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At least 865 records · Page 48

An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics

This project is motivated by the desire to develop numerical methods that will be useful in the study of compressible flows that exhibit aeroacoustic phenomena. Solutions to linear problems have been investigated through the development of a computer code based on the recent dispersion-relation-preserving (DRP) methodology. In regard to nonlinear problems, the class of essentially nonoscillatory (ENO) schemes have been considered as the primary candidates for solving aeroacoustic problems in which discontinuities are involved. Discontinuities in the solution itself (e.g. shocks) as well as in the geometry on which the problem is defined have been studied. Two-dimensional nonlinear problems were considered in order to determine if the one-dimensional results obtained in the first phase of this project were extendable to more realistic problems. Conclusions have been drawn in regard to the ability to numerically predict solutions of nonlinear problems with shocks to high-order accuracy.

Casper, Jay↗

Effect of Phenolic Matrix Microcracking on the Structural Response of a 3-D Woven Thermal Protection System

The effect of microcracking in the phenolic matrix of a three-dimensional woven thermal protection system (TPS) and the resulting material stiffness reduction was studied via a comparison of finite element analysis results from a linear analysis and an iterative linear analysis. A TPS is necessary to protect space vehicles from the aerodynamic heating of planetary entry. The Heatshield for Extreme Entry Environment Technology (HEEET) project has developed a TPS for use in high heat-flux and pressure missions. The material is a dual-layer continuous dry weave, which is then infiltrated with a low-density phenolic resin matrix to form a rigid ablator. The phenolic resin matrix does not have structural load transfer requirements, and testing has shown that the phenolic resin can fully satisfy thermal requirements when the matrix contains microcracks. Due to high stresses in the through-the-thickness direction of the material, phenolic microcracks may form in the matrix material, which would result in a reduction of stiffness. An exploratory study was conducted to determine if reduction in material stiffness would change the load paths and/or decrease the structural margins. A comparison was performed between a linear finite element analysis that did not take into account phenolic microcracking and an iterative linear finite element analysis that accounted for propagation of phenolic microcracking. Four subcases using varying assumptions were analyzed and the results indicate that the assumed strength at which the phenolic microcracking propagates was the critical parameter for determining the extent of microcracking in the phenolic matrix. Phenolic microcracking does not have an adverse effect on the structural response of the test article and is not a critical failure.

Langston, Sarah L.↗

Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM

We analyze an expansion of the generalized block Krylov subspace framework of [Electron. Trans. Numer. Anal., 47 (2017), pp. 100--126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and contains, as special cases, the block GMRES method and the new block Radau--Arnoldi method. Within this general setting, we present results that extend the interpolation property from the nonblock case to a matrix polynomial interpolation property for the block case, and we relate the eigenvalues of the projected matrix to the latent roots of these matrix polynomials. Some error bounds for these modified block FOM methods for solving linear systems are presented. We then show how cospatial residuals can be preserved in the case of families of shifted linear block systems. This result is used to derive computationally practical restarted algorithms for block Krylov approximations that compute the action of a matrix function on a set of several vectors simultaneously. Finally, we prove some error bounds and present numerical results showing that two modifications of FOM, the block harmonic and the block Radau--Arnoldi methods for matrix functions, can significantly improve the convergence behavior.

97 MATHEMATICS AND COMPUTING↗

Evolution of the SLATE linear algebra library

SLATE (Software for Linear Algebra Targeting Exascale) is a distributed, dense linear algebra library targeting both CPU-only and GPU-accelerated systems, developed over the course of the Exascale Computing Project (ECP). While it began with several documents setting out its initial design, significant design changes occurred throughout its development. In some cases, these were anticipated: an early version used a simple consistency flag that was later replaced with a full-featured consistency protocol. In other cases, performance limitations and software and hardware changes prompted a redesign. Sequential communication tasks were parallelized; host-to-host MPI calls were replaced with GPU device-to-device MPI calls; more advanced algorithms such as Communication Avoiding LU and the Random Butterfly Transform (RBT) were introduced. Early choices that turned out to be cumbersome, error prone, or inflexible have been replaced with simpler, more intuitive, or more flexible designs. Applications have been a driving force, prompting a lighter weight queue class, nonuniform tile sizes, and more flexible MPI process grids. Of paramount importance has been building a portable library that works across several different GPU architectures – AMD, Intel, and NVIDIA – while keeping a clean and maintainable codebase. Here we explore the evolving design choices and their effects, both in terms of performance and software sustainability.

