Rings and rigidity transitions in network glasses

Abstract

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 numberr = 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 ∆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.

The Structure of Silicate Melts: A Glass Perspective

“…The unstressed rigid phase is an intermediate phase (cf. Thorpe et al 2000), and the width (⌬r) of the intermediate phase and order of the transition are related to the median-range order of the network (Micoulaut & Phillips 2003). The identifi cation of an intermediate phase provides new theoretical and experimental challenges for understanding the explicit nature of the behavior of glasses and offers exciting possibilities for explaining a number of phenomena such as phase separation and the behavior of density and viscosity.…”

Material functionalities from molecular rigidity: Maxwell’s modern legacy

“…However, it has now become clear that such intriguing effects seem to result from adaptation or self-organization at the molecular level, in order to avoid the stresses imposed by increased bond density. 17 Apart from these more basic aspects of rigidity transitions, with the important body of data accumulated on chalcogenide and oxide glasses in the past few years, it has now also become evident that such isostatic glassy compositions defi ning an "intermediate phase" display a certain number of quite remarkable properties, such as an enhanced stability with respect to aging, 18 space-fi lling tendencies, 19 stress-free character, 20 and glass transitions with minimum enthalpic changes. 5 Undoubtedly, such anomalous properties will be used in the near future for the design of dedicated functionalities.…”

Recent advancement in metal containing multicomponent chalcogenide glasses

“…In 2003 Tanaka [51] reviewed the nanoscale structures of chalcogenide glasses and ins− pected surface modifications at nanometer resolution. Sub− sequently, Micoulaut et al [52] have shown three elastic phases of covalent networks [(I) floppy, (II) isostatically rigid, and (III) stressed−rigid], depending on a degree free− dom of material. They also suggested that the ring factor was responsible for high crystallization temperature in metallic/semi−metallic chalcogenide glasses.…”