Optimal control of 3D state-constrained induction heating problems with nonlocal radiation effects

The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditions for an associated optimal control problem are established

Optimal control of 3D state constrained induction heating problems with nonlocal radiation effects

The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditions for an associated optimal control problem are established

Analysis and feedback control of the scanning laser epitaxy process applied to nickel-base superalloys

Scanning Laser Epitaxy (SLE) is a new layer-by-layer additive manufacturing process being developed in the Direct Digital Manufacturing Laboratory at Georgia Tech. SLE allows for the fabrication of three-dimensional objects with specified microstructure through the controlled melting and re-solidification of a metal powder placed atop a base substrate. This dissertation discusses the work done to date on assessing the feasibility of using SLE to both repair single crystal (SX) turbine airfoils and manufacture functionally graded turbine components. Current processes such as selective laser melting (SLM) are not able to create structures with defined microstructure and often have issues with warping of underlying layers due to the high temperature gradients present when scanning a high power laser beam. Additionally, other methods of repair and buildup have typically been plagued by crack formation, equiaxed grains, stray grains, and grain multiplication that can occur when dendrite arms are separated from their main dendrites due to remelting. In this work, it is shown that the SLE process is capable of creating fully dense, crack-free equiaxed, directionally-solidified, and SX structures. The SLE process, though, is found to be currently constrained by the cumbersome method of choosing proper parameters and a relative lack of repeatability. Therefore, it is hypothesized that a real-time feedback control scheme based upon a robust offline model will be necessary both to create specified defect-free microstructures and to improve the repeatability of the process enough to allow for multi-layer growth. The proposed control schemes are based upon temperature data feedback provided at high frame rate by a thermal imaging camera. This data is used in both PID and model reference adaptive control (MRAC) schemes and drives the melt pool temperature during processing towards a reference melt pool temperature that has been found to give a desired microstructure in the robust offline model of the process. The real-time control schemes will enable the ground breaking capabilities of the SLE process to create engine-ready net shape turbine components from raw powder material.Ph.D

Multi-impurity adsorption model for modeling crystal purity and shape evolution during crystallization processes in impure media

ACKNOWLEDGMENTS Financial support provided by the European Research Council Grant No. [280106-CrySys] is gratefully acknowledged.Peer reviewe

Electricity from photovoltaic solar cells: Flat-Plate Solar Array Project final Report. Volume III: Silicon sheet: wafers and ribbons

The Flat-Plate Solar Array (FSA) Project, funded by the U.S. Government and managed by the Jet Propulsion Laboratory, was formed in 1975 to develop the module/array technology needed to attain widespread terrestrial use of photovoltaics by 1985. To accomplish this, the FSA Project established and managed an Industry, University, and Federal Government Team to perform the needed research and development. The primary objective of the Silicon Sheet Task of the FSA Project was the development of one or more low-cost technologies for producing silicon sheet suitable for processing into cost-eompetitive solar cells. Silicon sheet refers to high-purity crystalline silicon of size and thickness for fabrication into solar cells. The Task effort began with state-of-the-art sheet technologies and then solicited and supported any new silicon sheet alternatives that had the potential to achieve the Project goals. A total of 48 contracts were awarded that covered work in the areas of ingot growth and casting, wafering, ribbon growth, other sheet technologies, and programs of supportive research. Periodic reviews of each sheet technology were held, assessing the technical progress and the long-range potential. Technologies that failed to achieve their promise, or seemed to have lower probabilities for success in comparison with others, were dropped. A series of workshops was initiated to assess the state of the art, to provide insights into problems remaining to be addressed, and to support technology transfer. The Task made and fostered significant improvements in silicon sheet including processing of both ingot and ribbon technologies. An additional important outcome was the vastly improved understanding of the characteristics associated with high-quality sheet, and the control of the parameters required for higher efficiency solar cells. Although significant sheet cost reductions were made, the technology advancements required to meet the Task cost goals were not achieved. This FSA Final Report (JPL Publication 86-31, 5101-289, DOE/JPL 1012-125, October 1986) is composed of eight volumes, consisting of an Executive Summary and seven technology reports: Volume I: Executive Summary. Volume II: Silicon Material. Volume III: Silicon Sheet: Wafers and Ribbons Volume IV: High-Efficiency Solar Celis. Volume V: Process Development. Volume VI: Engineering Sciences and Reliability. Volume VII: Module Encapsulation. Volume VIII: Project Analysis and Integration. Two supplemental reports included in the final report package are: FSA Project: 10 Years of Progress, JPL Document 400-279. 5101-279, October 1985. Summary of FSA Project Documentation: Abstracts of Published Documents, 1975 to 1986, JPL Publication 82-79 (Revision 1),5101-221, DOE/JPL-1 012-76, September 1986

Analysis and Control of Microstructure in Binary Alloys

When metallic alloys solidify, various microstructures form inside the alloys. Most solidified alloys have a polycrystalline structure, which is an assembly of crystalline grains with boundaries between any two grains. Each grain is a single crystal with a unique crystalline orientation. Many physical properties of polycrystalline alloys are determined by the arrangement of these grains and grain boundaries. During solidification of a single crystal, microstructures with even smaller microscopic lengthscales form, such as dendritic and eutectic structures. The physical properties of single crystal alloys are largely influenced by the lengthscales of these structures. Therefore, the understanding and control of microstructure formation in solidification is important in order to achieve desired properties. Microstructures form while the system is not in equilibrium. What microstructures form is not based on minimization of free energy of the system, but depends on the dynamics of the solidification process, which is the focus of our study. We used an alloy model system, Succinonitrile-Coumarin152, to experimentally investigate dynamic selection and control of grain boundary structures and dendritic structures in binary alloys. We found that in a temperature gradient the grain boundaries drift toward the high temperature region in addition to the migration due to grain coarsening. We show how we can control grain boundary orientations by generating local temperature gradient through UV or laser heatings. We show that perturbations also permit accurate control of the microstructure within a single crystal during the directional solidification process. Dendritic patterns can be controlled either by guiding the initial formation of the pattern or by triggering subcritical transitions between stable microstructures. We also investigated the role of surface tension anisotropy on the stability of cellular/dendritic arrays using three crystals of different growth orientations with respect to the surface tension anisotropy. We found that the surface tension anisotropy affects the spacing between dendrites and stability via the surface tension perpendicular to the growth direction

Continuum Theory of Polymer Crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with $G \sim \exp(1/T \Delta T)$, where $G$ is the growth rate and $\Delta T$ is the super-cooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with $G \sim \Delta T$, for small $\Delta T$. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.Comment: 37 double-spaced pages including 8 figures, submitted to the Journal of Chemical Physic