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Microcomputer Modeling of Growth Processes of Single-Crystal Sheets and Fibers
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Authors: Thomas F. George (University of Missouri); Liliana Braescu; Agneta M. Balint (West Univ. of Timisoara); Laszlo Nanai (Univ. of Szeged); Stefan Balint (West Univ. of Timisoara) 
Book Description:
Fiber (rod) and sheet-shaped crystals with specified size for use as final products without additional machining are required in various applications of modern engineering. In order to avoid formation of internal mechanical stress in the crystal, lateral surface shaping without contact with container walls is preferred. As the crystal is not restricted by crucible walls, its cross-section is determined by the meniscus-shaping capillary forces and the heat and mass-exchange in the melt-crystal system. Any variation of the pulling rate, pressure, temperature gradient in the furnace, and melt temperature at the meniscus base leads to a change in the crystal cross-section and to pinch formation.

Over the past two decades, many experimental and theoretical studies have been reported on a powerful approach to crystal lateral surface shaping without contact with container walls, namely the so-called edge-defined film-fed growth (EFG) technique. The shape and size of a single crystal grown by EFG is determined by the shape and size of the meniscus, i.e., the liquid bridge retained between the die and the crystal, which depend on the radius or half-thickness of the die and other properties such as pulling rate, pressure, temperature gradient and melt temperature.

In this book, theoretical and numerical results are obtained using a nonlinear mathematical model of the EFG method. Theoretical results presented for fibers and sheets are rigorously obtained on the basis of the equations of the model. Numerical results are obtained on the basis of theoretical results using experimental data. Such results offer a complete package of the possibilities of the model for equipment designers and practical crystal growers.(from the Preface)

Table of Contents:
INTRODUCTION

CHAPTER 1 - MENISCUS EQUATION
1.1 - Meniscus equation for sheets
1.2 - Meniscus equation for fibers
1.3 - Conclusions

CHAPTER 2 - TEMPERATURE DISTRIBUTION AND HEAT FLUX
2.1 - Temperature distribution in the meniscus and in the crystal
2.2 - Heat flux at the interface before the pulling start
2.3. - Heat flux at the interface level after the pulling start at a given rate
2.4 - Conclusions

CHAPTER 3 - DYNAMICS OF THE INTERFACE, HALF-THICKNESS OF THE SHEET AND FIBER RADIUS
3.1 - System of differential equations which governs the evolution of the half-thickness of a sheet and height of the crystallization front
3.2 - Evolution of the fiber radius and height of the crystallization front
3.3 - Stationary states and their asymptotic stability for sheets
3.4 - Stationary states and their asymptotic stability for fibers
3.5 - Stable growth region and growth path of a sheet of given half-thickness
3.6 - Stable growth region and growth path of a fiber of given radius
3.7 - Conclusions

CHAPTER 4 - A CONTROL PROCEDURE FOR THE SHEET HALF-THICKNESS
AND FIBER RADIUS, BASED ON AN ESTIMATION OF THE REGION OF ATTRACTION
4.1 - Procedure to control the sheet half-thickness
4.2 - Procedure to control the fiber radius
4.3 - Conclusions

CHAPTER 5 - MINIMIZATION OF THE SURFACE NON-UNIFORMITY
5.1 - Minimization of the surface non-uniformity for Si sheets
5.2 - Minimization of the surface non-uniformity for Nd:YAG fibers
5.3 - Conclusions

REFERENCES

INDEX

   Binding: Hardcover
   Pub. Date: 2007
   ISBN: 1-60021-230-1
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
  
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Microcomputer Modeling of Growth Processes of Single-Crystal Sheets and Fibers