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Gravity induced free convection effects in melting phenomena for thermal control, predicting temperature distributions and solid-liquid interface profiles by two dimensional model
Investigation of the solidification behavior of spherical specimens of Ni-12 wt % Sn and Ni-1 wt % Ag that froze radially from the surface toward the center and cylindrical specimens of Al-33 wt % Cu eutectic that froze directionally under appropriately selected conditions of thermal gradient at the solid-liquid interface and growth rate. Possible effects of vacuum and low gravity conditions, under which the spherical specimens were processed, on observed nucleation and growth phenomena are discussed. A genetic explanation is given of observed microstructures, and the distributions of alloying elements is discussed. In directionally solidified eutectic specimens a comparison is made between statistically evaluated growth defects in Skylab and in ground specimens.
Absorption induced embrittlement of solid metals by certain liquid metals is analyzed through an Engel-Brewer calculation of the solid-liquid interaction energy, and of the effect of the latter in reducing fracture surface energy. The reduction in fracture surface energy is estimated by comparison of the electronic contribution to the solid-liquid interaction energy with solid-solid bond energy for some 40 liquid-solid couples. Regular solution theory is used to estimate mutual solubility as the relative difference in parameter values. Embrittlement can be predicted by using reduction in fracture surface energy and solubility parameter difference as critical variables. The effect of solute additions to the liquid on the degree of embrittlement is interpreted via the same two variables; the principal effect of solutes is to modify solubility relationships at the solid-liquid interface.
Electromagnetic force generated by radiofrequency coil is used to shape molten silicon. Shaping coil surrounds melt near solid-liquid interface and induces current in surface region of melt nearly equal to but opposite coil current.
Surface tension driven flow in a cylindrical melt suspended between two rods was investigated by numerical solution of the steady state differential equations for heat and momentum transfer. Radiation heating and electron beam heating were considered approximately. For small values of the driving force, one rotating ring was formed in the top half of the zone, and its mirror image in the bottom half. At larger driving forces, secondary cells form which probably would undergo oscillatory motion. The influence of Prandtl number, zone movement, and buoyancy on the convection was also studied. The primary resistance to mass transfer in the laminar regime was in the center of the zone rather than at the solid-liquid interfaces.
A numerical study of the conjugated problem of a separated supersonic flow field and a conductive solid wall with an embedded heat source is presented. Implicit finite-difference schemes were used to solve the two-dimensional time-dependent compressible Navier-Stokes equations and the time-dependent heat-conduction equation for the solid in both general coordinate systems. A detailed comparison between the thin-layer and Navier-Stokes models was made for steady and unsteady supersonic flow and showed insignificant differences. Steady-state and transient cases were computed and the results show that a temperature pulse at the solid-fluid interface can be used to detect the flow direction near the wall in the vicinity of separation without significant distortion of the flow field.
Experimental results are summarized, and it is pointed out that gravity-driven convection can alter the diffusive-advective mass transport behavior in the growth of crystals by physical vapor transport. Specially designed and constructed transparent furnaces are described which are being used to study the effects of gravity in the crystal growth of the compound semiconductors PbTe and CdTe. The theory underlying vapor transport behavior is reviewed, with attention given to the vapor-solid behavior of compound materials, to one-dimensional mass transport, and to gravity-induced (natural) convection. In the transparent furnaces, the quartz capillary tube mounted along the axis of the main quartz ampoule is used to measure the temperature at the growth surface (vapor-solid crystal interface) and the source, as well as the complete temperature profile along the axis of the tube. The light-pipe works to remove heat from the growth end of the ampoule by radiative heat transfer. The ampoules are sealed after being evacuated to the low 10 to the -8th torr range with a cryogenic vacuum pump.
At low solidification rates, the criterion for the onset of morphological instability parallels closely the criterion of constitutional supercooling. At somewhat larger rates of solidification, however, the results of the perturbation theory of morphological instability differ significantly from the predictions of constitutional supercooling. This arises because the critical wave length for instability decreases as solidification rate increases and thus the effects of capillarity (solid-liquid surface tension) play a strong stabilizing role. This gives rise to the concept of absolute stability, according to which the system will always be stable for a sufficiently large rate of solidification. This enhanced stabilization by capillarity is present only so long as local equilibrium is maintained at the solid-liquid interface. If the interfacial temperature drops below its equilibrium value by an amount dependent on growth rate, oscillatory morphological instabilities can occur. The differences among these various stability criteria are illustrated by means of some simple two-dimensional diagrams that should supplant the conventional plots of (temperature gradient)/(growth rate) vs. alloy concentration.
High growth rates which are the key to a successful low cost silicon ribbon technology is discussed. The heat of fusion is conducted along the grown ribbon for some distance before it can be dissipated. The conduction path is limited to the cross sectional area of the ribbon, since the solid-liquid interface is perpendicular to the pull direction. Horizontal ribbon growth is achieved by providing an extended solidification interface, parallel within a few degrees, to the pull direction. The heat of fusion need only be conducted through the thickness of the ribbon and is dissipated from the upper surface which comprises an area equal to the interface. Growth of up to 15cm wide ribbon and continuous growth of ribbons as long as 120 meters is demonstrated. Areal productivity as high as 2.7 sq/m/hr is shown for a single 15 cm ribbon, while typical values of approximately 1 sq/m/hr are obtained in the growth of 5 cm ribbon.
