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NASA NTRS1985

Dendritic solidification. I - Analysis of current theories and models. II - A model for dendritic growth under an imposed thermal gradient

A critical review of the present dendritic growth theories and models is presented. Mathematically rigorous solutions to dendritic growth are found to rely on an ad hoc assumption that dendrites grow at the maximum possible growth rate. This hypothesis is found to be in error and is replaced by stability criteria which consider the conditions under which a dendrite tip advances in a stable fashion in a liquid. The important elements of a satisfactory model for dendritic solidification are summarized and a theoretically consistent model for dendritic growth under an imposed thermal gradient is proposed and described. The model is based on the modification of an analysis due to Burden and Hunt (1974) and predicts correctly in all respects, the transition from a dendritic to a planar interface at both very low and very large growth rates.

Laxmanan, V.↗

NASA NTRS1996

Successful Isothermal Dendritic Growth Experiment (IDGE) Proves Current Theories of Dendritic Solidification are Flawed

The scientific objective of the Isothermal Dendritic Growth Experiment (IDGE) is to test fundamental assumptions about dendritic solidification of molten materials. "Dendrites"-- from the ancient Greek word for tree--are tiny branching structures that form inside molten metal alloys when they solidify during manufacturing. The size, shape, and orientation of the dendrites have a major effect on the strength, ductility (ability to be molded or shaped), and usefulness of an alloy. Nearly all of the cast metal alloys used in everyday products (such as automobiles and airplanes) are composed of thousands to millions of tiny dendrites. Gravity, present on Earth, causes convection currents in molten alloys that disturb dendritic solidification and make its precise study impossible. In space, gravity is negated by the orbiting of the space shuttle. Consequently, IDGE (which was conducted on the space shuttle) gathered the first precise data regarding undisturbed dendritic solidification. IDGE is a microgravity materials science experiment that uses an apparatus which was designed, built, tested, and operated by people from the NASA Lewis Research Center. This experiment was conceived by the principal investigator, Professor Martin E. Glicksman, from Rensselaer Polytechnic Institute in Troy, New York. The experiment was a team effort of Lewis civil servants, contractors from Aerospace Design & Fabrication Inc. (ADF), and personnel at Rensselaer.

Source record↗

NASA NTRS1985

Dendritic solidification. III - Some further refinements to the model for dendritic growth under an imposed thermal gradient

Some further refinements to a simple model for dendritic solidification in a binary alloy melt under an imposed positive thermal gradient are presented. Two new expressions for the dendrite tip undercooling have been obtained and shown to yield a limiting value of Delta T sub 0 and very small growth rates. Here Delta T sub 0 is the equilibrium solidification range of the alloy. At very large growth rates, all three tip undercooling expressions reach the same limiting value depending on the value of a dimensionless parameter lambda which is related to the effective diffusion distance ahead of the dendrite tip. The predicted tip undercoolings are, however, somewhat lower at intermediate growth rates. An improved calculation for the solute buildup at the dendrite tip due to curvature effects is also included.

Laxmanan, V.↗

NASA NTRS1986

Advanced dendritic web growth development and development of single-crystal silicon dendritic ribbon and high-efficiency solar cell program

Efforts to demonstrate that the dendritic web technology is ready for commercial use by the end of 1986 continues. A commercial readiness goal involves improvements to crystal growth furnace throughput to demonstrate an area growth rate of greater than 15 sq cm/min while simultaneously growing 10 meters or more of ribbon under conditions of continuous melt replenishment. Continuous means that the silicon melt is being replenished at the same rate that it is being consumed by ribbon growth so that the melt level remains constant. Efforts continue on computer thermal modeling required to define high speed, low stress, continuous growth configurations; the study of convective effects in the molten silicon and growth furnace cover gas; on furnace component modifications; on web quality assessments; and on experimental growth activities.

