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At least 397 records · Page 22

Durable and High-Performance SOECs Based on Proton Conductors for Hydrogen Production

Proton-conducting solid oxide electrolysis cells (P-SOECs) are a promising technology for cost-effective and efficient production of green hydrogen. Breakthroughs in materials development, optimization of cell structure, and achievement of high performance and durability are essential to significantly increase the commercial competitiveness of these technologies. The main objective of this project is to gain scientific knowledge for the rational design, fabrication, and demonstration of a robust, highly efficient, and low-cost SOEC technology based on a proton-conducting electrolyte membrane for hydrogen production. We focused on better understanding the degradation mechanisms of proton-conducting electrolytes, air electrodes, and catalyst materials under electrolysis mode to develop an effective strategy for rationalizing new materials that are vital for enhancing cell performance and durability. The scope includes enhancing the performance and durability of the electrolyte and electrode materials under realistic operating conditions, developing highly active and robust catalysts to minimize electrode losses while improving tolerance to contaminant poisoning, revealing the mechanism of enhanced activity and stability of the catalyst, and understanding the underlying degradation mechanisms. In addition, various characterization techniques were employed to gain a fundamental understanding of the materials’ behavior and their impact on cell performance, providing vital information to guide materials discovery and cell design. After defect chemistry engineering, the optimized donor and acceptor co-doped electrolytes BaMo/W 0.03 Ce 0.71 Yb 0.26 O 3-δ (BM/W03) showed substantially improved chemical stability against high concentrations of CO 2 and H 2 O compared to the state-of-the-art electrolyte (BaZr 0.1 Ce 0.7 Y 0.1 Yb 0.1 O 3-δ , BZCYYb1711) while maintaining comparable ionic conductivity and ionic transference number. To bypass the inherent trade-off between conductivity and chemical stability, we fabricated a bi-layer electrolyte composed of BZCYYb1711 coated with a highly-stable thin layer of BaHf 0.83 Yb 0.17 O 3-δ (BHYb). This bi-layer electrolyte displayed excellent chemical stability against high concentration CO 2 ; there was no detectable formation of BaCO 3 after exposure to 97% CO 2 (with 3% H 2 O) at 500 °C for 1000 hours and the rate of degradation in resistance was about 0.4% per 1,000 hours (kh). In contrast, the same BZCYYb1711 electrolyte without a BHYb coating degraded significantly under the same testing conditions; the degradation rate was increased to 5.1%/kh. In addition, a triple conducting air electrode Ba 0.9 Pr 0.1 Hf 0.1 Y0.1Co 0.8 O 3-δ (BPHYC) was developed by heavily doping transition metal ions into a proton-conducting material. This air electrode material, composed of 3 distinct phases, exhibits superior electrocatalytic activity due to the synergistic effect from the three component phases. Moreover, an active and durable catalyst, La 2 Ni 0.5 Fe 0.5 O 4+δ (LNF), was developed, showing excellent catalytic activity and contaminant tolerance, with a degradation rate of only 0.49%/kh when exposed to high concentrations of steam and Cr. Finally, single cells were constructed from the best electrolytes, electrodes, and catalyst coatings developed in this project. These cells demonstrated superior high current density at a given cell voltage, high roundtrip efficiency, and remarkable durability (up to 1000 hours of operation).

08 HYDROGEN↗

Critical Contribution of Imbalanced Charge Loss to Performance Deterioration of Si-Based Lithium-Ion Cells during Calendar Aging

