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Evolution of Dendritic Extended 3D Patterns during Directional Solidification: Microgravity Experiments in DECLIC-DSI onboard ISS and Phase-field Modeling

To characterize the dynamical formation of three-dimensional (3D) arrays of dendrites under diffusive growth conditions, in situ monitoring of a series of experiments on a transparent succinonitrile – 0.46 wt% camphor model alloy was carried out under low gravity in the DECLIC Directional Solidification Insert onboard the International Space Station. These experiments offer continuous interface observation and enable the construction of space-time evolution maps of dendrite location and primary spacing during directional solidification. We present the evolution of dendritic extended 3D patterns for a large range of parameters displaying different levels of side branching in both experiments and phase-field simulations. The combined and separate effects of macroscopic interface curvature and crystal mis-orientation are evidenced and detailed. In addition, the aligned dendritic array caused by the invasion of dendrites formed at the edge of the crucible border is investigated.

Kaihua Ji↗

NASA NTRS1984

Dynamics of dendritic pattern formation

This paper is a brief review of recent and ongoing developments in the theory of dendritic pattern formation. A marginal stability hypothesis has achieved some success in predicting dendritic growth rates, but a fully nonlinear dynamic theory of the dendritic growth mechanism has yet to be developed. A possible clue for the construction of such a theory is the existence of a class of one-dimensional models in which a pattern is found to spread into an unstable region by propagating at the slowest stable speed. This mathematical realization of the marginal stability mechanism has led to the development of a boundary layer model which describes localized dynamics of fully two- or three-dimensional solidification fronts and which retains some of the mathematical features of the propagating systems. Preliminary results of numerical calculations using the boundary layer model indicate that it is capable of probing fully nonlinear features of dendritic pattern formation.

Langer, J. S.↗

NASA NTRS1986

Transition from a planar interface to cellular and dendritic structures during rapid solidification processing

The development of theoretical models which characterize the planar-cellular and cell-dendrite transitions is described. The transitions are analyzed in terms of the Chalmers number, the solute Peclet number, and the tip stability parameter, which correlate microstructural features and processing conditions. The planar-cellular transition is examined using the constitutional supercooling theory of Chalmers et al., (1953) and it is observed that the Chalmers number is between 0 and 1 during dendritic and cellular growth. Analysis of cell-dendrite transition data reveal that the transition occurs when the solute Peclet number goes through a minimum, the primary arm spacings go through a maximum, and the Chalmers number is equal to 1/2. The relation between the tip stability parameter and the solute Peclet number is investigated and it is noted that the tip stability parameter is useful for studying dendritic growth in alloys.

Laxmanan, V.↗

NASA NTRS1987

Dendritic solidification in a binary alloy melt - Comparison of theory and experiment

A simple model for 'constrained' growth of an 'array' of cells or dendrites in a binary alloy melt, in the presence of a positive temperature gradient in the liquid ahead of the tips, is presented. The cell or dendrite tip radius is calculated by adopting both the 'ad hoc' assumption of minimum undercooling at the tips as well as the more recently proposed hypothesis of dendritic growth under conditions of 'marginal stability'. Theoretical predictions of the model have been compared with experimental data in binary succinonitrile-acetone alloys. It has been shown that, according to the present model, the 'marginally stable' state may be virtually indistinguishable from the 'minimum undercooled' state, under the usual conditions of dendritic growth.

Laxmanan, V.↗

NASA NTRS1987

Dendritic growth in a supercooled alloy melt

A simple model which describes the growth of an 'array' of dendrites into a supercooled, binary, alloy melt is presented. Solute diffusion is calculated by superposing the solutions given by Flemings and Zener, and also, by superposing the solutions given by Ivantsov and Flemings. A general expression for the transport solution is suggested from which all other dendrite growth models presented earlier may be obtained as special cases. It is shown that both 'free' and 'constrained' growth may be described by a single transport solution, which indicates that (1) both thermal and solutal effects will be important during 'free' growth in dilute alloys, (2) only solutal effects are predominant during 'free' growth in concentrated alloys and during 'constrained' growth. An examination of the relevant dimensionless parameters also suggests that all dendrite growth models, regardless of the assumptions used to determine the tip radius (marginal stability, minimum undercooling, maximum velocity, minimum entropy production) should predict the experimentally observed extrema in tip radius and growth velocity in dilute alloys, during 'free' dendritic growth. Experimental data in binary H2O-NaCl and succinonitrile-acetone solutions are shown to be in good agreement with the model.

Laxmanan, V.↗

NASA NTRS1988

Isothermal dendritic growth - A proposed microgravity experiment

This paper describes an isothermal dendritic growth experiment (IDGE), a microgravity-oriented spaceborne scientific experiment designed to obtain 'convection-free' dendritic growth and thereby provide a test of dendritic growth theory. The apparatus includes a controlled thermostatic bath capable of providing + or - 2 mK stability, a photographic data collection system, a crystal growth chamber ensuring 'free' dendritic growth, and an optical RAM camera for crystal growth detection. The experiment will be carried on essentially automatically aboard the Materials Science Laboratory in the cargo bay of the Space Shuttle. The results of preliminary ground-based studies are presented.

