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Theory and applications of electromagnetic levitation

A simple treatment of the electromagnetic levitation problem is presented, with emphasis placed on approximate formulas useful in planning and interpreting laboratory measurements. Consideration is also given to numerical solutions for fields, eddy currents, and Lorentz forces for rapidly varying applied fields, with particular reference made to traveling wave levitation experiments. Applications of levitation processing are briefly reviewed, including thermophysical property measurements, undercooling studies, containerless crystal growth, and continuous casting of cylinders.

Frost, R. T.↗

Quantitative Interferometry in the Severe Acoustic Environment of Resonant Supersonic Jets

There is renewed interest in the study of supersonic jets due to advances in high speed jet propulsion, supersonic combustion, and jet noise suppression for the next generation supersonic commercial transport. Understanding fundamental fluid dynamic and acoustic processes for these applications requires quantitative velocity, density and temperature measurements. In this paper we present data demonstrating a new, robust interferometer that can provide accurate data even in the presence of intense acoustic fields. This novel interferometer, the Liquid Crystal Point Diffraction Interferometer (LCPDI), was developed earlier for space flight experiments and is applied here to the case of a supersonic shock-containing jet. The LCPDI is briefly described, then integrated line-of-sight density data from the LCPDI for two underexpanded free jets are presented. The experimental shock spacings agree well with theory.

Mercer, Carolyn R.↗

Diffusion in Melts and Magmas

Diffusion results from random motion of particles and entities. Diffusion in melts and magmas is due to thermally excited random motion of atoms, ions, and clusters, and plays a critical role in magmatic and volcanic processes. In melts and magmas, diffusion is one of the two mechanisms of mass transfer; the other being bulk flow (referred to as convection or advection). When both are present, diffusion refers to the dispersive motion relative to the mean bulk flow in a given reference frame (Richter et al. 1998). Diffusion plays critical roles in controlling magma mixing (Watson 1982; Koyaguchi 1985, 1989; Lesher 1994; Huber et al. 2009; Guo and Zhang 2020), mineral growth and dissolution rates in magmas (e.g., Watson 1982; Harrison and Watson 1983; Zhang et al. 1989; Newcombe et al. 2014; Macris et al. 2018), bubble growth and dissolution rate in magmas (Sparks 1978; Proussevitch and Sahagian 1998; Liu and Zhang 2000; Zhang 2013), and elemental and isotope fractionation during mineral 2 growth and dissolution (Jambon 1980; Richter et al. 1999, 2003; Watson and Muller 2009; Chopra et al. 2012; Watkins et al. 2014, 2017; Holycross et al. 2016, 2018). As a result, diffusion also plays an essential role in explosive volcanic eruptions and magma crystallization. Furthermore, diffusion has important applications in geospeedometry (Lasaga 1983, 1998; Zhang 1994, 2008; Trail et al. 2016; Zhang and Xu 2016). Experimental investigation of diffusion in geologically relevant silicate melts began to flourish in the 1970’s when micro-analytical measurements of diffusion profiles became available. In addition to the vast number of papers published since then, numerous books and reviews are available for diffusion in silicate melts. Hofmann et al. (1974) edited a book titled “Geochemical Transport and Kinetics” published by Carnegie Institution of Washington. This was the first landmark book summarizing the field. Lasaga and Kirkpatrick (1981) edited a book “Kinetics of Geochemical Processes” as volume 8 of the Reviews in Mineralogy (later becoming Reviews in Mineralogy and Geochemistry) series. Zhang and Cherniak (2010) edited “Diffusion in Minerals and Melts” as volume 72 of Reviews of Mineralogy and Geochemistry series, in which one chapter focused on diffusion theory, five chapters on diffusion in silicate melts (Behrens 2010; Lesher 2010; Liang 2010; Zhang and Ni 2010; Zhang et al. 2010), and other chapters were on experimental, analytical, and computational methods, and diffusion in minerals. Several textbooks covered the principles and applications of diffusion theories (Kirkaldy and Young 1987; Shewmon 1989; Cussler 1997; Lasaga 1998; Zhang 2008; Vrentas and Vrentas 2016), and two classic books covered the mathematics of diffusion (Carslaw and Jaeger 1959; Crank 1975). In preparing for this review chapter, we thought carefully about what to cover for this vast field, and decided to briefly go through the fundamentals of diffusion (more complete review can be found in Chakraborty 1995; Zhang 2008, 2010) and solutions to often-encountered 3 diffusion problems, and then focus on post-2010 diffusion studies on silicate melts and magmas. Here, melts refer to (mostly natural) silicate liquid, and magmas refer to crystal-bearing and/or bubble-bearing melts in which the continuous phase is the melt. There is a large body of work on diffusion in glasses, especially in the materials science literature, which is not covered in this review.