Increasing the energy density of lithium-ion batteries, and thereby reducing costs, is a major target for industry and academic research. One of the best opportunities is to replace the traditional graphite anode with a high-capacity anode material, such as silicon. However, Si-based lithium-ion batteries have been widely reported to suffer from a limited calendar life for automobile applications. Heretofore, there lacks a fundamental understanding of calendar aging for rationally developing mitigation strategies. Both open-circuit voltage and voltage-hold aging protocols were utilized to characterize the aging behavior of Si-based cells. Particularly, a high-precision leakage current measurement was applied to quantitatively measure the rate of parasitic reactions at the electrode/electrolyte interface. The rate of parasitic reactions at the Si anode was found 5 times and 15 times faster than those of LiNi 0.8 Mn 0.1 Co 0.1 O 2 and LiFePO 4 cathodes, respectively. Here, the imbalanced charge loss from parasitic reactions plays a critical role in exacerbating performance deterioration. In addition, a linear relationship between capacity loss and charge consumption from parasitic reactions provides fundamental support to assess calendar life through voltage-hold tests. These new findings imply that longer calendar life can be achieved by suppressing parasitic reactions at the Si anode to balance charge consumption during calendar aging.

25 ENERGY STORAGE↗

Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov—Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in ma.ss-conserved cell polarity models.

97 MATHEMATICS AND COMPUTING↗

Evaluation of predictive correlation between flux expulsion and grain growth for superconducting radio frequency cavities

Abstract A series of experiments were carried out in an effort to develop a simple method for predicting the magnetic flux expulsion behavior of high purity niobium used to fabricate superconducting radio frequency (SRF) cavities. Using conventional metallographic characterizations in conjunction with high spatial resolution electron backscattered diffraction-orientation imaging microscopy, we find that the flux expulsion behavior of 1.3 GHz single cell SRF Nb cavities is significantly associated with the grain growth of the Nb material during heat treatment. Most of the Nb grains rapidly grew during 900 °C heat treatment, and were likely full-recrystallized with 1000 °C HT. When compared to the magnetic flux expulsion ratio ( B sc / B nc ) at Δ T = 5 K, the flux expulsion efficiency of the cavities increases with the increase of grain size. Most interestingly, 900 °C HT shows a roughly linear trend that suggests that this criterion could be used to predict the appropriate heat treatment temperature for sufficient flux expulsion behavior in SRF-grade Nb. This result can be used to see if flux expulsion can be predicted by examining the materials coming from Nb vendors, prior to cavity fabrication.

43 PARTICLE ACCELERATORS↗

Dermal Aged and Fetal Fibroblasts Realign in Response to Mechanical Strain

Integrins specifically recognize and bind extracellular matrix components, providing physical anchor points and functional setpoints. Focal adhesion complexes, containing integrin and cytoskeletal proteins, are potential mechanoreceptors, poised to distribute applied forces through the cytoskeleton. Pursuing the hypothesis that cells both perceive and respond to external force, we applied a stretch/relaxation regimen to normal human fetal and aged dermal fibroblast monolayers cultured on flexible membranes. The frequency and magnitude of the applied force is precisely controlled by the Flexercell Unit(Trademark). A protocol of stretch (20% elongation of the monolayer) at a frequency of 6 cycles/min caused a progressive change from a randomly distributed pattern of cells to a symmetric, radial distribution with cells aligned parallel to the applied force. We have coined the term 'orienteering' as the process of active alignment of cells in response to applied force. Cytochalasin D was added in graded doses to investigate the role of the actin cytoskeleton in force perception and transmission. A clear dose response was found; at high concentrations orienteering was abolished; and the drug's impact was reversible. The two cell strains used were similar in their alignment behavior and in their responses to cytochalasin D. Orienteering was influenced by cell density, and the cell strains studied differed in this respect. Fetal cells, unlike their aged counterparts, failed to orient at high cell density. In both cell strains, mid-density cultures aligned rapidly and sparse cultures lagged. These results indicate that both cell-cell adhesion and cytoskeleton integrity are critical in mediating the orienteering response. Differences between these two cell strains may relate to their expression of extracellular matrix molecules (fibronectin, collagen type 1) integrins and their relative binding affinities.

