Showing papers on "Directional solidification published in 1998"

Particle engulfment and pushing by solidifying interfaces: Part II. Microgravity experiments and theoretical analysis

Abstract: Results of the directional solidification (DS) experiments on particle engulfment and pushing by solidifying interfaces (PEP), conducted on the space shuttle Columbia during the Life and Microgravity Science (LMS) Mission, are reported. Two pure aluminum (99.999 pct) 9 mm cylindrical rods, loaded with about 2 vol pct 500µm-diameter zirconia particles, were melted and resolidified in the microgravity (µg) environment of the shuttle. One sample was processed at a stepwise increased solidification velocity and the other at a stepwise decreased velocity. It was found that a pushing/engulfment transition (PET) occurred in the velocity range of 0.5 to 1 µm/s. This is smaller than the ground PET velocity of 1.9 to 2.4 µm/s. This demonstrates that natural convection increases the critical velocity. A previously proposed analytical model for PEP was further developed. A major effort to identify and produce data for the surface energy of various interfaces required for calculation was undertaken. The predicted critical velocity for PET was 0.775 µm/s.

The creep and thermal stability characteristics of a unidirectionally solidified Al2O3/YAG eutectic composite

Abstract: Compressive creep characteristics at 1773, 1873, and 1973 K, oxidation resistance over 1000 h at a temperature of 1973 K in ambient air, and the thermal stability characteristics at 1973 K in ambient air of a unidirectionally solidified Al2O3/YAG eutectic composite were evaluated. At a test temperature of 1873 K and a strain rate of 10−4/s, the compressive creep strength of a eutectic composite manufactured by the unidirectional solidification method is approximately 13 times higher than that of a sintered composite with the same chemical composition. The insite eutectic composite also showed greater thermal stability, with no change in mass after an exposure of 1000 hours at 1973 K in ambient air. The superior high-temperature characteristics are closely related to such factors as (1) the in-situ eutectic composite having a microstructure, in which single crystal Al2O3 and single crystal YAG are three-dimensionally and continuously connected and finely entangled without grain boundaries and (2) no amorphous phase is formed at the interface between the Al2O3 and the YAG phases.

Evolution of dendritic patterns during alloy solidification: onset of the initial instability.

Abstract: The evolution of a dendritic pattern from a planar solid–liquid interface during directional solidification of a binary alloy was investigated experimentally. The model alloy used was the transparent organic crystal succinonitrile doped with the laser dye coumarin 152. The buildup of solute ahead of the initially stable planar interface and the subsequent instability of the planar front were measured in detail and compared with recent theoretical calculations by Warren and Langer [Warren, J. A. & Langer, J. S. (1993) Phys. Rev. E 47, 2702- 2712]. The fluorescence of coumarin 152 was used for direct observations of the evolution of the solute concentration profile ahead of the initially planar solid–liquid interface. UV absorption was used to produce thermal perturbations of the sample that generated spatially periodic modulations of the planar interface. This technique allows for measurement of both positive and negative linear growth coefficients (determined from the growth or decay rate of the modulation after the perturbation is switched off) for a large range of wave vectors. Measurements of the evolution of the concentration profile and the linear growth coefficients, and the occurrence of the initial instability, were in good agreement with the Warren–Langer predictions.

MC carbide formation in directionally solidified MAR-M247 LC superalloy

Abstract: MC-type carbide formation in MAR-M247 LC superalloy was systematically investigated using directional solidification and quenching methods in sample growth rates between 0.8×10−6 and 15×10−6 m s−1. The results indicate that carbide growth rate, carbide forming element enrichment and surrounding solid geometry determine carbide morphology and carbide composition. The carbide forming element enrichment and interface energy control carbide nucleation. Heterogeneous carbide nucleation can occur above the alloy liquidus temperature. Carbide forming element enrichment and trapping behavior of the solid–liquid interface control carbide growth, which occurs at inter-secondary γ-dendrite arm positions and the mushy zone bottom which are rich in carbide forming elements. At fast sample growth rates, the solid–liquid interface can trap carbide nuclei in front of it. This trapping tends to occur at the inter-secondary γ-dendrite arm region.

