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Phase-field model for crystallization in alkali disilicate glasses; Li$$_2$$O-2SiO$$_2$$, Na$$_2$$O-2SiO$$_2$$ and K$$_2$$O-2SiO$$_2$$

Kawaguchi, Munemichi  ; Uno, Masayoshi*

This study developed phase-field method (PFM) technique in oxide melt system by using a new mobility coefficient ($$L$$). The crystal growth rates ($$v_0$$) 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 $$v_0$$. Using the determined $$L$$, the crystal growth rates ($$v$$) in alkali disilicate glasses, Li$$_2$$O-2SiO$$_2$$, Na$$_2$$O-2SiO$$_2$$ and K$$_2$$O-2SiO$$_2$$ 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 ($$T_{rm m}$$) and the steep peak at around $$T_{rm m}$$-100 K. 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.

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Category:Materials Science, Ceramics

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