Numerical study to investigate the effect of partition block and ambient air temperature on interfacial heat transfer in liquid bridges of high Prandtl number fluid

Surface heat transfer at the liquid–air interface in liquid bridges of high Prandtl number fluid is known to affect the transitional characteristics appreciably. The heat transfer characteristics under microgravity conditions become much different from those of normal gravity mainly due to the absence of natural convection. The present study deals with numerical computations of flow and heat transfer characteristics in the liquid and surrounding air and also at the liquid–air interface of thermocapillary flow in liquid bridges of high Prandtl number fluid. The governing equations are solved in the coupled domain of the liquid bridge and the surrounding air with the help of available commercial CFD software. The results obtained for a range of Marangoni numbers indicate that by placing a partition block in the air region under normal gravity conditions, the surface heat transfer characteristics of microgravity conditions could be effectively mimicked. The effect of ambient temperature on the surface heat transfer has also been investigated and it has been found that the behavior of heat transfer at the interface changes from heat loss to heat gain when the ambient temperature is increased. Moreover, the presence of partition block under normal gravity suppresses surface heat loss as well as surface heat gain similar to microgravity conditions. Streamlines and temperature contours have been presented for various conditions in order to clarify the underlying physics more meaningfully. The computed profiles for velocity and temperature at the liquid–air interface have been validated against established experimental results.     

Control of multi-zone resistive heater in low temperature gradient BGO Czochralski growth with a weighing feedback,based on the global dynamic heat transfer model

The global heat transfer in a crystallization setup has been optimized to develop a strategy of control over a three-zone heater in the BGO Czochralski process, in order to provide invariable thermal conditions near the solid–liquid interface in the stage of a constant-diameter crystal growth. The functional related to the exactness of the heat balance condition at the crystallization front, i.e., the Stefan problem, was chosen as the target function. The optimization yielded unexpected results. The temperature of the lower heater should be lowered, relative to that of the middle heater, with increasing crystal length, whereas the temperature of the upper heater is to be raised. These recommendations were incorporated into a dynamic model of the oxide Czochralski process with a weighing control and into the control loop of the temperature regulators of a crystallization setup. A comparison of results of the time-dependent simulation with the real growth process confirmed that the new control strategy minimizes the deviation of the solid–liquid interface from the prescribed one, significantly decreases variations of interface shape during the process, and enables growth of high-quality crystals.     

Solutal convection around growing protein crystals and diffusional purification in Space

Convective and diffusional mass transport to an isolated crystal growing from solution, with slow linear interface kinetics, is considered analytically as a generic scaling model. We focus on the interface kinetics which is slow as compared to the diffusion mass transport which is typical of protein crystal growth. Independently, full-scale numerical solutions of transport equations around a cylindrical crystal, at the center of the bottom of a cylindrical cell filled with the solution, are found. The two approaches give results that agree over a wide range of parameters, providing dimensionless relationships that allow predictions of the contribution of convection and diffusion to mass transport. Requirements for microgravity level in Space experiments to achieve diffusional mass transport are estimated on the basis of these relationships. Coefficients of impurity distribution between a growing crystal and its solution, under the influences of convection and diffusion around the crystal, were numerically evaluated as functions of time. The results provide further support for the hypothesis concerning the role of the impurity depletion zone in the purification of a growing crystal. They also reveal that in general, the impurity distribution within the crystal is not homogeneous due to convection. The effects of various factors on growth kinetics and crystal purity are considered.     

Numerical simulation of a new SiC growth system by the dual-directional sublimation method

A new SiC growth system using the dual-directional sublimation method was investigated in this study. Induction heating and thermal conditions were computed and analyzed by using a global simulation model, and then the values of growth rate and shear stress in a growing crystal were calculated and compared with those in a conventional system. The results showed that the growth rate of SiC single crystals can be increased by twofold by using the dual-directional sublimation method with little increase in electrical power consumption and that thermal stresses can be reduced due to no constraint of the crucible lid and low temperature gradient in crystals.     

