Concave Interface Research Articles

<i>In Situ</i> Observation of Growth Process of δ Phase of 0.15% C Carbon Steel during Solidification

In situ observation of growth process of high temperature phase in 0.15% C carbon steel during solidification concerned with using Confocal Scanning Laser Microscope (CSLM), the growth rate of -phase has been measured. The results indicate that high temperature -phase grows at cell crystal way when the cooling speed reaches 2°C/min in 0.15% C carbon steel. The -phase of round or oval cross-sectional shaped may grow stably. The growth rate of -phase is gradually getting slow along with increasing of curvature radius. The variation of growth speed tends to be similar with different solid-liquid interface shapes of -phase. The growth rate of concave solid-liquid interface is faster than that of convex solid-liquid interface for phase. The smaller radius of curvature of phase is, the faster the growth rate reaches.

Application of optical beams to electrons in graphene

The technique of beam optics is applied to the description of the wave function of Dirac electrons. This approach is illustrated by considering electron transmission through simple nonhomogeneous structures, such as flat and bent p-n junctions and superlattices. We found that a convex p-n junction compresses the beam waist, while a concave interface widens it without loosing its focusing properties. At a flat p-n junction the waist of the transmitted Gaussian beam can be narrowed or widened, depending on the angle of incidence. A general condition is derived for the occurrence of beam collimation in a superlattice which is less stringent than previous discussed.

Negative Goos–Hänchen shift on a concave dielectric interface

We study the Goos-Hänchen shift (GHS) on a curved surface through numerical simulation by the boundary element method. A negative GHS is first discovered on a concave dielectric interface below the critical angle, accompanied by a large positive GHS on the convexity. The simulation shows that the GHS on a planar interface is the composition of the GHS from a concave and the corresponding convex interface. This work will enrich the study of the GHS for different curved surfaces, which will have potential applications in micro-optics and near-field optics.

Convection-induced peritectic macro-segregation proceeding at the directional solidification of Ti–46Al–8Nb intermetallic alloy

Authors extended the research on TiAl–Nb solidification/modeling reported in Kartavykh et al. (2010) [1]. Unidirectional counter-gravity (upward) melt solidification of Ti–46Al–8Nb (at.%) intermetallic alloy was performed in the three-zone resistive tube electro-furnace TEM 01-3M with power-down thermal profile operation. The laboratory refinement of this cylindrical ingot growth technique was developed in course of terrestrial preparation experiments in the furnace facility specially designed for a sounding rocket flight. Although Ti–46Al–8Nb is nominally slightly pro-peritectic composition, an axial elongated channel-like area with peritectically transformed microstructure was firstly observed in solidified ingots by SEM-BSE and EDX analyses, where Al content locally exceeds 47 at.%. For revealing the reasons of this microstructural inhomogeneity formation, the numerical modeling was applied. The real-time-scale 2D temperature field mapping, macro-scale study of melt hydrodynamics, heat-mass transfer, segregation effects, mushy zone evolution and solidification dynamics of TiAl–Nb melt/solid system have been performed accordingly. It was found that appearance of peritectic axial “spindle” in the solid is induced by the joint action of two factors in the melt: (i) rejection of Al solute ahead of the concave growth interface (dendrite tips front); (ii) development of weak laminar thermo-gravitational convective flow that picks up, pulls upward and stratifies an Al-enriched stream along the axis of melt column. The driving force of convection is a radial thermal gradient that depends on the furnace operational thermal conditions. To prevent the segregation, it was shown numerically that single regular convective cell could be broken into several cells by the appropriate variation of power-down cooling rate. The resulting uniform as-solidified microstructure of alloy produced confirms the modeling findings. Valuable data are obtained for the optimization of cast processes of TiAl-intermetallics.