Duncan, C. S.↗

NASA NTRS2001

Dendritic Alloy Solidification Experiment (DASE)

A space experiment, and supporting ground-based research, is proposed to study the microstructural evolution in free dendritic growth from a supercooled melt of the transparent model alloy succinonitrile-acetone (SCN-ACE). The research is relevant to equiaxed solidification of metal alloy castings. The microgravity experiment will establish a benchmark for testing of equiaxed dendritic growth theories, scaling laws, and models in the presence of purely diffusive, coupled heat and solute transport, without the complicating influences of melt convection. The specific objectives are to: determine the selection of the dendrite tip operating state, i.e. the growth velocity and tip radius, for free dendritic growth of succinonitrile-acetone alloys; determine the growth morphology and sidebranching behavior for freely grown alloy dendrites; determine the effects of the thermal/solutal interactions in the growth of an assemblage of equiaxed alloy crystals; determine the effects of melt convection on the free growth of alloy dendrites; measure the surface tension anisotropy strength of succinon itrile -acetone alloys establish a theoretical and modeling framework for the experiments. Microgravity experiments on equiaxed dendritic growth of alloy dendrites have not been performed in the past. The proposed experiment builds on the Isothermal Dendritic Growth Experiment (IDGE) of Glicksman and coworkers, which focused on the steady growth of a single crystal from pure supercooled melts (succinonitrile and pivalic acid). It also extends the Equiaxed Dendritic Solidification Experiment (EDSE) of the present investigators, which is concerned with the interactions and transients arising in the growth of an assemblage of equiaxed crystals (succinonitrile). However, these experiments with pure substances are not able to address the issues related to coupled heat and solute transport in growth of alloy dendrites.

Beckermann, C.↗

NASA NTRS2003

The Evolution of Dendrite Morphology during Isothermal Coarsening

Dendrite coarsening is a common phenomenon in casting processes. From the time dendrites are formed until the inter-dendritic liquid is completely solidified dendrites are changing shape driven by variations in interfacial curvature along the dendrite and resulting in a reduction of total interfacial area. During this process the typical length-scale of the dendrite can change by orders of magnitude and the final microstructure is in large part determined by the coarsening parameters. Dendrite coarsening is thus crucial in setting the materials parameters of ingots and of great commercial interest. This coarsening process is being studied in the Pb-Sn system with Sn-dendrites undergoing isothermal coarsening in a Pb-Sn liquid. Results are presented for samples of approximately 60% dendritic phase, which have been coarsened for different lengths of times. Presented are three-dimensional microstructures obtained by serial-sectioning and an analysis of these microstructures with regard to interface orientation and interfacial curvatures. These graphs reflect the evolution of not only the microstructure itself, but also of the underlying driving forces of the coarsening process. As a visualization of the link between the microstructure and the driving forces a three-dimensional microstructure with the interfaces colored according to the local interfacial mean curvature is shown.

Alkemper, Jens↗

NASA NTRS1986

Dendrite characteristics in directionally solidified Pb-8 pct Au and Pb-3 pct Pd alloys

The dendritic microstructure and solute compression profiles for Pb-8 pct Au and Pb-3 pct Pd alloy samples are examined. Two groups of models, the minimum undercooled dendrite tip model of Burden and Hunt (1974) and Laxmanan (1974, 1984) and marginal stability at the dendrite tip models of Trivedi (1980) and Laxmanan (1974) are used to predict growth behavior of the alloy samples. The experimentally observed dendrite tip radius, primary arm spacing, and liquid composition at the dendrite tip are compared with theoretical predictions. It is observed that the modified minimum undercooling dendrite tip model and both of the marginal stability models accurately predict dendritic behavior. It is concluded that quantitative comparison of the primary arm spacing measurements can not form the basis for distinguishing among the various dendrite growth models in a positive temperature gradient.

Tewari, S. N.↗

NASA NTRS1988

Dendritic solidification in binary alloys

Alloys generally solidify dendritically, and associated with that is the microsegregation of impurities. Pure metals also solidify in dendritic form as 'thermal' dendrites, which actually segregate the system's enthalpy. In this investigation, small additions of solute to succinonitrile have been studied and dendritic growth observed in a supercooled melt. This free dendritic growth-mode is similar to that experienced by equiaxed dendrites found in alloy castings. Observations of these free dendrites include measurement of velocity and tip radius of the dendrites at different supercoolings and solute concentrations.

