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NASA NTRS1983

Gravitational effects in dendritic growth

The theories of diffusion-controlled dendritic crystallization will be reviewed briefly, along with recently published critical experiments on the kinetics and morphology of dendritic growth in pure substances. The influence of the gravitational body force on dendrite growth kinetics will be shown to be highly dependent on the growth orientation with respect to the gravity vector and on the level of the thermal supercooling. In fact, an abrupt transition occurs at a critical supercooling, above which diffusional transport dominates the growth process and below which convective transport dominates. Our most recent work on binary mixtures shows that dilute solute additions influence the crystallization process indirectly, by altering the interfacial stability, rather than by directly affecting the transport mode. Directions for future studies in this field will also be discussed.

Glicksman, M. E.↗

NASA NTRS1984

Emitter formation in dendritic web silicon solar cells

The use of liquid dopants and liquid masks for p-n junction formation in dendritic web solar cells was investigated and found to be equivalent to the use of gaseous dopants and CVD SiO2 masks previously used. This results in a projected cost reduction of 0.02 1980$/Watt for a 25 MW/year production line, and makes possible junction formation processes having a higher throughput than more conventional processes. The effect of a low-energy (0.4 keV) hydrogen ion implant on dendritic web solar cells was also investigated. Such an implant was observed to improve Voc and Jsc substantially. Measurements of internal quantum efficiency suggest that it is the base of the cell, rather than the emitter, which benefits from the hydrogen implant. The diffusion length for electrons in the p-type base increased from 53 microns to 150 microns in one case, with dendritic web cell efficiency being boosted to 15.2 percent. The mechanism by which low-energy hydrogen ions can penetrate deeply into the silicon to effect the observed improvement is not known at this time.

Meier, D. L.↗

NASA NTRS1984

Dendritic solidification in a binary alloy melt: Steady-state versus morphological stability theories

A model for dendritic growth in a binary alloy melt, in the presence of a positive temperature gradient in the liquid, is presented. The model describes satisfactorily the transition from a dendritic interface to a planar interface at very low and very large growth rates. A dendrite tip stability parameter is derived, strictly from steady state considerations, without resorting to a perturbation analysis. The estimates of the parameter agree with those obtained by models based on perturbation analyses.

Laymanan, V.↗

NASA NTRS1986

The effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendrite

The Ivantsov (1947) analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite, an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change epsilon, and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero epsilon, but the effect is of order epsilon and hence is seen to be minor for most values of epsilon and dimensionless supercooling that occur in practice.

Mcfadden, G. B.↗

NASA NTRS1987

A critical examination of the dendrite growth models Comparison of theory with experimental data

Three dendrite growth models for directionally solidified succinonitrile-acetone, succinonitrile-salol, aluminum-copper, and lead-paladium alloys are evaluated. The characteristics of the Burden and Hunt (1974) model, the Laxmanan (1985) model, and the Trivedi (1980) model are described. The dendrite tip temperature, tip radius, liquid composition, and primary arm spacing for the alloys are analyzed in terms of growth speed, alloy composition, and temperature gradient. It is observed that the Burden and Hunt model accurately predicts the proper behavior of the parameters, but does not provide good quantitative predictions. A good fit between the experimental data and the Trivedi and Laxmanan models is detected. The advantages of the Trivedi marginal stability analysis and the Laxmanan minimum dendrite tip undercooling approaches are discussed.

Tewari, S. N.↗

NASA NTRS1987

Dendritic growth of undercooled nickel-tin. I, II

A comparison is made between high speed cinematography and optical temperature measurements of the solidification of an undercooled Ni-25 wt pct Sn alloy. The first part of this study notes that solidification during the recalescence period at all undercoolings studied occurred in the form of a dendritelike front moving across the sample surface, and that the growth velocities observed agree with calculation results for the dendrite growth model of Lipton et al. (1986); it is concluded that the coarse structure observed comprises an array of much finer, solute-controlled dendrites. In the second part, attention is given to the solidification of levitated metal samples within a transparent glass medium for the cases of two undercooled Ni-Sn alloys, one of which is eutectic and another hypoeutectic. The data obtained suggest a solidification model involving dendrites of very fine structure growing into the melt at temperatures near the bulk undercooling temperature.

