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Vertical solidification of dendritic binary alloys

Three numerical techniques are employed to analyze the influence of thermosolutal convection on defect formation in directionally solidified (DS) alloys. The finite-element models are based on the Boussinesq approximation and include the plane-front model and two plane-front models incorporating special dendritic regions. In the second model the dendritic region has a time-independent volume fraction of liquid, and in the last model the dendritic region evolves as local conditions dictate. The finite-element models permit the description of nonlinear thermosolutal convection by treating the dendritic regions as porous media with variable porosities. The models are applied to lead-tin alloys including DS alloys, and severe segregation phenomena such as freckles and channels are found to develop in the DS alloys. The present calculations and the permeability functions selected are shown to predict behavior in the dendritic regions that qualitatively matches that observed experimentally.

Heinrich, J. C.

On the drag of model dendrite fragments at low Reynolds number

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag vs Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendrite Stokes settling velocities are always less than that of a sphere of equal mass and volume. In the Stokes limit, the settling speed ratio is found to correlate well with the primary dendrite arm aspect ratio and a second dimensionless shape parameter which serves as a measure of the fractal-like nature of the dendrite models. These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings. The drag measurements may be used in numerical codes to calculate the movement of grains in a convecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.

Zakhem, R.

On the drag of model dendrite fragments at low Reynolds number

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag vs Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendrite Stokes settling velocities are always less than that of a sphere of equal mass and volume. In the Stokes limit, the settling speed ratio is found to correlate well with primary dendrite arm aspect ratio and a second dimensionless shape paremeter which serves as a measure of the fractal-like nature of the dendrite models. These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings. The drag measurements may be used in numerical codes to calculate the movement of grains in a convecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.

Zakhem, R.

IDGE - A test of dendritic growth theory using space flight

The isothermal Dendritic Growth Experiment (IDGE), to be performed on three of the United States Microgravity Payload (USMP) flights, starting with USMP-2, is designed to provide microgravity data on dendritic growth for a critical test of theory. Ground based test data using succinonitrile (SCN), from both a flight growth chamber and a laboratory growth chamber, are compared to theoretical calculations of dendritic tip velocities and radii. The comparison shows that the data from the flight chamber are consistent with the historical data and that dendritic growth in a microgravity environment should exhibit significant differences from the dendritic growth of SCN at g sub 0.

Glicksman, M. E.

The Isothermal Dendritic Growth Experiment (IDGE)

Dendritic solidification is one of the simplest examples of pattern formation where a structureless melt evolves into a ramified crystalline microstructure; it is a common mode of solidification in many materials, but especially so in metals and alloys. There is considerable engineering interest in dendrites because of the role dendrites play in the determination of microstructure, and thereby in influencing the physical properties of cast metals and alloys. Dendritic solidification provides important examples of non-equilibrium physics, pattern formation dynamics, and models for computational condensed matter and material physics. Current theories of dendritic growth generally couple diffusion effects in the melt with the physics introduced by the interface. Unfortunately, in terrestrial based experiments, convective effects in the melt alter the growth process in such a manner as to prevent definitive analysis of convective, diffusive or interfacial effects. Thus, the effective elimination of convection in the melt by operating experiments on orbit were required to produce high-fidelity data needed for achieving further progress. This simple fact comprised the scientific justification for the IDGE.

Glicksman, M. E.

Measurements of Dendritic Growth Velocities in Undercooled Melts of Pure Nickel Under Static Magnetic Fields

Dendritic growth velocities in undercooled melts of pure Ni have been intensively studied over the past fifty years. However, the literature data are at marked variance with the prediction of the widely accepted model for rapid dendritic growth both at small and at large undercoolings. In the present work, bulk melts of pure Ni samples of high purity were undercooled by glass fluxing treatment under a static magnetic field. The recalescence processes of the samples at different undercoolings were recorded using a high-speed camera, and were modeled using a software to determine the dendritic growth velocities. The present data confirmed the effect of melt flow on dendritic growth velocities at undercoolings below 100 K. A comparison of the present data with previous measurements on a lower purity material suggested an effect of impurities on dendritic growth velocities at undercoolings larger than 200 K as well.

Gao, Jianrong

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

Self-Healing Lithium Dendrites through Spontaneous Passivating Layer Formation for Stable Solid-State Lithium–Metal Batteries

All-solid-state lithium–metal batteries have attracted significant attention, owing to their high energy density and superior safety. However, lithium–metal penetration through the solid electrolyte, leading to short-circuiting, remains a critical failure mode that demands comprehensive mitigation strategies. Most existing strategies are effective only prior to the initiation of lithium-dendrite formation and fail once dendrites begin to propagate through the electrolyte. In this study, we propose a self-healing mechanism in which the penetrated lithium reacts with a self-healing agent to form a passivating layer along the particle boundaries. Lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) was incorporated into a Li 6 PS 5 Cl solid electrolyte as the self-healing agent to suppress lithium-dendrite propagation even after dendrite formation initiated under high current densities. The self-healing induced by LiTFSI was verified through comprehensive experimental analyses and was further demonstrated in a full-cell configuration. Moreover, LiTFSI incorporation plays an important role in increasing the critical current density by reducing the overall electronic conductivity of the solid electrolyte and facilitating the formation of a robust LiF-containing solid-electrolyte interphase.

25 ENERGY STORAGE

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.