Abstract
We have investigated numerically using the Metropolis Monte Carlo algorithm two-dimensional systems of about 3000 classical particles interacting via a Lennard-Jones potential and being subjected to periodic boundary conditions. In this model we consider metastable structures of small crystalline grains which are randomly oriented relative to each other and which are interconnected by a network of boundaries. The atomic structure within the grains being composed of about 500 atoms each is a nearly ideal triangular lattice. The network of boundaries however has a highly defective structure which is determined by the boundary conditions enforced by the crystalline grains. It is the objective of our work to develop a conceptually simple model for nanocrystalline materials, which can be used for a qualitative description of their complex properties. The main ingredient of the model is its property to relax into a metastable state consisting of intrinsically well ordered crystalline grains connected by a highly defective intergranular component. For that state we compute the static structure factor and the pair correlation function.
Similar content being viewed by others
References
Gleiter, H., in: Hanse, N., Horsewell A., Leffers T. (eds.): Deformation of polycrystals, pp. 15–21. 2nd. Riso Symp. Riso National Laboratory, Roskilde, Danmark (1981)
Birringer, H., Gleiter, H.: in Encyclopedia of materials science and engineering, (Suppl.) vol. 1 pp. 339–349. Cahn, R.W. (ed.). Oxford: Pergamon Press 1988
Gleiter, H.: Encyclop. Phys. Sci. Technol.10, 561 (1992)
Siegel, R.W.: MRS Bulletin, p. 60ff. (October 1990)
Gleiter, H.: Prog. Mat. Sci.33, 223 (1989)
Abraham, F.F.: Phys. Rep.80, 339 (1981)
Abraham, F.F.: Adv. Phys.35, 1 (1986)
Barker, J.A., Henderson, D., Abraham, F.F.: Physica106A, 226 (1981)
Kosterlitz, J.M., Thouless, D.J.: J. Phys. C: Solid State Phys.5, 124, 1972;6, 1181 (1973)
Halperin, B.I., Nelson, D.R.: Phys. Rev. Lett.41, 121 (1978)
Abraham, F.F.: Phys. Rev. B28, 7338 1983
Carlsson, A.E., in: Solid state physics, vol. 43, Seitz, F., Turnbull D. (eds.), New York: Academic Press 1990
Bak, P., Tang, C., Wiesenfeld, K.: Phys. Rev. A38, 364 (1988)
Hahn, W.: private Mitteilung
Zhu, X., Birringer, R., Herr, U., Gleiter, H.: Phys. Rev. B35, 9085 (1987)
Tiensu, V.H., Ergun, S., Alexander, L.E.: J. Appl. Phys.35, 1718 (1964)
Betts, F., Bienenstock, A.: J. Appl. Phys.43, 4591 1972
Haubold, T., Birringer, R., Lengler, B., Gleiter, H.: Phys. Lett. A135, 461 (1989)
Wagner, M.: Acta Metall.40, 957 (1992)
Wagner, W.: Phys. Rev. B45, 635 (1992)
Pirc, R., Holz, A.: Two-level systems in nanostructures materials (Preprint 1994)
Author information
Authors and Affiliations
Additional information
Work supported by Deutsche Forschungsgemeinschaft under grant No 841/8-1
Rights and permissions
About this article
Cite this article
Müller, S., Schwarz, M. On the structure and stability of nanoscale materials: a two-dimensional model. Z. Physik B - Condensed Matter 97, 503–510 (1995). https://doi.org/10.1007/BF01322431
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01322431