Crossover Scaling of Wavelength Selection in Directional Solidification of Binary Alloys

We simulate dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with an adaptive-mesh refinement. The spacing of primary branches is examined for a range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a non-trivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers, a result validated using published experimental data.Comment: 4 pages, four figures, submitted to Physical Review Letter

Influence of external flows on crystal growth: numerical investigation

We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K. Kassner, Phys. Rev. E {\bf 72}, 056703 (2005)] to simulate non-facetted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically. For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Peclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Peclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. At smaller anisotropy, a modification of the morphology diagram in the plane undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favour of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger. For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.Comment: 10 pages, 7 figures, accepted for Physical Review E; size of some images had to be substantially reduced in comparison to original, resulting in low qualit

Interface Morphology During Crystal Growth: Effects of Anisotropy and Fluid Flow

The effect of a parallel shear flow and anisotropic interface kinetics on the onset of instability during growth from a supersaturated solution is analyzed. The model used for anisotropy is based on the microscopic picture of step motion. A shear flow (linear Couette flow or asymptotic suction profile) parallel to the crystal solution interface in the same direction as the step motion decreases interface stability. A shear flow counter to the step motion enhances stability and for sufficiently large shear rates the interface is absolutely morphologically stable. For large wave numbers, the perturbed flow field can be neglected and a simple analytic approximation for the stability-instability demarcation is found

Step Bunching: Influence of Impurities and Solution Flow

Step bunching results in striations even at relatively early stages of its development and in inclusions of mother liquor at the later stages. Therefore, eliminating step bunching is crucial for high crystal perfection. At least 5 major effects causing and influencing step bunching are known: (1) Basic morphological instability of stepped interfaces. It is caused by concentration gradient in the solution normal to the face and by the redistribution of solute tangentially to the interface which redistribution enhances occasional perturbations in step density due to various types of noise; (2) Aggravation of the above basic instability by solution flowing tangentially to the face in the same directions as the steps or stabilization of equidistant step train if these flows are antiparallel; (3) Enhanced bunching at supersaturation where step velocity v increases with relative supersaturation s much faster than linear. This v(s) dependence is believed to be associated with impurities. The impurities of which adsorption time is comparable with the time needed to deposit one lattice layer may also be responsible for bunching; (4) Very intensive solution flow stabilizes growing interface even at parallel solution and step flows; (5) Macrosteps were observed to nucleate at crystal corners and edges. Numerical simulation, assuming step-step interactions via surface diffusion also show that step bunching may be induced by random step nucleation at the facet edge and by discontinuity in the step density (a ridge) somewhere in the middle of a face. The corresponding bunching patterns produce the ones observed in experiment. The nature of step bunching generated at the corners and edges and by dislocation step sources, as well as the also relative importance and interrelations between mechanisms 1-5 is not clear, both from experimental and theoretical standpoints. Furthermore, several laws controlling the evolution of existing step bunches have been suggested, though unambiguous conclusions are still missing. Addressing these issues is the major goal of the present project. The theory addressing the above problem, experimental methods, several figures which include: (1) the spatial wave numbers at which the system is neutrally stable as a function of growth velocity for linear kinetics and supersaturation for nonlinear kinetics; (2) a schematic of the experiment of lysozyme crystal growing under conditions of natural convection; (3) fluctuations in time, t, of the normal growth rate, R(t), vicinal slope, p(t) and Fourier Spectra of R(t), discussions and conclusions are presented

Flight Experiment to Study Double-Diffusive Instabilities in Silver-Doped Lead Bromide Crystals

A detailed study on the effect of convection on crystal quality was carried out by growing lead bromide crystals in transparent Bridgman furnace. Direct observations were made on the solid-liquid interface and a new kind of instability was observed. This could be explained on the basis of toroidal flow in the AgBr-doped lead bromide sample. With the increasing translation velocity, the interface changed from flat to depressed, and then formed a cavity in the center of the growth tube. The crystal grown at the lowest thermal Rayleigh number showed the highest quality and crystal grown at the largest thermal Rayleigh number showed the worst quality. Numerical studies were carried out to provide a framework for interpreting the observed convective and morphological instabilities, and to determine the critical (limiting) concentration of dopant for a particular growth velocity and gravity level. Theoretical instability diagrams were compared with data obtained from the experimental studies. These studies provided basic data on convective behavior in doped lead bromide crystals grown by the commercially important Bridgman process

Growth Mechanism of Nanowires: Ternary Chalcogenides

In the past two decades there has been a large rise in the investment and expectations for nanotechnology use. Almost every area of research has projected improvements in sensors, or even a promise for the emergence of some novel device technologies. For these applications major focuses of research are in the areas of nanoparticles and graphene. Although there are some near term applications with nanowires in photodetectors and other low light detectors, there are few papers on the growth mechanism and fabrication of nanowire-based devices. Semiconductor nanowires exhibit very favorable and promising optical properties, including high transparency and a several order of magnitude better photocurrent than thin film and bulk materials. We present here an overview of the mechanism of nanowire growth from the melt, and some preliminary results for the thallium arsenic selenide material system. Thallium arsenic selenide (TAS) is a multifunctional material combining excellent acousto-optical, nonlinear and radiation detection properties. We observed that small units of (TAS) nanocubes arrange and rearrange at moderate melt undercooling to form the building block of a nanowire. In some cases very long wires (less than mm) are formed. Since we avoided the catalyst, we observed self-nucleation and uncontrolled growth of wires from different places

