Showing papers on "Directional solidification published in 1985"

Diffusion on fractals.

Abstract: The issue of diffusion on fractals is addressed with stress on the question of how to generalize the diffusion equation for Euclidean lattices to the case of fractal lattices. Such an equation is proposed on the basis of scaling arguments. The solutions of this equation are interpreted as analytic envelopes of the exact probability distribution P(r,t) which is far from smooth. In fact it is shown that P(r,t) has discontinuities which appear self-similarly on all length scales. The exactly soluble examples of Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski gaskets embedded in general dimension d are analyzed. The predstudied by assuming that the sticking probability of the particles depends on the local orientation of the interface. Directional solidification is simulated by the deposition of particles undergoing biased random walks. Linearly stable patterns are generated if the basic features of the directional solidification experiments are taken into account. The resulting patterns are very similar to those observed experimentally.

Cellular Growth During Directional Solidification

Abstract: During steady state directional solidification of an alloy there is uniform motion of the sample relative to its thermal environment, and the solid­ liquid interface propagates at constant velocity. In the case of a single phase solid and a planar solid-liquid interface, there exist simple analytical solutions for the temperature and solute fields. Tiller et al (1) addressed the experimental observation that the solid-liquid interface is sometimes unstable; they associated this instability in interface shape with growth conditions for which there is constitutional supercooling. Subsequently, linear stability analyses (2--4) established a rigorous criterion for the stability of a planar interface subject to small disturbances. For small solidification velocities (typically < 10 2 cm s -1), the constitutional supercooling criterion and the stability criterion are quite similar, while at

Cellular interface morphologies in directional solidification. IV. The formation of deep cells.

Abstract: Much lheoretical research ovcr th€ last dccadc has be€n aimed at dcscribinS rhe evolution of sr€adity growing ccl-lular solidificalion inrcrfaces in a binary alloy.r-s These calculalions have d€scribed rhe formarion of mod€rate-amplitudc, tu,o-dimensional cellular interfac.s from thc planar srare, by eith€r decreasing th€ dimensionlGs tem-pcraturc gradimt G or incrersinS th€ dimcnsionless growlh vclocity P from thc crilical values predict€d by lincar thcory.6 Calculations of sparially p€riodic cclls are summariz€d in our recent paper5 for sotidificarion modets thal ac€ount differently for heat transfer in the melt and solid and for th€ €ffect of diffusion in rhe solid. These results and those in Rel 4 show that ccllular intcrfaccs with th€ same spatial wavelengrh i,:L. predicred by tinear theory evolve until rhey los€ srability to spalialy periodic cells c/i!h half this wavelensth. Th€ transition occurs as a sccondary bifurcation betwcen familics of cells with th€ two differcnl waveleDgths and marks rhc end, in rcrms of €ith€r G or P, of the cells with wavelengrh i-; onty cetls with l:1./2 exisr bevond this Doint. In all the crlculatioDs to date the metl-solid irrerface has !€€n reprEented by rhe Canesian-Mong.' projection /-,' {r) onto lhe planar fronr, where, measurB disranc€ in the gmwtft dir€ction and x is tangmr ro rhc tat inkF face. Usin8 rhis represenration, the sid6 of the rroov.s for rhc mosr defomed melt-\\olid interfa\". *or-be u*_ tical. Calculations itr Refs. 4 and 5 with a varicty of so_ lidification models were terminarcd when the Eroove violared rhis consrmint lo rh€ accuracy of rhe finir+ elemena appronmations used. To cmti'|uc th. crlcula-tions o[ c€lls with wavetenglh ,]t /2 requir€s a more com_ plex Inlerlac€ represenration rha! ajlows rhe surfac€ ro fold over as viewed from rhe oriSinal pla|E form. A {yltz€d ccll wilh such fotds is shown as Fic. l. In steady growrh, material sotidifying ar poitrl ,{ is Lnvccr ed throuSh lhe solid to point 8, where it r€mehs. Tbe concentration in rh€ solid neer , is determined bv rhe concentration frozen rn ar ,4 and by rhe amounr oi drf. fNion in thc solid. The material mettinS at , has a towcr concentration and a higher effectiv€ melting remp.rarure as a rcsult of the renekinS. The coupltng bet$ecn rhc melting and frcezrng on eirher sidc of a Drorrusron can lead to translation of thc fold atong rhe crli as a dcndritic sidearm. BeginninS wilh thc famous results of Jackson and …

Formation of solidification patterns in aggregation models.

Abstract: Generalizations of the diffusion-limited aggregation model are considered in order to simulate pattern formation during solidification. The two-dimensional clusters grown on a seed particle are initially circular but at later stages the process crosses over into dendritic growth. The effects of an anisotropic surface tension are studied by assuming that the sticking probability of the particles depends on the local orientation of the interface. Directional solidification is simulated by the deposition of particles undergoing biased random walks. Linearly stable patterns are generated if the basic features of the directional solidification experiments are taken into account. The resulting patterns are very similar to those observed experimentally.

