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A formula for the free energy difference between the undercooled liquid phase and the stable solid phase is derived for off-eutectic binary alloys in which the equilibrium solid/liquid transition takes place over a certain temperature range. The free energy change is then evaluated numerically for a Bi-25 at. pct Cd alloy modeled as a sub-subregular solution.
A concept is developed and described which allows to measure the heat capacity and the effective thermal conductivity of stable and undercooled liquid metals and alloys in an electromagnetic levitation apparatus. A proposal is made to use an ac pulse heating method which is used nowadays as a standard technique for precision measurement of low-temperature heat capacities. The ideal process parameters, including the drop diameter D, temperature T, and frequency of measurement omega, can be optimized when the following relations hold for the external and internal relaxation time constants tau-1 and tau-2, respectively: omega(tau-1) greater than 10 and omega(tau-2) less than 0.1. Then, heat capacity data can be obtained with an accuracy of better than 1 percent with D about 5 to 10 mm, T between 1200 and 1800 K, and omega between 0.1 and 1 Hz for typical metals and alloys.
The line-of-sight averaged, time-dependent dendrite tip concentrations for the diffusion dominated vertical directional solidification of a metal model (ammonium chloride and water) were obtained by extrapolating exponentially fit diffusion layer profiles measured using a laser interferometer. The tip concentrations were shown to increase linearly with time throughout the diffusion dominated growth process for an initially stagnant dendritic array. The process was terminated for the cases chosen by convective breakdown suffered when the conditionally stable diffusion layer exceeded the critical Rayleigh criteria. The transient tip concentrations were determined to significantly exceed the values predicted for steady state, thus producing much larger constitutional undercoolings. This has ramifications for growth speeds, arm spacings and the dendritic structure itself.
A combination of bulk undercooling in an electromagnetic levitation apparatus and splat quenching between two copper plates is used to process Nb-Si alloys in order to maximize rapid solidification conditions and minimize the effects of recalescence, with emphasis on the solidification of characteristics of alloys in the 21 to 27 at. pct Si range of composition. SEM and TEM as well as X-ray diffraction are used to characterize the microstructures of the processed samples. In the range of compositions studied, the splat-quenched drops always formed the tetragonal Nb3Si phase directly from the liquid. Drops solidified in the coil were characterized by the presence of the primary intermetallic Nb5Si3 and the absence of both peritectic Nb3Si and the equilibrium eutectic. In these cases, a metastable alpha-Nb + beta-Nb5Si3 eutectic formed. The results are discussed in terms of possible metastable configurations of the Nb-Si phase diagram as well as concepts of nucleation and growth kinetics applied to the Nb3Si and Nb5Si3 intermetallics.
The use of containerless processing in nucleation and microstructural studies of alloys is reviewed in terms of approaches and recent results. Drop-tube studies of niobium based on a statistical approach are discussed, and experiments are described which permit the study of the solidification front across the surface of a specimen. The various alloys studied are reviewed in terms of facilitated observations of metastability, chemical homogeneity, and microstructural refinement. Heterogeneous nucleation is reported for a preexponential factor of 10 exp 27 and a critical free energy of 46-56kT. The theoretical relationship between undercooling and solidification velocity correlates with containerless test observations at large solute concentrations. Containerless processing is effective for studying the properties of liquid metals or accessing the metastable thermodynamic regime.
Solidification of selected Mn-Al-C alloys during containerless levitation and rapid quenching has yielded the first report for a ferromagnetic metastable tau phase formed directly from the melt. Complete solidification to tau phase was interrupted by the competitive evolution of an equilibrium epsilon phase during recalescence. The amount of undercooling required to produce the metastable ferromagnetic tau phase in a Mn(0.55)Al(0.433)C(0.017) alloy during solidification was estimated as approximately 470 K based on differential thermal analysis results. When the alloy carbon content was increased to 3.4 at. pct, transition in structure development occurred so that the samples exhibited gamma 2 phase formation as well as tau and epsilon phases.
