Concentration distribution in solution crystal growth: effect of moving interface conditions

The linear diffusion-reaction theory with finite interface kinetics is employed to describe the dissolution and the growth processes. The results show that it is imperative to consider the effect of the moving interfaces on the concentration distribution at the growth interface for some cases. For small aspect ratio and small gravity magnitude, the dissolution and the growth interfaces must be treated as the moving boundaries within an angle range of 0 degrees < gamma < 50 degrees in this work. For large aspect ratio or large gravity magnitude, the effect of the moving interfaces on the concentration distribution at the growth interface can be neglected except for gamma < - 50 degrees.

The convection during NaClO3 crystal growth observed by the phase shift interferometer

An optical diagnostic system consisting of the Mach-Zehnder interferometer with the phase shift device and an image processor has been developed for the study of the kinetics of the crystal growing process. The dissolution and crystallization process of NaClO3 crystal has been investigated. The concentration distributions around a growing and dissolving crystal have been obtained by using phase-shift of four-steps theory for the interpretation of the interferograms. The convection (a plume flow) has been visualized and analyzed in the process of the crystal growth. The experiment demonstrates that the buoyancy convection dominates the growth rate of the crystal growing face on the ground-based experiment.

Progress In Modeling Of Fluid Flows In Crystal Growth Processes

Modeling of fluid flows in crystal growth processes has become an important research area in theoretical and applied mechanics. Most crystal growth processes involve fluid flows, such as flows in the melt, solution or vapor. Theoretical modeling has played an important role in developing technologies used for growing semiconductor crystals for high performance electronic and optoelectronic devices. The application of devices requires large diameter crystals with a high degree of crystallographic perfection, low defect density and uniform dopant distribution. In this article, the flow models developed in modeling of the crystal growth processes such as Czochralski, ammonothermal and physical vapor transport methods are reviewed. In the Czochralski growth modeling, the flow models for thermocapillary flow, turbulent flow and MHD flow have been developed. In the ammonothermal growth modeling, the buoyancy and porous media flow models have been developed based on a single-domain and continuum approach for the composite fluid-porous layer systems. In the physical vapor transport growth modeling, the Stefan flow model has been proposed based on the flow-kinetics theory for the vapor growth. In addition, perspectives for future studies on crystal growth modeling are proposed. (c) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

Growth Mechanism And Joint Structure Of Zno Tetrapods

Regular zinc oxide (ZnO) tetrapods with a flat plane have been obtained on Si(1 0 0) substrate via the chemical vapour deposition approach. The x-ray diffraction result suggests that these tetrapods are all single crystals with a wurtzite structure that grow along the (0 0 0 1) direction and corresponding electron backscatter diffraction analysis reveals the crystal orientation of growth and exposed surface. Furthermore, we find some ZnO tetrapods with some legs off and the angles between every two legs are measured with the aid of scanning electron microscopy and image analysis, which benefit to reveal the structure of ZnO tetrapods joint. The structure model and growth mechanism of ZnO tetrapods are proposed. Besides, the stable model of the interface was obtained through the density-functional theory calculation and the energy needed to break the twin plane junction was calculated as 5.651 J m(-2).

Diffusion dominated process for the crystal growth of a binary alloy

The pure diffusion process has been often used to study the crystal growth of a binary alloy in the microgravity environment. In the present paper, a geometric parameter, the ratio of the maximum deviation distance of curved solidification and melting interfaces from the plane to the radius of the crystal rod, was adopted as a small parameter, and the analytical solution was obtained based on the perturbation theory. The radial segregation of a diffusion dominated process was obtained for cases of arbitrary Peclet number in a region of finite extension with both a curved solidification interface and a curved melting interface. Two types of boundary conditions at the melting interface were analyzed. Some special cases such as infinite extension in the longitudinal direction and special range of Peclet number were reduced from the general solution and discussed in detail.

The asymptotic near-tip solution for mode-iii crack in steady growth in power hardening media

Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.

Grain growth in protoplanetary disks

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process.

