Validity of Resting Energy Expenditure Predictive Equations before and after an Energy-Restricted Diet Intervention in Obese Women

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Effects of Thermocapillary Convection on the Growth Process in Industrial 8-inch Silicon Czochralski Growth

Czochralski (CZ) crystal growth process is a widely used technique in manufacturing of silicon crystals and other semiconductor materials. The ultimate goal of the IC industry is to have the highest quality substrates, which are free of point defect, impurities and micro defect clusters. The scale up of silicon wafer size from 200 mm to 300 mm requires large crucible size and more heat power. Transport phenomena in crystal growth processes are quite complex due to melt and gas flows that may be oscillatory and/or turbulent, coupled convection and radiation, impurities and dopant distributions, unsteady kinetics of the growth process, melt crystal interface dynamics, free surface and meniscus, stoichiometry in the case of compound materials. A global model has been developed to simulate the temperature distribution and melt flow in an 8-inch system. The present program features the fluid convection, magnetohydrodynamics, and radiation models. A multi-zone method is used to divide the Cz system into different zones, e.g., the melt, the crystal and the hot zone. For calculation of temperature distribution, the whole system inside the stainless chamber is considered. For the convective flow, only the melt is considered. The widely used zonal method divides the surface of the radiation enclosure into a number of zones, which has a uniform distribution of temperature, radiative properties and composition. The integro-differential equations for the radiative heat transfer are solved using the matrix inversion technique. The zonal method for radiative heat transfer is used in the growth chamber, which is confined by crystal surface, melt surface, heat shield, and pull chamber. Free surface and crystal/melt interface are tracked using adaptive grid generation. The competition between the thermocapillary convection induced by non-uniform temperature distributions on the free surface and the forced convection by the rotation of the crystal determines the interface shape, dopant distribution, and striation pattern. The temperature gradients on the free surface are influenced by the effects of the thermocapillary force on the free surface and the rotation of the crystal and the crucible.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

Modeling of Ammonothermal Growth of Gallium Nitride Single Crystals

Ammonothermal growth of GaN crystals with a retrograde solubility has been modeled and simulated here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow in the porous charge is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. For the case of retrograde solubility, the charge is put above the baffle. The temperature difference between the dissolving zone and growth zone is found smaller than that applied on the sidewall of autoclave. The baffle opening has a strong effect on the nutrient transport and supersaturation of GaN species in the growth zone.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Transport Phenomena in Ammonothermal Growth of Gallium Nitride

GaN can be used to fabricate blue/green/UV LEDs and high temperature, high power electronic devices. Ideal substrates are needed for high quality III-nitride epitaxy, which is an essential step for the manufacture of LEDs. GaN substrates are ideal to be lattice matched and isomorphic to nitride-based films. Bulk single crystals of GaN can be grown from supercritical fluids using the ammonothermal method, which utilizes ammonia as fluid rather than water as in the hydrothermal process. In this process, a mineralizer such as amide, imide or azide is used to attack a bulk nitride feedstock at temperatures from 200 - 500癈 and pressures from 1 - 4 kbar. Baffle design is essential for successful growth of GaN crystals. Baffle is used to separate the dissolving zone from the growth zone, and to maintain a temperature difference between the two zones. For solubility curve with a positive coefficient with respect to temperature, the growth zone is maintained at a lower temperature than that in the dissolving zone, thus the nutrient becomes supersaturated in the growth zone. The baffle opening is used to control the mixing of nutrients in the two zones, thus the transfer of nutrient from the lower part to the upper part. Ammonothermal systems have been modeled here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. We investigated the effects of baffle opening and position on the transport phenomena of nutrient from dissolving zone to the growth zone. Simulation data have been compared qualitatively with experimental data.

Basic equations for ferroelectrics

A set of new formula of energy functions for ferroelectrics was proposed, and then the new basic equations were derived in this paper. The finite element formulation based on the new basic equations was improved to avoid the equivalent nodal load produced by remnant polarization. With regard to the fundamentals of mathematics and physics, the new energy functions and basic equations are reasonable for the material element of ferroelectrics in finite element analysis.

Torsion fracture behavior of drawn pearlitic steel wires with different heat treatments

In this paper, torsion fracture behavior of drawn pearlitic steel wires with different heat treatments was investigated. Samples with different heat treatments was investigated. Samples with different heat treatment conditions were subjected to torsion and tensile tests. The shear strain along the torsion sample after fracture was measured. Fracture surface of wires was examined by Scanning Electron Microscopy. In addition, the method of Differential Scanning Calorimetry was used to characterize the thermodynamic process in the heat treatment. A numerical simulation via finite element method on temperature field evolution for the wire during heat treatment process was performed. The results show that both strain aging and recovery process occur in the material within the temperature range between room temperature and 435 degrees C. It was shown that the ductility measured by the number of twists drops at short heating times and recovers after further heating in the lead bath of 435 degrees C. On the other hand, the strenght of the wire increases at short heating times and decreases after further heating. The microstructure inhomogeneity due to short period of heat treatment, coupled with the gradient characteristics of shear deformation during torsion results in localized shear deformation of the wire. In this situation, shear cracks nucleate between lamella and the wire breaks with low number of twists.