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A low gravity experiment to assess the effect of the presence of supercooled cloud droplets on the diffusional growth rate of ice crystals is described. The theoretical work and the feasibility studies are summarized. The nucleation of ice crystals in supercooled clouds is also discussed.
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.
The main focus is on solidification occurring in highly supercooled melts. Solidification rates in such melts are extremely high, an attractive feature from a commercial standpoint. Thus, the reported growth velocities for pure Ni and Co dendrites at a supercooling of 175 K are in excess of 180 km/hr. Rapidly quenched crystalline alloys produced by various atomization processes (e.g., centrifugal atomization or inert gas atomization) or melt spinning are examples of solidification processes, currently being intensively explored commercially, wherein extremely high solidification rates are achieved. Estimated dendrite tip growth rates are about 2 km/hr in a binary Al-4.5 wt % alloy, with a heat transfer coefficient of 6.4x10 sub 5 w/sq cm K or 15 cal/cu cm sK. In the limit, when the solidification rate exceeds a critical value, a glassy microstructure is obtained even in highly alloyed melts, which under normal conditions would solidity to form one or more crystalline phases. Glassy metals, also called metallic glasses, are candidate materials for distribution transformers because of their very low energy losses and are also being used in brazing and soldering applications.
During the directional solidification of alloys, solute inhomogeneities transverse to the growth direction arise due to morphological instabilities (leading to cellular or dendritic growth) and/or due to convection in the melt. In the absence of convection, the conditions for the onset of morphological instability are given by the linear stability analysis of Mullins and Sekerka. For ordinary solidification rates, the predictions of linear stability analysis are similar to the constitutional supercooling criterion. However, at very rapid solidification rates, linear stability analysis predicts a vast increase in stabilization in comparison to constitutional supercooling.
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.
Vapor pressures of solid and liquid ozone have been measured over a temperature range 87 to below 66 K. The experiment was performed under flow conditions, and the gas was analyzed by a precision mass spectrometer system. In the range of solid ozone two forms, supercooled and crystalline ozone, were found. A least-square fit of the data for crystalline ozone resulted in the equation log P(torr) = A + B/T, where A = 10.460 and B = -1021.6. The estimated uncertainty of the data is + or - 1.0 percent. A triple-point temperature of 79.6 + or - 0.3 K was found where supercooled and crystalline ozone data intersect.
The substitution of Y by Sm, Tb, Gd, and Ho in (BiYCa)3 FeSiGe)5O12 bubble garnet is shown to have large effects on the growth-induced anisotropy (GIA). The presently accepted film composition intended for 6-or 8-micron-period bubble memory devices demands partial substitution of Y by Gd and Ho. However, comparing films grown under the same growth conditions, it is observed that YGdHoBilG films posess less (GIA) than their Gd, Ho-free counterparts. Thus, to satisfy (GIA) requirements, the supercooling during growth must be increased by 20 K to 80 K with undesirable effects on defect densities. A new film composition containing Sm, Tb, and Gd has been formulated to satisfy all known material property specifications for 6- or 8-micron-period memory devices. It can be grown with only 45-50 K supercooling.
Meniscus-defined techniques for the growth of thin silicon sheets fall into two categories: vertical and horizontal growth. The interactions of the temperature field and the crystal shape are analyzed for both methods using two-dimensional finite-element models which include heat transfer and capillarity. Heat transfer in vertical growth systems is dominated by conduction in the melt and the crystal, with almost flat melt/crystal interfaces that are perpendicular to the direction of growth. The high axial temperature gradients characteristic of vertical growth lead to high thermal stresses. The maximum growth rate is also limited by capillarity which can restrict the conduction of heat from the melt into the crystal. In horizontal growth the melt/crystal interface stretches across the surface of the melt pool many times the crystal thickness, and low growth rates are achievable with careful temperature control. With a moderate axial temperature gradient in the sheet a substantial portion of the latent heat conducts along the sheet and the surface of the melt pool becomes supercooled, leading to dendritic growth. The thermal supercooling is surpressed by lowering the axial gradient in the crystal; this configuration is the most desirable for the growth of high quality crystals. An expression derived from scaling analysis relating the growth rate and the crucible temperature is shown to be reliable for horizontal growth.
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.
