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At least 73 records · Page 4

Interfacial wave theory of dendrite growth - Global mode solution and quantum condition

The signal feedback process at the edge of the dendrite tip is investigated, and the global instability mechanism of the system is derived. A mechanism is developed to describe a discrete set of unstable global modes for the system. Called WEASR, the method considers the wave emission at the turning point and signal reflections between the turning point and the front edge of the tip. It is shown that the method can obtain the asymptotic solutions for the unstable global modes and the quantum condition for the corresponding eigenvalues. A turning point called the pattern formation condition is shown to be crucial in the formation of dendritic structure and the choice of the final tip velocity. The wave emission process is outlined, and the importance of a signal feedback process at the edge of the dendrite tip is demonstrated. Parameters such as stability and surface tension can be analyzed in terms of their effects on WEASR modes.

Xu, Jian-Jun↗

Dendritic growth of undercooled nickel-tin. III

The paper is concerned with structures and microsegregations in undercooled droplets of Ni-25 wt pct Sn and eutectic Ni-32.5 wt pct Sn alloys. An analysis of experimental results suggests that all samples solidify dendritically and that the final structures are largely the result of ripening. Experimental data on minimum solute composition in the samples produced are bounded by two curves both of which assume equilibrium at all liquid-solid interfaces during recalescence and subsequent cooling. The eutectic alloy samples often show a dendritic structure over the surface in areas where shrinkage is present. This structure appears to be the remnant of an original growth structure in which only limited ripening occurred, due to the rapid removal of interdendritic liquid by shrinkage.

Wu, Y.↗

Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy

This paper is concerned primarily with the development of an analytic approach to the theory of steady-state velocity selection in the boundary-layer model of dendritic solidification. The two-dimensional version of this model with a fourfold crystalline anisotropy alpha in the surface tension is considered. By extending a WKB method introduced in an earlier paper, the alpha dependence of the selected growth rate is determined in the limit of small alpha; and this rate is studied for large alphas in the limit in which the dimensionless undercooling approaches unity. Portions of the paper are devoted to a reinterpretation of the mathematical structure of the solvability condition in problems of this kind.

Langer, J. S.↗

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.↗

Dendritic growth and structure of undercooled nickel base alloys

The principal objectives of this overall investigation are to: study means for obtaining high undercooling in levitation melted droplets, and study structures produced upon the solidification of these undercooled specimens. Thermal measurements are made of the undercooling, and of the rapid recalescence, to develop an understanding of the solidification mechanism. Comparison of results is made with the modeling studies. Characterization and metallographic work is done to gain an understanding of the relationship between rapid solidification variables and the structures so produced. In ground based work to date, solidification of undercooled Ni-25 wt percent Sn alloy was observed by high-speed cinematography and the results compared with optical temperature measurements. Also in ground based work, high-speed optical temperature measurements were made of the solidification behavior of levitated metal samples within a transparent glass medium. Two undercooled Ni-Sn alloys were examined. Measurements were carried out on samples at undercoolings up to 330 K. Microstructures of samples produced in ground based work were determined by optical metallography and by SEM, and microsegregation by electron microprobe measurements. A series of flight tests were planned to conduct experiments similar to the ground based experiments. The Space Shuttle Columbia carried an alloy undercooled experiment in the STS 61-C mission in January 1986. A sample of Ni-32.5 wt percent Sn eutectic was melted and solidified under microgravity conditions.

Flemings, M. C.↗

Interferometric measurements of a dendritic growth front solutal diffusion layer

An experimental study was undertaken to measure solutal distributions in the diffusion layer produced during the vertical directional solidification (VDS) of an ammonium chloride - water (NH4Cl-H2O) solution. Interferometry was used to obtain concentration measurements in the 1-2 millimeter region defining the diffusion layer. These measurements were fitted to an exponential form to extract the characteristic diffusion parameter for various times after the start of solidification. The diffusion parameters are within the limits predicted by steady state theory and suggest that the effective solutal diffusivity is increasing as solidification progresses.

Hopkins, John A.↗

Oxide Control for Silicon Crystal Growth

Web dendrite growth process pulls sheet of newly crystallized silicon from molten silicon. Jets of argon pull outside gas into melt cavity, preventing silicon oxide from passing through heat-shield hold and depositing on it. Generated by aspirators, reversed flow is used in web dendrite process, which produces sheets of single-crystal silicon for low-cost solar cells.

