The stability of thermocapillary convection in the floating zone for molybdenum (Mo) and lithium niobate (LiNbO3) has been studied using a linear theory. The input power induced by the heat source is assumed to be a Gaussian distribution. The steady, axisymmetric basic state is solved numerically using a finite difference method, employing the boundary-fitted curvilinear coordinate system. The linear disturbance equations for axisymmetric disturbances, which are partial differential equations, are treated by a mixed finite difference spectral method. The critical zone lengths and the critical input powers of Mo for axisymmetric disturbances are predicted. The thermocapillary instability of the LiNbO3 melt may not appear before the capillary instability (originating from the gas-melt interface) sets in.
