An axis symmetric 2D description of the growth process of a single crystal hollow tube, grown from the melt by pulling down method. Part.1

Abstract

This paper is the first part of an axis symmetric 2D description of a single crystal hollow tube growth process, grown from the melt, by micro- pulling--down (PD) method. The description concerns the following aspects: the free surfaces equations and the pressure differences accross the free surfces (section 2); limits of the pressure diferences \textit{$p_{i}$} and \textit{$p_{e}$} across the free surfaces (section 3); static stability of the capillary free surfaces (section 4). In section 5 the above aspects are numerically illustrated in the case of the growth of a silicon hollow tube of inner radius equal to $4.28x10^{-3}$[m] and outer radius equal to $4.72x10^{-3}$[m]. This part of the paper is helpfull to better understand the dependence of the shape and size of the tube, being to grown, on the pressure differences across the free surfaces and may help the manufacturing brfore seeding. In section 6 some general conclusions are given.