Three-dimensional numerical simulation of oxide melt flow in Czochralski configuration

Abstract

In order to understand the well-known surface pattern of oxide melt flow in a Czochralski crucible, a set of three-dimensional numerical simulations of LiNbO3 melt flow in a crucible (47mmφ×46mmh) with a rotating disc (23.5φmm, rotating at Ω) was conducted using the finite-difference method. The crucible bottom was assumed to be adiabatic and the side wall was heated by a constant heat flux. Several case studies with a constant temperature of the side wall were considered for comparison. The heat loss from the melt surface caused by radiation to the ambient at a constant temperature was taken into account. The disc/melt interface was assumed to be flat and at melting- point temperature. To investigate the role of surface tension in the melt flow, numerical simulations including and neglecting the Marangoni effect were conducted at each disc-rotation rate. When neglecting the Marangoni effect, the interaction between the buoyancy and the disc rotation produces a wavy ring-like pattern on the melt surface only at approximately Ω=40rpm. However, if the Marangoni effect is taken into account, a spoke pattern appears on the surface over a wide range of disc-rotation rate (0rpm⩽Ω⩽45rpm). At higher disc-rotation rates, the spoke pattern disappears. The flow in the bulk can be classified into three different types according to the disc-rotation rate, i.e., (1) thermally driven axisymmetric flow with no reverse flow at low rotation rates (0–20rpm), (2) thermally driven axisymmetric flow with reverse flow beneath the disc at moderate rotation rates (20–30rpm) and (3) nonaxisymmetric unsteady flow at higher rotation rates (⩾40rpm). The investigation of the effect of the thermal boundary condition indicated that these flow patterns are sensitive to the thermal boundary condition of the crucible side wall.