Phase-field model for crystallization in alkali disilicate glasses: Li₂O–2SiO₂, Na₂O–2SiO₂ and K₂O–2SiO₂

Abstract

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 (T_m) and the steep peak at around T_m–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.