Phase-field analyses for Y123 crystal growth

Abstract

A phase-field evolution equation (a kind of time dependent Ginzburg–Landau equation), in which order parameter ( φ) transition in width restricted within a unit grid, was solved using an implicit finite difference method. The direct implicit scheme would have an ability to correspond to a long-range order parameter correlation, which appeared around a phase transition. When the transition width is restricted within a unit grid, a skew directional finite difference is necessary to obtain an isotropic growth rate. Using these schemes, an isotropic growth shape was obtained for a single composition system with a latent heat free condition. In the case of a large latent heat condition, which is the case for Y123 crystal growth, we could obtain a faceted growth shape without using any anisotropic parameters.