Glicksman, M. E.↗

NASA NTRS1993

Thermosolutal convection and macrosegregation in dendritic alloys

A mathematical model of solidification, that simulates the formation of channel segregates or freckles, is presented. The model simulates the entire solidification process, starting with the initial melt to the solidified cast, and the resulting segregation is predicted. Emphasis is given to the initial transient, when the dendritic zone begins to develop and the conditions for the possible nucleation of channels are established. The mechanisms that lead to the creation and eventual growth or termination of channels are explained in detail and illustrated by several numerical examples. A finite element model is used for the simulations. It uses a single system of equations to deal with the all-liquid region, the dendritic region, and the all-solid region. The dendritic region is treated as an anisotropic porous medium. The algorithm uses the bilinear isoparametric element, with a penalty function approximation and a Petrov-Galerkin formulation. The major task was to develop the solidification model. In addition, other tasks that were performed in conjunction with the modeling of dendritic solidification are briefly described.

Poirier, David R.↗

NASA NTRS1993

Dendrite preventing separator for secondary lithium batteries

Dendrites are prevented from shorting a secondary lithium battery by use of a first porous separator, such as porous polypropylene, adjacent to the lithium anode that is unreactive with lithium and a second porous fluoropolymer separator between the cathode and the first separator, such as polytetrafluoroethylene, that is reactive with lithium. As the tip of a lithium dendrite contacts the second separator, an exothermic reaction occurs locally between the lithium dendrite and the fluoropolymer separator. This results in the prevention of the dendrite propagation to the cathode.

Shen, David H.↗

NASA NTRS1995

Space flight data from the isothermal dendritic growth experiment

The Isothermal Dendritic Growth Experiment (IDGE) is a NASA space flight experiment which flew as part of the United States Microgravity Payload (USMP-2), in early 1994. The IDGE measured dendritic growth rates, tip radii, and crystal morphologies of ultra-pure succinonitrile (CN-(CH2)2-CN) at supercoolings in the range from 0.05 - 2.0 K. Data taken in the form of slow-scan binary digitized images telemetered to the ground from orbit in near-real time, combined with the IDGE terrestrial data set, provide the first quantitative assessment of various theories on dendritic solidification and the effects of convection on dendritic growth.

Glicksman, M. E.↗

NASA NTRS1995

Dendrite preventing separator for secondary lithium batteries

Dendrites are prevented from shorting a secondary lithium battery by use of a first porous separator such as porous polypropylene adjacent the lithium anode that is unreactive with lithium and a second porous fluoropolymer separator between the cathode and the first separator such as polytetrafluoroethylene that is reactive with lithium. As the tip of a lithium dendrite contacts the second separator, an exothermic reaction occurs locally between the lithium dendrite and the fluoropolymer separator. This results in the prevention of the dendrite propagation to the cathode.

Shen, David H.↗

NASA NTRS1996

Macrosegregation During Dendritic Arrayed Growth of Hypoeutectic Pb-Sn Alloys: Influence of Primary Arm Spacing and Mushy Zone Length

Thermosolutal convection in the dendritic mushy zone occurs during directional solidification of hypoeutectic lead tin alloys in a positive thermal gradient, with the melt on the top and the solid below. This results in macrosegregation along the length of the solidified samples. The extent of macrosegregation increases with increasing primary dendrite spacings for constant mushy zone length. For constant primary spacings, the macrosegregation increases with decreasing mushy zone length. Presence of convection reduces the primary dendrite spacings. However, convection in the interdendritic melt has significantly more influence on the spacings as compared with that in the overlying melt, which is caused by the solutal buildup at the dendrite tips.

Tewari, S. N.↗

NASA NTRS2001

The Transient Dendritic Solidification Experiment (TDSE)

Dendritic solidification is a common mode of solidification. It is also an important model problem in nonequilibrium physics and pattern formation physics. Current theories couple the transfer of latent heat with selection mechanisms at the interface. Measurements of succinonitrile (SCN) dendrites in microgravity show reasonable agreement between heat transfer predictions and experiment. However, data and analysis for assessing interfacial physics theories are less definitive. We are studying, and will present data on, transient effects in dendritic growth of SCN. We employ the Clapeyron pressure/melting temperature effect to make a rapid change in a sample's hydrostatic pressure, and thereby rapidly change the specimen's melting temperature, forcing the dendrite to select a new steady-state. These initial measurements show some surprising and non-intuitive effects.