Youxue Zhang↗

Kinetics of Nucleation and Crystal Growth in Glass Forming Melts in Microgravity

This flight definition project has the specific objective of investigating the kinetics of nucleation and crystal growth in high temperature inorganic oxide, glass forming melts in microgravity. It is related to one1 of our previous NASA projects that was concerned with glass formation for high temperature containerless melts in microgravity. The previous work culminated in two experiments which were conducted aboard the space shuttle in 1983 and 1985 and which consisted of melting (at 1500 C) and cooling levitated 6 to 8 mm diameter spherical samples in a Single Axis Acoustic Levitator (SAAL) furnace. Compared to other types of materials, there have been relatively few experiments, 6 to 8, conducted on inorganic glasses in space. These experiments have been concerned with mass transport (alkali diffusion), containerless melting, critical cooling rate for glass formation, chemical homogeneity, fiber pulling, and crystallization of glass forming melts. One of the most important and consistent findings in all of these experiments has been that the glasses prepared in microgravity are more resistant to crystallization (better glass former) and more chemically homogeneous than equivalent glasses made on earth (1g). The chemical composition of the melt appears relatively unimportant since the same general results have been reported for oxide, fluoride and chalcogenide melts. These results for space-processed glasses have important implications, since glasses with a higher resistance to crystallization or higher chemical homogeneity than those attainable on earth can significantly advance applications in areas such as fiber optics communications, high power laser glasses, and other photonic devices where glasses are the key functional materials. The classical theories for nucleation and crystal growth for a glass or melt do not contain any parameter that is directly dependent upon the g-value, so it is not readily apparent why glasses prepared in microgravity should be more resistant to crystallization than equivalent glasses prepared on earth. Similarly, the gravity-driven convection in a fluid melt is believed to be the primary force field that is responsible for melt homogenization on earth. Thus, it is not obvious why a glass prepared in space, where gravity-driven convection is ideally absent, would be more chemically homogeneous than a glass identically prepared on earth. The primary objective of the present research is to obtain experimental data for the nucleation rate and crystal growth rate for a well characterized silicate melt (lithium disilicate) processed entirely in space (low gravity) and compare these rates with the nucleation and crystal growth rates for a similar glass prepared identically on earth (1g).

Day, Delbert E.↗

Solidification under microgravity conditions - Dendritic growth

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.

Glicksman, M. E.↗

Effective-Mass Theory For Inhomogeneous Semiconductors

Five papers present derivations in effective-mass theory for semiconducing materials of gradually varying spatial composition. In paper entitled "Position-Dependent Effective Masses in Semiconductor Theory," concept of spatially-varying effective masses reviewed and shown unworkable. Second paper considers compound semiconductor having gradual spatial variation of composition. Third paper shows effective masses depend on average of chemical composition over entire crystal. Pair of papers entitled "Forces Acting on Free Carriers in Semiconductors of Inhomogeneous Composition" show it is incorrect to apply extended Wannier-Slater theorem using spatially changing effective masses, and quasi-electric fields due to spatial variations in chemical composition do not depend explicitly on temperature.

Von Roos, Oldwig↗

Crystal Growth Research in Space

The objectives of this work are to develop growth techniques and theory leading to improved bulk growth of semiconductor single crystals. Ground based experiments will be complemented by experiments carried out in the low-g environment provided by the space shuttle. Analytical studies and laboratory investigations are being conducted to better define the causes of crystalline defects and inhomogeneities. The compound semiconductor lead-tin-telluride is being used as the modeling material. Theoretical techniques are being developed to predict the thermal and solutal fields which are present during bulk growth from a melt. Techniques for measuring the thermophysical properties of semiconductors at high temperatures have been developed. During the past year electrochemical etching techniques have been developed for delineation of inhomogeneous regions in crystals. Thermal diffusivity measurements have been completed for the solid and liquid phases of PbTe and PbSnTe. Preliminary results have been obtained on the effects on crystal morphology of gravity, interface shape and interaction between the melt and the container.