Chopra, M. A.↗

NASA NTRS1999

The Isothermal Dendritic Growth Experiment (IDGE)

The Isothermal Dendritic Growth Experiment (IDGE) constituted a series of three NASA-supported microgravity experiments, all of which flew aboard the space shuttle, Columbia. This experimental space flight series was designed and operated to grow and record dendrite solidification in the absence of gravity-induced convective heat transfer, and thereby produce a wealth of benchmark-quality data for testing solidification scaling laws. The data and analysis performed on the dendritic growth speed and tip size in Succinontrie (SCN) demonstrates that although the theory yields predictions that are reasonably in agreement with experiment, there are significant discrepancies. However, some of these discrepancies can be explained by accurately describing the diffusion of heat. The key finding involves recognition that the actual three-dimensional shape of dendrites includes time-dependent side-branching and a tip region that is not a paraboloid of revolution. Thus, the role of heat transfer in dendritic growth is validated, with the caveat that a more realistic model of the dendrite then a paraboloid is needed to account for heat flow in an experimentally observed dendrite. We are currently conducting additional analysis to further confirm and demonstrate these conclusions. The data and analyses for the growth selection physics remain much less definitive. From the first flight, the data indicated that the selection parameter, sigma*, is not exactly a constant, but exhibits a slight dependence on the supercooling. Additional data from the second flight are being examined to investigate the selection of a unique dendrite speed, tip size and shape. The IDGE flight series is now complete. We are currently completing analyses and moving towards final data archiving. It is gratifying to see that the IDGE published results and archived data sets are being used actively by other scientists and engineers. In addition, we are also pleased to report that the techniques and IDGE hardware system that the authors developed with NASA, are being currently employed on both designated flight experiments, like EDSE, and on flight definition experiments, like TDSE.

Glicksman, Martin E.↗

NASA NTRS1999

The Isothermal Dendritic Growth Experiment (IDGE): USMP-4 One-Year-Report

Dendrites describe the tree-like crystal morphology commonly assumed in many material systems--particularly in metals and alloys that freeze from supercooled or supersaturated melts. There remains a high level of engineering interest in dendritic solidification because of the role of dendrites in the determination of cast alloy microstructures. Microstructure plays a key role in determining the physical properties of cast or welded products. In addition, dendritic solidification provides an example of non-equilibrium physics and is one of the simplest non-trivial examples of dynamic pattern formation, where an amorphous melt, under simple starting conditions, evolves into a complex ramified microstructure. Although it is well-known that dendritic growth is controlled by the transport of latent heat from the moving solid-melt interface as the dendrite advances into a supercooled melt, an accurate, and predictive model has not been developed. Current theories consider: 1) the transfer of heat or solute from the solid-liquid interface into the melt, and 2) the interfacial crystal growth and growth selection physics for the interface. However, the effects of gravity-induced convection on the transfer of heat from the interface prevent either element from being adequately tested solely under terrestrial conditions. The Isothermal Dendritic Growth Experiment (IDGE) constituted a series of three NASA-supported microgravity experiments, all of which flew aboard the space shuttle, Columbia. This experimental space flight series was designed and operated to grow and record dendrite solidification in the absence of gravity-induced convective heat transfer, and thereby produce a wealth of benchmark-quality data for testing solidification scaling laws. The data collection from the on-orbit phase of the IDGE flight series is now complete. We are currently completing analyses and moving towards final data archiving.

