Modeling nonisothermal crystallization in a BaO∙2SiO₂ glass

The accuracy of a differential thermal analysis (DTA) technique for predicting the temperature range of significant nucleation is examined in a BaO∙2SiO₂ glass by iterative numerical calculations. The numerical model takes account of time-dependent nucleation, finite particle size, size-dependent crystal growth rates, and surface crystallization. The calculations were made using the classical and, for the first time, the diffuse interface theories of nucleation. The results of the calculations are in agreement with experimental measurements, demonstrating the validity of the DTA technique. They show that this is independent of the DTA scan rate used and that surface crystallization has a negligible effect for the glass particle sizes studied. A breakdown of the Stokes-Einstein relation between viscosity and the diffusion coefficient is demonstrated for low temperatures, near the maximum nucleation rate. However, it is shown that accurate values for the diffusion coefficient can be obtained from the induction time for nucleation and the growth velocity in this temperature range.