Nonequilibrium statistical mechanics of one-dimensional turbulence

The method of statistical mechanics is applied to the study of the one-dimensional model of turbulence proposed in an earlier paper. The closure problem is solved by the variational approach which has been developed for the three-dimensional case, yielding two integral equations for two unknown functions. By solving the two integral equations, the Kolmogorov k−5/3 law is derived and the (one-dimensional) Kolmogorov constant Ko is evaluated, obtaining Ko=0.55, which is in good agreement with the result of numerical experiments on one-dimensional turbulence.

Numerical Simulation of Heat Transfer and Kinetics in the Bulk Growth of Silicon Carbide

The growth process of 2-inch silicon carbide (SiC) single crystals by the physical vapor transport method (or modified Lely method) has been modeled and simulated. The comprehensive process model incorporates the calculations of radio frequency (RF) induction heating, heat and mass transfer and growth kinetics. The transport equations for electromagnetic field, heat transfer, and species transport are solved using a finite volume-based numerical scheme called MASTRAPP (Multizone Adaptive Scheme for Transport and Phase Change Process). Temperature distribution for a 2-inch growth system is calculated, and the effects of induction heating frequency and current on the temperature distribution and growth rate are investigated. The predicted results have been compared with the experimental data.

3D Finite Volume Scheme for Czochralski Crystal Growth

A general three-dimensional model is developed for simulation of the growth process of silicon single crystals by Czochralski technique. The numerical scheme is based on the curvilinear non-orthogonal finite volume discretization. Numerical solutions show that the flow and temperature fields in the melt are asymmetric and unsteady for 8’’ silicon growth. The effects of rotation of crystal on the flow structure are studied. The rotation of crystal forms the Ekman layer in which the temperature gradient along solid/melt surface is small.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

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.

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 Simulation of the Flow Field and Concentration Distribution in the Bulk Growth of Silicon Carbide Crystals

The physical vapor transport (PVT) method is being widely used to grow large-size single SiC crystals. The growth process is associated with heat and mass transport in the growth chamber, chemical reactions among multiple species as well as phase change at the crystal/gas interface. The current paper aims at studying and verifying the transport mechanism and growth kinetics model by demonstrating the flow field and species concentration distribution in the growth system. We have developed a coupled model, which takes into account the mass transport and growth kinetics. Numerical simulation is carried out by employing an in-house developed software based on finite volume method. The results calculated are in good agreement with the experimental observation.

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.

Phi 140 mm sapphire crystal growth by temperature gradient techniques and its color centers

Sapphire crystals, 140 mm in diameter and 90 turn in height, have been grown by temperature gradient techniques (TGT). The growth direction of the boule was fixed by means of Lane X-ray diffraction. A prominent 204 nm absorption band in TGT-Al2O3. which does not appear in single crystals grown by Czochralski method has been studied. Analysis further substantiates the F-center model of this band. Two relatively weaker bands absorbing at 232 nm and 254 nm were ascribed to F+ centers. F-type centers concentration was determined using Smakula's equation. (c) 2005 Elsevier B.V. All rights reserved.

Optimization of thermal environment during crystal growth of large-sized Nd : YAG by Temperature Gradient Technique

A finite-element model is employed to analysis the thermal environments in Temperature Gradient Technique (TGT) furnace during the growth of large-sized Nd:YAG crystal. The obtained results show that when the crucible is located at the lower position inside of the heater, a flatter solid-liquid interface is established, which makes it easier to obtain the core-free Nd:YAG crystal. Meanwhile, the lower crucible position can induce higher axial temperature gradient, which is beneficial to the release of latent heat. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bulk crystal growth and efficient diode-pumped laser performance of Yb 3+:Sc2SiO5

A bulk crystal of Yb:Sc2SiO5 (Yb:SSO) with favorable thermal properties was successfully obtained by the Czochralski method. The energy level diagrams for Yb:SSO crystal were determined by optical spectroscopic analysis and semi-empirical crystal-field calculations using the simple overlap model. The full width at half maximum of the absorption band centering at 976 nm was calculated to be 24 nm with a peak absorption cross-section of 9.2x10(-21) cm(2). The largest ground-state splitting of Yb3+ ions is up to 1027 cm(-1) in a SSO crystal host. Efficient diode-pumped laser performance of Yb:SSO was primarily demonstrated with a slope efficiency of 45% and output power of 3.55 W.