Expansion ratio dependence of lattice vibration of GaN using ab initio molecular dynamics calculations

Temperature dependence of Raman shift wavenumbers are important for the measurements of heat distribution of high-power GaN devices. In this study, calculated results of vibrational modes of ground state structure and some expanded structures of wurtzite type gallium nitride were presented using ab initio molecular dynamic (AIMD) simulations. Frequency analyses have been done for these calculated results and compared with the experimental results of temperature dependence of Raman spectra. Good agreement was achieved between the calculated and the experimental results quantitatively. AIMD would be a useful tool for the prediction of vibrating analysis for III-N systems.     

Computer simulation, thermodynamic and microstructural studies of benzamide–benzoic acid eutectic system

Phase diagram of benzamide–benzoic acid system has been studied by the thaw–melt method. Linear velocities of crystallization of the components and the eutectic mixture were determined at different undercoolings. Values of the heat of fusion were obtained from DSC studies. Excess Gibbs free energy, excess enthalpy and excess entropy of mixing were calculated. In order to know the nature of interaction between the two components, FT-IR spectral analyses were done. In addition to these studies, computer simulation has been done to obtain an idea about the interaction energy and the optimized geometry of the eutectic mixture. Microstructural studies showed the formation of an irregular structure in the eutectic mixture, which changed with aging and on addition of impurities.     

Phase diagram of growth mode for the SiGe/Si heterostructure system with misfit dislocations

The strain, surface and interface energies of the SiGe/Si (SiGe grown on Si) heterostructure system with and without misfit dislocations were calculated for the Frank–van der Merwe (FM), Stranski–Krastanov (SK) and Volmer–Weber (VW) growth modes essentially based on the three kinds of fundamental and simple structures. The free energies for each growth mode were derived from these energies, and it was determined as a function of the composition and layer thickness of SiGe on Si. By comparison of the free energies, the phase diagrams of the FM, SK and VW growth modes for the SiGe/Si system were determined. The (1 1 1) and (1 0 0) reconstructed surfaces were selected for this calculation. From the phase diagrams, it was found for the growth of SiGe on Si that the layer-by-layer growth such as the FM mode was easy to be obtained when the Ge composition is small, and the island growth on a wetting layer such as the SK mode was easy to be obtained when the Ge composition is large. The VW mode is energetically stable in the Ge-rich compositional range, but it is difficult for the VW mode to appear in the actual growth of SiGe on Si because the VW region is right above the SK region. The regions of the SK and VW modes for the (1 1 1) heterostructure are larger than those for the (1 0 0) one because the strain energy of the (1 1 1) face is larger than that of the (1 0 0) face. The regions of the SK and VW modes for the heterostructure with misfit dislocations are narrower than those for the one without misfit dislocations because the strain energy is much released by misfit dislocations. The phase diagrams roughly explain the behavior of the FM and SK growth modes of SiGe on Si.     

Ammonia-free chemical bath deposition of CdS films: tailoring the nanocrystal sizes

We report on the control of nanocrystal sizes in CdS nanocrystalline films prepared by ammonia-free chemical bath deposition technique. We studied the effect of deposition duration, bath temperature during deposition, and post-preparation heat treatment. Nanocrystals (NCs) with radii from 2.6 nm to more than 10 nm were prepared and characterised by transmission electron microscopy, X-ray diffraction, and optical photoluminescence and absorption spectroscopy. We observed cubic to hexagonal phase transition for large NCs prepared by the heat treatment.     

Nd:YVO4 crystal growth by Czochralski technique with a submerged plate

This paper is to investigate the growth of Nd:YVO₄ (yttrium vanadate) crystal by the modified Czochralski technique with a submerged plate. Numerical studies are performed to examine melt convection and heat transfer during Nd:YVO₄ growth. The attention is paid to study the effects of initial elevation of the submerged plate, crystal diameter, and melt level on melt inclusions. It is found that the increase in crystal rotation rate and crystal diameter, and the decrease in melt level will increase the axial temperature gradient at the edge and in the center of the crystal, and change the interface shape from convex to flat. The experiments are also carried out to confirm the feasibility of the proposed new technique for controlling melt inclusions in Nd:YVO₄ crystal growth.     

