Heat and Mass Transfer in the Growth of Titanium Doped Sapphire Material with the μ-PD Technique

Abstract

In this work we have studied the heat and the mass transfer of titanium doped sapphire in the growth domain. The growth of this material (Ti+3: Al2O3) is performed using a relatively recent growing technique that is the micro-pulling down (µ-PD) [1]. This method presents several advantages over other growing methods [2] and allows a stable growth of shaped material with very good quality [3]. In this study we established a numerical, two-dimensional finite volume model in cylindrical coordinates with an axisymmetric configuration. The flow, the thermal transfer and the mass transfer are modeled by the differential equations of conservation of the mass, of quantity of the movement, energy and the species. This problem, which takes into account the convection-diffusion coupling, is discretized using the Finite Volumes Method (FVM). We focus on the physical properties of the molten zone and on the radial and axial distribution of titanium in the sapphire crystal fiber. Our model is in good agreement with experimental results.