Wehrli, H. A. I.↗

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.↗

Silicon dendritic web growth

Technological goals for a silicon dendritic web growth program effort are presented. Principle objectives for this program include: (1) grow long web crystals front continuously replenished melt; (2) develop temperature distribution in web and melt; (3) improve reproductibility of growth; (4) develop configurations for increased growth rates (width and speed); (5) develop new growth system components as required for improved growth; and (6) evaluate quality of web growth.

Duncan, S.↗

Large area sheet task: Advanced dendritic web growth development

The growth of silicon dendritic web for photovoltaic applications was investigated. The application of a thermal model for calculating buckling stresses as a function of temperature profile in the web is discussed. Lid and shield concepts were evaluated to provide the data base for enhancing growth velocity. An experimental web growth machine which embodies in one unit the mechanical and electronic features developed in previous work was developed. In addition, evaluation of a melt level control system was begun, along with preliminary tests of an elongated crucible design. The economic analysis was also updated to incorporate some minor cost changes. The initial applications of the thermal model to a specific configuration gave results consistent with experimental observation in terms of the initiation of buckling vs. width for a given crystal thickness.

Duncan, C. S.↗

Large area sheet task. Advanced dendritic web growth development

The development of a silicon dendritic web growth machine is discussed. Several refinements to the sensing and control equipment for melt replenishment during web growth are described and several areas for cost reduction in the components of the prototype automated web growth furnace are identified. A circuit designed to eliminate the sensitivity of the detector signal to the intensity of the reflected laser beam used to measure melt level is also described. A variable speed motor for the silicon feeder is discussed which allows pellet feeding to be accomplished at a rate programmed to match exactly the silicon removed by web growth.

Duncan, C. S.↗

Large-area sheet task advanced dendritic web growth development

The thermal models used for analyzing dendritic web growth and calculating the thermal stress were reexamined to establish the validity limits imposed by the assumptions of the models. Also, the effects of thermal conduction through the gas phase were evaluated and found to be small. New growth designs, both static and dynamic, were generated using the modeling results. Residual stress effects in dendritic web were examined. In the laboratory, new techniques for the control of temperature distributions in three dimensions were developed. A new maximum undeformed web width of 5.8 cm was achieved. A 58% increase in growth velocity of 150 micrometers thickness was achieved with dynamic hardware. The area throughput goals for transient growth of 30 and 35 sq cm/min were exceeded.

Duncan, C. S.↗

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.↗

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.↗

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.↗

Convection and diffusion effects during dendritic solidification

A report is presented of the first quantitative measurements of dendritic growth at supercooling levels where convection instead of diffusion is the controlling heat transfer mechanism. Precautions similar to that used in an investigation conducted by Glicksman et al. (1976) were taken to insure 'free' dendritic growth conditions. Dendritic growth velocity was measured as a function of growth orientation at seventeen supercoolings which ranged from 0.043 C to 2 C. Selected but representative measurements of velocity versus orientation angle are shown in a graph. The relative growth velocity of a downward growing dendrite is found to be greater than that of a diffusion-limited dendrite. This result is consistent with that expected from the enhanced heat transfer arising from natural convection.

Glicksman, M. E.↗

Channel formation in Pb-Sn, Pb-Sb, and Pb-Sn-Sb alloy ingots and comparison with the system NH4Cl-H2O

The formation of segregation channels during the unidirectional solidification of base chilled ingots has been studied as a function of composition in binary Pb-Sn and Pb-Sb and ternary Pb-Sn-Sb alloys. The patterns of channel distribution were characterized in the binary and ternary systems and are described as functions of temperature gradients, growth rates, dendrite spacings, and interdendritic permeabilities. Channels appear to nucleate at random across a dendritic front and subsequently to interact as they propagate, decreasing in density across the front. Assuming that the interdendritic spacing is the characteristic distance for a liquid perturbation, yields critical effective Rayleigh numbers which lie within a factor of x 40 for both metallic and aqueous systems. This correlation is close, considering the sensitivity to any assumed dimension and the range of material properties involved, and is taken to support a model for channel nucleation occurring close to the dendritic growth front.

Hellawell, A.↗