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
type: Item
instance of: scholarly article
title: 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
zbMATH Open document ID: 1186.80012
DOI: 10.1155/2009/348538
author: Stefan Balint
author: Agneta M. Balint
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45830
review text: In this paper the author's presented the 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. The method presented in this paper locates the controllable part \(p\) of the pressure difference across the free surface. It is based on the solution of the differential equation describing the outer free and inner free surface with the boundary conditions. After some set of calculations they determined the melt column height (between the horizontal crucible melt level and the shaper top level) in the function of the pressure of the gas flow (introduced in the furnace for release the heat) in order to obtain the desired meniscus. They showed that the solution \(z_i=z_i(r)\) has to minimize the energy functional of the melt column. Based on the mathematical theorems proven in [\textit{St. Balint} and \textit{L. Tanasie}, Nonlinear Stud. 15, No.~4, 277--296 (2008; Zbl 1168.34008)], they formulate fifteen statements. The procedure presented in this paper is general and was numerically illustrated at many figures. It is worth to emphasize that novelty of this paper is the algorithm for the exact determination of which has to be used to the determination of the melt column height and the evolution of the effect of shaper radii. They didn't consider the thermal conditions in the problem.
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 5632472
zbMATH Keywords: free surface
zbMATH Keywords: energy functional
zbMATH Keywords: melt growth techniques
zbMATH Keywords: growth of single crystal tube
Wikidata QID: Q58648961
reviewed by: Jerzy August Gawinecki
MaRDI profile type: Publication
OpenAlex ID: W2093439458
cites work: Q3604142
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description: scientific article; zbMATH DE number 5632472