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Showing papers on "Directional solidification published in 1988"


Journal ArticleDOI
TL;DR: In this article, a melt-textured growth of polycrystalline YBa2Cu3O7−δ superconductor using directional solidification created an essentially 100% dense structure consisting of long, needle- or plate-shaped crystals preferentially aligned parallel to the a-b conduction plane.
Abstract: Melt‐textured growth of polycrystalline YBa2Cu3O7−δ superconductor using directional solidification created an essentially 100% dense structure consisting of long, needle‐ or plate‐shaped crystals preferentially aligned parallel to the a‐b conduction plane. The new microstructure, which completely replaces the previous granular and random structure in the sintered precursor, exhibits dramatically improved transport Jc values at 77 K of ∼17 000 A/cm2 in zero field and ∼4000 A/cm2 at H=1 T (as compared to ∼500 and ∼1 A/cm2, respectively, for the as‐sintered structure), with the severe field dependence of Jc (‘‘weak‐link’’ problem) no longer evident in the new melt‐textured material. The improvement in Jc is attributed to the combined effects of densification, alignment of crystals, and formation of cleaner grain boundaries. Microstructure and distribution of various phases present in the melt‐textured material are discussed in relation to the superconducting properties.

745 citations


Book
01 Jan 1988
TL;DR: In this paper, the Saffman-Taylor Finger is used to trace the shape of a curved flame growing from a supercooled liquid in a channel, and the shapes of a Needle Crystal Growing from a Supercooled Liquid.
Abstract: Introduction. The Saffman-Taylor Finger. Stationary Shapes of a Needle Crystal Growing from a Supercooled Liquid. Stationary Shapes of a Curved Flame Propagating in a Channel. Stability of Curved Fronts. Conclusion. References. Collected Papers. Planar Front Propagation. Dragging of a Liquid by a Moving Plate. Saffman-Taylor Finger. Dendrites. Directional Solidification. Raising Bubbles. Premixed Flames.

489 citations


Journal ArticleDOI
TL;DR: The quality of large semiconductor crystals grown from the melt for use in electronic and optoelectronic devices is strongly influenced by the intricate coupling of heat and mass transfer and melt flow in growth systems.
Abstract: The quality of large semiconductor crystals grown from the melt for use in electronic and optoelectronic devices is strongly influenced by the intricate coupling of heat and mass transfer and melt flow in growth systems. This paper reviews the present state of understanding of these processes starting from the simplest descriptions of solidification processes to detailed numerical calculations needed for quantitative modeling of processing with solidification. Descriptions of models for the vertical Bridgman-Stockbarger and Czochralski crystal growth techniques are included as examples of the level of understanding of industrially important methods.

279 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated particle behavior at the solid-liquid interface in Al-2 pct Mg and Al-6.1 pct Ni alloys and found that particles can be entrapped in the solid if adequate solidification rates and temperature gradients are used.
Abstract: Directional solidification results were obtained in order to investigate particle behavior at the solid-liquid interface in Al-2 pct Mg (cellular interface) and Al-6.1 pct Ni (eutectic interface) alloys. It is found that particles can be entrapped in the solid if adequate solidification rates and temperature gradients are used. Model results showed critical velocity values slightly higher than those obtained experimentally.

217 citations



Journal ArticleDOI
TL;DR: Dans une experience de solidification directionnelle sur une interface nematique isotrope en mouvement, on observe des modes solitaires se propageant a travers l'interface egalement l'instabilite d'Eckhaus.
Abstract: Dans une experience de solidification directionnelle sur une interface nematique isotrope en mouvement, on observe des modes solitaires se propageant a travers l'interface. On observe egalement l'instabilite d'Eckhaus. En presence de modes solitaires, le mecanisme de la selection des formes est dynamique

74 citations


Journal ArticleDOI
TL;DR: In this paper, experimental data from the literature for organic and metallic alloys and compared it with the predictions of the linear and the weakly non-linear theory, and found that the neutral stability curves, known to be very wide in the case of a subcritical bifurcation, are much narrow for a supercritical one.

52 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of small additions of Si, P, Cr, Mn, Ti, Al, and S to pure Fe-C eutectic, upon the transi-tion velocities from grey to white and white to grey cast iron, has been measured by varying the growth rate during directional solidification.
Abstract: The effect of small additions of Si, P, Cr, Mn, Ti, Al, and S to pure Fe-C eutectic, upon the transi-tion velocities from grey to white and white to grey cast iron, has been measured by varying the growth rate during directional solidification. As a result, it is found that alloying elements can be classified into three types: graphitizing (Si, Al, P, and S), carburizing (Cr), and “hysteretic effect” (Mn, Ti). The well-known influence of a thermal gradient (or the superheat) has been shown to af-fect only the grey-to-white transition. Growth undercoolings were measured as a function of growth rate, while the average lamellar spacings were determined from transverse sections of directionally solidified samples. A small addition of the element studied can have a marked effect upon these parameters.