As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

Logarithmic Potential Theory on Riemann Surfaces

We develop a logarithmic potential theory on Riemann surfaces which generalizes logarithmic potential theory on the complex plane. We show the existence of an equilibrium measure and examine its structure. This leads to a formula for the structure of the equilibrium measure which is new even in the plane. We then use our results to study quadrature domains, Laplacian growth, and Coulomb gas ensembles on Riemann surfaces. We prove that the complement of the support of the equilibrium measure satisfies a quadrature identity. Furthermore, our setup allows us to naturally realize weak solutions of Laplacian growth (for a general time-dependent source) as an evolution of the support of equilibrium measures. When applied to the Riemann sphere this approach unifies the known methods for generating interior and exterior Laplacian growth. We later narrow our focus to a special class of quadrature domains which we call Algebraic Quadrature Domains. We show that many of the properties of quadrature domains generalize to this setting. In particular, the boundary of an Algebraic Quadrature Domain is the inverse image of a planar algebraic curve under a meromorphic function. This makes the study of the topology of Algebraic Quadrature Domains an interesting problem. We briefly investigate this problem and then narrow our focus to the study of the topology of classical quadrature domains. We extend the results of Lee and Makarov and prove (for n ≥ 3) c ≤ 5n-5, where c and n denote the connectivity and degree of a (classical) quadrature domain. At the same time we obtain a new upper bound on the number of isolated points of the algebraic curve corresponding to the boundary and thus a new upper bound on the number of special points. In the final chapter we study Coulomb gas ensembles on Riemann surfaces.

From organism to population: the role of life-history theory

The role of life-history theory in population and evolutionary analyses is outlined. In both cases general life histories can be analysed, but simpler life histories need fewer parameters for their description. The simplest case, of semelparous (breed-once-then-die) organisms, needs only three parameters: somatic growth rate, mortality rate and fecundity. This case is analysed in detail. If fecundity is fixed, population growth rate can be calculated direct from mortality rate and somatic growth rate, and isoclines on which population growth rate is constant can be drawn in a ”state space” with axes for mortality rate and somatic growth rate. In this space density-dependence is likely to result in a population trajectory from low density, when mortality rate is low and somatic growth rate is high and the population increases (positive population growth rate) to high density, after which the process reverses to return to low density. Possible effects of pollution on this system are discussed. The state-space approach allows direct population analysis of the twin effects of pollution and density on population growth rate. Evolutionary analysis uses related methods to identify likely evolutionary outcomes when an organism's genetic options are subject to trade-offs. The trade-off considered here is between somatic growth rate and mortality rate. Such a trade-off could arise because of an energy allocation trade-off if resources spent on personal defence (reducing mortality rate) are not available for somatic growth rate. The evolutionary implications of pollution acting on such a trade-off are outlined.

Growth and its spectroscopic properties of Sm : YAP crystal

Sm3+-doped yttrium aluminum perovskite (YAP) single crystal was grown by Czochralski (CZ) method. The absorption and fluorescence spectra along the crystallographic axis b were measured at room temperature. Judd-Ofelt theory was used to calculate the intensity parameters (Omega(t)), the spontaneous emission probability, the branching ratio and the radiative lifetime of the state (4)G(5/2). The peak emission cross-sections were also estimated at 567, 607, and 648 nm wavelengths. (c) 2006 Elsevier B.V. All rights reserved.

Growth and spectral properties of Er:Gd2SiO5 crystal

Er3+ -doped Gd2SiO5 (Er:GSO) single crystal with dimensions of circle divide 35 x 40 mm(3) has been grown by the Czochralski method. The absorption and fluorescence spectra of the Er:GSO crystal were measured at room temperature. The spectral parameters were calculated based on Judd-Ofelt theory, and the intensity parameters Omega(2), Omega(4) and Omega 6 are obtained to be 6.168 x 10(-20), 1.878 x 10(-20), and 1.255 x 10(-20) cm(2), respectively. The emission cross-section has been calculated by Fuechtbauer-Ladenbury formula. (c) 2007 Elsevier B.V. All rights reserved.

