Arnon Chait

Transport modes during crystal growth in a centrifuge

Abstract A fully nonlinear three-dimensional numerical model for a centrifugal crystal growth experiment is presented. The model includes ampoule geometry and the experimentally obtained thermal profiles for the inner furnace steel cartridge insert. Results are presented based on both steady-state and fully transient models. The flow modes are presented resulting from Coriolis effects and from average resulting acceleration and the acceleration gradient, both acting on radial and axial thermal gradients. Thus far the model has been used to simulate growth at a particular experimental g equal to the value at which non-convective type impurity profiles were obtained. The flow modes resulting from different combinations of these forces can be of the same order of magnitude and interact with one another. The importance of the gradient acceleration is determined by the value of a new nondimensional number, called Ad. Thus, Coriolis effects and g gradients may have to be included in the model in order to obtain physically meaningful results. Implications of the resulting flow and thermal fields on the growing crystal at conditions available during centrifuge processing are also discussed.

Prediction of dislocation generation during Bridgman growth of GaAs crystals

Dislocation densities are generated in GaAs single crystals due to the excessive thermal stresses induced by temperature variations during growth. A viscoplastic material model for GaAs, which takes into account the movement and multiplication of dislocations in the plastic deformation, is developed according to Haasens theory. The dislocation density is expressed as an internal state variable in this dynamic viscoplastic model. The deformation process is a nonlinear function of stress, strain rate, dislocation density and temperature. The dislocation density in the GaAs crystal during vertical Bridgman growth is calculated using a nonlinear finite element model. The dislocation multiplication in GaAs crystals for several temperature fields obtained from thermal modeling of both the GTE GaAs experimental data and artificially designed data are investigated.

Thermal diffusion dominated dendritic growth : an analysis of the wall proximity effect

Abstract It is demonstrated that using a simple correction to the original Ivantsov solution to account for wall proximity effects is sufficient to describe the Peclet number microgravity data of Glicksman et al. [M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett. 73 (1994) 573; M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, ISLJ International 35 (1995) 1216; MRS Fall Meeting, Symp. P, Boston MA, 1995, in press] at low supercooling. The analytical correction provides for the enhanced diffusive heat transfer when the thermal diffusion length becomes comparable to the physical chamber dimension. The wall proximity effect is also responsible for the existence of a lower supercooling limit below which the dendrite cannot grow in a steady-state manner. It is concluded that Glicksmans USMP-2 microgravity data is thermal diffusion dominated and thus entirely appropriate for comparison with dendritic growth theories.

Magnetically damped convection and segregation in Bridgman growth of PbSnTe

Abstract The effects of an axially imposed magnetic field on convection and solute segregation during Bridgman growth of a non-dilute multicomponent system Pb 0.8 Sn 0.2 Te were studied using a finite-element model. The model considers heat and mass transport, fluid motion, solid/liquid-phase change and magnetic damping. The main objectives are to provide a quantitative understanding of the complex transport phenomena during solidification in a magnetic field, to provide estimates of the required magnetic field strength for low gravity growth, and to assess the role of magnetic damping for space and earth growth control. Numerical results for both vertical and horizontal growth configurations are presented. In addition to full-scale simulation, a revised scaling analysis is also presented.

Dynamic scaling in dendritic growth : significance of the initial nucleus size

Abstract This paper is concerned with the physical origin of one of the recently introduced dendrite tip scaling parameters [V. Pines, A. Chait, M. Zlatkowski, J. Crystal Growth 167 (1996) 777]. Using at least two parameters, σ 1 and σ 2 , the above quoted scaling analysis permits a consistent determination of the dendrite tip curvature radius and solidification velocity. In this work, the parameter σ 1 is shown to account for the divergence of the conventional dendrite tip scaling parameter, σ, at low supercooling. The parameter σ 1 is traced to the linear stage of development of the morphological instability of a small spherical nucleus placed in a supercooled melt. We demonstrate that σ 1 is proportional to the characteristic initial mean curvature of an unstable nucleus. The initial curvature may take different values depending on the origin of the unstable nucleus, and could be specified in a careful experimental setup.

