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NASA NTRS1985

Pattern selection in a boundary-layer model of dendritic growth in the presence of impurities

Presently analyzed, in the context of a boundary-layer model, is the problem of pattern selection in dendritic growth in a situation where impurities are present in the undercooled liquid. It is found that the tip-velocity selection criterion that has been proposed recently for the geometrical model and the boundary-layer model of a pure substance can be extended, in a nontrivial way, to this more complex situation where two coupled diffusion fields (temperature and solute) determine the interface dynamics. This model predicts a sharp enhancement of tip velocity in good qualitative agreement with experiment. This agreement is consistent with the conjecture that a solvability condition can be used to determine the operating point of the dendrite in the full nonlocal problem.

Karma, A.↗

NASA NTRS1985

Influence of dendrite network defects on channel segregate growth

The solidifying ingot interdendritic flow analysis in which channel segregates are assumed to be produced by interdendritic fluid flow dissolving channels in the primary dendrite network is presently refined by examining the flow through a dendrite network possessing a small defect. Attention is given to the section of the mushy zone in a solidifying casting. Since defects such as that presently treated are unavoidable in a real casting, a more reliable indication may be furnished of the occurrence of channel segregates.

Simpson, M.↗

NASA NTRS1985

Silicon dendritic web growth thermal analysis task

A thermal analysis model is presented which describes the dendritic ribbon process. The model uses a melt-dendrite interface which projects out of the bulk melt as the basic interpretation of the ribbon production process. This is a marked departure from the interpretations of the interface phenomena which were used previously. The model was extensively illustrated with diagrams and pictures of ribbon samples. This model should have great impact on the analyses of experimental data as well as on future design modifications of ribbon-pulling equipment.

Richter, R.↗

NASA NTRS1985

Structural defect characterization of silicon dendritic web ribbons

An EBIC study of the cross section of silicon dendritic web ribbon has revealed that recombination-active structural defects are mainly concentrated in the inner part of the ribbon, particularly at and near the twin plane, whereas the material near the surface has significantly fewer defects. An analysis of the distribution of etch pits due to slip dislocations created by shear stress indicates that a minimum in the dislocation density is frequently observed in the ribbon adjacent to the dendrite.

Cheng, L. J.↗

NASA NTRS1986

Dendritic microstructure in argon atomized superalloy powders

The dendritic microstructure of atomized nickel base superalloy powders (Ni-20 pct Cr, NIMONIC-80A, ASTROALOY, and ZHS6-K) was studied. Prealloyed vacuum induction melted ingots were argon-atomized, the powders were cooled to room temperature, and various powder-size fractions were examined by optical metallography. Linear correlations were obtained for the powder size dependence of the secondary dendrite arm spacing, following the expected d-alpha (R) to the m power dependence on the particle size for all four superalloy compositions. However, the Ni-20 pct Cr alloy, which had much coarser arm spacing as compared to the other three alloys, had a much larger value of m.

Tewari, S. N.↗

NASA NTRS1987

High temperature (900-1300 C) mechanical behaviour of dendritic web grown silicon ribbons - Strain rate and temperature dependence of the yield stress

The mechanical behavior of dendritic web Si ribbons close the melting point was studied experimentally. The goal of the study was to generate data for modeling the generation of stresses and dislocation structures during growth of dendritic web Si ribbons, thereby permitting modifications to the production process, i.e., the temperature profile, to lower production costs for the photovoltaic ribbons. A laser was used to cut specimens in the direction of growth of sample ribbons, which were then subjected to tensile tests at temperatures up to 1300 C in an Ar atmosphere. The tensile strengths of the samples increased when the temperature rose above 1200 C, a phenomena which was attributed to the diffusion of oxygen atoms to the quasi-dislocation sites. The migration to the potential dislocations sites effectively locked the dislocations.

Mathews, V. K.↗

NASA NTRS1986

The effect of gravity level on the average primary dendritic spacing of a directionally solidified superalloy

The effect of alternating low (0.01 g) and high (1.8 g) gravity force on the primary spacings in the dendrite structure in a directionally solidified Ni-based superalloy (PWA 1480, containing 5 pct Co, 10 pct Cr, 4 pct W, 12 pct Ta, 5 pct Al, 1.5 pct Ti, and the balance Ni) was investigated using samples solidified in a directional solidification furnace aboard the NASA KC-135 aircraft that made a series of low-g parabolas. The cross-section slices for each growth rate were polished and etched with Kallings II, and the primary dendritic arm spacings were measured using the method of Jacobi and Schwerdtfeger (1976). The arm spacings were found to fluctuate with gravity force, increasing as the gravity level decreased, and growing finer as gravity increased.

Mccay, M. H.↗

NASA NTRS1987

Dislocation dynamics and the viscoplastic buckling of dendritic web type silicon ribbon

The effect of dendrites (reinforced edges) on the residual stresses, dislocation densities and buckling behavior during growth of web type silicon ribbon is studied. A viscoplastic material response function (Haasen-Sumino model) is used to calculate the stresses and the disloction density at each point in the silicon ribbon. In addition, the role of dendrites on the viscoplastic buckling behavior of the ribbon is investigated. The critical thicknesses, the corresponding deflection shapes and lateral deflection speeds are calculated. These results are then compared with similar data obtained for flat plates.