Sawyer, Christine↗

Orientation and length of mammalian skeletal myocytes in response to a unidirectional stretch

Effects of mechanical forces exerted on mammalian skeletal muscle cells during development were studied using an in vitro model to unidirectionally stretch cultured C2C12 cells grown on silastic membrane. Previous models to date have not studied these responses of the mammalian system specifically. The silastic membrane upon which these cells were grown exhibited linear strain behavior over the range of 3.6-14.6% strain, with a Poisson's ratio of approximately 0.5. To mimic murine in utero long bone growth, cell substrates were stretched at an average strain rate of 2.36%/day for 4 days or 1.77%/day for 6 days with an overall membrane strain of 9.5% and 10.6%, respectively. Both control and stretched fibers stained positively for the contractile protein, alpha-actinin, demonstrating muscle fiber development. An effect of stretch on orientation and length of myofibers was observed. At both strain rates, stretched fibers aligned at a smaller angle relative to the direction of stretch and were significantly longer compared to randomly oriented control fibers. There was no effect of duration of stretch on orientation or length, suggesting the cellular responses are independent of strain rate for the range tested. These results demonstrate that, under conditions simulating mammalian long bone growth, cultured myocytes respond to mechanical forces by lengthening and orienting along the direction of stretch.

Non-NASA Center↗

Electrophoresis and isoelectric focusing of whole cell and membrane proteins from the extremely halophilic archaebacteria

The subunits from two purified halobacterial membrane enzymes (ATPase and nitrate reductase) behaved differently with respect to isoelectric focusing, silver staining and interaction with ampholytes. Differential behavior was also observed in whole cell proteins from Halobacterium saccharovorum regarding resolution in two-dimensional gels and silver staining. It is proposed that these differences reflect the existence of two classes of halobacterial proteins.

Stan-Lotter, Helga↗

Predicting non-linear stress–strain response of mesostructured cellular materials using supervised autoencoder

Recent breakthroughs in advanced manufacturing capabilities have made it possible to design and print sophisticated topologies of cellular structures using diverse engineering materials such as metals, polymers, and ceramics. In these architectured materials, it is often desirable to tailor the mechanical properties by altering the unit cell topology. This necessitates an in-depth understanding of how the topology of the unit cell structure affects the macroscopic behavior of the material in both the linear and the non-linear regimes encountered under large compression. Here, we have developed a machine learning (ML) approach capable of accelerating the prediction of the stress–strain response of a polymer-based cellular structure under uniaxial confined compression. As part of generating the training data for ML, 60,000 mesostructures were generated using a relatively novel approach based on cellular automata, and their corresponding stress–strain responses were obtained from the finite element simulations. Principal component analysis (PCA) was used to reduce the dimensionality of the stress–strain curves. With only 20 principal components, PCA captured 99.89% of the variance in the stress–strain curves while reducing the dimensionality by 5X. ML using supervised autoencoder was able to successfully speed up the prediction of the non-linear stress–strain response of a unit cell by up to 4600X. The proposed method can serve as an efficient data generation tool and a rapid means for predicting the structure–property relationship through accelerated forward modeling of cellular materials under compaction, in cases where the macroscopic stress–strain response is governed by the unit-cell topology.

36 MATERIALS SCIENCE↗

Evaluating temperature dependent degradation mechanisms of silicon-graphite electrodes and the effect of fluoroethylene carbonate electrolyte additive

Understanding and overcoming the relatively high rate of degradation observed with silicon (Si)-based anodes in lithium (Li)-ion batteries (LiBs) is crucial for developing cells with increased energy density. The capacity fade of Si-graphite (Gr) electrodes in electrolytes with and without 10 wt% fluoroethylene carbonate (FEC) is explored during cycling at temperatures of 25, 45, and 70 °C, focusing on the complex degradation modes arising from loss of active material, loss of Li inventory, and cell resistance growth. We first show the common half-cell testing cannot be used at elevated temperatures as the performance of Li metal overshadows the behavior of Si-Gr electrode. Symmetric cell configuration successfully eliminates the effect of foreign materials, and reveals that while the presence of FEC provides better passivation of Si, it also results in greater parasitic reactions at 70 °C and faster capacity fade. The electrolyte without FEC, on the other hand, shows higher capacity retention at 70 °C. Finally, we propose a multi-step test protocol which can successfully deconvolute the information on loss of Li inventory and of active material. By combining half-cell and symmetric cell test methods, we demonstrate that loss of active material is reduced at higher temperatures and the dominant mechanisms of capacity loss for Si-Gr electrodes at elevated temperatures is loss of Li inventory.

