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At least 163 records · Page 9

Thermosolutal convection during dendritic solidification of a binary alloy

The FEM model of Heinrich (1988) is presently extended to the case of dendritic vertical solidification under steady-state conditions. An analysis is conducted of the nonlinear governing equations for linear stability, and FEM calculations are performed in cases where instability has been predicted for Pb-Sn melt systems; the results obtained show that the model is more stable than the plane front liquid-solid model, and shows similar, finger-like covection when unstable. It is found that convection in the 'mush' zone is confined to the top of that region; convective motion is driven by convection in the bulk fluid, in the absence of natural convection.

Heinrich, Juan C.↗

Structure and Kinematics of a Complex Crater: Upheaval Dome, Southeast, Utah

Two vastly different phenomena, extraterrestrial impact and salt diapirism, have been proposed for the origin of Upheaval Dome. Upheaval Dome is a about 2.5-km-diameter structural dome surrounded by a 5-km-diameter ring structural depression, which is in turn flanked by extensive, nearly flat-lying Colorado Plateau strata. Seismic refraction data and geologic mapping indicate that the dome originated by the collapse of a transient cavity formed by impact; data also show that rising salt has had a negligible influence on dome development. Evidence for this includes several factors: (1) a rare lag deposit of impactite is present; (2) fan-tailed fracture surfaces (shatter surfaces) and a few shattercones are present; (3) the top of the underlying salt horizon is at least 500 m below the center of the dome, with no exposures of salt in the dome to support the possibility that a salt diapir has ascended through it; (4) sedimentary strata in the center are significantly imbricated by top-to-the-center thrust faulting and are complexly folded; (5) top-to-the-center low-angle normal faults are found at the perimeter of the structure; and (6) clastic dikes are widespread. The scarcity of melt rocks and shock fabrics is attributed to approximately 0.5 km of erosion; the structures of the dome reflect processes of complex crater development at a depth of about 0.5 km below the crater floor. Based on mapping and kinematic analysis, we infer that the dome formed mainly by centerward motion of rock units along listric faults. Outcrop-scale folding and upturning of beds, especially common in the center, largely resulted from this motion. In addition, we have detected some centerward motion of fault-bounded wedges resulting from displacements on subhorizontal faults that conjoin and die out within horizontal bedding in the perimeter of the structure. Collectively, the observed deformation accounts for the creation of both the central uplift and the encircling ring syncline.

Kriens, B. J.↗

Fault Offsets and Lateral Crustal Movement on Europa

Structural evidence is presented for tension cracking associated with strike slip faulting and crustal movement in the bright ice covered Galilean satellite Europa. The structure and morphology of wedge shaped bands argues that they formed as a result of the rotation and lateral displacement of crustal units bounded by near vertical faults penetrating through the brittle crustal layer. The significant rotation and lateral motion of crustal blocks near the anti-jove point on Europa, without graben formation, also argues that the lithosphere in the fractured area is mechanically decoupled from the solid silicate interior, by either warm ice at depth or liquid water. Ice at depth and at a large fraction of its melting temperature is expected to behave as a fluid over geologically short time intervals due to its extremely low viscosity relative to the cold, brittle ice near the surface. One proposed convection mechanism is thus considered unlikely as it would be difficult to transmit internal stress through a decoupling layer to the surface.

Schenk, P. M.↗

Emergent Relationships Among Sea Ice, Longwave Radiation, and the Beaufort High Circulation Exposed Through Parameter Uncertainty Analysis

Using a perturbed parameter ensemble of a coupled climate model, emerging relationships are identified between sea ice area, net surface longwave radiation, and the atmospheric circulation over the Beaufort gyre. There is a strong positive correlation between sea ice area and the net longwave radiation over the ocean-ice surface during the melting season and a negative correlation during the freezing season. The mechanisms responsible for the longwave radiation balance at the surface are mainly driven by sea ice variations in the freezing season and by clouds in the melting season. A strong positive (negative) correlation is also found between the fall (summer) total sea ice area in the Arctic and the sea level pressure over the Beaufort High region. It is argued that as sea ice coverage is lost, static stability losses are severe in fall, resulting in enhanced evaporation, vertical motions, and weakening of the general large-scale anticyclonic circulation of the Beaufort High.

