Effect of buoyancy and Marangoni forces on the dopant distribution in a single crystal fiber grown from the melt by edge-defined film-fed growth (EFG) method

Abstract

The dependence of the dopant distribution on the combined effect of the buoyancy and Marangoni forces, for two fibers (Nd:YAG and Nd:LiNbO 3) grown from the melt by EFG method with central capillary channel (CCC) shaper and melt replenishment, is analyzed. The partial differential equations used for describing the growth process are the incompressible Navier–Stokes equations in the Boussinesq approximation and the convection–conduction and conservative convection–diffusion equations. For numerical solutions, the finite-element numerical technique using COMSOL Multiphysics 3.3 software for a 2D axi-symmetric model is utilized. The Marangoni effect is taken into account, and for its implementation the weak form of the boundary application mode is employed. The computations are carried out in the stationary case, for different Grashof and Marangoni numbers corresponding to the heat expansion coefficients and surface tension temperature coefficients situated in ranges centered around the literature values: β∈[1.8×10 −6, 1.8×10 −4] K −1; d γ/d T∈[−3.5×10 −4, −3.5×10 −6] N m −1 K −1 for Nd:YAG, and β∈[1×10 −5, 1×10 −3] K −1; d γ/d T∈[3×10 −5, 3×10 −3] N m −1 K −1 for Nd:LiNbO 3. The combined effect of the buoyancy and Marangoni forces on the fluid flow and on the dopant distribution is analyzed.