Surface Modification at Nanoscale; Nanoparticle-Nanowire Transition

Binary, ternary and quaternary oxides and selenides have been developed and used in multiple applications including high power lasers, detectors, dielectric energy storage and variety of optical devices. These materials have been grown by Bridgman, physical vapor transport (PVT), chemical vapor transport (CVT) methods and flux methods in the form of bulk thin film, nanocrystals and nanowires. With increasing thrust of bio applications, nanoparticles it is essential to understand nucleation and nanomorphological transition during drug delivery, growth of nanoengineered bio composites in body, grain growth and final morphology. Addition of fluorides and selenides have increased significantly in synthetic tissue constituents because of some advantages in adhesion and stability. We have performed experiments on multinary oxides Sr-Ba-O-F, Se-Tl-As and Se-Pb-Sn-Se using several growth methods to demonstrate nanoparticle and nanowire transition. This study has great potential to increase surface area and also provides understanding to the mechanism of nanowire growth

Growth Mechanism of Nanowires: Binary and Ternary Chalcogenides

Semiconductor nanowires exhibit very exciting optical and electrical properties including high transparency and a several order of magnitude better photocurrent than thin film and bulk materials. We present here the mechanism of nanowire growth from the melt-liquid-vapor medium. We describe preliminary results of binary and ternary selenide materials in light of recent theories. Experiments were performed with lead selenide and thallium arsenic selenide systems which are multifunctional material and have been used for detectors, acousto-optical, nonlinear and radiation detection applications. We observed that small units of nanocubes and elongated nanoparticles arrange and rearrange at moderate melt undercooling to form the building block of a nanowire. Since we avoided the catalyst, we observed self-nucleation and uncontrolled growth of wires from different places. Growth of lead selenide nanowires was performed by physical vapor transport method and thallium arsenic selenide nanowire by vapor-liquid-solid (VLS) method. In some cases very long wires (>mm) are formed. To achieve this goal experiments were performed to create situation where nanowires grew on the surface of solid thallium arsenic selenide itself

Onset of Convection in Two Liquid Layers with Phase Change

We perform linear stability calculations for horizontal fluid bilayers that can undergo a phase transformation, taking into account both buoyancy effects and thermocapillary effects in the presence of a vertical temperature gradient. We compare the familiar case of the stability of two immiscible fluids in a bilayer geometry with the less-studied case that the two fluids represent different phases of a single-component material, e.g., the water-steam system. The two cases differ in their interfacial boundary conditions: the condition that the interface is a material surface is replaced by the continuity of mass flux across the interface, together with an assumption of thermodynamic equilibrium that in the linearized equations represents the Clausius-Clapeyron relation relating the interfacial temperature and pressures. For the two-phase case, we find that the entropy difference between the phases plays a crucial role in determining the stability of the system. For small values of the entropy difference between the phases, the two-phase system can be linearly unstable to either heating from above or below. The instability is due to the Marangoni effect in combination with the effects of buoyancy (for heating from below). For larger values of the entropy difference the two-phase system is unstable only for heating from below, and the Marangoni effect is masked by effects of the entropy difference. To help understand the mechanisms driving the instability on heating from below we have performed both long-wavelength and short-wavelength analyses of the two-phase system. The short-wavelength analysis shows that the instability is driven by a coupling between the flow normal to the interface and the latent heat generation at the interface. The mechanism for the large wavelength instability is more complicated, and the detailed form of the expansion is found to depend on the Crispation and Bond numbers as well as the entropy difference. The two-phase system allows a conventional Rayleigh-Taylor instability if the heavier fluid overlies the lighter fluid; applying a temperature gradient allows a stabilization of the interface

Dynamics of a faceted nematic-smectic B front in thin-sample directional solidification

We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 \mu m-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic - smectic B interface presents a facet in one direction -- the direction parallel to the smectic layers -- and is otherwise rough, and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V and the angle theta_{0} between the facet and the isotherms. We focus on the phenomena occurring immediately above the instability threshold when theta_{0} is neither very small nor close to 90^{o}. Under these conditions we observe drifting shallow cells and a new type of solitary wave, called "faceton", which consists essentially of an isolated macroscopic facet traveling laterally at such a velocity that its growth rate with respect to the liquid is small. Facetons may propagate either in a stationary, or an oscillatory way. The detailed study of their dynamics casts light on the microscopic growth mechanisms of the facets in this system.Comment: 12 pages, 19 figures, submitted to Phys. Rev.