Heating rate effects in time-dependent homogeneous nucleation in glasses

Nucleation kinetics of glass-ceramics is frequently determined using Tammann's double-stage heat-treatment. This method requires a complex deconvolution of the experimentally observed induction time (t(ind)), i.e. the intercept of the linear part of the crystal number density curve with the nucleation time axis, into two components. In this paper, double-stage heat treatments were performed, with heating rates between the nucleation and development temperatures covering two orders of magnitude, in samples of a homogeneously nucleating glass-forming system, lithium disilicate. Our results show that t(ind) increases with increasing heating rates with cubic root dependence. In accordance with the theory, t(ind) was split into the intrinsic time required to establish a steady-state cluster size distribution, tau (time-lag) at the nucleation temperature and an incubation time (t(i)), which is a size, heating rate and development temperature (T-d) dependent growth time. We demonstrate that the Collins-Kashchiev nucleation model performs poorly if t(i) is approximated by the time needed to experimentally detect the first crystal. In contrast, the Shneidman approach is consistent with theory. We found that at any given nucleation temperature, t(i) is a strong function of the heating rate, and is proportional to t(ind), whereas tau is a constant, as expected.