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Report No.

Phase-field mobility for crystal growth rates in undercooled silicates, SiO$$_2$$ and GeO$$_2$$ liquids

Kawaguchi, Munemichi   ; Uno, Masayoshi*

Phase-field mobility, $$L$$, and crystal growth rates in crystallization of 11 oxides or mixed oxides in undercooled silicates, SiO$$_2$$ and GeO$$_2$$ liquids were calculated with a simple phase-field model (PFM), and material dependence of the $$L$$ was discussed. Ratios between experimental crystal growth rates and the PFM simulation with $$L=1$$ were confirmed to be proportional to a power of $$frac{TDelta T}{eta}$$ on the solid/liquid interface process during the crystal growth in a log-log plot. We determined that parameters, $$A$$ and $$B$$, of the $$L=A(frac{k_{B}TDelta T}{6pi^{2}lambda^{3}eta T_{m} })^{B}$$ were $$A=6.7times 10^{-6}$$ to $$2.6$$m$$^4$$J$$^{-1}$$s$$^{-1}$$ and $$B=0.65$$ to $$1.3$$, which were unique for the materials. It was confirmed that our PFM simulation with the determined $$L$$ reproduced quantitively the experimental crystal growth rates. The $$A$$ has a proportional relationship with the diffusion coefficient of a cation molar mass average per unit an oxygen molar mass at $$T_{m}$$ in a log-log graph. The $$B$$ depends on the sum of the cation molar mass per the oxygen molar mass, $$frac{Sigma_{i}M_{i}}{M_{O}}$$, in a compound. In $$frac{Sigma_{i}M_{i}}{M_{O}}leq 25$$, the $$B$$ decreases with the cation molar mass increasing. The assumed cause is that the B represents the degree of the temperature dependence of the $$L$$. Since the cation molar mass is proportional to an inertial resistance of the cation transfer, the $$B$$ decreases with inverse of the cation molar mass. In crystallization of the silicates of heavy cation in $$frac{Sigma_{i}M_{i}}{M_{O}}geq 25$$, the $$B$$ saturates at approximately 0.67, which leads to $$T_{p}approx 0.9T_{m}$$.



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