Microstructural analysis of strip cast Nd–Fe–B alloys for high (BH)max magnets

Abstract: High energy density magnets >400 kJ/m3 are increasingly used in many applications. Conventional casting techniques for sintered magnets reveal the formation of a high quantity of α-Fe and large Nd-rich regions. New techniques, like strip casting, produce homogeneous and fine scaled microstructures and are already used for producing high (BH)max magnets. The fast cooling rate during strip casting suppresses the formation of α-Fe dendrites and of large Nd-rich pockets. Directional solidification causes a formation of columnar grains containing a typical arrangement of hard magnetic Nd2Fe14B regions and Nd-rich regions. The Nd regions occur as intragranular platelets as well as intergranular phases. Intragranular lamellae show a periodicity which corresponds to a eutectoidal solidification according to the composition of the liquid and are directed parallel to the temperature gradient during solidification. The lamellae show an average width of 150 nm, a spacing of 3 μm, and a length up to the size of the hard magnetic grains. The fine separation of the hard magnetic and Nd phases is advantageous for the milling of the alloy after hydrogen decripitation and improves sinterability of magnets. Although the microstructure of strip cast alloys is much finer than that of ordinary cast alloys, the alignment of the powder is not deteriorated and Br is not reduced due to a sufficient large interlamellar spacing between the Nd-rich platelets that enables the formation of single crystal powder particles after milling.

Modeling freckle formation in three dimensions during solidification of multicomponent alloys

Abstract: The formation of macrosegregation defects known as “freckles” was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-W alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.

Particle engulfment and pushing by solidifying interfaces: Part 1. Ground experiments

Abstract: Directional solidification experiments have been carried out to determine the pushing/engulfment transition for two different metal/particle systems. The systems chosen were aluminum/zirconia particles and zinc/zirconia particles. Pure metals (99.999 pct A1 and 99.95 pct Zn) and spherical particles (500 µm in diameter) were used. The particles were nonreactive with the matrices within the temperature range of interest. The experiments were conducted so as to ensure a planar solid/liquid (SL) interface during solidification. Particle location before and after processing was evaluated by X-ray transmission microscopy (XTM) for the Al/ZrO2 samples. All samples were characterized by optical metallography after processing. A clear methodology for the experiment evaluation was developed to unambiguously interpret the occurrence of the pushing/engulfment transition (PET). It was found that the critical velocity for engulfment ranges from 1.9 to 2.4 µm/s for Al/ZrO2 and from 1.9 to 2.9 µm/s for Zn/ZrO2.

Dendrite coarsening during directional solidification of Al–Cu–Mn alloys

Abstract: Steady state directional solidification of Al–3.75%Cu–1.5%Mn and Al–1%Cu–1.5%Mn dendritic monocrystals was interrupted for different lengths of time prior to quenching and dendrite coarsening kinetics were evaluated versus temperature. For a given alloy composition, the isothermal coarsening rate, expressed as the time variation of the normalized specific dendrite surface area, increased with temperature and decreased with time. It also decreased with increasing copper concentration. The secondary dendrite arm spacing increased with time and for shorter times, with decreasing temperature. For Al–3.75%Cu–1.5%Mn alloy this trend was reversed for times exceeding about 1.5 min. For all times the rate of increase of the spacing increased with temperature. Secondary dendrite arm spacing increased with time during solidification and with decreasing growth rate. The dependence of specific surface area on time was predicted reasonably well by combining a coarsening model which is valid for the earlier stages of coarsening with a model which is valid for later stages. Copper diffusion through the liquid was found to be the rate controlling step in dendrite coarsening. Experimental measurements of secondary arm spacing during isothermal coarsening, as well as during solidification agreed reasonably well with model predictions.