Clathrate-hydrate film growth along water/hydrate-former phase boundaries—numerical heat-transfer study

This paper describes two analytic models for the heat-transfer-controlled lateral growth of a clathrate-hydrate film along a planar interface between liquid water and an immiscible hydrate-forming fluid (or guest fluid), such as methane or carbon dioxide. The two models are different from each other only regarding the assumption of the film-front geometry. Either model assumes the film to be uniform and constant in thickness, ignoring possible changes in the thickness on a time scale relevant to its lateral growth. Another fundamental assumption employed in the model is that the film's hydrate-forming front is maintained at the hydrate/guest/water three-phase equilibrium temperature, thereby forming a two-dimensional temperature distribution in the surrounding three-phase space. Based on these assumptions, the transient, two-dimensional conductive heat transfer from the film front into the three phases is formulated and numerically solved to give the instantaneous rate of lateral film growth (i.e., the linear speed of the film-front) along the water/guest-fluid interface, while the film thickness is arbitrarily assumed as a fitting parameter. By comparing the predicted rates of film growth with the corresponding experimental data obtained with methane or carbon dioxide as the guest fluid, we estimated the film thickness to be about 10–20 μm for the methane hydrate at a pressure of 9.06 MPa and about 0.5 μm for the carbon-dioxide hydrate at a pressure of 5 MPa.     

Microstructure and composition analysis of group III nitrides by X-ray scattering

The importance of Group III-nitride structures for both light-emitting devices and high-power field effect transistors is well known (J.W. Orton, C.T. Foxon, Rep. Prog. Phys. 61 (1998) 1). In both cases, different alloy composition and doping levels or type are utilised and the device performance also depends critically on the interface quality and defect density. We have used high resolution X-ray scattering to measure the state of strain in the individual layers on an absolute scale to derive the alloy composition, i.e. we have avoided the conventional method of using the substrate as an internal reference since it could be strained. The composition and individual layer thickness are derived through simulation of the profile with this additional strain information and the best-fit profile is obtained with an automatic procedure. These structures are laterally inhomogeneous arising from defects breaking up the structure into narrow vertical columns of nearly perfect material and this produces significant broadening of the diffraction pattern. This broadening in the diffraction pattern has been modelled using an extended dynamical scattering model (P.F. Fewster, X-Ray Scattering from Semiconductors, Imperial College Press, World Scientific, Singapore, 2000) to yield the size distribution of perfect crystal regions. The measurement of the rotation about an axis defined by the growth direction of the GaN with respect to the sapphire is determined and is found to be small. However, a poor quality sample indicates that a large range of rotations is possible in these structures.     

Molecular dynamics simulations of the crystal–melt interface mobility in HCP Mg and BCC Fe

The temperature profile around the moving solid–liquid interface during non-equilibrium molecular dynamics (MD) simulations of crystallization and melting is examined for HCP Mg and BCC Fe. An evident spike (valley) is found around the solid–liquid interface during solidification (melting). Considering the effect of a non-uniform temperature distribution, it is found that, if the actual interface temperature is adopted to compute the interface mobility, rather than the thermostat temperature (or the mean temperature of the whole system), the kinetic coefficient is approximately a factor of two larger than previous estimates. Although the magnitude of the kinetic coefficient is larger than the previous estimates, the crystalline anisotropies derived in the current work are consistent with earlier calculations.     

Effect of steady ampoule rotation on radial dopant segregation in vertical Bridgman growth of GaSe

For vertical Bridgman growth of the nonlinear optical material GaSe in an ampoule sufficiently long that flow and dopant transport are not significantly influenced by the upper free surface, we show computationally that steady rotation about the ampoule axis strongly affects the flow and radial solid-phase dopant segregation. Radial segregation depends strongly on both growth rate U and rotation rate Ω over the ranges 0.25 μms⁻¹U3.0 μms⁻¹ and 0Ω270 rpm. For each growth rate considered, the overall radial segregation passes through two local maxima as Ω increases, before ultimately decreasing at large Ω. Rotation has only modest effects on interface deflection. Radial segregation computed using a model with isotropic conductivity (one-third the trace of the conductivity tensor) predicts much less radial segregation than the “correct” model using the anisotropic conductivity, with the segregation decreasing monotonically with Ω. Consideration of a model in which centrifugal acceleration is deliberately omitted shows that, as Ω increases, diminution and ultimately disappearance of the “secondary” vortex lying immediately above the interface is due to centrifugal buoyancy, while axial distension of the larger “primary” vortex above is due to Coriolis effects. These results, which are qualitatively different from those accounting for centrifugal buoyancy, suggest that several earlier computational and analytical predictions of rotating vertical Bridgman growth are either limited to rotation rates sufficiently low that centrifugal buoyancy is unimportant, or are artifacts associated with its neglect. The overall radial segregation depends approximately linearly on the product of and the growth rate U for the conditions considered, where is the segregation coefficient.     