Koss, M. B.↗

NASA NTRS2003

Convection Effects in Three-dimensional Dendritic Growth

A phase-field model is developed to simulate free dendritic growth coupled with fluid flow for a pure material in three dimensions. The preliminary results presented here illustrate the strong influence of convection on the three-dimensional (3D) dendrite growth morphology. The detailed knowledge of the flow and temperature fields in the melt around the dendrite from the simulations allows for a detailed understanding of the convection effects on dendritic growth.

Lu, Yili↗

NASA NTRS2012

Disruption of an Aligned Dendritic Network by Bubbles During Re-Melting in a Microgravity Environment

The quiescent Microgravity environment can be quite dynamic. Thermocapillary flow about "large" static bubbles on the order of 1mm in diameter was easily observed by following smaller tracer bubbles. The bubble induced flow was seen to disrupt a large dendritic array, effectively distributing free branches about the solid-liquid interface. "Small" dynamic bubbles were observed to travel at fast velocities through the mushy zone with the implication of bringing/detaching/redistributing dendrite arm fragments at the solid-liquid interface. Large and small bubbles effectively re-orient/re-distribute dendrite branches/arms/fragments at the solid liquid interface. Subsequent initiation of controlled directional solidification results in growth of dendrites having random orientations which significantly compromises the desired science.

Grugel, Richard N.↗

NASA NTRS2012

Primary Dendrite Array Morphology: Observations from Ground-based and Space Station Processed Samples

Influence of natural convection on primary dendrite array morphology during directional solidification is being investigated under a collaborative European Space Agency-NASA joint research program, "Microstructure Formation in Castings of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions (MICAST)". Two Aluminum-7 wt pct Silicon alloy samples, MICAST6 and MICAST7, were directionally solidified in microgravity on the International Space Station. Terrestrially grown dendritic monocrystal cylindrical samples were remelted and directionally solidified at 18 K/cm (MICAST6) and 28 K/cm (MICAST7). Directional solidification involved a growth speed step increase (MICAST6-from 5 to 50 micron/s) and a speed decrease (MICAST7-from 20 to 10 micron/s). Distribution and morphology of primary dendrites is currently being characterized in these samples, and also in samples solidified on earth under nominally similar thermal gradients and growth speeds. Primary dendrite spacing and trunk diameter measurements from this investigation will be presented.

Tewari, Surendra↗

NASA NTRS2012

Primary Dendrite Array: Observations from Ground-Based and Space Station Processed Samples

Influence of natural convection on primary dendrite array morphology during directional solidification is being investigated under a collaborative European Space Agency-NASA joint research program, Microstructure Formation in Castings of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions (MICAST). Two Aluminum-7 wt pct Silicon alloy samples, MICAST6 and MICAST7, were directionally solidified in microgravity on the International Space Station. Terrestrially grown dendritic monocrystal cylindrical samples were remelted and directionally solidified at 18 K per centimeter (MICAST6) and 28 K per centimeter (MICAST7). Directional solidification involved a growth speed step increase (MICAST6-from 5 to 50 millimeters per second) and a speed decrease (MICAST7-from 20 to 10 millimeters per second). Distribution and morphology of primary dendrites is currently being characterized in these samples, and also in samples solidified on earth under nominally similar thermal gradients and growth speeds. Primary dendrite spacing and trunk diameter measurements from this investigation will be presented.

Tewari, Surendra N.↗

NASA NTRS1979

Influence of convection on free growth of dendrite crystals from solution

The free growth of dendrites in a uniformly supercooled solution was examined using cine photography with a Schlieren optical system. Crystals were grown in the bulk of the solution from a centrally located capillary tube, nucleated at the interface with a liquid nitrogen cooled wire. Crystals propagated along the tube, the slower growing orientations eliminated, and emerged at the tip, usually growing parallel to the tube direction. For both sodium sulfate decahydrate from its solution and ice from sodium chloride solution, growth rate and fineness of dendrites increased with supercooling. In sodium sulfate, upward convection of the less dense depleted solution occurs; downward convection was observed for the rejected, more concentrated sodium chloride solution. In both cases, there was a spatial and temporal delay in the release of the convective plume from the moving dendrite tip. The role of this convection on the growth characteristics and the production of secondary crystals is examined. A proposed low-g experiment to examine differences in growth rate, crystal texture, and secondary nucleation in a reduced convective regime where molecular diffusion is the dominant transfer process is discussed.

Hallett, J.↗

NASA NTRS1982

The influence of acceleration forces on dendritic growth and grain structure

The results of experiments on the tin-15 wt pct lead system are presented, showing the effects on microstructure of solidification in the presence of acceleration forces from 0.0001 to 5 g for three cooling rates. An increase in the acceleration level is shown to drive fluid flow and cause dendrite remelting, fragmentation, and macrosegregation. The cooling rate impacts the final structure through its control of dendrite arm spacings and permeability to fluid flow. At the low (0.0001 g) acceleration, dendrite arm spacings deviated from the predicted relationship to cooling rate. An explanation for this anomaly is given which considers the temperature and concentration gradients in the low-gravity environment.

Johnston, M. H.↗