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It is shown that the dynamically selected velocity and tip radius of dendrites in the boundary-layer model of solidification have the special values which permit the existence of steady-state needle-crystal solutions. This result, in conjunction with considerations of stability, provides new insight concerning the validity of the marginal-stability hypothesis.
The distribution of slip dislocations in silicon dendritic web ribbons due to plastic deformation during the cooling phase of the growth was studied. The results show the existence of two distinguishable stress regions across the ribbon formed during the plastic deformation stage, namely, shear stress at the ribbon edges and tensile stress at the middle. In addition, slip dislocations caused by shear stress near the edges appear to originate at the twin plane.
The kinetic and morphological behavior of systems solidifying at small undercooling were investigated with emphasis on the role of convective and diffusive transport and the influence of gravity. A data base was established for pure succinonitrile which permits a comprehensive check on diffusional dendrite growth theory and the development of scaling laws to extend the theory to other material systems. A departure from diffusional-controlled growth was observed which becomes more significant at smaller undercoolings. A shuttle experiment is prepared to test the theory at the low undercoolings where convective effects begin to dominate.
A program to develop the technology of the silicon dendritic web ribbon growth process is examined. The effort is being concentrated on the area rate and quality requirements necessary to meet the JPL/DOE goals for terrestrial PV applications. Closed loop web growth system development and stress reduction for high area rate growth is considered.
Progress made in the study of defect characterization of silicon dendritic web ribbon is presented. Chemical etching is used combined with optical microscopy, as well as the electron beam induced current (EBIC) technique. Thermal annealing effect on carrier lifetime is examined.
Twenty-five minimodules composed of dendritic web solar cells with nominal glass size of 12 by 40 cm were provided for study. The modules were identical with respect to design, materials, and manufacturing and assembly processes to full scale modules. The modules were also electrically functional. These minimodules were fabricated to provide test vehicle for environmental testing and to assess reliability of process and design procedures. The module design and performance are outlined.
In the context of local models of solidification, it is suggested that the sidebranching which appears to be a characteristic feature of dendritic processes may be generated by selective amplification of noise near the tip and that, under some circumstances, thermal fluctuations may be strong enough to explain the observed effects. This proposal is discussed based on the two-dimensional boundary-layer model with kinetic crystalline anisotropy. Experimental methods to distinguish this stochastic process from a deterministic, dynamical sidebranching mechanism are suggested, including the possibility of space-based experiments.
The effect of a low-energy (0.4 keV), short-time (2-min), heavy-dose (10 to the 18th/sq cm) hydrogen ion implant on dendritic web silicon solar cells and material was investigated. Such an implant was observed to improve the cell open-circuit voltage and short-circuit current appreciably for a number of cells. In spite of the low implant energy, measurements of internal quantum efficiency indicate that it is the base of the cell, rather than the emitter, which benefits from the hydrogen implant. This is supported by the observation that the measured minority-carrier diffusion length in the base did not change when the emitter was removed. In some cases, a threefold increase of the base diffusion length was observed after implantation. The effects of the hydrogen implantation were not changed by a thermal stress test at 250 C for 111 h in nitrogen. It is speculated that hydrogen enters the bulk by traveling along dislocations, as proposed recently for edge-defined film-fed growth silicon ribbon.
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.
The microstructural development of binary alloys during directional solidification is studied. Cellular growth data for the Al-Cu and Pb-Sn binary alloy systems are analyzed in order evaluate the criteria of Kurz and Fisher (1981) and Trivedi (1984) for cellular-dendritic transition. It is observed that the experimental growth values do not correlate with the Kurz and Fisher or Trivedi data.
An analytic solution of the problem of velocity selection in a fully nonlocal model of dendritic crystal growth is presented. The analysis uses a WKB technique to derive and evaluate a solvability condition for the existence of steady-state needle-like solidification fronts in the limit of small under-cooling Delta. For the two-dimensional symmetric model with a capillary anisotropy of strength alpha, it is found that the velocity is proportional to (Delta to the 4th) times (alpha exp 7/4). The application of the method in three dimensions is also described.