Gates, Mark↗

In-Situ Laser-Induced-Desorption-Spectroscopy Diagnostic Deployment on the Linear Plasma Device CSDX

A calibrated laser induced desorption diagnostic (LIDS) concept is developed under this award for application to fusion relevant plasma materials interactions studies. Small areal amounts of hydrogenic release from a deuterium filled PMI target are measured and quantified when irradiated by a LID flash heat event on the target surface. Good success was demonstrated by this project with the PISCES-E rf plasma device at UCSD by fully quantified measurement and removal of D from W-D co-deposit layers in experiments. However, adapting the LIDS technique to D plasma exposed W targets in the linear plasma CSDX device, now labelled PISCES-Rf, was prone to several technical challenges ranging from target line of sight access, laser focusing, and loss of optical spectroscopic signal strength in the larger PISCES-Rf vacuum system. The results are summarized in this report.

08 HYDROGEN↗

Computational Imaging for Intelligence in Highly Scattering Aerosols (Final Report)

Natural and man-made degraded visual environments pose major threats to national security. The random scattering and absorption of light by tiny particles suspended in the air reduces situational awareness and causes unacceptable down-time for critical systems and operations. To improve the situation, we have developed several approaches to interpret the information contained within scattered light to enhance sensing and imaging in scattering media. These approaches were tested at the Sandia National Laboratory Fog Chamber facility and with tabletop fog chambers. Computationally efficient light transport models were developed and leveraged for computational sensing. The models are based on a weak angular dependence approximation to the Boltzmann or radiative transfer equation that appears to be applicable in both the moderate and highly scattering regimes. After the new model was experimentally validated, statistical approaches for detection, localization, and imaging of objects hidden in fog were developed and demonstrated. A binary hypothesis test and the Neyman-Pearson lemma provided the highest theoretically possible probability of detection for a specified false alarm rate and signal-to-noise ratio. Maximum likelihood estimation allowed estimation of the fog optical properties as well as the position, size, and reflection coefficient of an object in fog. A computational dehazing approach was implemented to reduce the effects of scatter on images, making object features more readily discernible. We have developed, characterized, and deployed a new Tabletop Fog Chamber capable of repeatably generating multiple unique fog-analogues for optical testing in degraded visual environments. We characterized this chamber using both optical and microphysical techniques. In doing so we have explored the ability of droplet nucleation theory to describe the aerosols generated within the chamber, as well as Mie scattering theory to describe the attenuation of light by said aerosols, and correlated the aerosol microphysics to optical properties such as transmission and meteorological optical range (MOR). This chamber has proved highly valuable and has supported multiple efforts inclusive to and exclusive of this LDRD project to test optics in degraded visual environments. Circularly polarized light has been found to maintain its polarization state better than linearly polarized light when propagating through fog. This was demonstrated experimentally in both the visible and short-wave infrared (SWIR) by imaging targets made of different commercially available retroreflective films. It was found that active circularly polarized imaging can increase contrast and range compared to linearly polarized imaging. We have completed an initial investigation of the capability for machine learning methods to reduce the effects of light scattering when imaging through fog. Previously acquired experimental long-wave images were used to train an autoencoder denoising architecture. Overfitting was found to be a problem because of lack of variability in the object type in this data set. The lessons learned were used to collect a well labeled dataset with much more variability using the Tabletop Fog Chamber that will be available for future studies. We have developed several new sensing methods using speckle intensity correlations. First, the ability to image moving objects in fog was shown, establishing that our unique speckle imaging method can be implemented in dynamic scattering media. Second, the speckle decorrelation over time was found to be sensitive to fog composition, implying extensions to fog characterization. Third, the ability to distinguish macroscopically identical objects on a far-subwavelength scale was demonstrated, suggesting numerous applications ranging from nanoscale defect detection to security. Fourth, we have shown the capability to simultaneously image and localize hidden objects, allowing the speckle imaging method to be effective without prior object positional information. Finally, an interferometric effect was presented that illustrates a new approach for analyzing speckle intensity correlations that may lead to more effective ways to localize and image moving objects. All of these results represent significant developments that challenge the limits of the application of speckle imaging and open important application spaces. A theory was developed and simulations were performed to assess the potential transverse resolution benefit of relative motion in structured illumination for radar systems. Results for a simplified radar system model indicate that significant resolution benefits are possible using data from scanning a structured beam over the target, with the use of appropriate signal processing.

