Model for the glass transition in amorphous solids based on fragmentation

A model for the glass transition in a heating process has been proposed. In the model, noncrystalline solids are assumed to be assemblies of pseudomolecules or structural units. When the noncrystalline solid is heated, a bond breaking process becomes dominant compared with a rebinding process of broken bonds. At high temperature, successive bond breaking causes the fragmentation of the solid and the fragment size becomes smaller as the temperature further increases. Consequently, the solid begins to show some viscous behavior when the fragment size reaches a critical value. To construct mathematical expressions for the fragmentation model, we employed a simple rate equation for the bond breaking process first and then obtained the temperature dependence of dangling bond density in a noncrystalline solid. Second, the expressions for the fragment density and size as a function of temperature were obtained based on the following assumptions: (1) bond breaking takes place mainly at the boundaries between pseudomolecules, (2) once buds of microcracks are generated, successive bond breaking occurs mostly at the tip of the microcracks, and (3) the fragments are Voronoy polyhedra. Finally, the diffusion coefficient in the system was obtained by assuming the vacancy mechanism in solids and then the temperature dependence of viscosity was derived through Stokes-Einstein relation. To examine the present model, applications of the model to the phase changes of a-Si in heating processes are carried out and the results were discussed.