25 ENERGY STORAGE↗

Amyloplast sedimentation dynamics in maize columella cells support a new model for the gravity-sensing apparatus of roots

Quantitative analysis of statolith sedimentation behavior was accomplished using videomicroscopy of living columella cells of corn (Zea mays) roots, which displayed no systematic cytoplasmic streaming. Following 90 degrees rotation of the root, the statoliths moved downward along the distal wall and then spread out along the bottom with an average velocity of 1.7 microm min(-1). When statolith trajectories traversed the complete width or length of the cell, they initially moved horizontally toward channel-initiation sites and then moved vertically through the channels to the lower side of the reoriented cell where they again dispersed. These statoliths exhibited a significantly lower average velocity than those sedimenting on distal-to-side trajectories. In addition, although statoliths undergoing distal-to-side sedimentation began at their highest velocity and slowed monotonically as they approached the lower cell membrane, statoliths crossing the cell's central region remained slow initially and accelerated to maximum speed once they reached a channel. The statoliths accelerated sooner, and the channeling effect was less pronounced in roots treated with cytochalasin D. Parallel ultrastructural studies of high-pressure frozen-freeze-substituted columella cells suggest that the low-resistance statolith pathway in the cell periphery corresponds to the sharp interface between the endoplasmic reticulum (ER)-rich cortical and the ER-devoid central region of these cells. The central region is also shown to contain an actin-based cytoskeletal network in which the individual, straight, actin-like filaments are randomly distributed. To explain these findings as well as the results of physical simulation experiments, we have formulated a new, tensegrity-based model of gravity sensing in columella cells. This model envisages the cytoplasm as pervaded by an actin-based cytoskeletal network that is denser in the ER-devoid central region than in the ER-rich cell cortex and is linked to stretch receptors in the plasma membrane. Sedimenting statoliths are postulated to produce a directional signal by locally disrupting the network and thereby altering the balance of forces acting on the receptors in different plasma membrane regions.

NASA Program Fundamental Space Biology↗

Genetically Controlled Iron Oxide Biomineralization in Encapsulin Nanocompartments for Magnetic Manipulation of a Mammalian Cell Line

Magnetic nanoparticles have proven invaluable for biomechanical investigations due to their ability to exert localized forces. However, cellular delivery of exogenous magnetic agents often results in endosomal entrapment, thereby limiting their utility for manipulating subcellular structures. This study characterizes and exploits fully genetically controlled biomineralization of iron-oxide cores inside encapsulin nanocompartments to enable magnetic-activated cell sorting (MACS) and magnetic cell manipulation. The fraction of MACS-retained cells showed substantial overexpression of encapsulins and exhibited both para- and ferrimagnetic responses with magnetic moments of 10 -15 A m 2 per cell, comparable to standard exogenous labels for MACS. Electron microscopy revealed that MACS-retained cells contained densely packed agglomerates of ≈30 nm iron oxide cores consisting of ultrafine quasicrystalline ordered nuclei within an amorphous matrix of iron, oxygen, and phosphorus. Scanning transmission X-ray microscopy, X-ray absorption spectroscopy, and Raman microspectroscopy confirmed that the iron-oxide species are consistent with ferric oxide (Fe 2 O 3 ). In addition, the encapsulin-overexpressing MACS-retained cells can be manipulated by a magnetic needle and regrown in patterns determined by magnetic gradients. This study demonstrates that the formation of quasicrystalline iron oxide with mixed para/ferrimagnetic behavior in the cytosol of mammalian cells enables magnetic manipulation without the delivery of exogenous agents.

