Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Inequalities for Single Crystal Tube Growth by Edge-Defined Film-Fed Growth Technique | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 732106 28 pages doi 2009 732106 Research Article Inequalities for Single Crystal Tube Growth by Edge-Defined Film-Fed Growth Technique Stefan Balint1 and Agneta M. Balint2 1 Department of Computer Science Faculty of Mathematics and Computer Science West University of Timisoara Blv. 4 300223 Timisoara Romania 2 Faculty of Physics West University of Timisoara Blv. 4 300223 Timisoara Romania Correspondence should be addressed to Agneta M. Balint balint@ Received 3 January 2009 Accepted 29 March 2009 Recommended by Yong Zhou The axi-symmetric Young-Laplace differential equation is analyzed. Solutions of this equation can describe the outer or inner free surface of a static meniscus the static liquid bridge free surface between the shaper and the crystal surface occurring in single crystal tube growth. The analysis concerns the dependence of solutions of the equation on a parameter p which represents the controllable part of the pressure difference across the free surface. Inequalities are established for p which are necessary or sufficient conditions for the existence of solutions which represent a stable and convex outer or inner free surfaces of a static meniscus. The analysis is numerically illustrated for the static menisci occurring in silicon tube growth by edge-defined film-fed growth EFGs technique. This kind of inequalities permits the adequate choice of the process parameter p. With this aim this study was undertaken. Copyright 2009 S. Balint and A. 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. 1. Introduction The first successful Si tube growth was reported in 1 . Also a theory of tube growth by . process is developed there to show the dependence .