44 citations


Journal ArticleDOI
TL;DR: In this paper, a modified particle engulfment theory was proposed to explain these observations, which showed that high translation rates, high gradients, high gravity levels, and higher density and lower thermal conductivity of the L2 phase favored the formation of fiber composite structure, while the opposite conditions resulted in structures consisting of L2 droplets in α matrix.
Abstract: Cu-Pb and Bi-Ga monotectic alloys of nominal hypermonotectic compositions were directionally solidified under various furnace translation rates, temperature gradients, and gravity levels. Gravity was varied by solidifying the alloys under ground conditions and in the furnace aboard NASA KC-135 aircraft, flying on parabolic trajectories. High translation rates, high gradients, high gravity levels, and higher density and lower thermal conductivity of the L2 phase favored the formation of fiber composite structure, while the opposite conditions resulted in structures consisting of L2 droplets in α matrix. A modified particle engulfment theory as originally enunciated by Ulhmannet al. is proposed to explain these observations.

38 citations


Journal ArticleDOI
TL;DR: In this article, the onset of buoyancy-driven instability during the directional solidification of a pure liquid with a strongly temperature-dependent viscosity and an arbitrary Prandtl number is investigated using linear stability theory.
Abstract: The onset of a buoyancy-driven instability during the directional solidification of a pure liquid with a strongly temperature-dependent viscosity and an arbitrary Prandtl number is investigated using linear stability theory. The Rayleigh number for this system contains the lengthscale Ls defined as the ratio of the thermal diffusivity of the liquid and the solidification velocity times the density ratio of the two phases. It is independent of the actual depth of the liquid and it reflects the fact that increasing the solidification velocity stabilizes the system. The theory also shows that the difference in material properties between the two phases and the properties of the solidifying interface itself cause the interface to look like a boundary of finite conductivity measured by a wavenumber-dependent Biot number. For large viscosity variations, convection occurs below a stagnant layer which forms just beneath the interface where the liquid is immobilized by its very large viscosity. The thickness of this layer is measured by the natural logarithm of the viscosity contrast in the liquid times the lengthscale Ls. In this limit, the influence of the solidifying boundary is shielded from the bulk liquid by the stagnant layer and so the effect of the Biot number on the critical Rayleigh number is small. However, inertial effects, being associated with the bulk liquid, are very important for small Prandtl numbers of the fluid far from the interface. The model has applications to the solidification of magma chambers or lava lakes and to the material processing of polymeric liquids.

38 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of antimony additions on the hardness and tensile properties of Al-Si eutectic alloy has been examined during directional solidification, provided that its concentration in the melt was maintained at ~0·1 wt-%, improved the mechanical properties by almost 20-25%, all effects being additive to those that can be gained through increasing the growth velocity of the samples.
Abstract: The effect of antimony additions on the hardness and tensile properties of Al–Si eutectic alloy has been examined during directional solidification. Antimony, provided that its concentration in the melt was maintained at ~0·1 wt-%, improved the mechanical properties of the eutectics by almost 20–25%, all effects being additive to those that can be gained through increasing the growth velocity of the samples. Mechanical properties were found to correlate directly with the spacing between the silicon particles of the eutectic phase of the solidification structure, a Hall–Petch type relationship existing between the yield strength and silicon particle spacing.MST/653

Journal ArticleDOI
TL;DR: In this article, a series of Hg(1-x)Zn(x)Te crystals were grown by directional solidification with x ranging from 0.15 to 0.22.

Journal ArticleDOI
TL;DR: In this article, 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 was performed.

Journal ArticleDOI
TL;DR: In this article, the role of mixed convection, caused by a forced Couette flow, during the directional solidification of tin in a toroidal mold is studied, and the macrostructure of the solidified melt is examined and the metallurgical findings (crystal growth) connected with the heat and fluid flow measurements.



Journal ArticleDOI
TL;DR: In this paper, a model of the solute exchanges during solidification is proposed in order to predict the amount of liquid remaining at each stage in the process, particularly at the last stage when all the eutectic liquid is frozen in.
Abstract: The crystallization of complex nickel-base hardfacing alloys is studied with reference to the ternary Ni-Si-B and quaternary Ni-Cr-B-Si systems. Quenched interrupted, directional solidification is employed to establish the solidification sequence. The transformation temperatures are measured by differential thermal analysis. Solid-state transformations occurring during the cooling process are described. A model of the solute exchanges during solidification is proposed in order to predict the amount of liquid remaining at each stage in the process, particularly at the last stage when all the eutectic liquid is frozen in.