Wu, Y.↗

NASA NTRS1986

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

An investigation of Pb-8 pct Au and Pb-3 pct Pd alloy specimens which have been partially directionally solidified and then quenched is performed in order to characterize their dendritic microstructural details and solute composition profiles. A controlled sectioning technique is employed to measure dendrite tip radii. It is found that most of the observed behavior is predicted quite well by a modification of the Burden and Hunt (1974) model proposed by Laxmanan (1984), in addition to the models based on the marginal stability approach. Results indicate that quantitative comparison of the primary arm spacing measurements can not form the basis of distinguishing among the various dendrite growth models in a positive temperature gradient.

Tewari, S. N.↗

NASA NTRS1987

On the role of convective motion during dendrite growth: Experiments under variable gravity, revised

Experiments show the effect of self induced convection on individual dendrite growth in uniformly supercooled samples and solidification of the resulting mush under conditions of high and low g. Convection is visualized by a Schlieren optical system or a Mach Zender interferometer. For ice crystals growing from the vapor in air, a slight reduction in linear growth rate occur under low g. For ice crystals growing from NaCl solution, dendrite tip velocities are unchanged, but subsequent mush solidification is enhanced through drainage channels under higher g. By contrast, sodium sulfate decahydrate dendrites growing from solution produce convective plumes which lead to higher tip growth rate only as the crystal growth direction approaches that of gravity. Convective plumes are laminar for small crystals under conditions of these experiments; the rise velocity of such plumes is greater than individual vortex rings under identical conditions. Convection effects are only present in solution under a critical supercooling less than about 5 C for sodium sulfate and 2 C for ice in NaCl since at higher supercooling the crystallization velocity, proportional to the square of the supercooling, exceeds the convective velocity, proportional to the square root of the supercooling. The role of convective velocity in bulk solidification is to give a large scale flow which under extreme cases may lead to extensive secondary crystal production, which alters the resulting crystal texture of the completely solidified melt.

Hallett, J.↗

NASA NTRS1988

Dendritic growth in the presence of convection

The motion of the freezing front between a dendritic crystal and a supercooled liquid is studied using an interface evolution equation derived from a boundary integral transformation of the transient convective-diffusion equation. A new steady-state theory is introduced that incorporates the effects of convection in dendritic growth. It is shown that in the absence of capillary effects the shape of the crystal-melt interface is a paraboloid of revolution, similar to that found in situations where diffusion is the sole heat transfer mechanism. A relation between the supercooling, the product of the tip velocity and tip radius, and the strength of the flow is derived which reduces to the well-known Ivantsov theory in the absence of convection. A non-linear interface-tracking algorithm is developed and used to study the temporal and spatial evolution of the dendritic interface. The important role of capillarity and convection on the interface dynamics is established and the response of the interface to finite amplitude disturbances is examined for the first time. Tip splitting is identified as the dominant destabilization mechanism in the limit of zero surface tension. Finite surface tension leads to interface stabilization, irrespective of the magnitude and structure of the external perturbations. Finally, convection significantly decreases the magnitude of the freezing velocity.

Beaghton, Pantelis John↗

NASA NTRS1988

Dendritic solidification under microgravity conditions

The Isothermal Dendritic Growth Experiment is undergoing development in cooperation with NASA-Lewis in order to test dendritic growth theory at small supercoolings in low earth orbit. The apparatus encompasses four major subsystems: a temperature-controlled thermostatic bath capable of millikelvin stability, a photographic data collection system, a crystal-growth chamber, and a start-detection system which initiates data collection. Comparisons are made with ground-based study methods for dendritic growth.

Glicksman, M. E.↗

NASA NTRS1987

Isothermal dendritic growth - A low gravity experiment

The Isothermal Dendritic Growth Experiment has been designed to test dendritic growth theory at low undercoolings, under microgravity conditions in the Space Shuttle Cargo Bay-borne Material Science Laboratory. The experiment will be essentially autonomous, although limited in-flight interaction through a computer interface is planned. A crystal growth chamber able to yield oriented single-crystal dendritic growth will be incorporated; 'seeding' the chamber with a crystal of the requisite orientation will not in itself meet this requirement.

