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At least 19 records

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy

A fully time-dependent linear stability analysis of the morphological stability of a planar interface during directional solidification of a binary alloy at constant velocity in the presence of an electric field, is performed. The electromigration of solute and the differing electrical conductivities of solid and liquid for a model in which the temperature gradient is constant are taken into account. The present results are compared with the constitutional supercooling criterion, and it is shown there may be substantial differences. A modified constitutional supercooling criterion which is valid over a large range of conditions is derived. It is also found under certain conditions that the onset of instability may be time dependent.

Wheeler, A. A.

Morphological Stability and Fluid Dynamics of Vapor Crystal Growth

A fundamental understanding of the conditions under which crystals can retain morphological stability, i.e., shape stability of the advancing interface, during growth from vapors was studied. Morphological stability (MS) is a necessary condition for the growth of homogeneous single crystals required for numerous device applications. For crystallization from melts, the MS concepts are well developed and are essentially based on heat and mass transfer conditions about the advancing interface. For crystallization from vapors, the MS requirements are more complex and not well understood. The added complexity arises from the fact that anisotropies in interfacial kinetics are typically stronger in crystallization from vapors than from melts. These pronounced anisotropies root in the distinctly lower atomic roughness of most vapor-solid interfaces.

Rosenberger, F.

Effect of anisotropic thermal conductivity on the morphological stability of a binary alloy

A linear morphological stability analysis is presented for a planar interface during unidirectional solidification of a binary alloy, in the case of a crystal having an anisotropic thermal conductivity. A dispersion relation shows that the onset of instability depends on the orientation of the growth direction with respect to principal crystallographic axes and on the orientation of the wavevector of the perturbation. The onset of instability can be either oscillatory (traveling waves) or nonoscillatory in time. For growth along a principal axis of the crystal there is an exchange of stabilities, and the onset of instability is nonoscillatory.

Coriell, S. R.

Convection and morphological stability during directional solidification

For growth of a vicinal face at constant velocity, the effect of anisotropic interface kinetics on morphological stability is calculated for a binary alloy. The dependence of the interface kinetic coefficient on crystallographic orientation is based on the motion and density of steps. Anisotropic kinetics give rise to traveling waves along the crystal-melt interface, and can lead to a significant enhancement of morphological stability. The stability enhancement increases as the orientation approaches a singular orientation and as the solidification velocity increases. Shear flows interact with the traveling waves and, depending on the direction of the flow, may either stabilize or destabilize the interface. Specific calculations are carried out for germanium-silicon alloys.

Coriell, Sam R.

Morphological Stability of Faceted Interfaces

The major focus of this investigation is to study the fundamentals of layer spreading mechanisms during growth of doped Ge (a facet forming material), and to determine the conditions for morphological instability of vicinal solid-liquid interfaces. The investigation will also lead to the determination of the effect of dopants on the layer growth kinetics, step free energy, and dopant capture by the advancing ledges. The theoretical treatment of growth of faceted interfaces indicates that the kinetics of a step on a growing vicinal interface considerably depends on its angle of inclination, the melt concentration, and characteristics of flow currents in the melt. The morphological stability of the interface also depends on these parameters, as well as on the density and spreading velocity of the steps. However, the treatment of the instability of the interface by the layer growth mechanism is rather difficult because it requires exact knowledge of the thermal and solutal fields, hydrodynamics of the melt, and supercooling at the interface. The results of recent space experiments of the principal investigator involving directional solidification of faceted Bi-Sn alloys have shown that the morphological stability of various crystallographic orientations is significantly affected by the anistropy in interfacial properties of the faceted alloy in general, and the interface kinetics in particular. These findings have also raised many important and fundamental questions, particularly with respect to the behavior of interfacial steps, which need to be addressed via additional groundbased and microgravity experiments. For the present investigation we will use a novel crystal growth technique which provides axial heat flux close to the solid-liquid boundary. The Axial Heat Processing (AHP) technique allows for precise control and determination of the heat and mass transfer close to the crystallization front, and the establishment of a planar interface over the entire cross-section of the growing crystal.

Abbaschian, Reza

Morphological stability and fluid dynamics of vapor crystal growth

Research on morphological stability and fluid dynamics of crystal growth is discussed. Interfacial heat and mass transfer research is discussed. The finding of surface roughening is a precursor to a solid-solid phase transition was further quantified. Progress was obtained with the mass spectroscopic characterization of GeSe-Ge I sub 4.