58 GEOSCIENCES↗

Low dimensional magnetic solids and single crystal elpasolites: Need for improved crystal growing techniques

The need for extensive crystal growing experiments to develop techniques for preparing crystals suitable for magnetic anisotropy measurements and detailed X-ray and neutron diffraction studies is rationalized on the basis of the unique magnetic properties of the materials and their hydrogen bonded structures which have many features in common with metalloenzyme and metalloprotein active sites. Single crystals of the single and mixed lanthanide species are prepared by the Bridgeman technique of gradient solidification of molten samples. The effects of crystal imperfections on the optical properties of these materials are an important part of the projected research. A series of a-amido acid complexes of first row transition metals were prepared which crystallize as infinite linear chains and exhibit low dimensional magnetic ordering (one or two) at temperature below 40 K.

Good, M. L.↗

Mission analysis flow sequencing optimization

This investigation is an extension of a project dealing with the problem of optimal use of ground resources for future space missions. This problem was formulated as a linear programming problem using an indirect approach. Instead of minimizing the inventory level of needed ground resources, the overlapping periods during which the same types of resources are used by various flights are minimized. The model was built upon the assumption that during the time interval under consideration, the costs of various needed resources remain constant. Under other assumptions concerning costs of resources, the objective function, in general, assumes a non-linear form. In this study, one case where the form of the objective function turns out to be quadratic is considered. Also, disadvantages and limitations of the approach used are briefly discussed.

Scott, M.↗

EVA Robotic Assistant Project: Platform Attitude Prediction

The Robotic Systems Technology Branch is currently working on the development of an EVA Robotic Assistant under the sponsorship of the Surface Systems Thrust of the NASA Cross Enterprise Technology Development Program (CETDP). This will be a mobile robot that can follow a field geologist during planetary surface exploration, carry his tools and the samples that he collects, and provide video coverage of his activity. Prior experiments have shown that for such a robot to be useful it must be able to follow the geologist at walking speed over any terrain of interest. Geologically interesting terrain tends to be rough rather than smooth. The commercial mobile robot that was recently purchased as an initial testbed for the EVA Robotic Assistant Project, an ATRV Jr., is capable of faster than walking speed outside but it has no suspension. Its wheels with inflated rubber tires are attached to axles that are connected directly to the robot body. Any angular motion of the robot produced by driving over rough terrain will directly affect the pointing of the on-board stereo cameras. The resulting image motion is expected to make tracking of the geologist more difficult. This will either require the tracker to search a larger part of the image to find the target from frame to frame or to search mechanically in pan and tilt whenever the image motion is large enough to put the target outside the image in the next frame. This project consists of the design and implementation of a Kalman filter that combines the output of the angular rate sensors and linear accelerometers on the robot to estimate the motion of the robot base. The motion of the stereo camera pair mounted on the robot that results from this motion as the robot drives over rough terrain is then straightforward to compute. The estimates may then be used, for example, to command the robot s on-board pan-tilt unit to compensate for the camera motion induced by the base movement. This has been accomplished in two ways: first, a standalone head stabilizer has been implemented and second, the estimates have been used to influence the search algorithm of the stereo tracking algorithm. Studies of the image motion of a tracked object indicate that the image motion of objects is suppressed while the robot crossing rough terrain. This work expands the range of speed and surface roughness over which the robot should be able to track and follow a field geologist and accept arm gesture commands from the geologist.

Nickels, Kevin M.↗

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

Nguyen, Nhan T.↗

Forecasting Lightning at Kennedy Space Center/Cape Canaveral Air Force Station, Florida

