Phase-field model for crystallization in alkali disilicate glasses: Li<sub>2</sub>O–2SiO<sub>2</sub>, Na<sub>2</sub>O–2SiO<sub>2</sub> and K<sub>2</sub>O–2SiO<sub>2</sub>

This study developed phase-field method (PFM) technique in oxide melt system by using a new mobility coefficient (L). The crystal growth rates (v0) obtained by the PFM calculation with the constant L were comparable to the thermodynamic driving force in normal growth model. The temperature dependence of the L was determined from the experimental crystal growth rates and the v0. Using the determined L, the crystal growth rates (v) in alkali disilicate glasses, Li2O–2SiO2, Na2O–2SiO2 and K2O–2SiO2 were simulated. The temperature dependence of the v was qualitatively and quantitatively so similar that the PFM calculation results demonstrated the validity of the L. Especially, the v obtained by the PFM calculation appeared the rapid increase just below the thermodynamic melting point (Tm) and the steep peak at around Tm–100K. Additionally, as the temperature decreased, the v apparently approached zero ms−1, which is limited by the L representing the interface jump process. Furthermore, we implemented the PFM calculation for the variation of the parameter B in the L. As the B increased from zero to two, the peak of the v became steeper and the peak temperature of the v shifted to the high temperature side. The parameters A and B in the L increased exponentially and decreased linearly as the atomic number of the alkali metal increased due to the ionic potential, respectively. This calculation revealed that the A and B in the L were close and reasonable for each other.