Glicksman, M. E.↗

NASA NTRS2003

Data and Modeling of Dendrites Subject to A Step Change in Pressure (TDSE)

There is considerable interest in dendritic solidification because of the influence dendrites have in the determination of microstructure, and thereby in the physical properties of cast metals and alloys. Current theories and models of dendritic growth generally couple diffusion effects in the melt with the physics of the interface. Data and subsequent analysis prior of the tip growth speed and radii of thermal succinonitrile dendrites in the near-convection free, on-orbit, free-fall environment demonstrate that these theories yield predictions that are reasonably in agreement with the results of experiment. However, data and analysis for assessing the interfacial physics component of theory are not sufficiently detailed or definitive. To study fundamental aspects of dendritic interface stability, we are measuring and modeling the kinetics and morphology of dendrites as they evolve from one well-defined steady state at a pre-set supercooling, through a transient stage, to a different well-defined steady state. More specifically, we subject succinonitrile dendrites, growing under steady-state conditions, to a rapid change in pressure. This leads to a rapid change in thermal driving force from the corresponding change in both the equilibrium melting temperature due to the Clapeyron effect, and a change in the far-field temperature due to adiabatic temperature changes in the bulk liquid and solid. Subsequently, we observe transformations from a well-characterized initial state into a new steady-state. Initial data reveal that the dendrite tip velocity changes almost as fast as the pressure charges, while the tip radius changes occur more slowly, taking from 10 60 seconds depending on the size of the step change and the final supercooling. Computer modeling of this process shows both agreements and disagreements with the experimental data. In making these observations and measurements, we are gaining new understandings of interfacial dynamics and state-selection physics.

Koss, Matthew B.↗

NASA NTRS1981

Fundamentals of dendritic solidification. I - Steady-state tip growth. II - Development of sidebranch structure

Systematic measurements of dendrite tip radius and growth velocity in succinonitrile reveal that consideration of dendrite tip stability should be incorporated into the heat transfer theory to determine the steady-state dendritic growth condition. The dendritic stability criterion measured is 2 alpha d0/VR squared = 0.0195, where V is the dendritic growth velocity, R is the dendritic tip radius, alpha is the liquid thermal diffusivity, and d0 is a capillary length defined in the text. Several dendritic stability models are reviewed and discussed in comparison to the present experimental results.

Huang, S.-C.↗

NASA NTRS1999

Equiaxed Dendritic Solidification Experiment (EDSE)

The objective of the research is to quantitatively determine and understand the fundamental mechanisms that control the microstructural evolution during solidification of an assemblage of equiaxed dendritic crystals. A microgravity experiment will be conducted to obtain benchmark data on the transient growth and interaction of up to four equiaxed crystals of a pure and transparent metal analog (succinonitrile, SCN) under strictly diffusion dominated conditions. Of interest in the experiment are the transient evolution of the primary and secondary dendrite tip speeds, the dendrite morphology (i.e., tip radii, branch spacings, etc.) and solid fraction, the tip selection criterion, and the temperature field in the melt for a range of initial supercoolings and, thus, interaction "strengths" between the crystals. The experiment thus extends the microgravity measurements of Glicksman and coworkers for steady growth of a single dendrite [Isothermal Dendritic Growth Experiment (IDGE), first flown on USMP-2] to a case where growth transients are introduced due to thermal interactions between neighboring dendrites - a situation more close to actual casting conditions. Corresponding earth-based experiments will be conducted to ascertain the influence of melt convection. The experiments are supported by a variety of analytical models and numerical simulations. The data will primarily be used to develop and test theories of transient dendritic growth and the solidification of multiple interacting equiaxed crystals in a supercooled melt.

Beckermann, C.↗

NASA NTRS1999

The Transient Dendritic Solidification Experiment (TDSE)

The study of steady-state dendritic growth has both validated many element of transport phenomena in dendritic growth, and yielded many new insights. Further development in simulation and modeling are needed, as is further understanding of the role of selection or scaling in dendritic growth. The TDSE contributes to the further study of dendritic phenomena by carefully measuring and modeling transient effects on dendritic growth. The major challenge encountered in measuring and analyzing the transient behavior of isothermal dendrites is defining precisely the initial conditions from which or to which the dendrite evolves. Our proposed pressure-mediated TDSE microgravity experiment, obviates this difficulty, because the transient occurs between two well-characterized steady-states, rather than between an ill-defined initial state and the final steady state. The major results expected are unique data on transient behavior that will extend the scientific bounds from the now well-understood thermal effects, and provide insight into interfacial dynamics where open questions remain.

