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DOE OSTI2021

LANL-UW Collaboration on LC-QTOF Datasets (Annual Report)

Prior to the application of non-targeted chemometric techniques (i.e., Fisher ratio analysis), pre-processing steps must be carried out on the data collected using liquid chromatography-quadrupole time of flight (LC-QTOF) mass spectrometry. Data compression is the most important pre-processing step due to the vast number of high-resolution mass channels (m/z; 0.0001 Da) collected. Our first approach was to bin the mass spectral dimension to 0.01 Da; however, this approach was computationally expensive and did not preserve the high-resolution data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Weak-Form Latent Space Dynamics Identification

This software showcases the enhanced capabilities of the Latent Space Dynamics Identification (LaSDI) algorithm through the application of the weak form, resulting in WLaSDI. WLaSDI first compresses the data, then projects it onto test functions, and subsequently learns the local latent space models. Notably, WLaSDI demonstrates significantly improved robustness to noise. Using weak-form equation learning techniques, WLaSDI achieves local latent space modeling. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form ensures robust and precise latent space recovery, enabling fast, robust, and accurate simulations. We demonstrate the efficacy of WLaSDI against LaSDI using several common benchmark examples, including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in 1D inviscid Burgers' simulations with up to 100% Gaussian white noise, WLaSDI maintains relative errors consistently below 6%, whereas LaSDI errors can exceed 10,000%. Similarly, in radial advection simulations, WLaSDI keeps relative errors below 16%, compared to potential errors of up to 10,000% with LaSDI. Additionally, WLaSDI achieves significant speedups, such as a 140X speedup in 1D Burgers' simulations compared to the corresponding full order model.

Choi, Youngsoo↗

DOE OSTI2023

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz–tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

LA-R43S6-L1 Postshot Report [Slides]

The Ranchero LA-R43S6-L1 test (formerly referred to as LA-43S-L1. The R specifically designates it is a Ranchero device and the 6 indicates a 6” high explosive charge diameter in anticipation of using larger diameters in the future.) was conducted on 3/8/17 with good success. The experiment was the first test of a “Swooped” Ranchero flux compression generator (FCG), and the load for the test was an aluminum imploding liner. In addition to the swoop, the stator was anodized to provide an insulating layer instead of one or more layers of polyethylene as had been the case for all earlier Ranchero tests. Using the Firing point TA-39-88 capacitor bank, 3.5 MA was delivered to the FCG for the initial magnetic field, and 36.4 MA were delivered to the load having an initial inductance of 2.5 nH. Implosion speeds over 1.1 cm/us were recorded, which exceeds previous LANL solid liner experimental results. The test was diagnosed with 18 PDV channels, 12 of which recorded liner implosion data, and the other 6 of which tracked the FCG armature during flux compression. These armature expansion data recorded during flux compression are the first of their kind, and it was previously unknown, due to unknown effects of the SF 6 in the flux compression volume, whether or not the expansion could be recorded using the PDV technique. Post shot 2D MHD calculations employed a complete external circuit model, and an improved flux diffusion model not available prior to the test. Results from these simulations show very good agreement with the experimental result. Four PDV channels recorded the liner implosion viewed radially outward from the center of the liner. All four of these probes recorded implosion velocities greater that 1 cm/µs, with the cylindrical center displaced by ~2 mm from actual center. Four PDV channels looked at +10° angles from the CMU wall, and four looked at -10° angles. A glide plane interaction is shown moving toward the center of the liner in MHD calculations, and PDV probes provide confirmation. The high explosive (HE) in the LA-R43S6-L1 test was PBX 9501 which had to be glued together in many pieces, and the test was preceded by a camera test to verify that the PBX 9501 could be assembled with acceptable tolerance in glue joints to prevent severing the armature during expansion. The camera test verified an acceptable armature performance, and results are given in complete detail in a post shot report LA-UR-19-20124, and summarized here. This report provides complete detail of the considerable body of data obtained on the test and in the post shot calculations. It is prepared in Power Point for ease of preparation and future review. Shot documentation available in the LANL on-line library are included as references, and non-referenceable documents will be cited and stored in an LA- R43S6-L1 post shot folder stored on an M-6 shared drive. Fabrication drawings are also maintained in an M-6 shared drive and paper files are available from M-6 personnel. This report will be maintained as a PowerPoint document on the shared drive, as well, since included movies will play and graphs from Excel files retain information in the PowerPoint versions. PDF versions are required for clearance and are not to large to send by e-mail.