Rosenberger, F. E.

Heat of mixing and morphological stability

A mathematical model, which incorporates heat of mixing in the energy balance, has been developed to analyze the morphological stability of a planar solid-liquid interface during the directional solidification of a binary alloy. It is observed that the stability behavior is almost that predicted by the analysis of Mullins and Sekerka (1963) at low growth velocities, while deviations in the critical concentration of about 20-25 percent are observed under rapid solidification conditions for certain systems. The calculations indicate that a positive heat of mixing makes the planar interface more unstable, whereas a negative heat of mixing makes it more stable, in terms of the critical concentration.

Nandapurkar, P.

Fluctuations of thermal conductivity and morphological stability

Compositional fluctuations of the binary alloy result in the corresponding fluctuations of the thermal conductivity of the material. During crystal growth, these fluctuations can significantly modify the local temperature fields at the liquid-solid interface. This, in turn, will affect the morphological stability of the growing interface. In this work, the temperature dependence of the thermal conductivity of the solid phase has been included into the Mullins-Sekerka formalism. A significant effect on the onset of the instability of planar interface has been predicted. It has been found, in particular, that for binary systems with the segregation coefficient above unity a flat interface is always unstable. The shape of the interface fluctuation should have a single harmonic character with a well defined wavelength.

Mazuruk, K.

Morphological stability in the presence of fluid flow in the melt

Recent experiments have shown that the presence of a vertical buoyancy-driven flow adjacent to an initially cylindrical crystal-melt interface may produce a time-dependent helical deformation of the interface, with a rotation period ranging from several minutes to many hours, depending upon the width of the melt. The temperature distribution is such that the interface is expected to be morphologically stable in the absence of fluid flow. A linear stability analysis reveals that the instability is due to a coupling between a basic hydrodynamic instability in the buoyant flow and the deformable boundary separating the two phases. The crystal-melt interface lowers the critical Grashof number of an analogous rigid-walled system by an order of magnitude for succinonitrile with a Prandtl number P = 22.8; furthermore, the hydrodynamic mode that is actually destabilized by the interface is not the least stable mode in the rigid-walled system for P = 22.8. The results show that the instability may be regarded either as a rather large alteration of a basic hydrodynamic instability by the crystal-melt interface, or as a significant modification of the morphological stability of the interface by the presence of the buoyant flow.

Mcfadden, G. B.

The Effect of Solidification Rate on Morphological Stability

At low solidification rates, the criterion for the onset of morphological instability parallels closely the criterion of constitutional supercooling. At somewhat larger rates of solidification, however, the results of the perturbation theory of morphological instability differ significantly from the predictions of constitutional supercooling. This arises because the critical wave length for instability decreases as solidification rate increases and thus the effects of capillarity (solid-liquid surface tension) play a strong stabilizing role. This gives rise to the concept of absolute stability, according to which the system will always be stable for a sufficiently large rate of solidification. This enhanced stabilization by capillarity is present only so long as local equilibrium is maintained at the solid-liquid interface. If the interfacial temperature drops below its equilibrium value by an amount dependent on growth rate, oscillatory morphological instabilities can occur. The differences among these various stability criteria are illustrated by means of some simple two-dimensional diagrams that should supplant the conventional plots of (temperature gradient)/(growth rate) vs. alloy concentration.

Sekerka, R. F.

Morphological stability and kinetics in crystal growth from vapors

The following topics are discussed: (1) microscopy image storage and processing system; (2) growth kinetics and morphology study with carbon tetrabromide; (3) photothermal deflection vapor growth setup; (4) bridgman growth of iodine single crystals; (5) vapor concentration distribution measurement during growth; and (6) Monte Carlo modeling of anisotropic growth kinetics and morphology. A collection of presentations and publications of these results are presented.

Rosenberger, Franz

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy. III - Weakly nonlinear theory

The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, the demarcation between supercritical and subcritical behavior is calculated as a function of processing conditions and material parameters. The bifurcation behavior is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.

Wheeler, A. A.

Morphological stability of a crystal growing in solution

A brief outline is given of the problem of the stability of growth of a polyhedral crystal growing in solution in the presence of supersaturation inhomogeneity. An experiment is proposed for a low gravity environment which should provide data for confrontation with the various theoretical approaches to this problem. The validity of this data rests on the assumption that growth occurs in a convection-free environment.