A fully time-dependent linear stability analysis of the morphological stability of a planar interface during directional solidification of a binary alloy at constant velocity in the presence of an electric field, is performed. The electromigration of solute and the differing electrical conductivities of solid and liquid for a model in which the temperature gradient is constant are taken into account. The present results are compared with the constitutional supercooling criterion, and it is shown there may be substantial differences. A modified constitutional supercooling criterion which is valid over a large range of conditions is derived. It is also found under certain conditions that the onset of instability may be time dependent.
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.
The motion of the freezing front between a needle-shaped crystal and a supercooled liquid is analyzed for situations where there is forced convection aligned with the crystal axis. 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 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.
Alloys generally solidify dendritically, and associated with that is the microsegregation of impurities. Pure metals also solidify in dendritic form as 'thermal' dendrites, which actually segregate the system's enthalpy. In this investigation, small additions of solute to succinonitrile have been studied and dendritic growth observed in a supercooled melt. This free dendritic growth-mode is similar to that experienced by equiaxed dendrites found in alloy castings. Observations of these free dendrites include measurement of velocity and tip radius of the dendrites at different supercoolings and solute concentrations.
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.
The theory and practice of containerless processing via electromagnetic (EM) levitation is reviewed briefly. The use of EM levitation for the processing of alloys is described with particular emphasis on the bulk melt supercooling phenomenon in a containerless environment. The various effects associated with rapid solidification via bulk melt supercooling are discussed with examples of Nb-Si alloys. It is suggested that a detailed analysis of such effects can be utilized to select the potentially most promising alloys for future space-based processing.
Experimental observations and a theoretical model for the onset and disappearance of condensation are provided for hypersonic flows of pure nitrogen at M = 10, 14, and 18. A method for analyzing the thermodynamic and flow properties of a partially condensed mixture from known supply conditions and measured Pitot pressure yields the local static pressure and temperature, mass fraction of the nitrogen condensed, and the Mach number of the partially condensed flow based on frozen sound speed. The transition between partially condensed-supercooled flow is found to occur at 22-25 K isobaric supercooling with the corresponding mass fraction condensed being 12-14 percent over a range of two orders of magnitude in local static pressure. The heat released and vapor mass removed during condensation ultimately raise the local pressure and temperature and reduce the flow Mach number.
Optical properties and spectral emissivities of liquid silicon, titanium, niobium, and zirconium were investigated by HeNe laser polarimetry at 632.8 nm. The metals were of a high purity and, except for zirconium, clean. The more demanding environmental requirements for eliminating oxide or nitride phases from zirconium were not met. Containerless conditions were achieved by electromagnetic levitation and heating. CO2 laser beam heating was also used to extend the temperature range for stable levitation and to heat solid silicon to form the metallic liquid phase. Corrections to previously reported calorimetric measurements of the heat capacity of liquid niobium were derived from the measured temperature dependence of its spectral emissivity. Property measurements were obtained for supercooled liquid silicon and supercooling of liquid zirconium was accomplished. The purification of liquid metals and the extension of this work on liquids to the measurement of thermodynamic properties and phase equilibria are discussed.
Submicron size monodisperse particles are of interest in many industrial and scientific applications. These include the manufacture of ceramic parts using fine ceramic particles, the production of thin films by deposition of ionized clusters, monodisperse seed particles for laser anemometry, and the study of size dependence of cluster chemical and physical properties. An inexpensive and relatively easy way to generate such particles is by utilizing the phenomenon of spontaneous condensation. The phenomenon occurs when the vapor or a mixture of a vapor and a noncondensing gas is expanded at a high expansion rate. The saturation line is crossed with the supercooled vapor behaving like a gas, until all of a sudden at the so called Wilson point, condensation occurs, resulting in a large number of relatively monodisperse droplets. The droplet size is a function of the expansion rate, inlet conditions, mass fraction of vapor, gas properties, etc. Spontaneous condensation of steam and water vapor and air mixture in a one dimensional nozzle was modeled and the resulting equations solved numerically. The droplet size distribution at the exit of various one dimensional nozzles and the flow characteristics such as pressure ratio, mean droplet radius, vapor and droplet temperatures, nucleation flux, supercooling, wetness, etc., along the axial distance were obtained. The numerical results compared very well with the available experimental data. The effect of inlet conditions, nozzle expansion rates, and vapor mass fractions on droplet mean radius, droplet size distribution, and pressure ratio were examined.