42 ENGINEERING↗

DOE OSTI2022

Deep learning for electron and scanning probe microscopy: From materials design to atomic fabrication

Machine learning and artificial intelligence (ML/AI) are rapidly becoming an indispensable part of physics research, with applications ranging from theory and materials prediction to high-throughput data analysis. In parallel, the recent successes in applying ML/AI methods for autonomous systems from robotics through self-driving cars to organic and inorganic synthesis are generating enthusiasm for the potential of these techniques to enable automated and autonomous experiment in imaging. Here, we discuss recent progress in application of machine learning methods in scanning transmission electron microscopy and scanning probe microscopy, from applications such as data compression and exploratory data analysis to physics learning to atomic fabrication.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A study of real-world micrograph data quality and machine learning model robustness

Abstract Machine-learning (ML) techniques hold the potential of enabling efficient quantitative micrograph analysis, but the robustness of ML models with respect to real-world micrograph quality variations has not been carefully evaluated. We collected thousands of scanning electron microscopy (SEM) micrographs for molecular solid materials, in which image pixel intensities vary due to both the microstructure content and microscope instrument conditions. We then built ML models to predict the ultimate compressive strength (UCS) of consolidated molecular solids, by encoding micrographs with different image feature descriptors and training a random forest regressor, and by training an end-to-end deep-learning (DL) model. Results show that instrument-induced pixel intensity signals can affect ML model predictions in a consistently negative way. As a remedy, we explored intensity normalization techniques. It is seen that intensity normalization helps to improve micrograph data quality and ML model robustness, but microscope-induced intensity variations can be difficult to eliminate.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Synchrotron radiography of Richtmyer–Meshkov instability driven by exploding wire arrays

We present a new technique for the investigation of shock-driven hydrodynamic phenomena in gases, liquids, and solids in arbitrary geometries. The technique consists of a pulsed power-driven resistive wire array explosion in combination with multi-MHz synchrotron radiography. Compared to commonly used techniques, it offers multiple advantages: (1) the shockwave geometry can be shaped to the requirements of the experiment, (2) the pressure (P > 300 MPa) generated by the exploding wires enables the use of liquid and solid hydrodynamic targets with well-characterized initial conditions (ICs), (3) the multi-MHz radiography enables data acquisition to occur within a single experiment, eliminating uncertainties regarding repeatability of the ICs and subsequent dynamics, and (4) the radiographic measurements enable estimation of compression ratios from the x-ray attenuation. In addition, the use of a synchrotron x-ray source allows the hydrodynamic samples to be volumetrically characterized at a high spatial resolution with synchrotron-based microtomography. This experimental technique is demonstrated by performing a planar Richtmyer–Meshkov instability (RMI) experiment on an aerogel–water interface characterized by Atwood number A0∼−0.8 and Mach number M∼1.5. The qualitative and quantitative features of the experiment are discussed, including the energy deposition into the exploding wires, shockwave generation, compression of the interface, startup phase of the instability, and asymptotic growth consistent with Richtmyer's impulsive theory. Additional effects unique to liquids and solids—such as cavitation bubbles caused by rarefaction flows or initial jetting due to small perturbations—are observed. It is also demonstrated that the technique is not shape dependent by driving a cylindrically convergent RMI experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Identifying Climate Patterns Using Clustering Autoencoder Techniques