54 ENVIRONMENTAL SCIENCES↗

Controlling colloidal crystals via morphing energy landscapes and reinforcement learning

We report a feedback control method to remove grain boundaries and produce circular shaped colloidal crystals using morphing energy landscapes and reinforcement learning–based policies. We demonstrate this approach in optical microscopy and computer simulation experiments for colloidal particles in ac electric fields. First, we discover how tunable energy landscape shapes and orientations enhance grain boundary motion and crystal morphology relaxation. Next, reinforcement learning is used to develop an optimized control policy to actuate morphing energy landscapes to produce defect-free crystals orders of magnitude faster than natural relaxation times. Morphing energy landscapes mechanistically enable rapid crystal repair via anisotropic stresses to control defect and shape relaxation without melting. This method is scalable for up to at least N = 10 3 particles with mean process times scaling as N 0.5 . Further scalability is possible by controlling parallel local energy landscapes (e.g., periodic landscapes) to generate large-scale global defect-free hierarchical structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

fp-tools

The output of a molecular dynamics simulation is a data file containing properties of the motion of the simulated particles as a function of time (e.g., positions, velocities). From this output, scientists can extract various properties which give insight into the physics of the system; for example, the radial distribution function can be computed from the particle positions, which gives insight into how close the system is to melting or freezing. Many publicly available codes to perform molecular dynamics simulations exist and have been well adopted by the scientific community (e.g., LAMMPS, VASP). However, it remains standard practice for scientists to write their own post-processing scripts to extract various properties of interest from the molecular dynamics simulation data. Since in many cases scientists are interested in the same set of “textbook” properties, there is a large duplication of effort in writing these post-processing scripts. Our proposed code, FP-Tools, is a C++ toolkit designed to help scientists extract and analyze quantities of interest from the output of a molecular dynamics simulation, eliminating the need for them to write these codes themselves and thus reducing this duplication of effort. The quantities which are computed by our code are well documented in the literature (either in publications or textbooks), and the algorithms we implement to compute these properties are also well known in the field. We are not introducing new science or methods here; rather, our primary goal is to provide a useful tool to the community in the form of a well-documented, easy to use package.

Hartman, Leah↗

The Arctic Ocean ice balance - A Kalman smoother estimate

The methodology of Kalman filtering and smoothing is used to integrate a 7-year time series of buoy-derived ice motion fields and satellite passive microwave observations. The result is a record of the concentrations of open water, first-year ice, and multiyear ice that we believe is better than the estimates based on the microwave data alone. The Kalman procedure interprets the evolution of the ice cover in terms of advection, melt, growth, ridging, and aging of first-year into multiyear ice. Generally, the regions along the coasts of Alaska and Siberia and the area just north of Fram Strait are sources of first-year ice, with the rest of the Arctic Ocean acting as a sink for first-year ice via ridging and aging. All the Arctic Ocean except for the Beaufort and Chukchi seas is a source of multiyear ice, with the Chukchi being the only internal multiyear ice sink. Export through Fram Strait is a major ice sink, but we find only about two-thirds the export and greater interannual variation than found in previous studies. There is no discernible trend in the area of multiyear ice in the Arctic Ocean during the 7 years.

Thomas, D. R.↗

Numerical modeling of Bridgman growth of PbSnTe in a magnetic field

In this work we study heat and mass transport, fluid motion, and solid/liquid phase change in the process of steady Bridgman growth of Pb(.8)Sn(.2)Te (LTT) in an axially-imposed uniform magnetic field under terrestrial and microgravity conditions. In particular, this research is concerned with the interrelationships among segregation, buoyancy-driven convection, and magnetic damping in the LTT melt. The main objectives are to provide a quantitative understanding of the complex transport phenomena during solidification of the nondilute binary of LTT, to provide estimates of the strength of magnetic field required to achieve the desired diffusion-dominated growth, and to assess the role of magnetic damping for space and earth based control of the buoyancy-induced convection. The problem was solved by using FIDAP and numerical results for both vertical and horizontal growth configurations with respect to the acceleration of gravity vector are presented.