Koss, M. B.↗

NASA NTRS2001

Equiaxed Dendritic Solidification Experiment (EDSE)

The objective of the research is to quantitatively determine and understand the fundamental mechanisms that control the microstructural evolution during equiaxed dendritic solidification. A microgravity experiment will be conducted to obtain benchmark data on the transient growth and interaction of up to four equiaxed crystals of a pure and transparent metal analog (succinonitrile, SCN) under strictly diffusion-dominated conditions. Of interest in the experiment are the transient evolution of the primary and secondary dendrite tip speeds, the dendrite morphology and solid fraction, the tip selection criterion, and the temperature field in the melt for a range of interaction "strengths" between the crystals. The experiment extends the microgravity measurements of Glicksman and co-workers isothermal dendritic growth experiment (IDGE) for steady growth of a single dendrite to a case where growth transients are introduced due to thermal interactions between neighboring dendrites - a situation closer to actual casting conditions. Corresponding Earth-based experiments will be conducted to ascertain the influence of melt convection. The experiments are supported by a variety of analytical models and numerical simulations. The data will be used to develop and test theories of transient dendritic growth and the solidification of multiple interacting equiaxed crystals in a supercooled melt.

Beckermann, C.↗

NASA NTRS1976

Web-dendritic ribbon growth

A web furnace was constructed for pulling dendritic-web samples. The effect of changes in the furnace thermal geometry on the growth of dendritic-web was studied. Several attempts were made to grow primitive dendrites for use as the dendritic seed crystals for web growth and to determine the optimum twin spacing in the dendritic seed crystal for web growth. Mathematical models and computer programs were used to determine the thermal geometries in the susceptor, crucible melt, meniscus, and web. Several geometries were determined for particular furnace geometries and growth conditions. The information obtained was used in conjunction with results from the experimental growth investigations in order to achieve proper conditions for sustained pulling of two dendrite web ribbons. In addition, the facilities for obtaining the following data were constructed: twin spacing, dislocation density, web geometry, resistivity, majority charge carrier type, and minority carrier lifetime.

Hilborn, R. B., Jr.↗

NASA NTRS1977

Dendritic web silicon for solar cell application

The dendritic web process for growing long thin ribbon crystals of silicon and other semiconductors is described. Growth is initiated from a thin wirelike dendrite seed which is brought into contact with the melt surface. Initially, the seed grows laterally to form a button at the melt surface; when the seed is withdrawn, needlelike dendrites propagate from each end of the button into the melt, and the web portion of the crystal is formed by the solidification of the liquid film supported by the button and the bounding dendrites. Apparatus used for dendritic web growth, material characteristics, and the two distinctly different mechanisms involved in the growth of a single crystal are examined. The performance of solar cells fabricated from dendritic web material is indistinguishable from the performance of cells fabricated from Czochralski grown material.

Seidensticker, R. G.↗

NASA NTRS1984

Free dendritic growth

Free dendritic growth refers to the unconstrained development of crystals within a supercooled melt, which is the classical 'dendrite problem'. Great strides have been taken in recent years in both the theoretical understanding of dendritic growth and its experimental status. The development of this field will be sketched, showing that transport theory and interfacial thermodynamics (capillarity theory) were sufficient ingredients to develop a truly predictive model of dendrite formation. The convenient, but incorrect, notion of 'maximum velocity' was used for many years to estimate the behavior of dendritic transformations until supplanted by modern dynamic stability theory. The proper combinations of transport theory and morphological stability seem to able to predict the salient aspects of dendritic growth, especially in the neighborhood of the tip. The overall development of cast microstructures, such as equiaxed zone formation, rapidly solidified microstructures, etc., also seems to contain additional non-deterministic features which lie outside the current theories discussed here.

Glicksman, M. E.↗