Abstract The complexity of growing spatiotemporal resolution of climate simulations produces a variety of climate patterns under different projection scenarios. This paper proposes a new data-driven climate classification workflow via an unsupervised deep learning technique that can dimensionally reduce the vast volume of spatiotemporal numerical climate projection data into a compact representation. We aim to identify distinct zones that capture multiple climate variables as well as their future changes under different climate change scenarios. Our approach leverages convolutional autoencoders combined with k -means clustering (standard autoencoder) and online clustering based on the Sinkhorn–Knopp algorithm (clustering autoencoder) across the conterminous United States (CONUS) to capture unique climate patterns in a data-driven fashion from the Geophysical Fluid Dynamics Laboratory Earth System Model with GOLD component (GFDL-ESM2G). The developed approach compresses 70 years of GFDL-ESM2G simulation at 0.125° spatial resolution across the CONUS under multiple warming scenarios to a lower-dimensional space by a factor of 660 000 and then tested on 150 years of GFDL-ESM2G simulation data. The results show that five climate clusters capture physically reasonable and spatially stable climatological patterns matched to known climate classes defined by human experts. Results also show that using a clustering autoencoder can reduce the computational time for clustering by up to 9.2 times when compared to using a standard autoencoder. Our five unique climate patterns resulting from the deep learning–based clustering of the lower-dimensional space thereby enable us to provide insights on hydrometeorology and its spatial heterogeneity across the conterminous United States immediately without downloading large climate datasets. Significance Statement This paper presents a data-driven climate classification approach using unsupervised deep learning to dimensionally reduce climate model outputs and to identify distinct climate regions for their future changes. Our approach compresses climate information for 70 years of Geophysical Fluid Dynamics Laboratory Earth System Model data across the conterminous United States (CONUS) at 0.125° spatial resolution. The results reveal that five climate clusters capture reasonable and stable climatological patterns matched to known climate patterns. The embedded clustering process in deep learning provides ×9.2 times faster execution than the k -means clustering technique. These results give us insight about climate spatial patterns and heterogeneity of hydrological patterns across the conterminous United States without downloading large climate datasets.

Kurihana, Takuya↗

DOE OSTI2023

Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition

This report demonstrates satisfactory data compression of SOLPS-ITER simulation output ranging from 2D fields, 1D profiles, and 0D scalar variables with a novel matrix decomposition approach. The singular value decomposition (SVD) scales poorly for large matrix sizes and is unsuited to the application on high dimensional data common to fusion plasma physics simulation. In this work, we employ the columns-submatrix-rows (CUR) matrix factorization technique in order to compute a low-rank approximation up to two orders of magnitude faster than the SVD, but within a nominal L2-norm relative error of ε = 10 –2 . In addition, the CUR approach maintains the original format of the data, in its extracted columns and rows, allowing for interpretable data storage at the original resolution of the simulation. We utilize an iterative algorithm to compute the CUR decomposition of simulation output by maximizing the volume, or linearly independent information content, of a low-rank submatrix contained within the data. Experiments over $\textit{n} × \textit{n}$ randomized test matrices with embedded rank-deficient features show that this maximum volume implementation of CUR matrix approximation has reduced asymptotic computational complexity on the order of n compared to the SVD, which scales approximately as $n^3$. These results show that the CUR technique can be used to effectively select time step snapshots (columns) of over 140 SOLPS-ITER output variables and the associated discretized coordinate timeseries (rows) allowing for reconstruction of the complete simulation dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

All Optical Neural Networks for Low Power Edge Computing

We developed a simplistic physics-based model of an all-optical neural network that mimics the encoder part of an autoencoder neural network for image compression. Our approach relies on the generation of a MATLAB-based model for both data compression and decompression and utilizes MATLAB's built-in autoencoder networks in combination with simple propagation of optical fields between layers constituting phase elements via Fourier transform. We optimize the phase elements using the particle swarm optimization technique and using our model, we demonstrate a compression ratio of 25% for 2828-pixel input images containing numeric digits from 0 to 9.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Model-independent versus model-dependent interpretation of the SDSS-III BOSS power spectrum: Bridging the divide

The traditional clustering analyses of galaxy redshift surveys compress the clustering data into a set of late-time physical variables in a model-independent way. This approach has recently been extended by an additional shape variable encoding early-time physics information. Here we apply this new technique, ShapeFit, to SDSS-III BOSS data and show that it matches the constraining power of alternative, model-dependent approaches, which directly constrain the model’s parameters adopting a cosmological model ab initio. ShapeFit is ~30 times faster, model independent, naturally splits early- and late-time variables, and enables a better control of observational systematics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Evolution of Pore Structure and Permeability of Rocks Under Hydrothermal Conditions (Final Report)