Yao, Minwu↗

Solute effects upon dislocation motion and recovery in Mg alloys (Final Report)

The objective the research was to develop a firmer understanding of the interactions between substitutional solute atoms and dislocations within Mg alloys. These interactions govern the absolute and relative mobilities of various types of dislocations in Mg (e.g., basal < a>, non-basal < a>, and pyramidal < c+a>). Furthermore, they have an impact on dislocation recovery processes (e.g., cross-glide, climb, rearrangement, and annihilation). Ultimately, solute-dislocation interactions strongly impact a) strain hardening, b) strain rate sensitivity, c) plastic anisotropy of textured polycrystals, d) texture evolution, e) dislocation substructures evolution, and even f) recrystallization behavior. It is broadly known that Mg alloys exhibit poor low temperature formability. Since formability is largely governed by properties (a) – (c) in this list, it is critical to develop a better understanding of solute-dislocation interactions, if one hopes to improve the situation. While the theory of static solute strengthening is well developed, especially for alloys with face centered cubic (FCC) crystal structures, there are outstanding questions related to applications to hexagonal close packed (HCP) crystal structures and dynamic strain aging (DSA) in materials of various structures. DSA has far-reaching implications for metal formability and, in the case of Mg alloys, appears to correlate with the so-called rare-earth (RE) texture which has been shown to benefit formability. The Portevin-Le Chatelier (PLC) effect, and associated negative strain rate sensitivity, occur at higher temperatures (>100℃) in Mg alloys as compared with similar Al alloys, even though they have similar melting points and solute diffusivities. Our preliminary research has shown that modern, physics-based models of DSA can be tuned to describe the behavior of Mg alloys if a rather higher activation enthalpy is assumed for cross-core diffusivity. While this partially explains the delay in DSA to higher temperatures, it is also hypothesized that this delay is due in part to the intrinsically more thermally activated (rate sensitive) nature of non-basal < a> dislocation motion which is required for macroscopic flow of Mg alloys, whereas octahedral slip in many FCC metals like aluminum is essentially athermal at room temperature. It was originally proposed to employ a combination of in-situ diffraction-based experimental characterization to validate existing theory. It was envisioned to perform in-situ transmission electron microscopy (TEM) to assess individual dislocation behavior and in-situ high-energy X-ray diffraction (HEXRD) techniques which were showing great promise for elucidating collective dislocation behavior, 2 including recovery, especially if the contributions to various forms of diffraction peak broadening (𝜂𝜂,𝜔𝜔,and 2𝜃𝜃) can be effectively integrated. Finally, it was envisioned to perform discrete dislocation dynamics (DDD) modeling approaches to aide in the interpretation of both TEM and HEXRD experiments. In the end, mechanical tests were performed on more complex Mg alloys which exhibited evidence of dynamic strain aging, and this led to the establishment of another project. Mechanical test data obtained at McMaster University served as the basis of an assessment of the applicability of Bazinski’s “stress equivalence” theory of solute strengthening to polycrystalline alloys of Mg. Although we did not succeed in applying the approach to Mg alloys, we did develop expertise with the HEXRD approach using a BCC, β-Ti alloy and demonstrated numerous new capabilities that may be applied to any polycrystalline material in collaboration with researchers at CHESS and around the world: (1) assessment of details of the elastoplastic transition (yielding) using a combination of HEXRD and full-field polycrystal plasticity modeling, (2) the first-ever experimental observation of strong stress rotation within the individual grains of a polycrystalline material, and (3) a comprehensive analysis of the grain-level dislocation density evolution based upon diffraction peak broadening along 𝜂𝜂,𝜔𝜔,and 2𝜃𝜃 directions. This final aspect allowed us to confirm that dislocations were gliding on multiple plane types and not restricted to {110} type planes, and it also provided clues as to why some grains were unloading during straining, with surprising implications for our understanding of the effects of geometrically necessary dislocations (GNDs). Finally, graduate student, Mohammed Shabana, developed a MATLAB code which confirmed the conclusions of Prof. Catalin Picu (Rensallear Polytechnic Institute, RPI) regarding the effect of solute-trapped, forest dislocations on the breaking stress of Lomer lock junctions in FCC metal alloys. He applied the same anisotropic line-tension model to a variety of dislocation junction configurations and found an inconsistency in the widely cited results of Dupuy and Fivel regarding the Hirth Lock, and he outlined an approach to extend these finding to HCP Mg alloys that we are still pursuing with discretionary fundings at UVA.