Growth of lamellar eutectic dendrites in undercooled melts

Abstract: Electromagnetic levitation is used to undercool bulk samples of eutectic Ni 21.4 at % Si alloys. Large undercoolings ΔT up to ΔT=220 K are achieved by containerless processing of the melts. Crystal growth velocities are measured as a function of undercooling. The growth kinetics during solidification of the eutectic alloys is controlled by atomic diffusion. A maximum in the relation of the growth velocity on undercooling is observed which is due to the progressively decreasing diffusion coefficient counteracting the enhancement of the driving force of crystallization with increasing undercooling. Microstructure analysis of as-solidified samples reveals colonies of eutectic lamellae enveloped by a nonplanar growth front of a dendritelike morphology. The experimental data are analyzed within current models of crystal growth taking into account a negative temperature gradient in front of the solidification front. While the thermal undercooling causes a dendriticlike morphology of the solidification front, co...

Model of banding in diffusive and convective regimes during directional solidification of peritectic systems

Abstract: The formation of banded microstructure in peritectic systems is examined theoretically in both diffusive and convective regimes. A rigorous model is developed in the diffusive regime that describes the non-steady-state growth of alternate solid α and β phase bands with a planar solid-liquid interface. The model is extended to incorporate the effect of convection by assuming that solute diffusion takes place within a boundary layer of constant thickness, with a uniform composition in the mixed liquid zone outside this layer. The model predicts that convection effects in a semi-infinite sample narrow the composition range over which extended banding can occur, and the spacing of bands is reduced compared to the diffusive growth model. In a finite length sample, convection is shown to lead only to the transient formation of bands. In this transient banding regime, only a few bands with a variable width are formed, and this transient banding process can occur over a wide range of compositions inside the two-phase peritectic region. Directional solidification studies in the Pb-Bi system show transient bands and agree qualitatively with these predictions. However, the basic mechanisms of band formation observed in this system is found to be significantly different from the one assumed in the model. A new mechanisms of banding is proposed in which continuous growth of both phases is present instead of nucleation at the boundary of the pre-existing phase. This mechanism yields an oscillatory structure with a shorter spatial periodicity than the band spacing predicted by the purely diffusive or boundary layer convective models.

An adjoint method for the inverse design of solidification processes with natural convection

Abstract: This paper presents a finite element algorithm based on the adjoint method for the design of a certain class of solidification processes. In particular, the paper addresses the design of directional solidification processes for pure materials such that a desired freezing front heat flux and growth velocity are achieved. This is the first time that an infinite-dimensional continuum adjoint formulation is obtained and implemented for the solution of such inverse/design problems with moving boundaries and Boussinesq incompressible flow. The present design problem belongs to a category of inverse problems in which one is looking for the unknown conditions in part of the boundary, while overspecified boundary conditions are supplied in another part of the boundary (here the freezing interface). The solidification design problem is mathematically posed as a whole time-domain optimization problem. The gradient of the cost functional is calculated using the solution of an appropriately defined continuous adjoint problem. The minimization process is realized by the conjugate gradient method via the solutions of the direct, adjoint and sensitivity sub-problems. The proposed methodology is demonstrated with the solidification of an initially superheated liquid aluminum confined in a square mold. The non-uniformity in the casting product in the direction of gravity due to the existence of natural convection in the melt is emphasized. The inverse design problem is then posed as finding the appropriate spatial-temporal variations of the boundary heat flux on the vertical mold walls that can eliminate or reduce the effects of convection on the freezing interface heat fluxes and growth velocity. The numerical example demonstrates the accuracy and convergence of the adjoint formulation. Finally, open related research design problems are discussed. © 1998 John Wiley & Sons, Ltd.

Onset of sidebranching in directional solidification

Abstract: We study the onset of sidebranching of growth cells in directional solidification of impure succinonitrile. Care is taken to obtain uniform cell spacing over large distances in order to use this variable as a true control parameter. Two sidebranching modes referring to different crystalline orientations are observed and their physical equivalence is shown. The onset of sidebranching is identified according to an order parameter and scanned with respect to pulling velocity, thermal gradient, and cell spacing. Its evolution with the control parameters surprisingly reveals that increasing thermal gradient at otherwise fixed velocity and cell spacing enhances sidebranching. These results show the need for improving the experimental characterization and the theoretical description of sidebranching in directional solidification.

