Nucleation and growth in cluster dynamics: A quantitative test of the classical kinetic approach

Nucleation and size dependent growth of nanometer sized crystalline particles in glassy media have been studied by numerically solving the Turnbull–Fisher master equations that describe the time evolution of cluster population. Time dependencies of the formation rate and number density are determined for large clusters (built of up to 2×105 formula units, containing 1.8×106 atoms). We demonstrate that the formation rate and number density of such clusters are well approximated by Shneidman’s asymptotically exact analytical solution. A quantitative test of the kinetic Turnbull–Fisher model has been performed: Evaluating the kinetic coefficients and interfacial parameters from the transient time and steady-state nucleation rates measured on six stoichiometric oxide glass compositions (lithium–disilicate, barium–disilicate, lithium–diborate, wollastonite, 1:2:3 and 2:1:3 soda–lime–silica glass compositions), we calculated the macroscopic growth rates and compared with experiments. For wollastonite, lithium–diborate and the 1:2:3 soda–lime–silica glass, differences of 2 to 4 orders of magnitude have been observed between theory and experiment. This inadequacy of the microscopic kinetic parameters in describing macroscopic growth cannot be explained by either the curvature effect on the interfacial free energy or the self-consistency correction for the cluster free energy. The origin of the discrepancy is discussed.