Modelling directional solidification
The influence of convection and freezing rate fluctuations on compositional homogeneity and crystalline perfection was studied.
Wilcox, William R.↗
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Double diffusive convection during directional solidification - Nonlinear analysis
The dynamics of doubly diffusive convective flow during the constant-velocity vertical solidification of binary melts to form single-phase solids is examined, summarizing the results of recent experimental and analytical investigations. The effects of horizontal temperature gradients are considered; the nonlinearities of the system and their numerical treatment are discussed; and numerical results are presented graphically for the solidification of a Pb melt containing 0.0015 wt pct Sn, with growth velocity 0.0002 cm/s and a temperature gradient of 200 K/cm in the liquid.
Coriell, S. R.↗
Cellular interface morphologies in directional solidification. II - The effect of grain boundaries
A singular perturbation analysis valid for small grain-boundary slopes is used with the one-sided model for solidification to show that grain boundaries introduce imperfections into the symmetry of the developing cellular interfaces which rupture the junction between the family of planar shapes and the bifurcating cellular families. Undulating interfaces are shown to develop first near grain boundaries, and to evolve with decreasing temperature gradient either by a smooth transition from the almost planar family or by a sudden jump to moderate-amplitude cellular forms, depending on the growth rate.
Ungar, Lyle H.↗
Petrov-Galerkin methods for natural convection in directional solidification of binary alloys
A Petrov-Galerkin finite element method is presented for calculation of the steady, axisymmetric thermosolutal convection and interface morphology in a model for vertical Bridgman crystal growth of nondilute binary alloys. The Petrov-Galerkin method is based on the formulation for biquadratic elements developed by Heinrich and Zienkiewicz and is introduced into the calculation of the velocity, temperature and concentration fields. The algebraic system is solved simultaneously for the field variables and interface shape by Newton's method. The results of the Petrov-Galerkin method are compared critically with those of Galerkin's method using the same finite element grids. Significant improvements in accuracy are found with the Petrov-Galerkin method only when the mesh is refined and when the formulation of the residual equations is modified to account for the mixed boundary conditions that arise at the solidification interface. Calculations for alloys with stable and unstable solute gradients show the occurrence of classical flow transitions and morphological instabilities in the solidification system.
Adornato, Peter M.↗
Analysis of low gravity tolerance of model experiments for space station: Preliminary results for directional solidification
It has become clear from measurements of the acceleration environment in the Spacelab that the residual gravity levels on board a spacecraft in low Earth orbit can be significant and should be of concern to experimenters who wish to take advantage of the low gravity conditions on future Spacelab missions and on board the Space Station. The basic goals are to better understand the low gravity tolerance of three classes of materials science experiments: crystal growth from a melt, a vapor, and a solution. The results of the research will provide guidance toward the determination of the sensitivity of the low gravity environment, the design of the laboratory facilites, and the timelining of materials science experiments. To data, analyses of the effects of microgravity environment were, with a few exceptions, restricted to order of magnitude estimates. Preliminary results obtained from numerical models of the effects of residual steady and time dependent acceleration are reported on: heat, mass, and momentum transport during the growth of a dilute alloy by the Bridgman-Stockbarger technique, and the response of a simple fluid physics experiment involving buoyant convection in a square cavity.
Alexander, J. Iwan D.↗
Convective effects on directional solidification of a simulated metal alloy
The first significant results of a ground-based experimental program which supports a low gravity space processing Spacelab experiment are reported. The phenomena which precipitate pluming and thus freckling in a metal alloy analog (ammonium chloride and water) are studied in detail and the sequential events leading to massive channeling and convection are optically documented. The pluming is shown to be other than a random burst of unstable fluid from a preferred channel but rather a natural occurrence resulting from a fundamental (Rayleigh-Benard) fluid dynamic instability at the density inversion interface. This extrapolates to critical size parameters appropriate to processing of actual metal alloys.
Mccay, T. D.↗
Directional solidification of flake and spheroidal graphite cast iron in low and normal gravity environment
A NASA KC-135 research aircraft, flying repeated low-g trajectories that yield 20-30 sec of 0.1-0.001 g microgravity, has been used to study microgravity solidification's elimination of sedimentation and convection (with formation of unique and advantageous microstructures) for the case of eutectic-composition cast irons. The solidification interface of hypereutectic flake and spheroidal graphite cast irons has been slowly advanced through a 4 mm-diameter rod sample. Sample solidification rates have been correlated with accelerometer data, while independently controlling thermal gradients and solidification rates.
Hendrix, J. C.↗
Heat flow control and segregation in directional solidification: Development of an experimental and theoretical basis for Bridgman-type growth experiments in a microgravity environment
Within the framework of the proposed research, emphasis was placed on application of magnetic fields to semiconductor growth systems. It was found that magnetic fields up to 3 kGauss do not affect the growth behavior nor the macro-segregation behavior in the system Ge(Ga). Applied fields are found to significantlty alter the radial dopant distribution, which is attributed to alterations in the spatial orientation of convective cells. Increasing the magnetic field to 30 kGauss is found to have a fundamental effect on dopant segregation. Emphasis is also placed on the potential of KC-135 flights for preliminary studies on the effects of reduced gravity environments on the wetting behavior of semiconductor systems in growth configuration. The limited number of experiments conducted does not allow any conclusions on the merits of KC-135 flights for semiconductor processing research.