36 MATERIALS SCIENCE↗

Collapse of Jahn-Teller phonons in La 1−x Sr x MnO 3 with weak magnetoresistance

Perovskite manganites are quantum materials exhibiting competing interactions inducing colossal magnetoresistance (CMR). The prevailing theory of CMR highlights the essential role of electron-phonon coupling (EPC), but mounting evidence suggests the underlying mechanism is more complicated. Here, we investigate phonons and spin-phonon coupling in ferromagnetic CMR manganites La 1−x Sr x MnO 3 (x=0.2,0.3) with relatively small CMR associated with melting of the magnetic order above room temperature. High-resolution neutron scattering experiments combined with density functional theory (DFT) show that the low-temperature ferromagnetic phase is conventional: neutron scattering from phonons agrees with DFT predictions and magnons follow sinusoidal dispersions. Fluctuating magnetic moments and low-energy phonons remain conventional in the high-temperature paramagnetic phase, indicating the Mn and La/Sr sublattices are not strongly perturbed by melting of ferromagnetism. In contrast, the Jahn–Teller-active optical oxygen vibrations collapse entirely above the Curie temperature, despite low CMR in these compositions, with some of the lost spectral weight reappearing as quasielastic scattering. We attribute this highly anomalous behavior to giant EPC in the charge and/or orbital channel. It drives cooperative diffusive motion of quasistatic carrier-trapping oxygen sublattice distortions once ferromagnetism disappears. We hypothesize the magnitude of magnetoresistance correlates with the rate of diffusion rather than with the strength of Jahn–Teller EPC.

36 MATERIALS SCIENCE↗

Sea Ice Drift Tracks From Autonomous Buoys in the MOSAiC Distributed Network

A network of autonomous, ice-tethered buoys was deployed around the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) experiment in late September 2019 for a year-long drift in the Arctic Transpolar Drift Stream. The buoys were deployed as part of the MOSAiC distributed network (DN) which included 12 multi-instrumented ice stations and an additional 116 GPS buoys distributed primarily within a 40 km radius of the MOSAiC Central Observatory. Buoy coverage within the DN was maintained with additional deployments throughout the year-long drift allowing for collection of data over a full sea ice growth and melt cycle. All GPS position data from buoys deployed within the DN have been assembled and processed into the collection of 216 quality-controlled buoy drift tracks presented in this dataset covering the period 26 September 2019 – 23 May 2021. The drift tracks in this collection are ideal for studies of dynamic sea ice motion around the MOSAiC experiment at cascading spatial scales ranging from 100s of meters to 100s of km.