Journal ArticleDOI
TL;DR: In this paper, the upward directional solidification of a dilute binary alloy in a tall, thin, two-dimensional slot is considered, and an asymptotic approach is used which relates the small heat loss to the thinness of the solidification cell, and solutions for the resulting melt convection, interface deflection, and the distribution of heat and solute.

Journal ArticleDOI
TL;DR: The algorithm for time integration combines a fully implicit Adams-Moulton algorithm with the Isotherm-Newton method for solving the nonlinear set of differential-algebraic equations that result from the spatial discretization of the moving-boundary problem.
Abstract: Galerkin finite element methods are presented for calculation of the dynamic transitions between planar and deep two-dimensional cellular interface morphologies in directional solidification of a binary alloy from models that include solute transport, the phase diagram, and the interfacial free energy between melt and crystals. The unknown melt-solid interface shape is accounted for in the finite element formulation by mapping the equations to a fixed domain. Novel nonorthogonal transformations are introduced combining cylindrical and Cartesian coordinate interface representations for approximating the deep cellular interfaces that evolve from a planar solidification front. The algorithm for time integration combines a fully implicit Adams-Moulton algorithm with the Isotherm-Newton method for solving the nonlinear set of differential-algebraic equations that result from the spatial discretization of the moving-boundary problem. The fully implicit scheme is found to be more accurate and efficient than an explicit predictor-corrector algorithm. Sample calculations show the connectivity between families of shapes with resonant spatial wavelengths.


Journal ArticleDOI
TL;DR: The competition between stable and metastable solidification in Fe-C-X alloys has been studied theo-retically, with particular regard to phase stability, nucleation, and growth processes.
Abstract: The competition between stable and metastable solidification in Fe-C-X alloys has been studied theo-retically, with particular regard to phase stability, nucleation, and growth processes. The effects of small additions of Si, P, Cr, Mn, Ti, Al, and S upon the transition velocities from grey to white and from white to grey in directional solidification are related to their influence on the eutectic tempera-tures, and nucleation and growth undercoolings. It is shown that the consequences of simultaneously adding Si and Cr upon the transition velocities can be deduced from the results of adding of Si and Cr separately only when the detailed effects of these elements upon phase stability, nucleation, and growth are known. The well-known carburizing effect of a high thermal gradient (superheat) has been shown to influence only the nucleation process. A three-phase austenite-graphite-cementite mi-crostructure resulting from the cooperative growth of a double stable/metastable eutectic has been observed for the first time.

Journal ArticleDOI
TL;DR: An experimental study to evaluate and characterize the effects of inverted density layers during the directional solidification of metal alloys is described in this paper, where the temporal history of the layers in front of a dendritic interface for directionally solidified ammonium-chloride 72-wt% water is presented based on photographic data taken using a laser schlieren system and compared with predicted values.
Abstract: An experimental study to evaluate and characterize the effects of inverted density layers during the directional solidification of metal alloys is described. The temporal history of the inverted density layers in front of a dendritic interface for directionally solidified ammonium-chloride 72-wt-% water is presented based on photographic data taken using a laser schlieren system and compared with predicted values. Data are given for both 1- and low-g solidification runs and the stability of the layer is discussed. The reduction of buoyancy effects is shown to be significant and the impact of reducing gravity level on freckling in metal alloys is speculated.

Journal ArticleDOI
TL;DR: In this article, the effect of rigid side walls on the onset of solutal convection in the melt is investigated for upward solidification of a binary alloy and the physics is described by the Navier-Stokes equations in the Boussinesq approximation and by the balance of solute, which is coupled with the appropriate boundary conditions.
Abstract: In this study the effect of rigid side walls on the onset of solutal convection in the melt is investigated for upward solidification of a binary alloy. The physics is described by the Navier–Stokes equations in the Boussinesq approximation and by the balance of solute, which is coupled with the appropriate boundary conditions. By using a Tau–Chebyshev spectral method the numerical resolution of the perturbed system has been carried out for two alloys: lead–tin, which is the reference in the literature, and lead–thallium, which is currently under study. For both cases the lateral confinement has a stabilizing effect for all the aspect ratios that have been considered.