Numerical study of convection-induced peritectic macro-segregation effect at the directional counter-gravity solidification of Ti–46Al–8Nb alloy

Unidirectional counter-gravity (upward) melt solidification of Ti–46Al–8Nb (at%) intermetallic alloy was performed in the three-zone resistive tube electro-furnace with power-down thermal profile operation. The laboratory refinement of cylindrical ingots growth technique was developed in course of terrestrial preparation experiments in the facility specially designed for a sounding rocket flight. Despite Ti–46Al–8Nb is nominally slightly pro-peritectic composition, an axial elongated channel-like area with peritectically-transformed microstructure was observed in solidified ingots, where Al content locally exceeds 47 at%. For revealing the reasons of this microstructural inhomogeneity formation, the numerical modeling was applied. The real-time-scale 2D temperature field mapping, macro-scale study of melt hydrodynamics, heat–mass transfer, segregation effects, mushy zone evolution and solidification dynamics of TiAl–Nb melt/solid system have been performed accordingly. It was found that appearance of peritectic axial “spindle” in the solid is induced by the joint action of two factors in the melt: (i) rejection of Al solute ahead of the concave growth interface (dendrite tips front); (ii) development of weak laminar thermo-gravitational convective flow that picks-up, pulls upward and stratifies an Al-enriched stream along the axis of melt column. The driving force of convection is a radial thermal gradient that depends on the furnace operational thermal conditions. To prevent the segregation, it was shown numerically that single regular convective cell could be broken into several cells by the appropriate variation of power-down cooling rate. The resulting uniform as-solidified microstructure of alloy obtained confirms the modeling findings.

A simple numerical solution to the Ward–Tordai equation for the adsorption of non-ionic surfactants

A simple numerical scheme for solving the equation of Ward and Tordai (1946) for the diffusion-controlled adsorption of non-ionic surfactants to interfaces is proposed and pseudo-code, as well as C++ source code, is provided. The scheme utilises the trapezium rule of numerical integration and the accuracy and robustness of the method is enhanced by the bisection method of root-finding. The scheme is efficient and flexible in that it can be used with any adsorption isotherm and is readily modified for solving the problem of adsorption onto a convex interface. This scheme is not suggested for the adsorption onto a concave interface and the confusions that have previously arisen in relation to this problem are discussed.

Interface shape control using localized heating during Bridgman growth

Numerical calculations were performed to assess the effect of localized radial heating on the melt–crystal interface shape during vertical Bridgman growth. System parameters examined include the ampoule, melt and crystal thermal conductivities, the magnitude and width of localized heating, and the latent heat of crystallization. Concave interface shapes, typical of semiconductor systems, could be flattened or made convex with localized heating. Although localized heating caused shallower thermal gradients ahead of the interface, the magnitude of the localized heating required for convexity was less than that which resulted in a thermal inversion ahead of the interface. A convex interface shape was most readily achieved with ampoules of lower thermal conductivity. Increasing melt convection tended to flatten the interface, but the amount of radial heating required to achieve a convex interface was essentially independent of the convection intensity.

On crucible effects during the growth of cadmium zinc telluride in an electrodynamic gradient freeze furnace

The CrysMAS code of the Crystal Growth Laboratory, Fraunhofer IISB, is applied to reveal conditions occurring in electrodynamic gradient freeze furnaces during the growth of cadmium zinc telluride crystals. Of particular interest are heat transfer and growth conditions associated with crucibles of different design, one constructed of graphite and the other of pyrolytic boron nitride (PBN). Under identical furnace set-point schedules, the two systems exhibit very different behaviors. Specifically, the temperature field through the cone region of the PBN crucible displays much steeper axial thermal profiles and promotes convex solid–liquid interface shapes (rather than the concave shapes computed for the graphite crucible). Both systems exhibit a concave interface during growth through the cylindrical part of the crucible. However, the axial thermal profile through the graphite-crucible charge is considerably more offset from the set-point profile of the furnace due to significant axial heat flows through the crucible walls. These factors argue in favor of the PBN crucible; however, comparatively larger radial gradients in the PBN system could lead to higher dislocation levels.