Crystal growth and spectral properties of Sm:GdVO4

The 2 at.% Sm:GdVO4 crystal was grown by the Czochralski method. The segregation coefficient of Sm3+ ion in this crystal is 0.98. The crystal structure of the Sm:GdVO4 crystal was determined by X-ray diffraction analysis. Judd-Ofelt theory was used to calculate the intensity parameters (Omega(i)), the spontaneous emission probability, the luminary branching ratio and the radiative lifetime of the state (4)G(5/2). The stimulated emission cross-sections at 567, 604 and 646 nm are calculated to be 5.92 x 10(-21), 7.62 x 10(-21) and 5.88 x 10(-21) cm(2), respectively. The emission cross-section at 604 nm is 4.4 times lager than that in Sm: YAP at 607 nm. (C) 2007 Elsevier B.V. All rights reserved.

On the growth and form of the gut.

The developing vertebrate gut tube forms a reproducible looped pattern as it grows into the body cavity. Here we use developmental experiments to eliminate alternative models and show that gut looping morphogenesis is driven by the homogeneous and isotropic forces that arise from the relative growth between the gut tube and the anchoring dorsal mesenteric sheet, tissues that grow at different rates. A simple physical mimic, using a differentially strained composite of a pliable rubber tube and a soft latex sheet is consistent with this mechanism and produces similar patterns. We devise a mathematical theory and a computational model for the number, size and shape of intestinal loops based solely on the measurable geometry, elasticity and relative growth of the tissues. The predictions of our theory are quantitatively consistent with observations of intestinal loops at different stages of development in the chick embryo. Our model also accounts for the qualitative and quantitative variation in the distinct gut looping patterns seen in a variety of species including quail, finch and mouse, illuminating how the simple macroscopic mechanics of differential growth drives the morphology of the developing gut.

Fluid-structure interaction with mean flow: Over-scattering and unstable resonance growth

It is known theoretically [1-3] that infinitely long fluid loaded plates in mean flow exhibit a range of unusual phenomena in the 'long time' limit. These include convective instability, absolute instability and negative energy waves which are destabilized by dissipation. However, structures are necessarily of finite length and may have discontinuities. Moreover, linear instability waves can only grow over a limited number of cycles before non-linear effects become dominant. We have undertaken an analytical and computational study to investigate the response of finite, discontinuous plates to ascertain if these unusual effects might be realized in practice. Analytically, we take a "wave scattering" [2,4] - as opposed to a "modal superposition" [5] - view of the fluttering plate problem. First, we solve for the scattering coefficients of localized plate discontinuities and identify a range of parameter space, well outside the convective instability regime, where over-scattering or amplified reflection/transmission occurs. These are scattering processes that draw energy from the mean flow into the plate. Next, we use the Wiener-Hopf technique to solve for the scattering coefficients from the leading and trailing edges of a baffled plate. Finally, we construct the response of a finite, baffled plate by a superposition of infinite plate propagating waves continuously scattering off the plate ends and solve for the unstable resonance frequencies and temporal growth rates for long plates. We present a comparison between our computational results and the infinite plate theory. In particular, the resonance response of a moderately sized plate is shown to be in excellent agreement with our long plate analytical predictions. Copyright © 2010 by ASME.

Au@Si-n: Growth behavior, stability and electronic structure

The configurations, stability, and electronic structure of AuSin (n = 1-16) clusters have been investigated within the framework of the density functional theory at the B3PW91/LanL2DZ and PW91/DNP levels. The results show that the Au atom begins to occupy the interior site for cages as small as Si-11 and for Si-12 the Au atom completely falls into the interior site forming Au@Si-12 cage. A relatively large embedding energy and small HOMO-LUMO gap are also found for this Au@Si-12 structure indicating enhanced chemical activity and good electronic transfer properties. All these make Au@Si-12 attractive for cluster-assembled materials.