ALE method in the EFG crystal growth technique

Abstract

Using the arbitrary Lagrangian–Eulerian (ALE) method, an accurate description of the melt flow and impurity distribution in a time-dependent domainΩ(t), t ∈ [0, T], is performed. The procedure is developed for a crystal fiber grown from the melt by the edge-defined film-fed growth (EFG) technique, on the basis of the finite-element method using COMSOL multiphysics software. For this, an EFG system without melt replenishment (the melt level in the crucible decreases in time) is considered. By coupling three application modes – incompressible Navier–Stokes, moving mesh arbitrary Lagrangian–Eulerian, and convection–diffusion – it is illustrated, in the time-dependent case, how the pull of the crystal, with a constant rate v _in , generates the fluid flow, and it is shown how the resulting fluid flow and deformed geometry determine the impurity distribution in the melt and in the crystal.