Angela C. Bliss↗

Spatiotemporal mapping of mesoscopic liquid dynamics

The study of liquid dynamics at mesoscopic scales is still strewn with difficulty due to limitations in theory and experiment. Historically, significant attention has been given to the analysis of space-time correlation functions and their frequency-Fourier transforms at a few discrete wave numbers. The massive computing power afforded by modern high performance computing clusters and the advent of a wide-angle neutron spin-echo spectrometer, however, have unlocked a more intuitive and fruitful approach to this problem. Using molecular dynamics simulations, here we demonstrate the benefits of spatiotemporally mapping intermediate scattering functions on a dense grid of correlation times and wave numbers. Four model systems are investigated: a Lennard-Jones liquid, a coarse-grained bead-spring polymer, a molten sodium chloride, and a poly(ethylene oxide) melt. We show that the spatiotemporal mapping approach is particularly useful for elucidating the mesoscopic dynamics in these liquids, where several underlying mechanisms, such as molecular relaxations, hydrodynamic modes, and nonhydrodynamic excitations, are potentially at play. Therefore, compared to the traditional method, direct visualization of density space-time correlation functions on two-dimensional color maps permits appraisals of complicated dynamical behavior at mesoscales in a global manner. For example, the scaling relations between space and time for different types of molecular motions can be straightforwardly identified on these plots, without any model-dependent analysis. Additionally, we show how theoretical ideas regarding collective mesoscopic dynamics, such as the classical hydrodynamic theory, the convolution approximation, and a recently proposed phenomenological model, can be discussed in terms of the global features of spatiotemporal maps of intermediate scattering functions. The new perspective offered by the spatiotemporal mapping method should prove useful for the study of liquid dynamics in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Energy amplification in plasma crystals due to multiple torsions

Interacting torsions are examined within a two-dimensional monolayer crystal suspended in an argon complex plasma for 1–10 W discharge powers and pressures of 135–155 mTorr. Two torsions embedded in a lattice are shown to amplify the kinetic energy and range of motion of particles located between the torsions to nearly three times that observed in single torsion systems. It is also shown that multiple torsions can interact via amplified particle energy when separated by up to 14 interparticle distances (Δ). The torsion separation distance also showed a positive linear trend with power and a slightly positive correlation with the pressure. This amplification of energy is possible due to the fact that multiple torsions in a lattice increase the interparticle distance of the lattice by 16% more than single torsion systems, leading to additional freedom of motion in the lattice plane. These combined findings show that multiple torsions heat the lattice differently depending on their separation from the other torsion. The midpoint particles between torsions absorb the majority of energy from the two torsions, and energy addition at the midpoint is nonlinear. The addition of more torsions to the lattice may lead to melting of the plasma crystal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Non-linear resonance of fluids in a crystal growth cavity

In the microgravity environment, the effect of gravity on fluid motion is much reduced. Hence, secondary effects such as vibrations, jitters, surface tension, capillary effects, and electromagnetic forces become the dominant mechanism of fluid convection. Numerous studies have been conducted to investigate fluid behavior in microgravity with the ultimate goal of developing processes with minimal influence from convection. Industrial applications such as crystal growth from solidification of melt and protein growth for pharmatheutical application are just a few examples of the vast potential benefit that can be reaped from material processing in space. However, a space laboratory is not immune from all undesirable disturbances and it is imperative that such disturbances be well understood, quantifiable, and controlled. Non-uniform and transient accelerations such as vibrations, jitters, and impulsive accelerations exist as a result of crew activities, space vehicle maneuvering, and the operations of on-board equipment. Measurements conducted on-board a U.S. Spacelab showed the existence of vibrations in the frequency range of 1 to 100 Hz with a dominant mode of 17 Hz and harmonics of 54 Hz. The observed vibration is not limited to any coordinate plane but exists in all directions. Similar situation exists on-board the Russian MIR space station. Due to the large structure of its design, the future International Space Station will have its own characteristic vibration spectrum. It is well known that vibration can exert substantial influence on heat and mass transfer processes, thus hindering any attempts to achieve a diffusion-limited process. Experiments on vibration convection for a liquid-filled enclosure under one-g environment showed the existence of different flow regimes as vibration frequency and intensity changes. Results showed the existence of a resonant frequency, near which the enhancement is the strongest, and the existence of a high frequency asymptote. Numerical simulations of vibration convection have been conducted by Yurkov, Fu and Shieh, and by Wang. These analyses considered a two-dimensional air-filled cell under weightlessness condition and showed results similar to those of the experiments. It is not yet known whether resonance convection can be triggered by jitter alone or whether it requires the interaction of jitter with other convective forces in low gravity. An order of magnitude analysis, however, can be used to show the dependence of the resonance frequency on the fluid Prandtl number. Even though the onset of resonance convection may depend on other factors, results indicates that fluids with low Prandtl numbers are more susceptible to resonance than those with high Prandtl numbers. The current study is aimed at gaining additional insights to this problem using germanium as working fluid. Germanium was chosen for this analysis because of its common usage in solidification process and its relatively low Prandtl number (Pr = 0.02).

