Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-18T01:11:44.323Z Has data issue: false hasContentIssue false
  • English
  • Français

Size dependent thermal vibrations and melting in nanocrystals

Published online by Cambridge University Press:  03 March 2011

Frank G. Shi
Frank G. Shi
Affiliation:
School of Engineering, University of California, Irvine, California 92717
Get access

Abstract

A simple model for the size-dependent amplitude of the atomic thermal vibrations of a nanocrystal is presented which leads to the development of a model for the size dependent melting temperature in nanocrystals on the basis of Lindemann's criterion. The two models are in terms of a directly measurable parameter for the corresponding bulk crystal, i.e., the ratio between the amplitude of thermal vibrations for surface atoms and that for interior ones. It is shown that the present model for the melting temperature offers not only a qualitative but even an excellent quantitative agreement with the experimentally observed size-dependent superheating, as well as melting point suppression in both the supported and embedded metallic and semiconductor nanocrystals.

Type
Articles
Information
Journal of Materials Research , Volume 9 , Issue 5 , May 1994 , pp. 1307 - 1314
Copyright
Copyright © Materials Research Society 1994

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

1Somoriai, C. A., Chemistry in Two Dimensions: Surfaces (Cornell University Press, Ithaca, NY, 1981).Google Scholar
2Borel, J. P., Surf. Sci. 106, 1 (1981), and references therein.CrossRefGoogle Scholar
3Solliard, C., Solid State Commun. 51, 947 (1984), and references therein.CrossRefGoogle Scholar
4Rossouw, C. J. and Donnelly, S. E., Phys. Rev. Lett. 55, 2960 (1985); Evens, J.H. and Mazey, D.J., J. Phys. F 15, LI (1985).CrossRefGoogle Scholar
5Beck, T. L., Jellinek, J., and Berry, R. S., J. Chem. Phys. 87, 545 (1987); Honeycutt, J. D. and Andersen, H. C., J. Phys. Chem. 91, 4950 (1987); Ercolessi, F., Andreoni, W., and Tosatti, E., Phys. Rev. Lett. 66, 911 (1991); Cheng, H. P. and Berry, R. S., Phys. Rev. A 45, 7969 (1992); Ajayan, P.M. and Marks, L.D., Phys. Rev. Lett. 60, 595 (1988); Chui, S.T., Phys. Rev. B 46, 4233 (1992); Zhou, M. Y. and Sheng, P., Phys. Rev. B 43, 3460 (1991); Childless, J.R., Chien, C. L., Zhou, M. Y., and Sheng, P., Phys. Rev. B 44 11689 (1991); Wautelet, M., J. Phys. D 24, 343 (1991).CrossRefGoogle Scholar
6Allen, G. L., Bayless, R. A., Gile, W. W., and Jesser, W. A., Thin Solid Films 144, 297 (1986).CrossRefGoogle Scholar
7Castro, T., Reifenberger, R., Choi, E., and Andres, R. P., Phys. Rev. B 42, 8548 (1990).CrossRefGoogle Scholar
8Allen, G. L., Gile, W. W., and Jesser, W. A., Acta Metall. 28, 169 (1980).Google Scholar
9Boyce, J. B. and Stutzmann, M., Phys. Rev. Lett. 54, 562 (1985).CrossRefGoogle Scholar
10Skripov, V. P., Koverda, V. P., and Skokov, V. N., Phys. Status Solidi A 66, 109 (1981).CrossRefGoogle Scholar
11Goldstein, A. N., Echer, CM., and Alivisatos, A.P., Science 256, 1425 (1992).CrossRefGoogle Scholar
12Unruh, K. M., Patterson, B. M., and Shah, S. I., J. Mater. Res. 7, 214 (1992).CrossRefGoogle Scholar
13Lereah, Y., Deutscher, G., Cheyssac, P., and Kofman, R., Europhys. Lett. 12, 709 (1990); Kofman, R., Cheyssac, P., Garrigos, R., Lereah, Y., and Deutscher, G., Z. Phys. D20, 267 (1991).CrossRefGoogle Scholar
14Saka, H., Nishikawa, Y., and Imura, T., Philos. Mag. A57, 895 (1988).CrossRefGoogle Scholar
15Zhang, D. L. and Cantor, B., Acta Metall. Mater. 39, 1595 (1991).CrossRefGoogle Scholar
16Ohashi, T., Kuroda, K., and Saka, H., Philos. Mag. B65, 1052 (1992).Google Scholar
17Gråbæk, L., Bohr, J., Johnson, E., Johansen, A., S-Rristensen, L., and Andersen, H.H., Phys. Rev. Lett. 64, 934 (1990); Grlbask, L., Bohr, J., Andersen, H. H., Johansen, A., Johnson, E., S-Kristensen, L., and Robinson, I.K., Phys. Rev. B 45, 2628 (1992).CrossRefGoogle Scholar
18Hoshino, K. and Shimamura, S., Philos. Mag. A40, 137 (1979); Couchman, P. R. and Ryan, C. L., Philos. Mag. A37, 369 (1978).CrossRefGoogle Scholar
19Ivlev, V. I., Sov. Phys. Solid State 33, 909 (1991).Google Scholar
20Matsushita, E. and Nakanishi, A., J. Phys. Soc. Jpn. 39, 1415 (1975); Matsushita, E. and Matsushita, T., Prog. Theor. Phys. 59, 15 (1978); Matsushita, E. and Siegel, E., Scripta Metall. 13, 913 (1979).CrossRefGoogle Scholar
21Gryaznov, V. G., Gurskii, M. A., Trusov, L. I., and Aivazov, A. A., Sov. Phys. Solid State 24, 297 (1982).Google Scholar
22Cai, Z-X., Mahanti, S. D., Antonelli, A., Khanna, S. N., and Jena, P., Phys. Rev. B 46, 7841 (1992); Jellinek, J. and Garzon, I.L., Z. Phys. D20, 242 (1991).CrossRefGoogle Scholar
23Friedel, J., Surf. Sci. 106, 582 (1981).CrossRefGoogle Scholar
24Lindemann, F. A., Phys. Z. 11, 609 (1910).Google Scholar
25Hasegawa, M., Hoshino, K., and Watabe, M., J. Phys. F.: Metal Phys. 10, 619 (1980); Frenkel, A., Shasha, E., Gorodetsky, O., and Voronel, A., Phys. Rev. B 48, 1283 (1993).CrossRefGoogle Scholar
26Wallis, R. F., Prog, in Surf. Sci. 4, 233 (1974); Nesterenko, B.A. and Borodkin, A. D., Sov. Phys. Solid State 19, 127 (1977).CrossRefGoogle Scholar
27Buffat, Ph. and Borel, J. P., Phys. Rev. A 13, 2287 (1976).CrossRefGoogle Scholar
28Pócza, J. F., Barna, A., and Barna, P. B., J. Vac. Sci. Technol. 6, 472 (1969).CrossRefGoogle Scholar