Composition dependence of glass transition temperature and fragility. I. A topological model incorporating temperature-dependent constraints

We present a topological model for the composition dependence of glass transition temperature and fragility. Whereas previous topological models are derived for zero temperature conditions, our approach incorporates the concept of temperature-dependent constraints that freeze in as the system is cooled from high temperature. Combining this notion of temperature-dependent constraints with the Adam-Gibbs model of viscosity, we derive an analytical expression for the scaling of glass transition temperature and fragility in the binary Gex Se1-x system. In the range of 0≤_x≤_1/3, we reproduce the modified Gibbs-DiMarzio equation of Sreeram [J. Non-Cryst. Solids 127, 287 (1991)] but without any empirical fitting parameters. The modified Gibbs-DiMarzio equation breaks down for 1/3<x≤2/5, where the glass transition temperature decreases with increasing germanium content.