A temperature gradient stage design for optical microscopy is described. Exceptional thermal stability is the major feature. The stage is used to study crystal growth phenomena occurring at the solid-liquid interface. The apparatus is designed to use transparent organic solutions as models for the study of metal-like solidification. The stage provides a controlled thermal environment for unidirectional solidification of low melting temperature materials. Freezing rate is regulated by mechanically sliding in the stage a thin glass cell containing the materials being studied. Two cell assemblies are described. One type is used for convection-free and the other for controlled forced convection studies of the solidification interface.
The optimum conditions for crystal growth are usually achieved either by suppressing convective fluid flows (e.g., by the use of a low-gravity environment) or by over-riding thermal and solutal convection by the use of a strong stirring action. A novel stirring technique has been developed which involves subjecting a vertical crucible to a circle in a horizontal plane (without rotation). Use of an amplitude of 3 mm at a frequency of approx 6 Hz produced complete mixing of a non-uniform aqueous liquid in a few seconds. The mixing action involved the downward flow of liquid in the outer annulus of the liquid, driven by surface waves. When the downward flowing liquid reaches the bottom of the crucible, it is reflected in a central, upward flowing spiral. This flow pattern should be beneficial for crystal growth by the Bridgman method since it will sweep impurities away from the walls and produce a more convex solid-liquid interface. Initial attempts to apply the new stirring technique to CdTe crystal growth did not show significant improvement in the number of crystals nucleated, but the interface shape appeared to be close to that predicted.
The objective of this work has been to evaluate whether or not Marangoni flow could be suppressed in molten metals by the presence of very thin oxide films. Experimental work has been carried out on molten Sn under UHV conditions. A disk floating zone arrangement was developed to allow in situ Auger examination of molten surfaces. An electron energy loss technique was developed which allows detection of continuous tin oxide films of 6 A or greater. Experiments were planned to detect the effects of oxide formation upon Marangoni flow by measuring: (1) temperature profiles, (2) solid liquid interface shapes, (3) macrosegregation, and (4) the onset of oscillatory Marangoni flow by detecting oscillating temperature variations. Work on (4) showed that oscillatory temperature variations of frequency or = 10 Hz were not present in the disk float zone geometry under conditions of Ma = 4300 with an oxide free molten surface. The disk float zone geometry was modeled with a finite element analysis and temperature and velocity profiles were determined.
The objective of the research is to develop tools of use in explaining the results of directional solidification experiments in space. These tools consist of mathematical and experimental models. Experiments are also being flown at low-g to validate the ground-based results. Many metals and semiconductors directionally solidified in space had a diameter less than that of the containing ampoule. In fact this occurred whenever the ampoule contained a gas space. This phenomenon has been attributed in a vague way to lack of wetting of the ampoule wall by the melt. The actual liquid behavior by use of low temperature analogs is being observed aboard the KC-135. In the first flight, water was placed in plastic ampoules (not wet) with ceramic end plugs which were wet by the water to simulate a solid-liquid interface. Unfortunately during storage prior to the flight the water began to wet the ampoule wall. Discrete bubbles formed down the axis of the ampoules. New ampoule materials are being used now, with testing for stability prior to the next flight. A theoretical model has also been developed for this phenomenon.
Understanding how liquid phase particles are engulfed or pushed during freezing of a monotectic is addressed. The additional complication is that the solid-liquid interface is nonplanar due to constitutional undercooling. Some evidence of particle pushing where the particles are the liquid phase of the montectic was already observed. Cellular freezing of the succinonitrile-glycerol system also occurred. Only a few compositions were tested at that time. The starting materials were not especially pure so that cellular interface observed was likely due to the presence of unkown impurities, the major portion of which was water. Topics addressed include: the effort of modeling the particle pushing process using the computer, establishing an apparatus for the determination of phase diagrams, and the measurement of the temperature gradients with a specimen which will solidify on the temperature gradient microscope stage.
Thermodynamic models are developed for the processes which controlled the evolution of the surface Ganymede, an icy Jovian satellite assumed to have a rock-rich core surrounded by a water-ice mantle. Account is taken of a heat pulse which would have arisen from a Rayleigh-Taylor instability at a deep-seated liquid-solid water interface, rapid fracturing from global stresses imposed by warm ice diapiric upwelling, impacts by large meteorites, and resurfacing by ice flows (rather than core formation). Comparisons are made with existing models for the evolution of Callisto, and the difficulties in defining a mechanism which produced the groove terrain of Ganymede are discussed.
The shape of a stationary solid-liquid interface in a temperature gradient near a grain boundary in a pure material is calculated for anisotropic crystal-melt surface tension and equal thermal conductivities of crystal and melt. Results are compared with those for the well-known problem of the two-dimensional equilibrium shape of a crystal. For small anisotropy, the resulting interface shapes have continuously turning tangents but differ in detail from the grain boundary groove shapes that have been calculated for isotropic surface tension. For larger anisotropy, the interface shapes have discontinuities in slope as a result of missing orientations.
Numerical experiments are used to study thermally driven flows which occur during vertical Bridgman crystal growth of a single component fluid. The solid-liquid interface was specified as parabolic and flow patterns were calculated for various insulation thicknesses, Grashof, Prandtl, and Biot numbers. When the melt is on top and the gravity vector is axially downward it is shown that flow persists as long as a radial temperature gradient is present. If the interface is convex, as viewed from the liquid, a single cell is observed. A concave interface exhibits multiple counterrotating cells. The insulation thickness and Grashof, Prandtl, and Biot numbers influence the flow in a quantitative manner.
Finite element modeling is dominated by geometric modeling type operations. Therefore, an effective interface to geometric modeling requires access to both the model and the modeling functionality used to create it. The use of a dynamic interface that addresses these needs through the use of boundary data structures and geometric operators is discussed.