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
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.
scientific article; zbMATH DE number 5632472
scientific article