Satellite images of large volcanic explosions reveal that the tops of volcanic eruptions columns are much cooler than the surrounding atmosphere. It is proposed that this effect occurs whenever a mixture of hot volcanic ash and entrained air ascends sufficiently high into a stably stratified atmosphere. Although the mixture is initially very hot, it expands and cools as the ambient pressure decreases. It is shown that cloud-top undercoolings in excess of 20 C may develop in clouds that penetrate the stratosphere, and it is predicted that, for a given cloud-top temperature, variations in the initial temperature of 100-200 C may correspond to variations in the column height of 5-10 km. It is deduced that the present practice of converting satellite-based measurements of the temperature at the top of volcanic eruptions columns to estimates of the column height will produce rather inaccurate results and should therefore be discontinued.
The stability of a solid-liquid interface in a hypercooled melt is studied, taking into account attachment kinetics, surface energy, and surface energy in the heat balance. There is a basic-state solution with the planar interface moving at constant speed. Linear-stability theory gives a long-wave absolute-stability limit. Near this point a string model is introduced in which a thermal-boundary-layer approximation is used and an evolution equation for the interface is obtained. In a limiting case this interface equation reduces to a Kuromoto-Sivashinsky equation. Comparison with experimental and numerical results are discussed, and a conceptual picture of unconstrained growth for all undercoolings is addressed.
The focus of this work is the numerical simulation of interface motion during solidification of pure materials. First, the applicability of the oft-used quasi-stationary approximation for interface motion is assessed. It is seen that such an approximation results in poor accuracy for nontrivial Stefan numbers. Solution of the full set of equations including grid movement terms yields close agreement with analytical results. Next, a generic interface tracking procedure is designed, which overcomes restrictions of single-valuedness of the interface imposed by commonly used mapping methods. This method incorporates with ease interface phenomena involving curvature, which assume importance at the smaller scales of a deformed interface. The method is then applied to study the development of a morphologically unstable phase interface. The issue of appropriate scaling has been addressed. The Gibbs-Thomson effect for curved interfaces has been included. The evolution of the interface, with the competing mechanisms of undercooling and surface tension is found to culminate in tip-splitting, cusp formation and persistent cellular development.
Liquidus temperatures were determined for the titanium-aluminum system at compositions ranging from 41 to 62 at. pct Al. The measurements were obtained by inducing solidification of slightly undercooled melts under containerless processing conditions using electromagnetic levitation. Absolute temperatures were determined by optical pyrometry in combination with independent measurements of spectral emissivities by laser polarimetry. The present liquidus temperatures are in agreement with two sets of literature values and are consistent with a set of solid-state literature data. These values exceed those selected in one recent proposed phase diagram revision by about 30 K and are as much as 40 to 60 K higher than those in another proposed revision.
Optical properties (including spectral emissivity, refractive index, and extinction coefficient) of liquid Ti-Al alloys were measured as functions of temperature (including temperatures up to 350 K below the equilibrium liquidus temperatures), using laser ellipsometry at 632.8 nm. The experiments were conducted under containerless conditions, using electromagnetic levitation and heating supplemented by CO2 laser beam heating. It is shown that the emissivities of liquid Ti-Al alloy vary with temperature in a manner that can be understood by the same theories which are applicable to solid metals, for regions near to and above the liquidus temperature. At temperatures below the liquidus temperature, the optical properties of highly undercooled liquid Ti-Al alloys are not dependent on temperature.
Computed results are presented describing the transient evolution of the velocity and the temperature fields in a levitation-melted, electromagnetically-positioned metallic sample under microgravity, for conditions, when the heating current is switched off. Thus the calculations trace the evolution from one steady state corresponding to the simultaneous operation of both the heating and the positioning coils to that corresponding to the operation of the positioning coils only. The calculations have shown that the velocity field will decay much more rapidly than the temperature field, so that the cooling and subsequent undercooling and recalescence of the samples should take place from an essentially stagnant melt, meeting the original objectives of the experiment. The computed results for the velocity decay appear to agree with asymptotic calculations and also appear to follow the scaling laws.
NASA has planned three flight experiments, designated as the Isothermal Dendritic Growth Experiment (IDGE), to be performed on three of the United States Microgravity Payload (USMP) flights. IDGE is designed to provide microgravity data on dendritic growth for a critical test of theory. Terrestrial gravity, g sub 0, and the associated phenomenon of buoyancy driven convection, prevent a truly quantitative test of pure, diffusocapillary dendritic growth theory. However, recent theoretical analysis provides a fluid mechanics framework for estimating the effects of reduced gravity on the dendritic solidification of pure succinonitrile (SCN), the model material selected for the first IDGE flight. The results (dendritic tip radii and velocities) of the recent fully integrated ground-based tests on the IDGE prototype engineering hardware is in general agreement with the 'historical' ground based data for SCN. At undercoolings of 0.5 K or less, a microgravity environment of approximately 10 exp -3 g sub 0 or lower would have a significant difference from the g sub 0 dendritic growth of SCN.