Selection of doublet cellular patterns in directional solidification through spatially periodic perturbations

Abstract: Pattern formation at the solid-liquid interface of a growing crystal was studied in directional solidification using a perturbation technique. We analyzed both experimentally and numerically the stability range and dynamical selection of cellular arrays of {open_quotes}doublets{close_quotes} with asymmetric tip shapes, separated by alternate deep and shallow grooves. Applying an initial periodic perturbation of arbitrary wavelength to the unstable planar interface allowed us to force the interface to evolve into doublet states that would not otherwise be dynamically accessible from a planar interface. We determined systematically the ranges of wavelength corresponding to stable singlets, stable doublets, and transient unstable patterns. Experimentally, this was accomplished by applying a brief UV light pulse of a desired spatial periodicity to the planar interface during the planar-cellular transient using the model alloy Succinonitrile-Coumarin 152. Numerical simulations of the nonlinear evolution of the interface were performed starting from a small sinusoidal perturbation of the steady-state planar interface. These simulations were carried out using a computationally efficient phase-field symmetric model of directional solidification with recently reformulated asymptotics and vanishing kinetics [A. Karma and W.-J. Rappel, Phys. Rev. E {bold 53} R3017 (1996); Phys. Rev. Lett. {bold 77}, 4050 (1996); Phys. Rev. E {bold 57}, 4323 (1998)], whichmore » allowed us to simulate spatially extended arrays that can be meaningfully compared to experiments. Simulations and experiments show remarkable qualitative agreement in the dynamic evolution, steady-state structure, and instability mechanisms of doublet cellular arrays. {copyright} {ital 1998} {ital The American Physical Society}« less

A numerical investigation of steady convection in mushy layers during the directional solidification of binary alloys

Abstract: We present a numerical study of steady convection in a two-dimensional mushy layer during the directional solidification of a binary mixture. The calculations reveal the internal structure of strongly nonlinear states featuring upflow which has been focused into solid-free regions known as chimneys. The mushy layer is modelled as a porous medium whose permeability is a function of the local solid fraction. The mushy layer is coupled to a chimney that is modelled as a narrow vertical channel where lubrication scalings are used to simplify the Navier–Stokes equations. We use these methods to exhibit solutions which give the detailed structure of the temperature, solute, flow and solid-fraction fields within the mushy layer. A key finding of the numerics is that there are two distinct chimney solutions at low Rayleigh numbers, presumably corresponding to stable and unstable portions of a subcritical solution branch. We also explore the relationship between convective solutions with and without chimneys.

Anisotropy-driven dynamics of cellular fronts in directional solidification in thin samples

Abstract: We present an experimental investigation of the influence of interfacial anisotropy on the cellular growth patterns observed in directional solidification of the ${\mathrm{CBr}}_{4}\ensuremath{-}8\mathrm{}\mathrm{mol}%$ ${\mathrm{C}}_{2}{\mathrm{Cl}}_{6}$ alloy at pulling velocities less than twice the cellular-threshold velocity. The experiments are performed with single-crystal samples about 8 mm wide and 12 \ensuremath{\mu}m thick. In such samples, the solidification dynamics is essentially two dimensional, and the effective anisotropy of the system can be varied by changing the orientation of the (face centered cubic) crystal with respect to the solidification setup, as was previously established by S. Akamatsu, G. Faivre, and T. Ihle [Phys. Rev. E, 51, 4751 (1995)]. We find that the cellular pattern is unstable at all values of the spacing \ensuremath{\lambda} for crystal orientations corresponding to a vanishing effective interfacial anisotropy. For the other crystal orientations, i.e., for a nonvanishing effective interfacial anisotropy, stable cellular patterns are found over a finite-width \ensuremath{\lambda} range. The various modes of instability limiting this range are described. In particular, we show that a homogeneous tilt bifurcation exists for some orientations of the ``degenerate'' type (i.e., such that a {110} plane of the crystal is parallel to the growth direction and perpendicular to the sample plane). This bifurcation is not spontaneous, however, but a consequence of the particular symmetry of the effective interfacial anisotropy of the system for this crystal orientation.