Wang, Francis C.↗

Magnetic Susceptibility Effects and Lorentz Damping in Diamagnetic Fluids

A great number of crystals (semi-conductor and protein) grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity and g-jitter. Both static and dynamic (rotating or travelling wave) magnetic fields can be used to reduce the effects of convection in materials processing. In semi-conductor melts, due to their relatively high electrical conductivity, the induced Lorentz force can be effectively used to curtail convective effects. In melts/solutions with reduced electrical conductivity, such as aqueous solutions used in solution crystal growth, protein crystal growth and/or model fluid experiments for simulating melt growth, however, the variation of the magnetic susceptibility with temperature and/or concentration can be utilized to better damp fluid convection than the Lorentz force method. This paper presents a comprehensive, comparative numerical study of the relative damping effects using static magnetic fields and gradients in a simple geometry subjected to a thermal gradient. The governing equations are formulated in general terms and then simplified for the numerical calculations. Operational regimes, based on the best damping technique for different melts/solutions are identified based on fluid properties. Comparisons are provided between the numerical results and available results from experiments in surveyed literature.

Ramachandran, Narayanan↗

Chaotic motion of Europa and Ganymede and the Ganymede-Callisto dichotomy

Europa and Ganymede may have undergone an episode of chaotic motion before the establishment of the current Laplace resonance involving the three inner GAlilean satellites. During this episode, the orbital eccentricities of both satellites may have increased dramatically. As a result, the mechanical stresses due to tidal deformation of the satellites' icy lithospheres may have been large enough to result in extensive fracturing, and tidal heating may have melted water ice in the mantles of both satellites, triggering the geological activity that has modified their surfaces since the heavy cratering period. The tidal effects on Ganymede during this episode provide an explanation of the dichotomy between it and Callisto, which have similar bulk properties but very different geological histories.

Tittemore, William C.↗

Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence

When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. In this work, a background of these set of observations will be given followed by a presentation of our results on the digital particle tracking analysis that has been performed on a number of available videos. The analysis indicates that the levitated drop attains a constant rotational speed during the melting phase and formation of the co-rotating axi-symmetric laminar toroidal structures. However, the rate of axial rotation increases dramatically during the deformation of the toroidal structures anti their breakup into chaotic entities. This new data suggests an interaction between the flow inside the levitated molten drop and the driving coils in the experiments. Possible mechanisms for this interaction will be reviewed. The data will also be used to make an assessment of existing theories on droplet rotation.

Abedian, B.↗

Low frequency vibrational stirring - A new method for rapidly mixing solutions and melts during growth

A new method for rapidly stirring liquids has been developed which may be useful in crystal growth applications. The method involves the introduction of orthogonally coupled low frequency vibrations to fluids contained in cylindrical crucibles. A mathematical model has been developed to describe the influence of this vibrational stirring method on fluid flow. The optimum sloshing frequencies calculated for a specific system geometry were very close to those observed experimentally. A systematic study of the fluid flow induced by the vibrational motion was carried out at room temperature using aqueous solutions containing glycerine. Preliminary experiments were carried out to study the effect of vibrational stirring on interface shape and position during the Bridgman growth of CsCdCl3, a model system.

Liu, W.-S.↗