The physical and transport properties of porous rocks can be altered by a variety of diagenetic, metamorphic, and tectonic processes, and the changes that result are of critical importance to such industrial applications as resource recovery, carbon dioxide sequestration, and waste isolation in geologic formations. The associated interrelationships between rocks, pore fluids and deformation are also key to understanding many natural processes, including dynamic metamorphism, fault mechanics, fault stability and pressure solution creep. In this project, we investigated the changes of permeability and pore geometry owing to inelastic deformation by solution-transfer, brittle fracturing and dislocation creep. In particular, we studied the coupling between pore fluids and deformation in fluid-filled quartz, calcite, mudstones and ultramafic rocks and examine the effects of coupled mechanical and chemical processes on the evolution of porosity and permeability under hydrothermal conditions. The investigations used a combination of techniques, that included triaxial laboratory experiments; uniaxial compressive loading with in situ observations of microstructure; permeability under hydrostatic compression; observations of microstructure using optical and electron microscopes, and micro-CT imaging; and numerical calculations. Laboratory experiments were designed to provide mechanical and transport data under conditions that isolate the particular mechanisms responsible for the changes. The data obtained were used to quantify changes in surface roughness, porosity, pore dimensions and their spatial fluctuations. The results of the experiments and data from image analyses were compared to the results of network, finite-difference and other numerical models to verify the validity of experimentally established relations between permeability and other rock properties. A bibliography for the period from 2015-2019 is appended below. New results obtained in the final year and the unfunded extension period are detailed below.

58 GEOSCIENCES↗

DOE OSTI2021

The Cost of Decarbonization and Energy Upgrade Retrofits for US Homes

Cost is a major barrier when upgrading homes to reduce carbon emissions required to meet DOE’s climate-related goals. This report summarizes a nationwide effort to gather home energy upgrade project cost data along with household energy performance data. The goal was to develop cost benchmarks and to guide future R&D efforts aimed at cost compression and scaling of the residential upgrade market. The cost data were compiled for both total project costs and costs of individual measures. The majority of energy savings were modeled, with some models using measured site data for calibration. The database was analyzed using clustering techniques to find common energy and CO2 reduction approaches. The individual measures were combined into archetypal solutions to determine least-cost approaches to maximizing energy and carbon savings. Several financial analyses were preformed to examine other cost metrics beyond first cost. Project data was obtained for 1,739 projects, from 15 states and 12 energy programs, with a total of 10,512 individual measures. The database includes a wide-array of projects, ranging from single-measure HVAC upgrades to net-zero energy whole home remodels. Projects were predominantly single-family detached dwellings with wood frame construction. Most of the data was obtained from energy programs because they had recorded the necessary information and were willing to share with this study. This sample of convenience can provide broad guidance and national cost benchmarks, but lacks sufficient detail to draw more disaggregated conclusions, such as geographical trends. The majority of data contributions were obtained without compensation from sources where the required data was already in some sort of structured format. We compensated sources to enter data from individual projects into a structured data format for about 500 projects, with an average cost of about $40 per project. The database was highly skewed to lower cost, lower impact projects due to the nature of the sample of convenience. Less than 10% of projects had savings greater than 50%. The cost data for individual measures in the database are being used in other DOE efforts on residential energy use/decarbonization. This data collection effort should continue in order to provide the best-informed guidance for DOE and industry R&D, as well as deployment efforts (including policy and program planning).

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Classical and quantum compression for edge computing: the ubiquitous data dimensionality reduction

Edge computing aims to address the challenges associated with communicating and transferring large amounts of data generated remotely to a data center in a timely and efficient manner. A central pillar of edge computing is local (i.e., at- or near-source) data processing capability so that data transfer to a data center for processing can be minimized. Data compression at the edge is therefore a natural component of edge workflows. Here we present a survey of data compression algorithms with a focus on edge computing. Not all compression algorithms can accommodate the data type heterogeneity, tight processing and communication time constraints, or energy efficiency requirement characteristics of edge computing. We discuss specific examples of compression algorithms that are being explored in the context of edge computing. We end our review with a brief survey of emerging quantum compression techniques that are of importance in quantum information processing, including the proposed concept of quantum edge computing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗

DOE OSTI2025

Universal method for the optimization of HDC coating uniformity on non-planar, non-stationary substrates for inertial confinement fusion targets