Pseudogenization of the tumor-growth promoter angiogenin in a leaf-eating monkey

Physiological functions of human genes may be studied by gene-knockout experiments in model organisms such as the mouse. This strategy relies on the existence of one-to-one gene orthology between the human and mouse. When lineage-specific gene duplication occurs and paralogous genes share a certain degree of functional redundancy, knockout mice may not provide accurate functional information on human genes. Angiogenin is a small protein that stimulates blood-vessel growth and promotes tumor development. Humans and related primates only have one angiogenin gene, while mice have three paralogous genes. This makes it difficult to generate angiogenin-knockout mice and even more difficult to interpret the genotype-phenotype relation from such animals should they be generated. We here show that in the douc langur (Pygathrix nemaeus), an Asian leaf-eating colobine monkey, the single-copy angiogenin gene has a one-nucleotide deletion in the sixth codon of the mature peptide, generating a premature stop codon. This nucleotide deletion is found in five unrelated individuals sequenced, and therefore is likely to have been fixed in the species. Five colobine species that are closely related to the douc langur have intact angiogenin genes, suggesting that the pseudogenization event was recent and unique to the douc langur lineage. This natural knockout experiment suggests that primate angiogenin is dispensable even in the wild. Further physiological studies of douc largurs may offer additional information on the role of this cancer-related gene in normal physiology of primates, including humans. Our findings also provide a strong case for the importance of evolutionary analysis in biomedical studies of gene functions. (C) 2003 Elsevier Science B.V. All rights reserved.

Age structure, growth and mortality estimates of an endemic Ptychobarbus dipogon (Regan, 1905) (Cyprinidae: Schizothoracinae) in the Lhasa River, Tibet

Ptychobarbus dipogon is an endemic fish in the Yarlung Tsangpo River, but its biology is poorly known. We sampled 582 specimens (total length, TL, between 70.6 and 593.0 mm) from April 2004 to August 2006 in the Lhasa River, Tibet. We estimated ages based on the counts of alternating opaque and translucent zones (annuli) in thin transverse sections of lapilli otoliths. Ages ranged from 1(+) to 23(+) years for males and 1(+) to 44(+) for females. The observed 44(+) years was the oldest reported for schizothoracine fishes. Females attained a larger size than males. The TL weight relationship was W=7.12 x 10(-6)TL(3.006) for combined sexes. The growth parameters fitted von Bertalanffy growth functions were L-infinity = 598.66 mm, k=0.0898 year(-1), t(0)=-0.7261 year and W-infinity = 1585.38 g for females and L-infinity = 494.23mm, k=0.1197 year(-1), t(0)=-0.7296 year and W-infinity = 904.88g for males. The longevities of 32.7 year for females and 24.3 year for males were similar to the observed ages. Using an empirical model we estimated the instantaneous rate of total mortality (Z) at 0.28 per year in the lower reaches. Z in the upper and middle stocks was close to the M because of unexploited or lightly exploited stock. Protracted longevity, slow growth, low natural mortality and large body size were typical characteristics of P. dipogon. The current declining trend of P. dipogon could be prevented by altering fishing regulations.

The Essential Role of Endogenous Ghrelin in Growth Hormone Expression during Zebrafish Adenohypophysis Development

Ghrelin, a multifunctional hormone, including potent GH stimulation activity, has been suggested to be important during embryonic development. Expression of ghrelin has been confirmed in the zebrafish pancreas during embryonic stages. Interfering with ghrelin function using two specific antisense morpholino oligonucleotides causes defects during zebrafish embryonic development. In ghrelin morphants the expression of GH was abolished in zebrafish somatotropes, whereas the expression patterns of the other key molecules involved in hypothalamic-pituitary development and distinct pituitary hormones genes remain largely intact at the appropriate time during zebrafish adenohypophysis development. Effective rescue of the ghrelin morphants with exogenous ghrelin mRNA showed that the correct gene had been targeted. Moreover, by analyzing the efficiencies of the ghrelin morphants rescue experiments with various forms of exogenous mutant ghrelin mRNAs, we also demonstrated the essentiality of the form acyl-ghrelin on GH stimulation during zebrafish adenohypophysis development. Our in vivo experiments, for the first time, also provided evidence of the existence of functional obestatin in the C-terminal part of zebrafish proghrelin peptides. Our research here has demonstrated that zebrafish is a unique model for functional studies of endogenous ghrelin, especially during embryonic development. (Endocrinology 150: 2767-2774, 2009)

Effects of ammonium on growth, nitrogen and carbohydrate metabolism of Potamogeton maackianus A. Benn

Growth, nitrogen and carbohydrate metabolism in relation to eutrophication were studied for a submerged plant Potamogeton maackianus, a species common in East Asian shallow lakes. The plants were grown in six NH4+-N concentrations (0.05, 0.50, 1.00, 3.50, 5.00 and 10.00 mg/L) for six days. NH4+-N levels in excess of 0.50 mg/L inhibited the plant growth. The relationships between external NH4+-N availability and total nitrogen (TN), protein-N, free amino acid-N (FAA-N) and NH4+-N in plant tissues, respectively, conformed to a logarithmic model suggesting that a feedback inhibition mechanism may exist for ammonium uptake. The response of starch to NH4+-N was fitted with a negative, logarithmic curve. Detailed analysis revealed that the influx NH4+-N had been efficiently incorporated into organic-N and eventually stored as protein at the expense of starch accumulation. These data suggest that this species may be able to tolerate high levels of ammonium when dissolved oxygen is sufficient.