Rings and rigidity transitions in network glasses

TL;DR

This paper analytically investigates the elastic phases and transitions in covalent network glasses, revealing two distinct transitions influenced by ring structures and medium-range order, with implications for materials like Ge-Se and Si-Se.

Contribution

It introduces a model accounting for small rings and medium-range order, predicting two phase transitions instead of one in network glasses, supported by comparison to experimental data.

Findings

Identification of two elastic phase transitions in network glasses.

The width and nature of the phases depend on ring fractions and medium-range order.

Comparison with Group IV chalcogenides supports the model's predictions.

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 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.