Crouch, R. K.↗

Physics and Chemistry of Te and HgTe-based Ternary Melts

Historically, the theoretical treatment of the liquid phases has always been more difficult and complicated than that for solid and gas phases. A liquid has no lattice structure as crystalline solids and the atoms/molecules in the liquid can migrate through it relatively rapidly. On the other hand, it is also interacting with many other atoms/molecules so that the simplifications of the kinetic theory of gases cannot be employed. For more complicated liquids, such as the liquids of high ionicity and those containing hydrogen bonds and electric dipoles, the understanding is far from complete. At the same time, accurate information on the physics and chemistry of semiconductor melts is needed for the quantitative descriptions of the process of crystal growth from melt. The pre-crystallization phenomena in the liquid phase are critical because the properties of the grown crystals depend on the state and structure of the melt as well as the thermal history of the melt during solidification process. However, the data on the liquid phase, such as thermophysical properties of semiconductor melts are scarce, especially for the HgTe-based II-VI ternary compound semiconductors because of their high vapor pressure and extreme toxicity. Analysis of the thermophysical properties of the melt can provide information about structural transitions of the melt during the solidification process. From a broader point of view, the structure of liquids is much more complicated than the crystalline solids, especially the relaxation behavior through different thermal histories. The theory of hetero-phase fluctuations of liquids is applicable to any many-body systems including condensed-matter physics, field theory, physics of nuclear-matter, cosmology, biology and even sociology. This book summarizes the physics and chemistry from the experimental measurements and theoretical analyses of phase diagram, thermodynamic properties, density, thermal conductivity, viscosity, and electrical conductivity on the binary, pseudo-binary and ternary melts of the most advanced IR-detector material systems of HgCdTe and HgZnTe as well as the analyses of these results. The main objectives of this study are: (1) to provide the phase diagrams and thermodynamic properties of Hg-Cd-Te and Hg-Zn-Te systems through quantitatively fitting the experimental data by assuming an associated solution model for the liquid phase, (2) to experimentally measure the thermophysical properties of the Hg-Cd-Te and Hg-Zn-Te melts, including density, viscosity, electrical conductivity and thermal conductivity as functions of temperature and composition and (3) to enhance the fundamental knowledge of hetero-phase fluctuations and relaxation phenomena in the melts and extend our understanding of the solidification process in order to interpret the experimental results of crystal growth so as to improve the melt growth processes of the compound semiconductor. The physics and chemistry of Te and HgTe-based ternary melts were explored through the studies of the structural transformation during melting, the supercooling during solidification, the relaxation phenomena after rapid cooling of the melts and the metal-semiconductor transition in the melts through the analyses of electrical conductivity and Lorenz number. An in-depth study on the thermophysical properties and their time-dependent structural dynamic processes taking place in the vicinity of the solid-liquid phase transition of the narrow homogeneity range HgTe-based ternary semiconductors as well as the analysis of the homogenization process in the melt will also be presented.

Thermophysical properties↗

Solidification of II-VI Compounds in a Rotating Magnetic Field

This project is aimed at using a rotating magnetic field (RMF) to control fluid flow and transport during directional solidification of elemental and compound melts. Microgravity experiments have demonstrated that small amounts of residual acceleration of less than a micro-g can initiate and prolong fluid flow, particularly when there is a static component of the field perpendicular to the liquid solid interface. Thus a true diffusion boundary layer is not formed, and it becomes difficult to verify theories of solidification or to achieve diffusion controlled solidification. The RMF superimposes a stirring effect on an electrically conducting liquid, and with appropriate field strengths and frequencies, controlled transport of material through a liquid column can be obtained. As diffusion conditions are precluded and complete mixing conditions prevail, the technique is appropriate for traveling solvent zone or float zone growth methods in which the overall composition of the liquid can be maintained throughout the growth experiment. Crystals grown by RMF techniques in microgravity in previous, unrelated missions have shown exceptional properties. The objective of the project is two-fold, namely (1) using numerical modeling to simulate the behavior of a solvent zone with applied thermal boundary conditions and demonstrate the effects of decreasing gravity levels, or an increasing applied RMF, or both, and (2) to grow elements and II-VI compounds from traveling solvent zones both with and without applied RMFs, and to determine objectively how well the modeling predicts solidification parameters. Numerical modeling has demonstrated that, in the growth of CdTe from a tellurium solution, a rotating magnetic field can advantageously modify the shape of the liquid solid interface such that the interface is convex as seen from the liquid. Under such circumstances, the defect structure is reduced as any defects which are formed tend to grow out and not propagate. The flow of liquid, however, is complex due to the competing flow induced by the rotating magnetic field and the buoyancy driven convection. When the acceleration forces are reduced to one thousandth of gravity, the flow pattern is much simplified and well controlled material transport through the solvent zone can be readily achieved. Triple axis diffractometry and x-ray synchrotron topography have demonstrated that there is no significant improvement in crystal quality for HgCdTe grown on earth from a tellurium solution when a rotating magnetic field is applied. However, modeling shows that the flow in microgravity with a rotating magnetic field would produce a superior product.