The velocity-selection phenomenon in dendritic solidification is investigated theoretically. A WKB-type solvability condition is derived which is applicable to two- and three-dimensional symmetric and one-sided models; this condition is then solved numerically to obtain existence conditions for steady-state needle crystals. Numerical results are presented in graphs and discussed with reference to published numerical and experimental data.
NASA's KC-135, which flies a cyclic parabolic route designed to furnish periods of low gravity alternating with periods of high gravity, has been used to directionally solidify a superalloy and a FE-C-Si alloy. Probable transient effects, due to the rapid changes in the gravity levels, must be taken into account. An effort is presently made to show that experimental design is especially critical in the case of dendritic directional solidification experiments in which mixed gravity modes occur; inappropriate design easily leads to anomalous structures and data.
The Isothermal Dendritic Growth Experiment (IDGE) is a microgravity materials science experiment scheduled to fly in the cargo bay of the shuttle on the United States Microgravity Payload (USMP) carrier. The experiment will be operated by real-time control software which will not only monitor and control onboard experiment hardware, but will also communicate, via downlink data and uplink commands, with the Payload Operations Control Center (POCC) at NASA George C. Marshall Space Flight Center (MSFC). The software development approach being used to implement this system began with software functional requirements specification. This was accomplished using the Yourdon/DeMarco methodology as supplemented by the Ward/Mellor real-time extensions. The requirements specification in combination with software prototyping was then used to generate a detailed design consisting of structure charts, module prologues, and Program Design Language (PDL) specifications. This detailed design will next be used to code the software, followed finally by testing against the functional requirements. The result will be a modular real-time control software system with traceability through every phase of the development process.
An investigation of solute redistribution during dendritic solidification with diffusion in the solid has been performed using numerical techniques. The extent of diffusion is characterized by the instantaneous and average diffusion parameters. These parameters are functions of the diffusion Fourier number, the partition ratio and the fraction solid. Numerical results are presented as an approximate model, which is used to predict the average diffusion parameter and calculate the composition of the interdendritic liquid during solidification.
Experiments were carried out to measure the growth speed, V, and dendritic tip radius, R, of highly purified cyclohexanol. The data show that VR-squared = constant over the entire experimentally observed supercooling range, Delta T is between 0.1 and 1 K. The stability parameter estimated from this result indicates that sigma(asterisk) = 0.027, a value in good agreement with the values of sigma(asterisk) found for the cubic plastic crystals succinonitrile pivalic acid. Cyclohexanol differs from other carefully measured plastic crystals in that the viscosity of its melt at the melting point is about 20 times higher, so gravity-induced convection remains weak even at small supercoolings.
A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing the computed results with the results of an analytical solution derived by Kobayashi (1988) for the assumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a parabolic rate of the advancement of the solid/liquid interface. The flexibility of the method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.
The Isothermal Dendritic Growth Experiment (IDGE) is a microgravity materials science experiment scheduled to fly in the cargo bay of the shuttle on the United States Microgravity Payload (USMP) carrier. The experiment will be operated by real-time control software which will not only monitor and control onboard experiment hardware, but will also communicate, via downlink data and unlink commands, with the Payload Operations Control Center (POCC) at NASA George C. Marshall Space Flight Center (MSFC). The software development approach being used to implement this system began with software functional requirements specification. This was accomplished using the Yourdon/DeMarco methodology as supplemented by the Ward/Mellor real-time extensions. The requirements specification in combination with software prototyping was then used to generate a detailed design consisting of structure charts, module prologues, and Program Design Language (PDL) specifications. This detailed design will next be used to code the software, followed finally by testing against the functional requirements. The result will be a modular real-time control software system with traceability through every phase of the development process.