60 APPLIED LIFE SCIENCES↗

High-performance all-solid-state Li–S batteries enabled by an all-electrochem-active prelithiated Si anode

The development of all-solid-state Li–S batteries has been greatly impeded by dendrite growth and dendrite penetration, which are both related to the Li metal anode. As a compromised alternative, we report lithium silicide (Li x Si) as a dendrite-free and high-capacity anode with Li source. Here, the as-synthesized Li x Si is relatively soft, highly electronically conductive, and with a high Li diffusivity. These distinctive properties make Li x Si anode viable as an “all-electrochem-active” electrode (consisted of 100 wt.% Li x Si). Compared with the typical composite electrode, the all-electrochem-active electrode not merely maximizes the electrode-level energy density but also minimizes the electrolyte-related interfacial degradation. Li x Si symmetric cell demonstrates a reversible cycling at 4 mA cm –2 for over 320 h. Stress change and morphological evolution of the Li x Si electrode are investigated upon dealloying/alloying. When paired with a S cathode (active mass loading of 3 mg cm –2 ), Li x Si–S full cell shows a good cycling behavior over 500 cycles and rate performance (69% capacity retained at 1.2C) even at 25 °C.

25 ENERGY STORAGE↗

Dynamical Janus Interface Design for Reversible and Fast-Charging Zinc–Iodine Battery under Extreme Operating Conditions

Aqueous zinc (Zn) iodine (I 2 ) batteries have emerged as viable alternatives to conventional metal-ion batteries. However, undesirable Zn deposition and irreversible iodine conversion during cycling have impeded their progress. Here, to overcome these concerns, we report a dynamical interface design by cation chemistry that improves the reversibility of Zn deposition and four-electron iodine conversion. Due to this design, we demonstrate an excellent Zn-plating/-stripping behavior in Zn||Cu asymmetric cells over 1000 cycles with an average Coulombic efficiency (CE) of 99.95%. Moreover, the Zn||I 2 full cells achieve a high-rate capability (217.1 mA h g –1 at 40 A g –1 ; C rate of 189.5C) at room temperature and enable stable cycling with a CE of more than 99% at -50 °C at a current density of 0.05 A g –1 . In situ spectroscopic investigations and simulations reveal that introducing tetraethylammonium cations as ion sieves can dynamically modulate the electrode–electrolyte interface environment, forming the unique water-deficient and chloride ion (Cl – )-rich interface. Such Janus interface accounts for the suppression of side reactions, the prevention of ICl decomposition, and the enrichment of reactants, enhancing the reversibility of Zn-stripping/-plating and four-electron iodine chemistry. This fundamental understanding of the intrinsic interplay between the electrode–electrolyte interface and cations offers a rational standpoint for tuning the reversibility of iodine conversion.

25 ENERGY STORAGE↗

Drizzle, Turbulence, and Density Currents Below Post Cold Frontal Open Cellular Marine Stratocumulus Clouds

Nine cases of postcold frontal marine stratocumulus clouds exhibiting open cellular mesoscale organization are analyzed to characterize the drizzle, turbulence, and density currents below them. Data collected by the vertically pointing Doppler cloud radar and multiple lidars part of the Atmospheric Radiation Measurement (ARM) Eastern North Atlantic (ENA) site are used in these analyses. A total of 251 drizzle shafts passed over the site with 76 shafts sampled for more than 15 min by the vertically pointing instruments. On average the drizzle shafts were ~18 km wide with below-cloud drizzle water path of ~40 g m −2 , cloud base rain rate of 7.78 mm day −1 , and cloud base drizzle modal diameter of 393 μm. The widths of the drizzle shafts did not exhibit any relationship with the cloud base rain rate, below-cloud drizzle water path, and the total water removed from the cloud. The downdrafts in the lowest 500 m within the drizzle cells strengthened with increasing cloud base rain rates, while the updrafts within drizzle cells did not exhibit this behavior. On average, the surface air density, pressure, water vapor mixing ratio, and wind speed along the background wind during the drizzle shaft were higher by 1.88 g m −3 , 8.60 Pa, 0.24 g kg −1 , and 1.22 m s −1 , respectively, from their background values. On the other hand, the surface air temperature was lower by 0.43 K during the drizzle shaft than its background value. The coincident measurements highlight the drizzle-turbulence-surface coupling in these cloud systems.