Tsai, C. T.↗

NASA NTRS1987

Dynamics of dendritic sidebranching in the two-dimensional symmetric model of solidification

Within a WKB approximation, the evolution of time-dependent deformations of the needle crystal solution of the two-dimensional symmetric model of solidification is studied. It is found that perturbations with fixed small frequencies are initially amplified as they propagate from near the tip down the dendrite but ultimately decay. Localized wave packets behave rather differently; the packet continues to grow exponentially as it moves to arbitrarily large distances from the tip. The relevance of these results to sidebranching of dendrites is discussed.

Barber, Michael N.↗

NASA NTRS1987

Dendritic sidebranching in the three-dimensional symmetric model in the presence of noise

The time-dependent behavior of sidebranching deformations in the three-dimensional symmetric model of dendritic solidification is studied within a WKB approximation. Localized wave packets generated by pulses in the neighborhood of the tip are found to grow in amplitude and to spread and stretch as they move down the sides of the dendrite. This behavior is shown to imply that noise in the solidifying medium is selectively amplified in such a way as to produce a fluctuating train of sidebranches in qualitative agreement with experimental observations. A rough estimate indicates that purely thermal noise is probably not quite strong enough to fit the data.

Langer, J. S.↗

NASA NTRS1988

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.↗

NASA NTRS1987

Resistivity and thickness effects in dendritic web silicon solar cells

The decrease of minority carrier lifetime as resistivity decreases in dendritic-web silicon solar cells is addressed. This variation is shown to be consistent with the presence of defect levels in the bandgap which arise from extended defects in the web material. The extended defects are oxide precipitates (SiOx) and the dislocation cores they decorate. Sensitivity to this background distribution of defect levels increases with doping because the Fermi level moves closer to the majority carrier band edge. For high-resistivity dendritic-web silicon, which has a low concentration of these extended defects, cell efficiencies as high as 16.6 percent (4 sq cm, 40 ohm-cm boron-doped base, AM1.5 global, 100 mW/sq cm, 25 C JPL LAPSS1 measurement) and a corresponding electron lifetime of 38 microsec have been obtained. Thickness effects occur in bifacial cell designs and in designs which use light trapping. In some cases, the dislocation/precipitate defect can be passivated through the full thickness of web cells by hydrogen ion implantation.

Meier, D. L.↗

NASA NTRS1988

On dendritic growth in undercooled melts

The role of gravity-dependent convection in the steady-state growth of dendrites in undercooled melts is investigated theoretically. The model described by Huang and Glicksman (1981) is extended and refined, using the concept of a thermal diffusion boundary layer (Burton et al., 1987) to characterize the dendritic interface. Theoretical predictions are presented in graphs and shown to be in good general agreement with published experimental data on succinonitrile. The need for careful space experiments to clarify the role of nongravity-dependent convection is indicated.

Ohsaka, K.↗

NASA NTRS1989

Interfacial wave theory for dendritic structure of a growing needle crystal. I - Local instability mechanism. II - Wave-emission mechanism at the turning point

The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.

Xu, Jian-Jun↗

NASA NTRS1990

Stability of dendritic arrays

An approximate method for studying steady-state properties and linear stability of the dendritic arrays that are formed in directional solidification of alloys is proposed. This analysis is valid at high growth rates where the primary spacing between dendrites is larger than the velocity-dependent solutal diffusion length. A neutral stability boundary is computed and it is found that, in the situations where the results should be valid, the experimental data of Somboonsuk, et al. (1984) lie in the stable region, well away from the boundary.

Warren, James A.↗

NASA NTRS1992

The transition from columnar to equiaxed dendritic growth in proeutectic, low-volume fraction copper, Pb-Cu alloys

Lead, 17.1, 11.2, and 5 volume fraction copper (14, 9, and 4 wt pct Cu) alloys have been directionally solidified at constant growth velocities ranging from 1 to 100 microns/s. Serially increasing the growth velocity within this range results in a graded microstructural transition from fully columnar, albeit segregated, copper dendrites in a lead matrix to one consisting only of equiaxed grains. The imposed velocity necessary to effect fully equiaxed growth is found to drop rapidly as the volume fraction of copper is decreased. Factors which complicate the controlled, directional solidification of these alloys are discussed and the experimental results are interpreted in view of, and seen to be in qualitative agreement with, Hunt's theory on the transition from columnar to equiaxed growth of dendrites.

Kim, Shinwoo↗

NASA NTRS1992

Asteroid core crystallization by inward dendritic growth

The physics of the asteroid core crystallization process in metallic asteroids is investigated, with special attention given to the initial conditions for core crystallization, the manner of crystallization, the mechanisms acting in the stirring of the liquid, and the effects of elements such as sulfur on crystallization of Fe-Ni. On the basis of theoretical considerations and the published data on iron meteorites, it is suggested that the mode of crystallization in asteroid core was different from the apparent outward concentric crystallization of the earth core, in that the crystallization of asteroidal cores commenced at the base of the mantle and proceeded inward. The inward crystallization resulted in complex dendritic growth. These dendrites may have grown to lengths of hundreds of meters or perhaps even as large as the core radius, thereby dividing the core into separate magma chambers.

Haack, Henning↗

NASA NTRS1993

Numerical model for dendritic solidification of binary alloys

A finite element model capable of simulating solidification of binary alloys and the formation of freckles is presented. 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. Numerical simulations are shown in which an NH4Cl-H2O mixture and a Pb-Sn alloy melt are cooled. The solidification process is followed in time. Instabilities in the process can be clearly observed and the final compositions obtained.

Felicelli, S. D.↗