Gillies, D. C.↗

A comparison of the reduction of convection by a magnetic field and a microgravity environment

The relative effectiveness of magnetic damping and the microgravity environment of space for suppressing buoyancy driven convection in semiconductor crystal melts was analyzed using flow estimates based on the convection driven by a single vertical heated plate. The results show that convection can be more than a factor of 10 weaker in space. If a strong magnetic field is applied in space, the convection can be reduced by a factor of 1000 over similarly magnetically damped convection in an earth-bound laboratory. The heated plate estimates were checked by comparing them with exact boundary layer theory for the nonmagnetic problem in the same configuration and they were found to be accurate.

Fowlis, William W.↗

Neutron stars.

Current theories of stellar evolution are examined, giving attention to neutrino emission processes and stellar collapse. Neutrinos can transfer energy produced in the collapsing core to the outer parts of the star. If the remaining core does not exceed a certain mass, it can remain in this highly condensed state to form a neutron star. The properties of neutron matter are discussed, taking into account the superfluid state, the crystallization of matter at subnuclear densities, aspects of rotation, and the magnetic field.

Chiu, H. Y.↗

Macromolecular Crystallization in Microgravity

The key concepts that attracted crystal growers, macromolecular or solid state, to microgravity research is that density difference fluid flows and sedimentation of the growing crystals are greatly reduced. Thus, defects and flaws in the crystals can be reduced, even eliminated, and crystal volume can be increased. Macromolecular crystallography differs from the field of crystalline semiconductors. For the latter, crystals are harnessed for their electrical behaviors. A crystal of a biological macromolecule is used instead for diffraction experiments (X-ray or neutron) to determine the three-dimensional structure of the macromolecule. The better the internal order of the crystal of a biological macromolecule then the more molecular structure detail that can be extracted. This structural information that enables an understanding of how the molecule functions. This knowledge is changing the biological and chemical sciences with major potential in understanding disease pathologies. Macromolecular structural crystallography in general is a remarkable field where physics, biology, chemistry, and mathematics meet to enable insight to the basic fundamentals of life. In this review, we examine the use of microgravity as an environment to grow macromolecular crystals. We describe the crystallization procedures used on the ground, how the resulting crystals are studied and the knowledge obtained from those crystals. We address the features desired in an ordered crystal and the techniques used to evaluate those features in detail. We then introduce the microgravity environment, the techniques to access that environment, and the theory and evidence behind the use of microgravity for crystallization experiments. We describe how ground-based laboratory techniques have been adapted to microgravity flights and look at some of the methods used to analyze the resulting data. Several case studies illustrate the physical crystal quality improvements and the macromolecular structural advances. Finally, limitations and alternatives to microgravity and future directions for this research are covered.

Snell, Edward H.↗

Ginzburg-Landau theory for the solid-liquid interface of bcc elements. II - Application to the classical one-component plasma, the Wigner crystal, and He-4

The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.

Zeng, X. C.↗

Reassignment of the Iron (3) Absorption Bands in the Spectra of Mars

Absorption features in the near-infrared and visible region reflectance spectra of Mars have been assigned to specific Fe (3+) crystal-field and o(2-) yields Fe(3+) charge transfer transitions. Recently, near-ultraviolet absorption spectra of iron oxides were obtained and the energies of o(2-) yields Fe(3+) charge-transfer (LMCT) transitions were determined from accurate SCF-X # alpha-SW molecular orbital calculations on (FeO6)(9-) and (FeO4)(5-) clusters. Both the theoretical and experimental results, together with existing data in the literature, show that some of the previous Fe(3+) band assignments in the spectra of Mars need to be revised. The theory of Fe(3+) spectra in minerals is discussed and applied to the spectrum of Mars.

Sherman, D. M.↗

Transparent magnetic state in single crystal Nd(1.85)Ce(0.15)CuO(4-y) superconductors