The Applied Meteorology Unit (AMU) developed a set of statistical forecast equations that provide a probability of lightning occurrence on Kennedy Space Center (KSC) I Cape Canaveral Air Force Station (CCAFS) for the day during the warm season (May September). The 45th Weather Squadron (45 WS) forecasters at CCAFS in Florida include a probability of lightning occurrence in their daily 24-hour and weekly planning forecasts, which are briefed at 1100 UTC (0700 EDT). This information is used for general scheduling of operations at CCAFS and KSC. Forecasters at the Spaceflight Meteorology Group also make thunderstorm forecasts for the KSC/CCAFS area during Shuttle flight operations. Much of the current lightning probability forecast at both groups is based on a subjective analysis of model and observational data. The objective tool currently available is the Neumann-Pfeffer Thunderstorm Index (NPTI, Neumann 1971), developed specifically for the KSCICCAFS area over 30 years ago. However, recent studies have shown that 1-day persistence provides a better forecast than the NPTI, indicating that the NPTI needed to be upgraded or replaced. Because they require a tool that provides a reliable estimate of the daily thunderstorm probability forecast, the 45 WS forecasters requested that the AMU develop a new lightning probability forecast tool using recent data and more sophisticated techniques now possible through more computing power than that available over 30 years ago. The equation development incorporated results from two research projects that investigated causes of lightning occurrence near KSCICCAFS and over the Florida peninsula. One proved that logistic regression outperformed the linear regression method used in NPTI, even when the same predictors were used. The other study found relationships between large scale flow regimes and spatial lightning distributions over Florida. Lightning, probabilities based on these flow regimes were used as candidate predictors in the equation development. Fifteen years (1 989-2003) of warm season data were used to develop the forecast equations. The data sources included a local network of cloud-to-ground lightning sensors called the Cloud-to-Ground Lightning Surveillance System (CGLSS), 1200 UTC Florida synoptic soundings, and the 1000 UTC CCAFS sounding. Data from CGLSS were used to determine lightning occurrence for each day. The 1200 UTC soundings were used to calculate the synoptic-scale flow regimes and the 1000 UTC soundings were used to calculate local stability parameters, which were used as candidate predictors of lightning occurrence. Five logistic regression forecast equations were created through careful selection and elimination of the candidate predictors. The resulting equations contain five to six predictors each. Results from four performance tests indicated that the equations showed an increase in skill over several standard forecasting methods, good reliability, an ability to distinguish between non-lightning and lightning days, and good accuracy measures and skill scores. Given the overall good performance the 45 WS requested that the equations be transitioned to operations and added to the current set of tools used to determine the daily lightning probability of occurrence.

Lambert, Winfred↗

KELT-22Ab: A Massive, Short-Period Hot Jupiter Transiting a Near-solar Twin

We present the discovery of KELT-22Ab, a hot Jupiter from the KELT-South survey. KELT-22Ab transits the moderately bright (V11.1) Sun-like G2V star TYC 7518-468-1. The planet has an orbital period of P = 1.3866529 0.0000027 days, a radius of = -R 1.285+ R P 0.071 J 0.12 , and a relatively large mass of = - M 3.47+ M P 0.14 J 0.15 . The star has = - + R 1.099 0.046 R 0.079 , = - + M 1.092 0.041 M 0.045 , = - T 5767+ eff 49 50 K, = - log g 4.393+0.0600.039 (cgs), and [m/H]=+ -0.259+0.0830.085; thus other than its slightly super-solar metallicity, it appears to be a near-solar twin. Surprisingly, KELT-22A exhibits kinematics and a Galactic orbit that are somewhat atypical for thin-disk stars. Nevertheless, the star is rotating rapidly for its estimated age, and shows evidence of chromospheric activity. Imaging reveals a slightly fainter companion to KELT-22A that is likely bound, with a projected separation of 6″ (∼1400 au). In addition to the orbital motion caused by the transiting planet, we detect a possible linear trend in the radial velocity of KELT-22A, suggesting the presence of another relatively nearby body that is perhaps non-stellar. KELT-22Ab is highly irradiated (as a consequence of the small semimajor axis of a R = 4.97), and is mildly inflated. At such small separations, tidal forces become significant. The configuration of this system is optimal for measuring the rate of tidal dissipation within the host star. Our models predict that, due to tidal forces, the semimajor axis is decreasing rapidly, and KELT-22Ab is predicted to spiral into the star within the next Gyr.