Cellular pattern dynamics on a concave interface in three-dimensional alloy solidification

Three-dimensional interface patterns are common in condensed matter, whose dynamical behavior is still deserving clarification. The dynamics of cellular patterns formed at the concave solid-liquid interface during directional solidification in a cylinder of a transparent alloy is studied by means of bright-field live imaging. For each pulling velocity, in situ observation shows that the asymptotic cellular pattern, which establishes with time, is characterized by the continuous birth of a large number of cells at a circular source of morphological instability on the periphery, the sustained collective gliding of the whole cellular array down the interface slope, and the elimination of coarse cells at the central sink. This very peculiar dynamics is the specific signature of the cell advection imposed by interface curvature for the concave situation in three-dimensional solidification. It follows from the comparison between experimental cell gliding and pure slope advection that an additional mechanism of pattern advection is active. It is attributed to fluid flow interaction, estimated on the basis of the Forth and Wheeler traveling wave equations.

Effect of an applied static magnetic field on silicon dissolution into a germanium melt

An experimental investigation has been undertaken to explore the benefits of an applied static magnetic field on silicon transport into a germanium melt in a crucible configuration similar to that used in the liquid phase diffusion (LPD) and Czochralski growth systems. The measured concentration profiles with and without an applied magnetic field showed a very similar shape, while the amount of silicon transport into the melt was slightly higher in the samples processed under magnetic field. There was, however, a substantial difference in the dissolution interface shape. Without field, a flat stable interface is observed. In the presence of an applied field, the dissolution interface remains flat in the center but dramatically curves back into the source material near the wall. This indicates a far higher dissolution rate at the edges of the silicon source. It appears that the altered flow structure in the melt, due to the applied magnetic field, has increased transport at the dissolution interface near the crucible wall. In LPD growth the silicon transport is higher through the center of the melt and leads to a change in the interface shape from a concave interface towards the melt to a convex interface towards the melt at growth conclusion. The present experimental results indicate that an applied static field may be used to enhance silicon transport in LPD to obtain a more favorable (flatter) growth interface for less inclusions in the grown crystals.

Visualization study on coalescence between pair of water drops on inclined surfaces

Visualization experimental investigation on the phenomena and dynamic behavior of coalescence between two equal-size water drops on inclined surfaces is reported in this paper. The effects of inclination angle of the surface and drop size on the dynamics of liquid bridge, fore/back contact angle and triple-phase contact line of the coalescent drop are discussed. The results show that highly concave interface around the liquid bridge and highly convex interface at the retracted top-side parts of two drops built surface tension gradient to drive the interior liquid flow in early stage of the coalescence, while changeable surface tension gradient between highly convex interface at the forepart and near flattened interface at the back part of the coalescent drop and adverse gravity induced the interior flow and the oscillation process later. Coalescence promoted the motion of the coalescent drop on the inclined surface. The released surface energy and potential energy compensated the internal viscous dissipation and the friction, and the fraction for friction increased with increasing inclination angle and drop size. For coalescence of small drops on the inclined surface, the triple-phase contact line, liquid bridge radius and fore/back contact angle of the coalescent drop behaved as periodic damped oscillations. Larger inclination angle of the surface induced severe oscillations for the displacement of back-end and fore contact angle of the coalescent drop while subdued oscillations for the displacement of front-end and back contact angle as well as higher frequency and smaller amplitude for liquid bridge radius. For large drops coalescence, the displacements of front-end and back-end monotonously increased, the liquid bridge radius reduced rapidly without oscillation after passing through a peak value, and the fore/back contact angle increased/decreased quickly with slight oscillation to reach a stable value.

Use of a traveling magnetic field in VGF growth: Flow reversal and resulting dopant distribution

The melt flow in a model of a vertical gradient freeze facility under the action of a traveling magnetic field (TMF) is studied numerically. The radial temperature gradient over a concave solidification interface drives a radially converging flow which may cause an undesirable dopant concentration peak on the axis. We study the characteristics of such a flow for parameters beyond the previously reported linear regime. An upward directed TMF induces a body force which counteracts buoyancy. We report conditions under which the TMF reverses the flow direction for a wide parameter range. These conditions depend primarily on the product of the thermal gradient and the interface deflection. The simulation of the dopant transport demonstrates that the concentration peak disappears as soon as the flow direction changes.

