DOI: 10.1209/epl/i2002-00471-9


Europhys. Lett., 57 (3) , pp. 423-429 (2002)

Vibrations of amorphous, nanometric structures: When does continuum theory apply?

J. P. Wittmer¹, A. Tanguy¹, J.-L. Barrat¹ and L. Lewis<sup>2

1</sup>  Département de Physique des Matériaux, CNRS, Université de Lyon 43 Boulevard du 11 Novembre, 69622 Villeurbanne Cedex, France
²  Département de Physique, Université de Montréal C.P. 6128, Succ. Centre-Ville, Montréal, Québec, Canada H3C 3J7

jwittmer@dpm.univ-lyon1.fr

(Received 13 September 2001; accepted in final form 15 November 2001)

Abstract
We investigate the low-frequency end of the vibrational spectrum in small (nanometric) disordered systems. Using numerical simulation and exact diagonalization for simple two-dimensional models, we show that continuum elasticity, applied to these systems, actually breaks down below a length scale of typically 30 to 50 molecular sizes. This length scale is likely related to the one which is generally invoked to explain the peculiar vibrational properties of glassy systems.

PACS
72.80.Ng - Disordered solids.
65.60.+a - Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc..
61.46.+w - Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals.


© EDP Sciences 2002