The thickness uniformity of chemical vapor deposited (CVD) diamond coatings on non-planar, non-stationary substrates depends on both the intrinsic instantaneous coating thickness distribution (ICTD) of the coating conditions used and, if applicable, on the frequency of substrate reorientation. While important for many CVD diamond applications, the relative impact of the ICTD and substrate reorientation on the coating thickness uniformity has not been studied. In this work, we systematically investigate the effect of these factors for microwave-plasma chemical vapor deposition (MPCVD) of diamond (referred to as high density carbon (HDC) in the inertial confinement fusion (ICF) community) coatings on spherical, rolling substrates. This coating technique is used to fabricate capsules for ICF experiments, which require extreme coating uniformity with <0.3 % thickness variation (so-called Mode 1 or M1) to ensure symmetric compression of imploding targets. To extract the otherwise unobservable reorientation timescale (Δt), Monte Carlo simulations were performed using experimental ICTD data as input. This combined approach confirms scaling relationships between the substrate reorientation timescale as well as coating thickness and coating uniformity, as expected from a 3D random walk. Simulations confirm that M1 is Rayleigh-distributed and scales as (Δt) 1/2 , consistent with the randomization of two angles that determine orientation of a sphere. We also demonstrate that, under the conditions studied, Δt is the dominant factor in determining thickness uniformity while the intrinsic ICTD has minimal impact. Finally, experiments show that Δt can be affected by total batch size under constant agitation conditions due to space constraints that limit the capsule reorientation kinetics. In conclusion, this study highlights the utility of a combined experiment-simulation approach as a general methodology for understanding and improving coating uniformity on non-planar, non-stationary substrates.

Capsule↗

DOE OSTI2020

Nuclear data uncertainty propagation and modeling uncertainty impact evaluation in neutronics core simulation

Uncertainty analysis is a critical requirement in reactor simulation as it is used to quantify the reliability of best-estimate calculation. A comprehensive uncertainty analysis should characterize all sources of uncertainties in a computationally-feasible and scientifically-defendable manner. Here we employ a well-established reduced order modeling (ROM) based uncertainty quantification methodology to propagate uncertainties throughout neutronic calculations. ROM relies on recent advances in randomized data mining techniques applied to large data streams. In our proposed implementation, the nuclear data uncertainties are first propagated from multi-group level through lattice physics calculation to generate few-group parameter uncertainties, described using a vector of mean values and a covariance matrix. Employing an ROM-based compression of the covariance matrix, the few-group uncertainties are then propagated through downstream core simulation in a computationally efficient manner. This straightforward approach, albeit efficient as compared to brute force forward and/or adjoint-based methods, often employs a number of assumptions that have been unquestioned in the literature of neutronic uncertainty analysis. This manuscript argues that these assumptions could introduce another source of uncertainty referred to as modeling uncertainties, whose magnitude needs to be quantified in tandem with nuclear data uncertainties. Thus, our primary goal is to explore the interactions between these two uncertainty sources in order to assess whether modeling uncertainties have an impact on parameter uncertainties. To explore this endeavor, the impact of a number of modeling assumptions on core attributes uncertainties is quantified. The study employs a CANDU reactor model, with Serpent and NEWT as lattice physics solvers and NESTLE-C as core simulator. The modeling assumptions investigated include those related with the uncertainty propagation method employed, e.g., deterministic vs. stochastic, the few-group energy structure employed to represent the cross-sections, the resonance treatment in lattice physics calculation, the reference values for the cross-section, and the number of samples employed to render ROM compression. Results indicate that some of the modeling assumptions could have a non-negligible impact on the core responses propagated uncertainties, highlighting the need for a more comprehensive approach to combine parameter and modeling uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Shear strength measurements and hydrostatic compression of rhenium diboride under high pressures

Shear strength measurements have been carried out on rhenium diboride, ReB 2 , to a pressure of 74 GPa using a Radial X-ray Diffraction (R-XRD) technique in a diamond anvil cell using platinum as an internal x-ray pressure standard. The R-XRD result has provided a unique insight into the deformation of hexagonal crystal lattice under non-hydrostatic compression and variation of shear strength with increasing pressure. From R-XRD data, we have estimated hydrostatic component of compression to determine an equation of state of rhenium diboride yielding a bulk modulus of K 0 = 366 ± 25 GPa with a pressure derivative $K^{'}_{0}$ = 4.3 ± 0.5 in good agreement with hydrostatic density functional theory calculations. Here, the average lower bound of shear strength (τ) from various diffraction planes was then calculated using the measured interplanar d-spacing (d m ) and hydrostatic component of d-spacing (d p ) to be shown to approach 6.7 ± 0.4 GPa at 70 GPa. Our results show that the anisotropic compression effects observed in ReB 2 under hydrostatic compression are correlated to electronic structure changes under compression as predicted by theoretical calculations.

36 MATERIALS SCIENCE↗