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 Ribbon Growth by Edge-Defined Film-Fed Growth Technique | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 381604 14 pages doi 2008 381604 Research Article Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique Stefan Balint1 and Agneta M. Balint2 1 Computer Science Department West University of Timisoara Bulv. 4 300223 Timisoara Romania 2 Faculty of Physics West University of Timisoara Bulv. 4 300223 Timisoara Romania Correspondence should be addressed to Agneta M. Balint balint@ Received 24 July 2007 Revised 26 November 2007 Accepted 16 February 2008 Recommended by Kok Teo A second-order nonlinear differential equation of which some solutions describe the static meniscus free surface the static liquid bridge free surface between the shaper and the crystal surface occurring in single crystal ribbon growth is analyzed. The analysis is focusing on the dependence of the solutions of the equation on the pressure difference p across the free surface. Inequalities are deduced for p which are necessary or sufficient conditions for the stable and convex free surface of a static meniscus. The obtained results are numerically illustrated in the case of a silicon single crystal ribbon growth. The advantage of these kinds of inequalities is that from them special results can be gleaned concerning the experiment planning and technology design. With this aim this study was undertaken. Copyright 2008 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 According to 1 modern engineering needs crystals with prescribed shapes and sizes ribbon- rod- and tube-shaped crystals that allow one to use them as final products without additional machining. Therefore crystals of specified sizes and shapes are required to be grown from