High-temperature electrostatic levitator provides independent control of levitation and heating of sample in vacuum. Does not cause electromagnetic stirring in molten sample (such stirring causes early nucleation in undercooling). Maintenance of levitating force entails control of electrostatic field and electrical charge on sample.
Measurements of thermophysical properties of undercooled liquids often require some kind of levitator which isolates samples from container walls. We introduce in this presentation a high temperature/high vacuum electrostatic levitator (HTHVESL) which promises some unique capabilities for the studies of thermophysical properties of molten materials. Although substantial progress has been made in the past several months, this technology is still in the development stage, therefore, in this presentation we only focus on the present state of the HTHVESL(1) and point out other capabilities which might be realized in the near future.
Broadly speaking, our efforts have been concentrated in two aspects of directional solidification: (A) a more complete theoretical understanding of convection effects in a Bridgman apparatus; and (B) a clear understanding of scalings of various features of dendritic crystal growth in the sensitive limit of small capillary effects. For studies that fall within class A, the principal objectives are as follows: (A1) Derive analytical formulas for segregation, interfacial shape and fluid velocities in mathematically amenable asymptotic limits. (A2) Numerically verify and extend asymptotic results to other ranges of parameter space with a view to a broader physical understanding of the general trends. With respect to studies that fall within class B, the principal objectives include answering the following questions about dendritic crystal growth: (B1) Are there unsteady dendrite solutions in 2-D to the completely nonlinear time evolving equations in the small surface tension limit with only a locally steady tip region with well defined tip radius and velocity? Is anisotropy in surface tension necessary for the existence of such solutions as it is for a true steady state needle crystal? How does the size of such a local region depend on capillary effects, anisotropy and undercooling? (B2) How do the different control parameters affect the nonlinear amplification of tip noise and dendritic side branch coarsening?
Compound chondrules are considered to be the product of collisions between molten chondrules during chondrule formation Wasson, J. T. et al. (1994) have argued that some compound chondrules are formed when a chondrule with an accretional rim experienced a flash-melting event similar to a chondrule-forming event. We have designed experiments to investigate the formation of compound chondrules by both methods. Experiments were performed on a Deltech vertical muffle tube furnace to form synthetic chondrules to use as accretion rim material. For our experimental conditions, it is clear that compound chondrules can only be made by a collisional event. Our changes maintain their spherical shape and produce distinct boundaries between charges that are similar to natural compound chondrules. Furthermore, collision event(s) between chondrules will cause nucleation if they are molten and undercooled, thus producing chondrule textures. Flash melting chondrules with accretionary rims will not produce compound chondrules but will produce new chondrules with new textures.
A theoretical model is used to describe and investigate the effects of simultaneous crystallization, radiation loss, and entrainment of cooler material on the temperature of a well-mixed core of an active aa lava flow. Entrainment of crust, levee debris, and base material into the interior of active flows has been observed, but the degree of assimilation and the thermal consequences are difficult to quantify. The rate of entrainment can be constrained by supplementing the theoretical model with information on the crystallization along the path of the flow and estimation of the radiative loss from the flow interior. Application of the model is demonstrated with the 1984 Mauna Loa flow, which was erupted about 30 C undercooled. Without any entrainment of cooler material, the high crystallization rates would have driven temperatures in the core wall above temperatures measured by thermocouple and estimated from glass geothermometry. One plausible scenario for this flow, which agrees with available temperature and crystallinity measurements, has a high initial rate of entrainment during the first 8 hours of travel (a mass ratio of entrained material to fluid core of about 15% if the average temperature of the entrained material was 600 C), which counterbalances the latent heat from approximately 40% crystallization. In this scenario, the model suggests an additional 5% crystallization and a 5% entrainment mass ratio over the subsequent 16-hour period. Measurements of crystallization, radiative losses, and entrainment factors are necessary for understanding the detailed thermal histories of active lava flows.