Knicole Colon↗

Ultraviolet Spectropolarimetry Conservative and Nonconservative Mass Transfer in OB Interacting Binaries

The current consensus is that at least half of the OB stars are formed in binary or multiple star systems. The evolution of OB stars is greatly influenced by whether the stars begin as close binaries, and the evolution of the binary systems depend on whether the mass transfer is conservative or nonconservative. FUV/NUV spectropolarimetry is poised to answer the latter question. This paper discusses how the Polstar spectropolarimetry mission can characterize the degree of nonconservative mass transfer that occurs at various stages of binary evolution, from the initial mass reversal to the late Algol phase, and quantify its amount. The proposed instrument combines spectroscopic and polarimetric capabilities, where the spectroscopy can resolve Doppler shifts in UV resonance lines with 10 km/s precision, and polarimetry can resolve linear polarization with 10 −3 precision or better. The spectroscopy will identify absorption by mass streams and other plasmas seen in projection against the stellar disk as a function of orbital phase, as well as scattering from extended splash structures, including jets. The polarimetry tracks the light coming from material not seen against the stellar disk, allowing the geometry of the scattering to be tracked, resolving ambiguities left by the spectroscopy and light-curve information. For example, nonconservative mass streams ejected in the polar direction will produce polarization of the opposite sign from conservative transfer accreting in the orbital plane. Time domain coverage over a range of phases of the binary orbit are well supported by the Polstar observing strategy. Special attention will be given to the epochs of enhanced systemic mass loss that have been identified from IUE observations (pre-mass reversal and tangential gas stream impact). We show how the history of systemic mass and angular momentum loss/gain episodes can be inferred via ensemble evolution through the r–q diagram. Combining the above elements will significantly improve our understanding of the mass transfer process and the amount of mass that can escape from the system, an important channel for changing the final mass and ultimate supernova of a large number of massive stars found in binaries at close enough separation to undergo interaction.

Geraldine J. Peters↗

Assessing Bare-Ice Albedo Simulated By MAR Over the Greenland Ice Sheet (2000–2021) and Implications for Meltwater Production Estimates

Surface mass loss from the Greenland ice sheet (GrIS) has accelerated over the past decades, mainly due to enhanced surface melting and liquid water runoff in response to atmospheric warming. A large portion of runoff from the GrIS originates from exposure of the darker bare ice in the ablation zone when the overlying snow melts, where surface albedo plays a critical role in modulating the energy available for melting. In this regard, it is imperative to understand the processes governing albedo variability to accurately project future mass loss from the GrIS. Bare-ice albedo is spatially and temporally variable and contingent on non-linear feedbacks and the presence of light-absorbing constituents. An assessment of models aiming at simulating albedo variability and associated impacts on meltwater production is crucial for improving our understanding of the processes governing these feedbacks and, in turn, surface mass loss from Greenland. Here, we report the results of a comparison of the bare-ice extent and albedo simulated by the regional climate model Modèle Atmosphérique Régional (MAR) with satellite imagery from the Moderate Resolution Imaging Spectroradiometer (MODIS) for the GrIS below 70∘ N. Our findings suggest that MAR overestimates bare-ice albedo by 22.8 % on average in this area during the 2000–2021 period with respect to the estimates obtained from MODIS. Using an energy balance model to parameterize meltwater production, we find this bare-ice albedo bias can lead to an underestimation of total meltwater production from the bare-ice zone below 70∘ N of 42.8 % during the summers of 2000–2021.

albedo↗

Final Report: Next Generation Diamond Drumhead X-Ray Optics

Problem / Opportunity Statement: Future high-impact scientific applications at synchrotron and Free-Electron Laser (FEL) X-ray sources require the development of processing and mounting methods for ultra-thin diamond crystals to meet the most challenging needs of pioneering research at next generation light source facilities. These methods should be capable of manufacturing crystal plates as thin as 10 micrometers over an area of a few mm2, and with a surface cut in different crystal orientations, such as the diamond {100}, {111}, {110} and {113} planes. Project Purpose and Approach: In Phase I, Great Lakes Crystal Technologies (GLCT) partnered with Stonybrook University (SUNY) to created thin diamond drumhead crystals. The purpose of the Phase I project is to transfer the drumhead membrane window etching technology from SUNY to GLCT. Testing of a device using the beamline at Stanford Linear Accelerator Laboratory was initially planned, however, a delay on the part of a third party service provided required us to get beamline testing done at Argonne National Laboratory. Phase I Taskwork: Testing of a high purity diamond plate thinning and etching process was performed. By SUNY and GLCT. Plates were sent to a third party service provider for thinning to ~100 microns, however, delays required that GLCT develop an in-house thinning process to complete the taskwork. GLCT successfully developed this in-house capability even though it was initially planned to be part of the Phase II Taskwork. Multiple practice and deliverable plates were provided to SUNY to be etched into the target drumhead devices. GLCT practiced and refined an in-house plate thinning process and produced five plates with thicknesses in the 60 – 150 micron range. Processing of the plates has begun and will continue in a no-cost extension period necessitated by the third party service provider delay. GLCT also procured and installed a reactive ion etching/inductively coupled plasma system. In addition, one of the thinned plates was measured at the Applied Photon Source at APL for a pre-processing assessment of the crystalline strain. After processing the plate into a drumhead and annealing, a post-processing assessment of the strain will be performed. Phase I Results: The initial data from GLCT’s plate thinning process development, SUNY’s drumhead etching processing, and characterization at APS/ANL demonstrate our teams capabilities to achieve the project goals. Commercial Applications & Benefits: The proposed technology will benefit advanced x-ray science performed at BNL and the 70+ additional advanced beamlines around the world. There are also a number of medical and homeland security applications which could benefit from the technology.