Journal ArticleDOI
TL;DR: In this paper, a finite element model is used for the study of thermosolutal convection in binary alloys during vertical directional solidification under the assumption of a planar undeformable interface with constant growth velocity.
Abstract: A finite element model is used for the study of thermosolutal convection in binary alloys during vertical directional solidification under the assumption of a planar undeformable interface with constant growth velocity. The fluid region is modeled as a two-dimensional viscous incompressible flow that satisfies the Boussinesq approximation, coupled with two convective-diffusion equations for thermal and solute transport. Results obtained for the case of an infinitely wide layer of fluid, assuming that the flow is cyclic in that direction, are in excellent agreement with previously calculated ones and give the first independent verification of the results. Calculations for a finite layer of fluid, bounded by solid adiabatic vertical walls, are also performed, and the results discussed.

Journal ArticleDOI
TL;DR: This work presents an alternative asymptotic approach that isolates and preserves the crucially important nonlinearities in their original form, and thus preserves the proper behavior at large amplitudes during pattern formation.
Abstract: Directional solidification in the presence of an impurity may be described by a set of impurity-concentration and thermal-diffusion equations coupled at a free boundary. Small deviations of the interface from planarity can be described by a single fourth-order equation. This equation is derived by a long-wavelength, small-amplitude expansion in the limit of a small distribution coefficient. We present an alternative asymptotic approach that isolates and preserves the crucially important nonlinearities in their original form, and thus preserves the proper behavior at large amplitudes during pattern formation. The resulting evolution equation is in better agreement with the physical phenomena of front destabilization and droplet creation than are previously presented models. The formation of different solidification patterns is numerically elucidated.

Journal ArticleDOI
TL;DR: In this paper, various Cu-Pb-Al alloys were directionally solidified under 1g conditions and alternating high-g/low-g conditions (achieved using NSAS's KC-135 aircraft) as a means of studying the influence of interfacial energies and gravitational levels on the resulting microstructures.
Abstract: Various Cu-Pb-Al alloys were directionally solidified under 1-g conditions and alternating high-g/low-g conditions (achieved using NSAS's KC-135 aircraft) as a means of studying the influence of interfacial energies and gravitational levels on the resulting microstructures. Directional solidification of low Al content alloys was found to result in samples with coarser more irregular microstructures than in alloys with high Al contents under all the gravity conditions considered. Structures are correlated with interfacial energies, growth rates, and gravitational levels.

Journal ArticleDOI
TL;DR: In this paper, aluminum-6.1 wt. pct. nickel-silicon carbide composites were directionally solidified at different translation rates and temperature gradients, under variable gravity levels.
Abstract: Aluminum-6.1 wt. pct. nickel-silicon carbide composites containing varying volume fractions and particle sizes of SiC were directionally solidified at different translation rates and temperature gradients, under variable gravity levels. High-gravity, high-volume fractions of particles or high effective viscosity of liquid favored the engulfment of particles by the melt interface. Solidification under low gravity seemed to deflocculate the SiC particle agglomerates, while opposite results were obtained when solidifying under high gravity. Intercellular spacings were higher under low gravity solidfication.

Journal ArticleDOI
TL;DR: In this paper, the suitability of the KC-135 environment for directional solidification of monotectic alloys is discussed, and differences within these regions are examined, and a suitability for the flight of the aircraft is discussed.
Abstract: Hypermonotectic copper-lead alloys were directionally solidified at unit gravity on earth and also in the cyclic gravitational environment attainable during flight of NASA's KC-135 aircraft. In both cases macrosegregation developed that consisted of an initial lead-rich phase above which an aligned composite structure of apparent monotectic composition grew. Differences within these regions are examined, and the suitability of the KC-135 environment for directional solidification of monotectic alloys is discussed.


Proceedings ArticleDOI
01 Jan 1988
TL;DR: In this article, numerical calculations of the solute and fluid flow fields in the melt have been carried out using finite differences in a two-dimensional, time-dependent model that assumes a planar crystal-melt interface and allows timedependent gravitational accelerations.
Abstract: During directional solidification of a binary alloy at constant velocity, buoyancy-driven fluid flow may occur due to the solute gradients generated by the solidification process. Numerical calculations of the solute and fluid flow fields in the melt have been carried out using finite differences in a two-dimensional, time-dependent model that assumes a planar crystal-melt interface and allows time-dependent gravitational accelerations. The container walls are rigid and perfectly insulating for solute. For constant vertical gravitational accelerations, as the solutal Rayleigh number is varied, multiple steady states and time-dependent states may occur. The bifurcation from the quiescent state may be subcritical or transcritical, depending on the aspect ratio of the container. Calculations have also been performed for a gravitational acceleration that is assumed to be uniform in magnitude with its direction rotating uniformly. Numerical results have been obtained for a Schmidt number of 10 and a gravitational acceleration of 0.0001 G. The maximum variation in the solute concentration at the crystal-melt interface is calculated for various values of the rotation rate of the gravitational acceleration.