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Crystal Growth Process (crystal + growth_process)
Selected AbstractsCombined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growthCRYSTAL RESEARCH AND TECHNOLOGY, Issue 8 2009F. Mokhtari Abstract In order to understand the influence of crucible geometry combined with natural convection and Marangoni convection on melt flow pattern, temperature and pressure fields in silicon Czochralski crystal growth process, a set of numerical simulations was conducted. We carry out calculation enable us to determine temperature, pressure and velocity fields in function of Grashof and Marangoni numbers. The essential results show that the hemispherical geometry of crucible seems to be adapted for the growth of a good quality crystal and the pressure field is strongly affected by natural and Marangoni convection and it is more sensitive than temperature. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1: non-rotating seedCRYSTAL RESEARCH AND TECHNOLOGY, Issue 6 2007M. H. Tavakoli Abstract For the seeding process of oxide Czochralski crystal growth, the flow and temperature field of the system as well as the seed-melt interface shape have been studied numerically using the finite element method. The configuration usually used initially in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and non-rotating seed crystal. At first the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF coil was calculated. Using this heat source the fluid flow and temperature field were determined in the whole system. We have considered two cases with respect to the seed position: (1) before and (2) after seed touch with the melt. It was observed that in the case of no seed rotation (,seed = 0), the flow pattern in the bulk melt consists of a single circulation of a slow moving fluid. In the gas domain, there are different types of flow motion related to different positions of the seed crystal. In the case of touched seed, the seed-melt interface has a deep conic shape towards the melt. It was shown that an active afterheater and its location with respect to the crucible, influences markedly the temperature and flow field of the gas phase in the system and partly in the melt. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Crystal temperature control in the Czochralski crystal growth processAICHE JOURNAL, Issue 1 2001Antonios Armaou This work proposes a control configuration and a nonlinear multivariable model-based feedback controller for the reduction of thermal gradients inside the crystal in the Czochralski crystal growth process after the crystal radius has reached its final value. Initially, a mathematical model which describes the evolution of the temperature inside the crystal in the radial and axial directions and accounts for radiative heat exchange between the crystal and its surroundings and motion of the crystal boundary is derived from first principles. This model is numericully solved using Galerkin's method and the behaviour of the crystal temperature is studied to obtain valuable insights which lead to the precise formulation of the control problem, the design of a new control configuration for the reduction of thermal gradients inside the crystal and the derivation of a simplified 1-D in a space dynamic model. Then, a model reduction procedure for partial differential equation systems with time-dependent spatial domains (Armaou and Christofides, 1999) based on a combination of Galerkin's method with approximate inertial manifolds is used to construct a fourth-order model that describes the dominant thermal dynamics of the Czochralski process. This low-order model is employed for the synthesis of a fourth-order nonlinear multivariable controller that can be readily implemented in practice. The proposed control scheme is successfully implemented on a Czochralski process used to produce a 0.7 m long silicon crystal with a radius of 0.05 m and is shown to significantly reduce the axial and radial thermal gradients inside the crystal. The robustness of the proposed controller with respect to model uncertainty is demonstrated through simulations. [source] Preparation and characterization of poly(butylene terephthalate)/poly(ethylene terephthalate) copolymers via solid-state and melt polymerizationJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 5 2007M. A. G. Jansen Abstract To increase the Tg in combination with a retained crystallization rate, bis(2-hydroxyethyl)terephthalate (BHET) was incorporated into poly(butylene terephthalate) (PBT) via solid-state copolymerization (SSP). The incorporated BHET fraction depends on the miscibility of BHET in the amorphous phase of PBT prior to SSP. DSC measurements showed that BHET is only partially miscible. During SSP, the miscible BHET fraction reacts via transesterification reactions with the mobile amorphous PBT segments. The immiscible BHET fraction reacts by self-condensation, resulting in the formation of poly(ethylene terephthalate) (PET) homopolymer. 1H-NMR sequence distribution analysis showed that self-condensation of BHET proceeded faster than the transesterification with PBT. SAXS measurements showed an increase in the long period with increasing fraction BHET present in the mixtures used for SSP followed by a decrease due to the formation of small PET crystals. DSC confirmed the presence of separate PET crystals. Furthermore, the incorporation of BHET via SSP resulted in PBT-PET copolymers with an increased Tg compared to PBT. However, these copolymers showed a poorer crystallization behavior. The modified copolymer chain segments are apparently fully miscible with the unmodified PBT chains in the molten state. Consequently, the crystal growth process is retarded resulting in a decreased crystallization rate and crystallinity. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 882,899, 2007. [source] Kinetic Model for Crystallization in White Ceramic GlazesJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 1 2001Agustin Escardino Theoretical equations have been developed for crystal growth rate in layers of small frit (glass) particles during firing. Throughout the process, the crystalline and the glassy phases have different compositions; therefore, the system can be considered a pseudo-two-component system consisting of a crystallizable component (structural unit) and a noncrystallizable mixture of several components. The concentration of the crystallizable component decreases in the residual glassy phase during the crystal growth process, on integrating at the surfaces of crystals having the same composition. Throughout the crystal growth process, a concentration gradient of the crystallizable component is therefore produced in the glassy phase, which results in mass transport by diffusion of this component from the bulk residual glassy phase to the surfaces of the crystals. Equations have been derived assuming that the diffusion step of the crystallizable component through the residual glassy phase is the overall crystal growth process rate-controlling step. [source] A stochastic formulation for the description of the crystal size distribution in antisolvent crystallization processesAICHE JOURNAL, Issue 8 2010M. Grosso Abstract A stochastic approach to describe the crystal size distribution dynamics in antisolvent based crystal growth processes is here introduced. Fluctuations in the process dynamics are taken into account by embedding a deterministic model into a Fokker-Planck equation, which describes the evolution in time of the particle size distribution. The deterministic model used in this application is based on the logistic model, which shows to be adequate to suit the dynamics characteristic of the growth process. Validations against experimental data are presented for the NaCl,water,ethanol antisolvent crystallization system in a bench-scale fed-batch crystallization unit. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] | ||||||||||