Dispersion relation of surface plasmon wave propagating along a curved metal-dielectric interface

The dispersion relations of surface plasmon wave (SPW) propagating along a convex or concave metal-dielectric interface with a radius of curvature are studied by solving the root of a characteristic equation in terms of Bessel and Hankel functions of complex order numerically. For the convex geometry, a metallic circular cylinder embedded in a dielectric host is modeled, whereas for the concave one, a dielectric cylinder in a metallic host is modeled. We found that the phase velocity of SPW along a convex interface is always less than that of SPW along a planar one. On the contrary, the phase velocity of a concave case is faster than that of a planar one. For both cases, the attenuation constants are larger than a planar one, due to the radial radiation of the energy into the surrounding medium, except the dissipation in the metal.

Strong optical transport of a square-lattice photonic crystal due to the self-collimation effect and negative refraction effect

We investigate the optical transport properties of a square-lattice photonic crystal structure formed by air holes in a dielectric background with concave interface. A strong focusing beam of a point source is formed while a good-quality focus of a plane wave can also be formed by the photonic crystal structure. The focusing properties of the photonic crystal structure show that the self-collimation effect mainly occurs inside the photonic crystal region whereas the negative refraction effect occurs near the concave interface. A high efficiency of manipulation of the light propagation is realized. Contributions to the wave transport inside the photonic crystal region are different for the spatial frequencies in different zones because higher spatial frequencies are generated, mainly arising from the periodic potential of the finite photonic crystal structure.

Viscous resuspension in a tube: The impact of secondary flows resulting from second normal stress differences

The viscous resuspension of non-neutrally buoyant particles has been modeled as a competition between the rate of shear-induced diffusion and sedimentation or as a balance between gradients in the particle stress and gravity. Typically, however, the rheology of the suspension has been modeled using a simple concentration-dependent Newtonian viscosity. In this paper, we demonstrate through theory and comparison with existing experimental results that the anisotropy of the total stress tensor must be included to accurately describe the resuspension process in a tube. At steady state, the isotropic model predicts a secondary current within the tube cross section that flows downwards at the center and upwards near the sidewalls, resulting in a concave upward interface between the clear suspending fluid and the particles [K. Zhang and A. Acrivos, Int. J. Multiphase Flow 20, 579 (1994)]. In contrast, with the inclusion of the known non-Newtonian suspension rheology, the secondary current profile is reversed: upwards near the center and downwards near the walls. This leads to a concave downward shape of the interface between the suspending fluid and the suspension and is in quantitative agreement with the experimental measurements of Altobelli et al. [J. Rheol. 35, 721 (1991)].

Focusing Properties in Photonic Crystal Structure Formed byAir Holes in Dielectric Background with Concave Interface

We investigate the focusing properties of photonic crystal structureswith a concavo-concave as the photonic crystal boundary. The photoniccrystal is constituted by air holes parallelly distributed in a uniformdielectric. A good-quality focus of a plane wave can appear out of thephotonic crystal structure, and a strong far field focus is also formedfrom the photonic crystal interface. A negative-refractive beam at thefrequency 0.195 (2πc/a) for the excited Bloch wave mode near theBrillouin zone edges under all incident angles are obtained bysimulation.

Polytype Control in 6H-SiC Grown via Sublimation Method

6H-SiC ingots were grown with different growth interfaces at different rates via the sublimation method. A model for the step flow growth mechanism is proposed to interpret the occurrence of 15R-SiC inclusions in the 6H-SiC single crystal. The results show that the 15R-SiC occurs more easily on the convex and the concave interface than on the slight convex interface and 15R-SiC inclusion also occurs when the growth rate of 6H-SiC exceeds the critical rate of 300 %m/h with the slight convex interface at the seed temperature 2250°C.

