Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-19T06:36:43.205Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological Origin of the Surface Singularities in Glasses

Published online by Cambridge University Press:  25 February 2011

Richard Kerner
Richard Kerner*
Affiliation:
Département de Mécanique Analytique, 4 Place Jussieu, 75230 Paris Cedex 05, France.
Get access

Abstract

A model of CRN in two dimensions is presented, composed of equilateral but not equiangular polygons with a constant coordination number = 3; in a simplified version only pentagons, hexagons and heptagons are present in the network. We introduce the mean potential energy per atom averaged over a typical cell containing three adjacent polygons; we assume that although the thermal equilibrium is not attained for single atoms, it is attained on the level of these cells, so that we can apply the virial theorem for the cells. Then we minimize the free energy which contains the configuration entropy contribution. In terms of two variables P and δ (hexagon frequency and mean bond angle deviation) we get the surfaces of constant energy. Under stress the energy configurations cease to be one-connected, and the 0-th homotopy group is no more trivial. This can give rise to surface singularities (cracks).

Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 61: Symposium P – Defects in Glasses , 1985 , 39
Copyright
Copyright © Materials Research Society 1986

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

[1] Kerner, R., Phys. Rev. B 28, 756–561 (1983).CrossRefGoogle Scholar
[2] Kerner, R., Journal of non-Crystalline Solids, 71, 19–27 (1985).CrossRefGoogle Scholar
[3] Santos, D.M. Lucas Ferreira dos, Journal de Physique, 45 (1984).CrossRefGoogle Scholar
[4] Kepler, J., De Nive Sexangula, Tampach, ed., Frankfurt (1611); see also A.L. Mackay, Physics Bulletin, Nov. 1976, 495.Google Scholar
[5] Kerner, R., Santos, D.M. dos, Comptes Rendus Acad. Sci. Paris, 295–300, (1982); also D.M. dos Santos (to appear).Google Scholar
[6] Toulouse, G., Kléman, M., J. Physique Lett., 37 L149 (1976).CrossRefGoogle Scholar
[7] Kléman, M., Michel, L., Toulouse, G., J. Physique Lett., 38 L 195, (1977).CrossRefGoogle Scholar