Rigidity transitions and constraint counting in amorphous networks: Beyond the mean-field approach
Laboratoire de Physique Théorique des Liquides,
Université Pierre et Marie Curie Boite 121, CNRS UMR 7600 -
4, Place Jussieu, 75252 Paris Cedex 05, France
Accepted: 27 March 2002
We study rigidity transitions in covalent amorphous networks using size-increasing cluster approximations and constraint-counting algorithms. Possible consequences of the presence of self-organization are examined. The analysis reveals two transitions instead of the usual (mean-field) single transition: one from a floppy to an isostatic rigid phase at a mean coordination number where the number of floppy modes vanishes and a second one from an isostatic to a stressed rigid phase at . The value of the two critical mean coordination numbers as well as the width of the intermediate phase depend very strongly on the presence of medium-range order elements such as rings.
PACS: 61.43.Fs – Glasses / 62.20.-x – Mechanical properties of solids
© EDP Sciences, 2002