Glicksman, M. E.↗

NASA NTRS1987

Solidification under microgravity conditions - Dendritic growth

The experimental approach and apparatus of a zero-gravity active crystal growth experiment to test dendritic growth theory at low supercoolings are discussed. The experiment consists of 20 experimental cycles. Estimates have been made as to how low gravitational accelerations would have to be reduced to observe convection-free dendritic growth at supercoolings from 0.01-1.0 K. The experiment requires temperature control of + or - 2 mK and photographic resolution of a few microns with a depth of field of + or - 6 mm. The thermostatic bath and temperature control system, photographic system, growth chamber, and dendrite detection system are described in detail.

Glicksman, M. E.↗

NASA NTRS1988

Isothermal dendritic growth: A low gravity experiment

The Isothermal Dendritic Growth Experiment is an active crystal growth experiment designed to test dendritic growth theory at low undercoolings where convection prohibits such studies at 1 g. The experiment will be essentially autonomous, though limited in-flight interaction through a computer interface is planned. One of the key components of the apparatus will be a crystal growth chamber capable of achieving oriented single crystal dendritic growth. Recent work indicates that seeding the chamber with a crystal of the proper orientation will not, in and of itself, be sufficient to meet this requirement. Additional flight hardware and software required for the STS flight experiment are currently being developed at NASA Lewis Research Center and at Rensselaer Polytechnic Institute.

Glicksman, M. E.↗

NASA NTRS1988

Dendritic solidification of alloys in low gravity

The effect of low gravity during solidification on primary and secondary dendrite spacings is investigated. Dendritic spacing data for iron-carbon-type alloys and superalloys which were directionally solidified during aircraft low-g trajectories are examined. The low-g data data are compared with data for metal model materials and binary alloys, and theoretical models to explain the dendritic spacing are considered.

Curreri, P. A.↗

NASA NTRS1989

Thermosolutal convection during dendritic solidification

This paper presents a mathematical model for directional solidification of a binary alloy including a dendritic region underlying an all-liquid region. It is assumed initially that there exists a nonconvecting state with planar isotherms and isoconcentrates solidifying at a constant velocity. The stability of this system has been analyzed and nonlinear calculations are performed that show the effect of convection in the solidification process when the system is unstable. Results of calculations for various cases defined by the initial temperature gradient at the dendrite tips and varying strength of the gravitational field are presented for systems involving lead-tin alloys. The results show that the systems are stable for a gravitational constant of 0.0001 g(0) and that convection can be suppressed by appropriate choice of the container's size for higher values of the gravitational constant. It is also concluded that for the lead-tin systems considered, convection in the mushy zone is not significant below the upper 20 percent of the dendritic zone, if al all.

Heinrich, J. C.↗

NASA NTRS1989

Flight hardware and tele-operations supporting the Isothermal Dendritic Growth Experiment aboard the Space Shuttle

The Isothermal Dendritic Growth Experiment, which is expected to fly on the Space Shuttle to study dendritic solidification of molten metals such as iron and aluminum, is examined. Succinonitrile and pivalic acid are substitued for metals to permit visualiztion of dendritic growth. The technical features of the apparatus are described, including temperature control, the photographic system, and slow scan television. The teleoperations techniques for the experiment are discussed in detail.

Winsa, E.↗

NASA NTRS1989

Dendrites, viscous fingers, and the theory of pattern formation

Recent developments in the theory of pattern formation in dendritic crystal growth and viscous fingering in fluids are reviewed. Consideration is given to the discovery that weak capillary forces act as singular perturbations which lead to selection mechanisms in dendritic crystal growth and fingering patterns. Other topics include the conventional thermodynamic model of the solidification of a pure substance from its melt, fingering instability, pattern selection, the solvability theory, dendritic growth rates, the bubble effect discovered by Couder et al. (1986), the dynamics of pattern-forming systems, and snowflake formation.

Langer, J. S.↗

NASA NTRS1990

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↗