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At least 19 records

Boundary-layer analysis for the convection/diffusion transition in dendritic growth

The supercooling dependence of dendritic growth kinetics under the influence of convective heat transport is investigated theoretically and experimentally with emphasis on theoretical prediction of the supercooling level at which the transition from diffusion-controlled to convection-controlled dendritic growth occurs. It is shown that the crossover between diffusive and convective transport depends on the relative thickness of the Stefan length compared with the thermal boundary layer. These lengths become equal at a supercooling which may be calculated from diffusion theory and fluid mechanics. It is also shown that the crossover supercooling varies weakly with the gravitational acceleration, melt viscosity, and the volumetric expansion coefficient.

Glicksman, M. E.

Influence of diffusion and convective transport on dendritic growth in dilute alloys

Experimentation has been carried out in which the kinetics and morphology of dendritic growth were measured as a function of thermal supercooling, solute concentration, and spatial orientation of the dendritic growth axis. The crystal growth system studied is succinonitrile, NC(CH2)2CN, with additions of argon (up to 0.1 mole percent). This system is especially useful as a model for alloy studies because kinetic data are available for high purity (7-9's) succinonitrile. The influence of the solute, at fixed thermal supercooling, is to increase the growth velocity and correspondingly decrease intrinsic crystal dimensions. Morphological measurements are described in detail relating tip size, perturbation wavelength, supercooling, and solute concentration. The analysis of these effects based on morphological stability theory is also discussed, and experiments permitting the separation of convective and diffusive heat transport during crystal growth of succinonitrile are described. The studies underscore the importance of gravitationally-induced buoyancy effects on crystal growth.

Glicksman, M. E.

Convective flow during dendritic growth

A review is presented of the major experimental findings obtained from recent ground-based research conducted under the SPAR program. Measurements of dendritic growth at small supercoolings indicate that below approximately 1.5 K a transition occurs from diffusive control to convective control in succinonitrile, a model system chosen for this study. The key theoretical ideas concerning diffusive and convective heat transport during dendritic growth are discussed, and it is shown that a transition in the transport control should occur when the characteristic length for diffusion becomes larger than the characteristic length for convection. The experimental findings and the theoretical ideas discussed suggest that the Fluid Experiment System could provide appropriate experimental diagnostics for flow field visualization and quantification of the fluid dynamical effects presented here.

Glicksman, M. E.

Web-dendritic growth

The effects of various machine design parameters on the growth of web dendritic silicon ribbon were investigated. Ribbons were grown up to lengths of one meter, with widths increasing linearly up to one cm at the point of termination of growth. Thermal data were collected and evaluated for actual seeding and growth with variations in parameters affecting heat loss. It was found that for suitable growth, the mechanical system should be very rigid and stable, and the tolerances and specifications of the quartz crucibles must be far tighter than normal quartz tolerances. The widening rates of the ribbons were found to be a function of the temperature gradient rather than the temperature differences alone. A twin spacing in the seed of 3 microns to 2 microns was found to be unfavorable for growth; whereas spacing of 0.9 microns to 2 microns and 8 microns to 2 microns were favorable. Thermal modeling studies of the effects of furnace design parameters on the temperature distributions in melt and the growth of the dendritic web ribbon showed that the pull rate of the ribbon is strongly dependent on the temperature of the top thermal shield, the spacing between this shield and the melt, and the thickness of the growing web.

Hilborn, R. B.

Convective heat transfer during dendritic growth

Axial growth rate measurements were carried out at 17 levels of supercooling between 0.043 C and 2 C, a temperature range in which convection, instead of diffusion, becomes the controlling mechanism of heat transfer in the dentritic growth process. The growth velocity, normalized to that expected for pure diffusive heat transfer, displays a dependence on orientation. The ratio of the observed growth velocity to that for convection-free growth and the coefficients of supercooling are formulated. The dependence of normalized growth rate in supercooling is described for downward growing dendrites. These experimental correlations can be justified theoretically only to a limited extent.

Glicksman, M. E.

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.

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.

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.

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.

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.

Computer modeling of dendritic web growth processes and characterization of the material

High area throughput rate will be required for the economical production of silicon dendritic web for solar cells. Web width depends largely on the temperature distribution on the melt surface while growth speed is controlled by the dissipation of the latent heat of fusion. Thermal models were developed to investigate each of these aspects, and were used to engineer the design of laboratory equipment capable of producing crystals over 4 cm wide; growth speeds up to 10 cm/min were achieved. The web crystals were characterized by resistivity, lifetime and etch pit density data as well as by detailed solar cell I-V data. Solar cells ranged in efficiency from about 10 to 14.5% (AM-1) depending on growth conditions. Cells with lower efficiency displayed lowered bulk lifetime believed to be due to surface contamination.

Seidensticker, R. G.

Large area sheet task: Advanced Dendritic Web Growth Development

A melt level control system was implemented to provide stepless silicon feed rates from zero to rates exactly matching the silicon consumed during web growth. Bench tests of the unit were successfully completed and the system mounted in a web furnace for operational verification. Tests of long term temperature drift correction techniques were made; web width monitoring seems most appropriate for feedback purposes. A system to program the initiation of the web growth cycle was successfully tested. A low cost temperature controller was tested which functions as well as units four times as expensive.

Duncan, C. S.

Large-area sheet task advanced dendritic web growth development

Thermal models were developed that accurately predict the thermally generated stresses in the web crystal which, if too high, cause the crystal to degenerate. The application of the modeling results to the design of low-stress experimental growth configurations will allow the growth of wider web crystals at higher growth velocities. A new experimental web growth machine was constructed. This facility includes all the features necessary for carrying out growth experiments under steady thermal conditions. Programmed growth initiation was developed to give reproducible crystal starts. Width control permits the growth of long ribbons at constant width. Melt level is controlled to 0.1 mm or better. Thus, the capability exists to grow long web crystals of constant width and thickness with little operator intervention, and web growth experiments can now be performed with growth variables controlled to a degree not previously possible.

Duncan, C. S.

Large-area sheet task advanced dendritic web growth development

The thermal stress model was used to generate the design of a low stress lid and shield configuration, which was fabricated and tested experimentally. In preliminary tests, the New Experimental Web Growth Facility performed as designed, producing web on the first run. These experiments suggested desirable design modifications in the melt level sensing system to improve further its performance, and these are being implemented.

Duncan, C. S.

Large-area sheet task advanced dendritic web growth development

The computer code for calculating web temperature distribution was expanded to provide a graphics output in addition to numerical and punch card output. The new code was used to examine various modifications of the J419 configuration and, on the basis of the results, a new growth geometry was designed. Additionally, several mathematically defined temperature profiles were evaluated for the effects of the free boundary (growth front) on the thermal stress generation. Experimental growth runs were made with modified J419 configurations to complement the modeling work. A modified J435 configuration was evaluated.

Duncan, C. S.