59 BASIC BIOLOGICAL SCIENCES↗

A Comprehensive Numerical and Experimental Study for the Passive Thermal Management in Battery Modules and Packs

Cooling plates in battery packs of electric vehicles play critical roles in passive thermal management systems to reduce risks of catastrophic thermal runaway. In this work, a series of numerical simulations and experiments are carried out to unveil the role of cooling plates (both between cells and a bottom plate parallel to the cell stack) on the thermal behavior of battery modules and packs under nail penetrations. First, we investigated the role of side cooling plates on the thermal runaway propagation mitigation in battery modules (1S3P) and packs (3S3P) by varying the key parameters of the side cooling plates, such as plate thicknesses, thermal contact resistances, and materials. Then, three important factors for passive thermal management systems are identified: (i) thermal mass of side cooling plates, (ii) interfacial thermal contact resistances, and (iii) the effective heat transfer coefficients at exterior surfaces. The roles of bottom cooling plates on thermal runaway propagation mitigation in 1S3P and 1S5P battery modules are numerically investigated by comparing the thermal behavior of the modules with only side cooling plates and with both side and bottom cooling plates.

25 ENERGY STORAGE↗

Development of High Temperature (>700°C) molten Salt Pump Technology for Gen3 Solar Power Tower Systems

Generation 3 Concentrating Solar Power (CSP) Systems require thermal energy storage that can efficiently receive solar heat and deliver it to a working fluid at temperatures greater than 700°C. For liquid systems, the thermal transfer fluid must be phase stable over large temperature ranges. High temperature molten salts meet this criteria, but are difficult liquids to handle. The high heat and salt content can be very corrosive to several different materials that are wetted by the liquid salt. For power tower collectors, the molten salt must be pumped under high pressure to the top of the collector tower. These pumps have impellers and shafts as part of their rotating elements, and under load, require bearings to control shaft movement while rotating. These high temperature pumps require submerged bearings, and thus bearing materials that can withstand the temperature and molten salt contact over long periods of time. This is essential for keeping pump maintenance costs low, and downtime to a minimum. Long running bearing materials is an enabling technology for integrated liquid systems in Generation 3 CSP Systems. Keeping costs low and systems reliable are critical for the broad adoption of Gen 3 CSP Systems. Hayward Tyler, Inc (HTI) proposed development of journal bearing materials for use in vertical pumps designed for pumping high temperature molten salt on both the hot and cold sides of the solar power tower. To complete this objective, HTI utilized the testing capabilities of Oak Ridge National Laboratory (ORNL) and High Temperature System Design (HTSD). Materials would first be selected for static corrosion testing, then downselected for tribological testing. Successful tribologically tested materials would then be downselected for use in additional test regimes. Ten samples were selected for static corrosion testing. Three passed the static testing regime. Two of these materials were downselected for ball material in tribological testing against three metallic alloys: Sintered Y2O3 Partially Stabilized Zirconia YTZP and Silicon Nitride, Grade 147-31N. HTI also proposed collecting data from a thorough bearing test regime using a test rig designed and built as part of this project, and also a conceptual design for a high temperature molten salt vertical pump. HTI withdrew from the project prior to completion of this work and this report reflects only the work completed prior to withdrawal. The completed work produced two papers, one manuscript submitted for publication, and one paper published in the journal Solar Energy Materials and Solar Cells. The papers are: “Tribological behavior of ceramic-alloy bearing contacts in molten salt lubrication for concentrating solar power” and “Material Selection and Corrosion Studies Of Candidate Bearing Materials For Use In Molten Chloride Salt."

14 SOLAR ENERGY↗

Bernal model - A simple equilibrium theory of close-packed liquids.

The Bernal model of a hard-sphere liquid is used in conjunction with an extension of the cell method to predict the behavior of liquid argon near melting. The entropy of disorder associated with the Bernal state is deduced. The model is found to be applicable to liquid metals.

Caron, L. G.↗