Several experimental studies have been reported as evidence of Josephson coupling between the superconducting layers in the highly anisotropic oxide such as the Bi2Sr2CaCu2O8 and Tl2Ba2CuO6 systems. These include the large penetration depth of 100 mu m measured, ac and dc Josephson effects. Recently two critical temperatures corresponding to Josephson coupling in between the layers and the Berezinskii-Kosterlitz-Thouless transition in the ab-plane have been directly observed in the transport measurements. If the field is applied parallel to the superconducting layers, the magnetic excitation is not the conventional Abrikosov vortices, but the Josephson vortices which extend lambda(sub ab) in the c-axis direction and lambda(sub J) = gamma s in the plane (s is the interlayer distance, gamma is the anisotropy constant). Because of the weak screening effect associated with the Josephson vortices, there have been predictions of magnetic transparent states at magnetic field above a characteristic field H(sub J), a behavior distinctively different from that of the type-II superconductors. In this paper, we report an experimental result which illustrates a transition from the Meissner state to the magnetic transparent state in single crystal of Nd(1.85)Ce(0.15)CuO(4-y). Magnetization has been measured as a function of temperature and field in the magnetic field parallel or close to ab-plane geometry. For a fixed magnetic field, the magnetization shows a two-step transition in M(T); for a fixed temperature, the magnetization shows an abrupt change to almost zero value above a characteristic field H(sub J), an indication of magnetic transparent state. The data of magnetization as a function of field clearly deviates from the behavior predicted by the Abrikosov theory for type-II superconductors. Instead, the data fit well into the picture of Josephson decoupling between the CuO2 layers.

Zuo, F.↗

Magnetic fields and nonuniform structures of the Moon

Direct magnetic measurements performed by space probes demonstrated the existence of small-scale, stationary surface magnetic fields on the Moon. The magnetic field averaged over a region of approximately 600 km was found to be no larger than approximately 10(exp -5) G, that of the regions approximately 100-200 km is approximately 10(exp -5) to 10(exp -4) G, and that of approximately 10-100 km reaches approximately 10(exp -3) G. Investigations of certain lunar rocks reveal stable residual magnetization, which could have been acquired during the crystallization of the rocks in the presence of the outer magnetic field, provided such a field existed at the initial stage of lunar evolution. Estimates show that 4 x 10(exp 9) yr ago the field was small, then it rose to approximately 1.3 G at the beginning of 3.9 x 10(exp 9) yr with a subsequent exponential decrease during the period of 3.9 x 10(exp 9) yr to 3.2 x 10(exp 9) yr ago. Small-scale fields have been explained by some authors as due to mechanical impacts produced by meteors. The theory of this effect is not elaborated in detail. This can in no way explain the paleomagnetic data. These data are commonly explained as a result of the dynamo action in the liquid lunar core.

Dolginov, A. Z.↗

Equiaxed Dendritic Solidification Experiment (EDSE)

The objective of the research is to quantitatively determine and understand the fundamental mechanisms that control the microstructural evolution during equiaxed dendritic solidification. A microgravity experiment will be conducted to obtain benchmark data on the transient growth and interaction of up to four equiaxed crystals of a pure and transparent metal analog (succinonitrile, SCN) under strictly diffusion-dominated conditions. Of interest in the experiment are the transient evolution of the primary and secondary dendrite tip speeds, the dendrite morphology and solid fraction, the tip selection criterion, and the temperature field in the melt for a range of interaction "strengths" between the crystals. The experiment extends the microgravity measurements of Glicksman and co-workers isothermal dendritic growth experiment (IDGE) for steady growth of a single dendrite to a case where growth transients are introduced due to thermal interactions between neighboring dendrites - a situation closer to actual casting conditions. Corresponding Earth-based experiments will be conducted to ascertain the influence of melt convection. The experiments are supported by a variety of analytical models and numerical simulations. The data will be used to develop and test theories of transient dendritic growth and the solidification of multiple interacting equiaxed crystals in a supercooled melt.

Beckermann, C.↗

Equiaxed Dendritic Solidification Experiment (EDSE)

The objective of the research is to quantitatively determine and understand the fundamental mechanisms that control the microstructural evolution during solidification of an assemblage of equiaxed dendritic crystals. A microgravity experiment will be conducted to obtain benchmark data on the transient growth and interaction of up to four equiaxed crystals of a pure and transparent metal analog (succinonitrile, SCN) under strictly diffusion dominated conditions. Of interest in the experiment are the transient evolution of the primary and secondary dendrite tip speeds, the dendrite morphology (i.e., tip radii, branch spacings, etc.) and solid fraction, the tip selection criterion, and the temperature field in the melt for a range of initial supercoolings and, thus, interaction "strengths" between the crystals. The experiment thus extends the microgravity measurements of Glicksman and coworkers for steady growth of a single dendrite [Isothermal Dendritic Growth Experiment (IDGE), first flown on USMP-2] to a case where growth transients are introduced due to thermal interactions between neighboring dendrites - a situation more close to actual casting conditions. Corresponding earth-based experiments will be conducted to ascertain the influence of melt convection. The experiments are supported by a variety of analytical models and numerical simulations. The data will primarily be used to develop and test theories of transient dendritic growth and the solidification of multiple interacting equiaxed crystals in a supercooled melt.

Beckermann, C.↗