrossRefGoogle Scholar
43.Gallas, M. R. and Piermarini, G. J., J. Am. Ceram. Soc. 77, 2917 (1994).CrossRefGoogle Scholar
44.Xie, C., Zhang, L., and Mo, C., Nanostruc. Mater. 4, 113 (1994).CrossRefGoogle Scholar
45.Mayo, M. J., Siegel, R. W., Liao, Y. X., and Nix, W. D., J. Mater. Res. 7, 973 (1992).CrossRefGoogle Scholar
46.Mayo, M. J., Siegel, R. W., Narayanasamy, A., and Nix, W. D., J. Mater. Res. 5, 1073 (1990).CrossRefGoogle Scholar
47.Cottom, B. A. and Mayo, M. J., Scripta Mater. 34, 809 (1996).CrossRefGoogle Scholar
48.Kingery, W. D., Bowen, H. K., and Uhlman, D. R., Introduction to Ceramics, 2nd ed. (John Wiley & Sons, New York, 1976).Google Scholar