Anomaly in dendritic growth data — effect of density change upon solidification

Abstract We examine recent dendritic growth data obtained by Glicksman and co-workers [M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett. 73 (1994) 573; M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, ISIJ Int. 35 (1995) 1216; MRS Fall Meeting, Symp. P, Boston, MA, 1995, in press; M.E. Glicksman, M.B. Koss, L.T. Bushnell and J.C. LaCombe, in: Modelling of Casting, Welding and Advanced Solidification Processes VII, Eds. M. Cross and J. Campbell, (The Minerals, Metals and Materials Society, 1995); private communication] in microgravity. These authors have pointed out an anomaly in the data, when compared with theoretical predictions. In particular, a systematic deviation of the growth Pe´clet number from an Ivantsovs theory was noted at the intermediate supercooling range. This work considers effects due to density change upon solidification. This requires a careful reexamination of the definition of material parameters, and an evaluation of effects due to the solidification-induced fluid flow (“Stefan wind”). A consistent application of carefully obtained material parameters clearly eliminates the discrepancy between the theory and experimental data. However, the effect of fluid flow due to the solid-melt density change is shown to be of minor importance to the particular experiment and material under consideration. We conclude by presenting an Ivantsovs theory modified for the wall proximity effect and corrected for density change upon solidification that matches the entire range of supercooling levels used in Glicksmans experiments.

Lateral or radial segregation in solidification of binary alloy with a curved liquid-solid interface

This paper deals with steady state lateral or radial segregation of solute in solidification of a binary alloy with a curved solid-liquid interface. It is an extension of the work of Coriell and Sekerka and of Coriell et al. for interface shapes that meet the crucible wall at an arbitrary angle, as is commonly found in experiments. This work is limited to the diffusion controlled growth regime in which the Peclet number Pe = Vl/D is large, and where the interface deflection is small. In the definition of Peclet number V is the growth rate, l is a characteristic length, and D is the binary diffusion coefficient of the solute in the liquid. We present analytical expressions for lateral and radial segregation which can be readily evaluated, given the material properties, growth velocity, and an interface shape obtained from experiment.

Dynamic scaling in dendritic growth

Abstract We use simple scaling analysis to examine the fundamental relations in dendritic growth between dynamic parameters such as dendrite tip radius and growth velocity, and the dimensionless net heat flux through the dendrite surface (Peclet number). The resulting relations are then expanded in powers of the Peclet number. It is demonstrated that for a small Peclet number, a two term expansion is sufficient to fit the entire range of data in supercooling of Glicksmans recent microgravity experiment [M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett. 73 (1994) 573; M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, ISIJ Int. 35 (1995) 1216; MRS Fall Meeting, Symp. P, Boston, MA, 1995, in press]. We also show that conventional theories using a single parameter are not supported from basic scaling arguments, nor do they correspond to experimental observations.

Lunar and Martian Dust: Evaluation and Mitigation

Dust is a ubiquitous phenomenon which must be explicitly addressed during upcoming robotic and human planetary exploration missions. The near term plans to revisit the moon as a stepping stone to further exploration of Mars and beyond brings places a primary emphasis on evaluation and mitigation of lunar dust. Comprised of regolith particles ranging in size from tens of nanometers to microns, lunar dust is a manifestation of the complex interaction of the lunar soil with multiple mechanical, electrical, and gravitational effects. Charged dust particles could levitate in the solar wind plasma environment, and may mediate significant differential charging effects with potential harmful consequences, as well as pose toxicological health problems when inhaled. This work outlines the scientific basis for lunar dust behavior, it’s characteristics and potential effects, and surveys several potential strategies for its control and mitigation both for surface operations and inside the habitable working volumes of a lunar outpost. This paper presents a preliminary analysis of dust as a component of the lunar environment, an assessment of it’s potential impacts on lunar exploration, as well as a perspective on lessons learned and information still to be gained from prior exploration. Also presented are the current perspective and planning for dust management activities within NASA’s Exploration Technology Development Program.

Equiaxed dendritic solidification in supercooled melts

The growth of equiaxed dendrites from a pure supercooled melt is examined. We propose modifications to the classical Ivantsov theory that allow for consideration of multiple interacting dendrites. The modified theory reveals the existence of a steady-state dendritic solidification mode in a frame of reference moving with the dendrite tip. This regime should be valid from the onset of nucleation to the commencement of time-dependent coarsening when the mass of the solid becomes comparable to the liquid mass in the solidification chamber. This regime is characterized by a reduced (relative to the single dendrite case) heat flux leading to slower solidification rates, but with the same level of supercooling. We study the effects of the relative proximity and number of interacting dendrites through a numerical example of solidification of succinonitrile, a common material used in many experiments. The data show that the model predicts a new steady growth regime that is different than the steady growth law of a single dendrite as described by Ivantsov theory.