Total pressure‐controlled PVT SiC growth for polytype stability during using 2D nucleation theory

A total pressure‐controlled physical vapor transport growth method that stabilizes SiC polytype is proposed. The supersaturation of carbon during SiC growth changed as a function of the growth time due to changes in the temperature difference between the surfaces of the source and the grown crystal. Supersaturation also varied as a function of the pressure inside the furnace. Therefore, modification of the pressure as a function of growth time allowed for constant supersaturation during growth. The supersaturation was calculated based on classical thermodynamic nucleation theory using data for heat and species of Si₂C and SiC₂ transfer in a furnace obtained from a global model. Based on this analysis, a method for polytype‐stabilized SiC growth was proposed that involves decreasing the pressure as a function of growth time. The 4H‐SiC prepared using this pressure‐controlled method was more stable than that of 4H‐SiC formed using the conventional constant‐pressure method.     

Thermodynamic modeling of the system As–Fe combined with first-principles total energy calculations

A thermodynamic model has been developed for the system As–Fe by combining the Calphad approach and the first-principles total energy calculations. Our first-principles calculations are based on the projector augmented wave method within the generalized gradient approximation. We performed these calculations because the experimental values for the enthalpy of formation of the compounds As₂Fe, AsFe and AsFe₂ may have a large uncertainty. Our results indicate significantly more negative values for the enthalpy of formation of these compounds relative to the experimentally established values. We demonstrate that applying our first-principles results in a thermodynamic analysis based on the Calphad approach leads to a calculated phase diagram and thermodynamic properties which are not significantly different from experimental data.     

Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.     

In situ optical monitoring of AlGaN thickness and composition during MOVPE growth of AlGaN/GaN microwave HFETs

Real-time spectral reflectometry has been implemented to monitor the MOVPE growth of AlGaN/GaN microwave HFET structures. The aim is to monitor and control the thickness and composition of the thin AlGaN layer during growth. In order to extract useful information from the in situ spectra the optical constants of AlGaN as a function of alloy composition are required at the growth temperature (1050°C). As the first step to obtaining the high temperature optical constants, a room temperature spectroscopic ellipsometry study (energy range 1.65–4.95 eV) has been carried out on thin AlGaN films of various thickness (30 and 100 nm) and aluminium content (0.15 and 0.25). The multilayer model of each sample from the ellipsometry study is used to generate a reflectance spectrum which is compared with the in situ spectral reflectometry spectrum of the same sample acquired at room temperature to verify the technique. Further work is in progress to model the bandgap and optical constants of GaN and AlGaN at growth temperature.     

A new thermal assembly design for the directional solidification of transparent alloys

A modified design of the thermal assembly is presented for the directional solidification of transparent alloys that eliminates the radial temperature gradient and minimizes the curvature of the interface. An additional booster heater is designed, and the position of the heater is shown to be critical in obtaining a flat interface. A full-scale numerical calculation, carried out for succinonitrile-0.5 wt% Salol, shows that the interface concavity can be reduced gradually by placing the booster heater just above the cold end and by adjusting the temperature of the booster heater while keeping the hot and cold zone temperatures fixed. Experimental measurements of temperatures at the wall and at the center have been carried out systematically by using two calibrated thermocouples, and the observed thermal profiles have been shown to strongly support the numerical prediction. When a macroscopically flat interface is obtained, it is shown that columnar growth away from the ampoule wall can be observed and photographed. The effects of thermal gradient and the temperature setting of the booster heater on the planarity of the interface are discussed.     

Crystal growth of PbFCl by modified Bridgman method

Lead fluoride chloride (PbFCl) crystal was grown by modified Bridgman method. The result of X-ray powder diffraction pattern (XRD) was well accordant with the data of JCPDS card. The transmittance spectrum was first reported without absorption band from 270 to 800 nm. Three emission bands were first observed at room temperature when excited by ultraviolet light.