Quayle, Paul↗

Density weighted angular redshift fluctuations: a new cosmological observable

We propose the use of angular fluctuations in the galaxy redshift field as a new way to extract cosmological information in the Universe. This new probe $\delta z (\hat{\mathbf {n}})$ consists of the statistics of sky maps built by projecting redshifts under a Gaussian window of width σz centred upon a redshift zobs, and weighted by the galaxy density field. We compute the angular power spectrum of the $\delta z (\hat{\mathbf {n}})$ field in both numerical simulations and in linear perturbation theory. From these, we find that the $\delta z (\hat{\mathbf {n}})$ field (i) is sensitive to the underlying density and peculiar velocity fields; (ii) is highly correlated, at the $\gtrsim 60\, {{\ \rm per\ cent}}$ level, to the line-of-sight projected peculiar velocity field; (iii) for narrow windows (σz < 0.03), it is almost completely uncorrelated to the projected galaxy angular density field under the same redshift window; and (iv) it is largely unaffected by multiplicative and additive systematic errors on the observed number of galaxies that are redshift-independent over ~σz. We conclude that $\delta z (\hat{\mathbf {n}})$ is a simple and robust tomographic measure of the cosmic density and velocity fields, complementary to angular clustering, that will contribute to more complete exploitations of current and upcoming galaxy redshift surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Spinning Rocket Simulator Turntable Design

Contained herein is the research and data acquired from the Turntable Design portion of the Spinning Rocket Simulator (SRS) project. The SRS Project studies and eliminates the effect of coning on thrust-propelled spacecraft. This design and construction of the turntable adds a structural support for the SRS model and two degrees of freedom. The two degrees of freedom, radial and circumferential, will help develop a simulated thrust force perpendicular to the plane of the spacecraft model while undergoing an unstable coning motion. The Turntable consists of a ten-foot linear track mounted to a sprocket and press-fit to a thrust bearing. A two-inch high column grounded by a Triangular Baseplate supports this bearing and houses the slip rings and pressurized, air-line swivel. The thrust bearing allows the entire system to rotate under the moment applied through the chain-driven sprocket producing a circumferential degree of freedom. The radial degree of freedom is given to the model through the helically threaded linear track. This track allows the Model Support and Counter Balance to simultaneously reposition according to the coning motion of the Model. Two design factors that hinder the linear track are bending and twist due to torsion. A Standard Aluminum "C" channel significantly reduces these two deflections. Safety considerations dictate the design of all the components involved in this project.

Miles, Robert W.↗

Materials Data on Na5CuSO2 by Materials Project

Na5CuSO2 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are two inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded in a linear geometry to four equivalent S2- and two equivalent O2- atoms. All Na–S bond lengths are 3.24 Å. Both Na–O bond lengths are 2.29 Å. In the second Na1+ site, Na1+ is bonded in a 2-coordinate geometry to two equivalent S2- and two equivalent O2- atoms. Both Na–S bond lengths are 3.02 Å. Both Na–O bond lengths are 2.31 Å. Cu1+ is bonded in a linear geometry to two equivalent O2- atoms. Both Cu–O bond lengths are 1.81 Å. S2- is bonded to twelve Na1+ atoms to form SNa12 cuboctahedra that share corners with four equivalent SNa12 cuboctahedra, faces with four equivalent SNa12 cuboctahedra, and faces with eight equivalent ONa5Cu octahedra. O2- is bonded to five Na1+ and one Cu1+ atom to form ONa5Cu octahedra that share corners with six equivalent ONa5Cu octahedra and faces with four equivalent SNa12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–16°.

36 MATERIALS SCIENCE↗