We collect and critically analyze extensive literature data, including our own, on three important kinetic processes—viscous flow, crystal nucleation, and growth—in lithium disilicate (Li₂O·2SiO₂) over a wide temperature range, from above T_m to 0.98T_g where T_g ≈ 727 K is the calorimetric glass transition temperature and T_m = 1307 K, which is the melting point. We found that crystal growth mediated by screw dislocations is the most likely growth mechanism in this system. We then calculated the diffusion coefficients controlling crystal growth, $D_{eff}^U$ , and completed the analyses by looking at the ionic diffusion coefficients of Li⁺¹, O²⁻, and Si⁴⁺ estimated from experiments and molecular dynamic simulations. These values were then employed to estimate the effective volume diffusion coefficients, $D_{eff}^V$ , resulting from their combination within a hypothetical Li₂Si₂O₅ “molecule”. The similarity of the temperature dependencies of 1/η, where η is shear viscosity, and $D_{eff}^V$ corroborates the validity of the Stokes-Einstein/Eyring equation (SEE) at high temperatures around T_m. Using the equality of $D_{eff}^V$ and $D_{eff}^{\eta }$ , we estimated the jump distance λ ∼ 2.70 Å from the SEE equation and showed that the values of $D_{eff}^U$ have the same temperature dependence but exceed $D_{eff}^{\eta }$ by about eightfold. The difference between $D_{eff}^{\eta }$ and $D_{eff}^U$ indicates that the former determines the process of mass transport in the bulk whereas the latter relates to the mobility of the structural units on the crystal/liquid interface. We then employed the values of η(T) reduced by eightfold to calculate the growth rates U(T). The resultant U(T) curve is consistent with experimental data until the temperature decreases to a decoupling temperature $T_d^U\approx 1.1-1.2T_g$ , when $D_{eff}^{\eta }$ begins decrease with decreasing temperature faster than $D_{eff}^U$ . A similar decoupling occurs between $D_{eff}^{\eta }$ and $D_{eff}^{\tau }$ (estimated from nucleation time-lags) but at a lower temperature$T_d^{\tau }\approx T_g$ . For T > T_g the values of $D_{eff}^{\tau }$ exceed $D_{eff}^{\eta }$ only by twofold. The different behaviors of $D_{eff}^{\tau }\left(T\right)$ and $D_{eff}^U\left(T\right)$ are likely caused by differences in the mechanisms of critical nuclei formation. Therefore, we have shown that at low undercoolings, viscosity data can be employed for quantitative analyses of crystal growth rates, but in the deeply supercooled liquid state, mass transport for crystal nucleation and growth are not controlled by viscosity. The origin of decoupling is assigned to spatially dynamic heterogeneity in glass-forming melts.

In the present paper, some further results of application of the generalized Gibbs’ approach [J. W. P. Schmelzer et al., J. Chem. Phys. 112, 3820 (2000); 114, 5180 (2001); 119, 6166 (2003)] to describing new-phase formation processes are outlined. The path of cluster evolution in size and composition space is determined taking into account both thermodynamic and kinetic factors. The basic features of these paths of evolution are discussed in detail for a simple model of a binary mixture. According to this analysis, size and composition of the clusters of the newly evolving phase change in an unexpected way which is qualitatively different as compared to the classical picture of nucleation-growth processes. As shown, nucleation (i.e., the first stage of cluster formation starting from metastable initial states) exhibits properties resembling spinodal decomposition (the size remains nearly constant while the composition changes) although the presence of an activation barrier distinguishes the nucleation process from true spinodal decomposition. In addition, it is shown that phase formation both in metastable and unstable initial states near the classical spinodal may proceed via a passage of a ridge of the thermodynamic potential with a finite work of the activation barrier even though (for unstable initial states) the value of the work of critical cluster formation (corresponding to the saddle point of the thermodynamic potential) is zero. This way, it turns out that nucleation concepts—in a modified form as compared with the classical picture—may govern also phase formation processes starting from unstable initial states. In contrast to the classical Gibbs’ approach, the generalized Gibbs’ method provides a description of phase changes both in binodal and spinodal regions of the phase diagram and confirms the point of view assuming a continuity of the basic features of the phase transformation kinetics in the vicinity of the classical spinodal curve.