Elwell, D.

Morphological stability and fluid dynamics of vapor crystal growth

Progress is reported in establishing the capabilities of thermal deflection spectroscopy for measurements of the concentration field around a growing crystal. Work was completed on the inclusion of the next nearest neighbor interaction into a surface roughness model and the resulting formalism was applied to copper, zinc, and lead. Other work in mass spectroscopy and vapor transport is discussed.

Rosenberger, F. E.

Dendritic solidification in a binary alloy melt: Steady-state versus morphological stability theories

A model for dendritic growth in a binary alloy melt, in the presence of a positive temperature gradient in the liquid, is presented. The model describes satisfactorily the transition from a dendritic interface to a planar interface at very low and very large growth rates. A dendrite tip stability parameter is derived, strictly from steady state considerations, without resorting to a perturbation analysis. The estimates of the parameter agree with those obtained by models based on perturbation analyses.

Laymanan, V.

A numerical and analytical study of nonlinear bifurcations associated with the morphological stability of two-dimensional single crystals

The nonlinear stability of a two-dimensional single crystal of pure material in an undercooled melt is studied both analytically and numerically. The quasi-steady state approximation is used for the thermal fields, and the effects of different solid and liquid thermal conductivities, isotropic interfacial growth kinetics, and isotropic surface tension are included. The bifurcation analysis is performed by calculating the instantaneous value of the fundamental component of the local normal growth speed for an interface perturbed by a single Fourier shape component. Numerically, the fundamental component of the interfacial growth speed is found by Fourier analysis of the solution to an integrodifferential equation obeyed at the interface. Analytically, an expansion technique is used to derive a solvability condition defining each of these bifurcation points. The analytical and numerical results are in very close agreement. Almost all of the bifurcations are subcritical, and the results are presented by giving values of the Landau coefficient as a function of the different dimensionless parameters used in the model.

Brush, L. N.

Investigating Morphological Stability of Faceted Interfaces with Axial Heat Processing (AHP) Technique

Successful processing of homogeneous semiconductor single crystals from their melts depends strongly on precise control of thermal and fluid flow conditions near the solid/liquid interface. In this project, we utilize a novel crystal growth technique called Axial Heat Processing (AHP) that uses a baffle, positioned inside the melt near the interface, to supply and/or conduct heat axially to the interface. The baffle, which may or may not have a heater encased in it, can promote more stable and planar growth as well as reduce buoyancy driven convection. The latter is because the baffle reduces the aspect ratio of the melt as it separates the melt into three sections, above the baffle, in the feed gap between the baffle and the crucible wall, and below the baffle between the baffle base and the interface. AHP also enables a close monitoring and/or control of thermal boundaries near the solid/liquid interface during crystal growth by means of thermocouples placed in the baffle. The interface is kept planar when a heating element in the baffle is used. However, a proper choice of melt height is necessary to keep the interface planar when using the baffle without a heater. This study addresses the influence of melt height and growth velocity on the segregation profile of AHP-grown Sb doped Ge single crystals.

Abbaschian, Reza

Steps in Solution Growth: Revised Gibbs-Thomson Law, Turbulence and Morphological Stability

Two groups of new phenomena revealed by AFM and high resolution optical interferometry on crystal faces growing from solutions will be discussed. 1. Spacing between strongly polygonized spiral steps with low less than 10(exp -2) kink density on lysozyme and K- biphtalate do not follow the Burton-cabrera-Frank theory. The critical length of the yet immobile first Short step segment adjacent to a pinning defect (dislocation, stacking fault) is many times longer than that following from the step free energy. The low-kink density steps are typical of many growth conditions and materials, including low temperature gas phase epitaxy and MBE. 2. The step bunching pattern on the approx. 1 cm long { 110) KDP face growing from the turbulent solution flow (Re (triple bonds) 10(exp 4), solution flow rate approx. 1 m/s) suggests that the step bunch height does not increase infinitely as the bunch path on the crystal face rises, as is usually observed on large KDP crystals. The mechanism controlling the maximal bunch width and height is based on the drag of the solution depleted by the step bunch down thc solution stream. It includes splitting, coagulation and interlacing of bunches

Chernov, A. A.