Witt, A. F.↗
Morphological instabilities in directional solidification of a binary alloy - End effects
This paper considers the unidirectional solidification of a binary alloy for which the liquid and solid phases are bounded by endwalls. In order to account for the transport of latent heat and solute, thermal and solutal boundary layers must be placed at the solidifying interface. Further, under the assumption of fixed temperature gradients, the presence of the endwalls leads to a velocity of solidification that decreases with time, and hence to an unsteady basic state having a planar interface. From a stability analysis of this state, a nonlinear long-wave evolution equation of Sivashinsky type is derived, with modified coefficients, that shows how the onset of cellular structure is delayed by the presence of endwalls.
Young, Gerald W.↗
Shallow cells in directional solidification
The existing theory on two-dimensional transitions (appropriate to thin parallel-plate geometries) is presented in such a way that it is possible to identify easily conditions for the onset of shallow cells. Conditions are given under which succinonitrile-acetone mixtures should undergo supercritical bifurcation in experimentally accessible ranges. These results suggest a means for the quantitative test of the Mullins and Sekerka (1964) model and its weakly nonlinear extensions.
Merchant, G. J.↗
Convective instabilities during directional solidification
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Mccay, T. D.↗
Hydrodynamic interactions in directional solidification
A binary liquid undergoes unidirectional solidification. The one-dimensional steady state is susceptible to morphological instability that causes the solid/liquid interface to change from a planar state to a cellular pattern. This paper examines the effects on this transition of volume-change convection, buoyancy-driven convection or forced flows. It emphasizes how flows alter stability limits, create scale and pattern changes in morphology, and create, through coupling, new instabilities. Emphasis is placed on the physical mechanisms of the interactions.
Davis, Stephen H.↗
A novel approach to determine the heat transfer coefficient in directional solidification furnaces
The heat transfer coefficient between a molten charge and its surroundings in a Bridgman furnace was determined using an approach utilizing in-situ temperature measurement. The ampoule containing an isothermal melt was suddenly moved from a higher temperature zone to a lower temperature zone. The temperature-time history was used in a lumped-capacity cooling model to evaluate the heat transfer coefficient between the charge and the furnace. The experimentally determined heat transfer coefficient was of the same order of magnitude as the value estimated by standard heat transfer calculations.
Banan, Mohsen↗
Morphological instability in rapid directional solidification
Mullins and Sekerka (1964) showed for fixed temperature gradient that the planar interface is linearly stable for all pulling speeds V above some critical value, the absolute stability limit. Near this limit, where solidification rates are rapid, the assumption of local equilibrium at the interface may be violated. Here, nonequilibrium effects are incorporated into a linear stability analysis of the planar front by allowing the segregation coefficient and interface temperature to depend on V in a thermodynamically consistent way. The absolute stability limit of the cellular mode is modified. A new oscillatory state is formed which, in the absence of latent heat, has a critical wavenumber of zero; by itself this instability would lead to the formation of solute bands in the solid. This mode has its own absolute-stability limit determined by solute trapping and kinetics. Under certain conditions, there exists a window of stability above the steady absolute-stability boundary and below the oscillatory-stability boundary; here the planar segregation-free state is restabilized.
Merchant, G. J.↗
Three-dimensional flow transport modes in directional solidification during space processing
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Arnold, W. A.↗
Instability during directional solidification - Gravitational effects
After an elementary introduction to solidification, recent research that attempts to understand the interaction of fluid flow with a crystal-melt interface under gravitational influence using linear stability analysis is reviewed. Recent numerical calculations of fluid flow and interface morphology during alloy solidification are briefly discussed.
Coriell, S. R.↗
An experimental approach to determine the heat transfer coefficient in directional solidification furnaces
The heat transfer coefficient between a molten charge and its surroundings in a Bridgman furnace was experimentally determined using in-situ temperature measurement. The ampoule containing an isothermal melt was suddenly moved from a higher temperature zone to a lower temperature zone. The temperature-time history was used in a lumped-capacity cooling model to evaluate the heat transfer coefficient between the charge and the furnace. The experimentally determined heat transfer coefficient was of the same order of magnitude as the theoretical value estimated by standard heat transfer calculations.
Banan, Mohsen↗
Thermal effects in rapid directional solidification - Linear theory
We study the morphological instability of the planar solid/liquid interface for a unidirectionally-solidified dilute binary mixture. We use a model developed by Boettinger et al. (1985, 1986), Aziz (1982), and Jackson et al. (1980), which allows for nonequilibrium effects on the interface through velocity-dependent segregation and attachment kinetics. Two types of instabilities are found in the linear stability analysis: (1) a cellular instability, and (2) an oscillatory instability driven by disequilibrium effects. Merchant and Davis (1990) characterized these instabilities subject to the frozen-temperature approximation (FTA). The present work relaxes the FTA by including the effects of latent heat and the full temperature distribution. Thermal effects slightly postpone the onset of the cellular instability but dramatically postpone the onset of the oscillatory instability; however, the absolute-stability conditions, at which at high speed the cellular and oscillatory instabilities are suppressed, remain unchanged from the FTA.
Huntley, D. A.↗