Phase-Field Modeling of Crystal Growth on the Surface and in the Volume of Na(2)O–2CaO–3SiO(2) Glass under Periodic Temperature Conditions

[Image: see text] We performed modeling of two- and three-dimensional phase-field methods (2D- and 3D-PFM) for crystal growth on the surface and in the volume of Na(2)O–2CaO–3SiO(2) glass to investigate crystal growth behaviors under periodic temperature conditions. In this study, the periodic temperature conditions were set to 993 K for 180 s and 873 K for 252 s repeatedly. Phase-field mobilities, L(S) and L(B), were determined to compare with the experimental surface crystal growth rate, u(S), and the volume crystal growth rate, u(B), at 873–1023 K. 2D-PFM with L(S) and L(B) reproduced quantitatively the temperature dependence of u(S) and u(B). The parameters of L(S) and L(B) were consistent with those of 11 kinds of silicate melts, considering the surface and bulk diffusion coefficients. 3D-PFM simulated the single- and multinucleated crystal growth behaviors: the single-nucleated crystal simulation revealed that a ring was formed around the pre-existing crystal by heterogeneous nucleation. These radii obtained by 3D-PFM were comparable to the experimental values. The multinucleated crystal simulation revealed the contact and interaction between the crystals, e.g., new crystal rings could not be formed at the contacting region. In random nucleation, the 3D-PFM simulation demonstrated the crystal shape of the multinucleated crystals under periodic temperature conditions. It was comparable to the experimental photographs obtained by Yuritsyn et al.