Cellular interface morphologies in directional solidification. III - The effects of heat transfer and solid diffusivity

Abstract: The shape and stability of two-dimensional finite-amplitude cellular interfaces arising during directional solidification are compared for several solidification models that account differently for latent heat released at the interface, unequal thermal conductivities of melt and solid, and solute diffusivity in the solid. Finite-element analysis and computer-implemented perturbation methods are used to analyze the families of steadily growing cellular forms that evolve from the planar state. In all models a secondary bifurcation between different families of finite-amplitude cells exists that halves the spatial wavelength of the stable interface. The quantitative location of this transition is very dependent on the details of the model. Large amounts of solute diffusion in the solid retard the growth of large-amplitude cells.

Solutal convection and morphological instability in directional solidification of binary alloys

Abstract: We study the effect of the coupling between front deformation and solutal convection on the position of the bifurcation from the planar quiescent state of a dilute binary alloy submitted to directional solidification. We set up a perturbation treatment of the coupling between the «bare» (Mullins-Sekerka and solutal convective) bifurcations. We show that the shift of the Mullins-Sekerka bifurcation is extremely small at usual values of the applied thermal gradient, and is accurately predicted by the first order perturbation expression. The shift of the convective bifurcation, though much larger, can also be calculated with very good accuracy in the same range of values of the thermal gradient with the help of the first order approximation. We give a qualitative interpretation of these results in terms of an effective Rayleigh number and of the mismatch between the critical wavevectors of the uncoupled system Etude de l'effet du couplage entre la deformation du front solide-liquide et la convection solutale sur la position de la bifurcation a partir de l'etat plan quiescent pour un alliage binaire dilue soumis a un processus de solidification dirigee. Developpement d'un traitement de perturbation du couplage entre les bifurcations «nues» correspondant aux instabilites de Mullins-Sekerka et de convection solutale classiques. Interpretation qualitative des resultats obtenus en termes d'un nombre de Rayleigh effectif et de l'ecart entre les vecteurs d'onde critiques en l'absence de couplage

Solutal convection and morphological instability in directional solidification of binary alloys. - II. Effect of the density difference between the two phases

Abstract: We extend the perturbative analysis of the coupling between front deformation and solutal convection performed in a recent article [3] to include the effect of «advection», i.e. of the flow induced by the density change associated with solidification. We study the resulting shifts of the bifurcation from the stationary planar front regime. We show that, for the convective branch, the effect of advection is comparable to that of the convection-deformation coupling, while, for the morphological branch, it is by far dominant Extension de l'analyse de perturbation du couplage entre deformation de front et convection solutale pour tenir compte de l'effet de l'«advection», c'est-a-dire de l'ecoulement induit par la variation de densite qui accompagne la solidification. Etude du deplacement de la bifurcation a partir du regime stationnaire a front plan

Crystallographically aligned metal–oxide composite made by reduction of a directionally solidified oxide–oxide eutectic

Abstract: Aligned metal–oxide composite materials have been grown from the melt by directional solidification at eutectic composition of several binary metal–oxide systems. The resulting microstructures consist of metallic fibres ∼1 µm in diameter imbedded in an oxide matrix1,2. The occurrence of such fibrous structures, as opposed to lamellar structures, corresponds to eutectic compositions for which the volume fraction of the minor component is <30% (ref. 3). The work reported here presents a different route to the fabrication of aligned metal–oxide composites, making the production of fine–scale lamellar microstructures possible. The method consists of the chemical reduction of lamellar oxide–oxide eutectic structures in conditions of temperature and partial pressure of oxygen in which only one of the oxides is transformed to the corresponding metal. We show here how the method can be successfully applied to the preparation of aligned Ni–ZrO2 lamellar structures.

N ‐ CuInS2 / Sulfide ‐ Polysulfide Electrochemical Photovoltaic Cells

Abstract: Large-grained photovoltaic n-CuInS2 was prepared by directional solidification. The as-grown material had doping levels of approximately 6 x 10 to the 16th per cu cm, a minority carrier diffusion length of approximately 1 micron, and a maximum efficiency of 6.4 percent in a sulfide-polysulfide electrolyte under simulated AM2 conditions. CuInS2 thin films were also made by an elemental vacuum evaporation technique with observed efficiencies of 2 percent. These electrodes had high doping densities (equal to or greater than 10 to the 17th), short diffusion lengths (approximately 0.05 micron), and recombination dominated I-V behavior. 31 references.

Preparation and electrical properties of a directionally solidified Ge‐TiGe2 eutectic

Abstract: Directional solidification of a Ge‐TiGe2 eutectic yields an array of aligned TiGe2 fibers in a Ge matrix. These aligned metallic fibers result in a highly anisotropic material such that the ratio of the resistivities perpendicular and parallel to the rods is typically 102–103 at room temperature and even larger at low temperatures. The resistivity of these semiconductor based eutectic composites is examined as a function of the type and concentration of donors. A significant distinction in the resistivity perpendicular to the rods is observed between composites with a p‐type and n‐type Ge matrix. This difference is analyzed in terms of the depletion layers at the metal‐semiconductor junction, as well as the high density of crystalline defects in the Ge created by the two phase solidification and cooling stresses.

