Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 348538, 22 pages
doi:10.1155/2009/348538
Research Article

On the Creation of a Stable Drop-Like Static Meniscus, Appropriate for the Growth of a Single Crystal Tube with Prior Specified Inner and Outer Radii

Stefan Balint1 and Agneta M. Balint2

1Faculty of Mathematics and Computer Science, West University of Timisoara, Bulv. V.Parvan 4, 300223 Timisoara, Romania
2Faculty of Physics, West University of Timisoara, Bulv. V.Parvan 4, 300223 Timisoara, Romania

Received 22 February 2009; Revised 6 May 2009; Accepted 24 May 2009

Academic Editor: Ben T. Nohara

Copyright © 2009 Stefan Balint and Agneta M. Balint. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A theoretical procedure for the creation of a stable drop-like static meniscus, appropriate for the growth of a single crystal tube, with a priori specified inner and outer radius, is presented. The method locates the controllable part p of the pressure difference across the free surface. It consists in a set of calculus, which leads to the determination of the melt column height (between the horizontal crucible melt level and the shaper top level) in function of the pressure of the gas flow (introduced in the furnace for release the heat) in order to obtain the desired meniscus. The procedure is presented in general and is numerically illustrated for InSb tubes. The novelty is the algorithm for the exact determination of p, which has to be used, the determination of the melt column height, and the evaluation of the effect of shaper radii. The setting of the thermal conditions, which assure that for the obtained static meniscus the solidification conditions are satisfied at the “right” places, is not considered here.