Onset of rigidty in glasses: from random to self-organized networks

We review in this paper the signatures of a new elastic phase that is found in glasses with selected compositions. It is shown that in contrast with random networks, where rigidity percolates at a single threshold, networks that are able to self-organize to avoid stress will remain in an almost stress- free state during a compositional interval, an intermediate phase, that is bounded by a flexible phase and a stressed rigid phase. We report the experimental signatures and describe the theoretical efforts that have been accomplished to characterize the intermediate phase. We illustrate one of the methods used in more detail with the example of Group III chalcogenides and finally suggest further possible experimental signatures of self-organization.Comment: 27 pages, 6 figures, Proceedings of the Conference on Non-Crystalline Materials 10, to appear in Journal of Non-Crystalline Solid

Rings and rigidity transitions in network glasses

Three elastic phases of covalent networks, (I) floppy, (II) isostatically rigid and (III) stressed-rigid have now been identified in glasses at specific degrees of cross-linking (or chemical composition) both in theory and experiments. Here we use size-increasing cluster combinatorics and constraint counting algorithms to study analytically possible consequences of self-organization. In the presence of small rings that can be locally I, II or III, we obtain two transitions instead of the previously reported single percolative transition at the mean coordination number $\bar r=2.4$, one from a floppy to an isostatic rigid phase, and a second one from an isostatic to a stressed rigid phase. The width of the intermediate phase $~ \bar r$ and the order of the phase transitions depend on the nature of medium range order (relative ring fractions). We compare the results to the Group IV chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate phase has been obtained, and for which estimates of ring fractions can be made from structures of high T crystalline phases.Comment: 29 pages, revtex, 7 eps figure