Method for production of combustion turbine blade having a hybrid structure

Abstract: A process of fabricating directionally solidified turbine blades for combustion turbines, in which a mold containing molten metal is cooled in a controlled fashion so that solidification occurs slow enough to allow directional solidification beginning at the airfoil end. The solidification is monitored and magnetic mixing of the remaining molten metal is started at approximately the beginning of solidification of said root section and the rate of cooling of said blade is increased to a rate faster than at which directional solidification occurs. A blade is produced with a directionally solidified airfoil section and a fine grained root section.

Method of reducing casting time

Abstract: An improved method of casting an article decreases the time required to cast the article without affecting the quality of the article. When a directionally solidified (DS) casting is made, molten metal is poured into a mold cavity. One end of the mold cavity is exposed to a chill plate which initiates solidification of the molten metal. As the metal solidifies, a dendritic structure grows upwardly into the mold cavity. Molten metal is disposed in the interstices of the uppermost portions of dendritic structure. As the metal in the mold cavity cools, the molten metal in the interstices solidifies and the dendritic structure, including a region containing some molten metal in the interstices, continues to grow upwardly toward the upper end of the mold cavity. The directional solidification of the metal in the mold cavity is promoted by slowly withdrawing the mold from a furnace as the molten metal solidifies. In accordance with the present invention, when the upper end of the dendritic structure reaches the upper end of the mold cavity, the rate of withdrawal of the mold from the furnace is substantially increased to accelerate the solidification of the remaining molten metal.

Superalloy microstructural variations induced by gravity level during directional solidification

Abstract: The Ni-base superalloy MAR-M246 (Hf) was directionally solidified during low gravity maneuvers aboard a NASA KC-135 aircraft. Gravity force variations during this process yielded a concomitant variation in microstructure and microsegregation. Secondary dendrite arm spacings are noted to be larger in the low-g portion; this, in turn, decreases the extent of interdendritic segregation. The amount of Hf in both the carbides and interdendritic eutectic increases as the gravity force diminishes. Fewer carbides are present in the low-g regions.

Polygon cross section seed for directional solidification

Abstract: in the directional solidification of single crystal castings the seed crystal (90) is specially fit within the starter section (92) of the mold (93) to minimize angular rotation to less than 0.6 degrees. Preferably the seed (90) is polygon shaped in cross section and has planar sides.

Method and apparatus for growing single crystal bodies

Abstract: A method and apparatus for use in growing single crystal bodies. The method includes directional solidification techniques in which a boule is pulled from a thermally controlled melt on a substantially continuous basis while the melt is continuously replenished from feed stock. The process is carried out in a vacuum and with or without a melt overflow. The apparatus includes a shallow through crucible (26), multiple pulling zones (40) and continuous silicon feed means (24) controlled by the melt level.

Precipitation of Titanium and Zirconium Sulfides during Uni-directional Solidification

Abstract: Morphologies, chemical compositions and distribution of sulfide inclusions in steel have been examined on uni-directionally solidified iron alloy containing about 0.1% sulfur and one of sulfide forming elements; Mn about 1%, Ti about 0.5 or 1%, and Zr about 0.1 or 0.3%.The results obtained are summarized as follows;(1) Almost all of titanium and zirconium sulfides are observed in an interdendritic space in the morphology of Type II. The number density and mean diameter of these sulfides are approximately same as those for MnS.(2) In titanium added alloys many sulfide colonies consisting of rod- and/or plate-like TiS are observed, whose area fraction amounts to 0.2.(3) Rod- and plate-like inclusions observed in zirconium dded alloys make solid solution with manganese sulfide to form (Zr, Mn)3S4(Zr/Mn molar ratio: 0.4-3.5) and approach to a spherical form in the existence of manganese with about 1%.(4) The supersaturation for these sulfides to precipitate in the solidification sequence has been evaluated by use of phosphorus content in the steel matrix adjacent to a given sulfide precipitate. The supersaturation for sulfide precipitation is evaluated as follows;MnS : 1.0-1.7, TiS : 1.0-1.7, Zr3S4: 3.0-10 where the equilibrium relations between sulfur and sulfide forming elements determined by authors, and solute enrichment during solidification are taken into account.

Casting Process Developments for Improving Quality

Abstract: This paper presents a short synopsis of the important developments in casting/solidification processes, as well as the important advances in the conventional methods. These developments are discussed related to quality aspects. The position of each process with respect to practice, as well as expected gains in cost, are examined. The paper briefly features the author’s work on innovative processes (directional solidification, rheocasting, squeeze-casting and rapid solidification) as well as work of other investigators on developments in conventional methods.

Orbital Processing of Aligned Magnetic Composites

Abstract: Experiments will be conducted on the space shuttle in which aligned, two-phase magnetic composites will be grown by plane front directional solidification. The objectives are to: (1) identify and quantitatively evaluate the influences of gravitationally driven thermo-solutal convection on contained plane front solidification of binary, eutectic, off-eutectic, and peritectic magnetic composites; (2) to evaluate the effectiveness of micro-g processing as a means of damping convection; and (3) to evaluate the uniqueness of micro-g processing relative to the best of terrestrial convection damping.