Characterization of Dual Substrate Binding Sites in the Homodimeric Structure of Escherichia coli mRNA Interferase MazF

MazF and MazE constitute a so-called addiction module that is critical for bacterial growth arrest and eventual cell death in response to stress. The MazF toxin was recently shown to possess mRNA interferase (MIase) activity, and acts as a protein synthesis inhibitor by cleaving cellular mRNA. As a cognate regulator, the short-lived antitoxin, MazE, inhibits MazF MIase activity and hence maintains the delicate homeostasis between these two components. In the present study, we have shown that the MazF homodimer contains two symmetric binding sites, each of which is capable of interacting with a MazE C-terminal peptide, MazEp(54-77). The slow exchange phenomenon between free and peptide-bound MazF on the NMR timescale indicates relatively high affinities for MazEp(54-77) at both sites (Kd,K'd < 10(-7) M). However, the observed sequential binding behavior suggests a negative cooperativity between the two sites (Kd < K'd). A 13 base single-stranded DNA, employed as an uncleavable RNA substrate analog, can also bind to both sites on the MazF homodimer with moderate affinity (Kd approximately 10(-5) -10(-6) M). Chemical shift perturbation data deduced from NMR experiments indicates that the two binding sites for the MazEp peptide coincided with those for the single-stranded DNA competitive inhibitor. These dual substrate-binding sites are located on the concave interface of the MazF homodimer, consisting of a highly basic region underneath the S1-S2 loop and two hydrophobic regions containing the H1 helix of one subunit and the S3-S4 loop of the opposing subunit. We show that the MazF homodimer is a bidentate endoribonuclease equipped with two identical binding sites for mRNA processing and that a single MazE molecule occupying one of the binding sites can affect the conformation of both sites, hence efficiently hindering the activity of MazF.

The interface inversion process during the Czochralski growth of high melting point oxides

High melting point oxides show an interface inversion from a convex interface shape to a flat or concave interface when grown after the Czochralski method with constant crystal rotation rate and increasing crystal radius (as in the shoulder region). Under the described conditions one observes during YAG-growth a sudden and uncontrollable interface change, called interface flip, at a certain critical crystal rotation rate. We describe model experiments and numerical simulations of this inversion process. We show that it is connected with a flow transition at a certain critical rotational Reynolds number Re c. This Re c increases with the convex interface deflection and with the strength of the buoyant-thermocapillary flow near the free melt surface towards the crystal. A self-amplifying process, involving the back-melting of the crystal cone, starts when Re c is reached. The dynamics of the back-melting is explained. A more vigerous interface inversion process is expected for systems with large interface deflections and for systems with smaller dynamic Bond number, e.g. smaller crucibles.

Time-dependent magnetic field influence on GaAs crystal growth by vertical Bridgman method

The paper deals with the numerical investigation of time-dependent magnetic field influence on GaAs crystal growth by vertical Bridgman method. Fully unsteady numerical simulation is performed for three types of dynamic magnetic fields: rotating magnetic field (RMF), axial alternating magnetic field (AMF) and travelling magnetic field (TMF). The fields of stream function in the melt, temperature and dopant distribution in the melt and in the grown crystal with and without magnetic field are obtained and analyzed. RMF is found to pose significant influence on both azimuthal and meridional melt flows towards their intensification, and to substantially reduce the interface deflection. Higher magnetic field intensity results in the crystal–melt interface shape change from a concave interface to W-shaped one. At certain value of magnetic field intensity the steady-state flow regime becomes unstable and the transition to time-dependent regime is observed. The influence of AMF on GaAs crystal growth is found to be similar to that of static magnetic field. Application of travelling magnetic field significantly changes the flow structure, the interface shape and the dopant distribution in a melt and grown crystal. Depending on the propagation direction it can make either positive or negative effect on the resulting flow structure.