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At least 37 records · Page 2

A Novel Rotating Flexure-Test Technique for Brittle Materials with Circular Geometries

The four-point bend test is one of the simplest and often the preferred flexural strength evaluation method for brittle materials. In this loading mode, fracture often initiates from a critical surface (or subsurface) flaw when subjected to a tensile stress state. However, if the critical flaw exists on the compression side of the test specimen, it may not activate to grow a crack and hence the resulting flexural strength will be higher than the true value. The goal of this study is to measure the true flexural strength of a solid or hollow cylindrical brittle specimen by ensuring that failure occurs at its weakest point by rotating along its longitudinal axis, thereby exposing and activating its critical surface flaw during a four-point bend test. A novel test fixture has been designed and fabricated, and the true flexural strengths of cylindrical brittle and quasi-brittle tubular specimens have been measured and compared to existing experimental data obtained through traditional four-point bend tests. In this work, experimental results showcase the orientation dependance on flexural strength for various materials. Additionally, similarities between experimental findings and those available in literature, including observations of fracture surfaces and relationships between surface roughness and material strength, are discussed.

36 MATERIALS SCIENCE↗

VTO FY20Q4 quarterly report

Project Objective.This project has three objectives: (1) tuning microstructures of 3D-printed SSE separators,(2) determining material and processing compatibilities with cathode printing,and (3)3D printing of sintering-free SSE separators.Project Impact.All-solid-state lithium batteries are difficult to process due to the brittleness of ceramic materials, poor solid-solid contact, and electrolyte-electrode stability issues. As a result, the energy and power density and also cycling stability are far from satisfying. This project will address fabrication difficulties by using state-of-the-art 3D-printing techniques that can introduce 3D interfaces and architectures to enhance solid-solid contact and reduce charge transfer resistance. Success will benefit the DOE by establishing the best manufacturing methods for ASSBsto achieve VTO goals on the performance of beyond Li-ion batteries. Approach.The project employs 3D-printing techniques to manufacture SSEs and related components for ASSBs. The team starts with direct ink writing (DIW) to develop ink recipes with desired rheological properties and explore post-sintering approaches to achieve high densification. In parallel with DIW3D printing, the team also explores other 3D printing options, such as projection microstereolithography (PuSL). Both sintering and sintering-free approaches can gain benefit from 3D printing and therefore will be investigated.Out-Year Goals.The team will determine particle sizes and morphologies as well as post-processing conditions that deliver good ionic conductivity and charge transfer properties of LLZTO separators. They will examine co-sintering of LLZTO/cathode and determine the effects of material, particle size, surface coating, and sintering conditions.Collaborations.Microstructures, ionic conductivities, and mechanical properties will be provided to the LLNL simulation team, led by PI B. Wood, for establishing and validating phase-field modeling methods.

36 MATERIALS SCIENCE↗

Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns

Abstract This paper develops a deep learning tool based on neural processes (NPs) called the Peri-Net-Pro, to predict the crack patterns in a moving disk and classifies them according to the classification modes with quantified uncertainties. In particular, image classification and regression studies are conducted by means of convolutional neural networks (CNNs) and NPs. First, the amount and quality of the data are enhanced by using peridynamics to theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, case studies are conducted with the prototype microelastic brittle (PMB), linear peridynamic solid (LPS), and viscoelastic solid (VES) models obtained by using the peridynamic theory. The case studies are performed to classify the images by using CNNs and determine the suitability of the PMB, LBS, and VES models. Finally, a regression analysis is performed on the crack pattern images with NPs to predict the crack patterns. The regression analysis results confirm that the variance decreases when the number of epochs increases by using the NPs. The training results gradually improve, and the variance ranges decrease to less than 0.035. The main finding of this study is that the NPs enable accurate predictions, even with missing or insufficient training data. The results demonstrate that if the context points are set to the 10th, 100th, 300th, and 784th, the training information is deliberately omitted for the context points of the 10th, 100th, and 300th, and the predictions are different when the context points are significantly lower. However, the comparison of the results of the 100th and 784th context points shows that the predicted results are similar because of the Gaussian processes in the NPs. Therefore, if the NPs are employed for training, the missing information of the training data can be supplemented to predict the results.

Mathematics↗

Unveiling the structural transformations in glassy solid electrolyte adapted to high-stress cycles

Brittleness of glass–ceramic and ceramic ion conductors is considered as a main roadblock for their implementation as electrolytes in solid-state batteries where the fractures often occur due to the pressure exerted by metallic lithium. In this regard, nano- and micro-scale ductility of the solid electrolyte allows reducing such pressure without formation of cracks. Among different types of solid state ion conductors, phosphate invert glasses seem to be promising in achieving such ductility. We report the mechanical behavior of lithium phosphorous oxynitride (LiPON) invert glass probed by static and cyclic nanoindentation. Repeated application of high intensity stress results in densification and shear deformation of material allowing LiPON to accommodate the ~ 22% nominal strain imposed by the nanoindenter without cracking. Ability to do this under repeated loading indicates robustness of LiPON when used in lithium metal batteries under cyclic charge and discharge. Using Raman spectroscopy with unsupervised K-means clustering we reveal pressure-induced formation of P 2 O 7 units which migrate to the periphery of the residual hardness impressions with cycling resulting in surface morphology of LiPON superficially similar to that of deformed bulk metallic glass.

36 MATERIALS SCIENCE↗

Lightweight single-phase Al-based complex concentrated alloy with high specific strength

Developing light yet strong aluminum (Al)-based alloys has been attracting unremitting efforts due to the soaring demand for energy-efficient structural materials. However, this endeavor is impeded by the limited solubility of other lighter components in Al. Here, we propose to surmount this challenge by converting multiple brittle phases into a ductile solid solution in Al-based complex concentrated alloys (CCA) by applying high pressure and temperature. We successfully develop a face-centered cubic single-phase Al-based CCA, Al 55 Mg 35 Li 5 Zn 5 , with a low density of 2.40 g/cm 3 and a high specific yield strength of 344×10 3 N·m/kg (typically ~ 200×10 3 N·m/kg in conventional Al-based alloys). Our analysis reveals that formation of the single-phase CCA can be attributed to the decreased difference in atomic size and electronegativity between the solute elements and Al under high pressure, as well as the synergistic high entropy effect caused by high temperature and high pressure. The increase in strength originates mainly from high solid solution and nanoscale chemical fluctuations. Our findings could offer a viable route to explore lightweight single-phase CCAs in a vast composition-temperature-pressure space with enhanced mechanical properties.

42 ENGINEERING↗

CabanaPD

CabanaPD is a meshfree peridynamics application built with Cabana and Kokkos. Kokkos enables performance portability across hardware architectures and Cabana provides particle capabilities including multi-node MPI support. The main components of CabanaPD are particle initialization, neighbor list generation, force and energy computation, time integration, and multi-node particle communication. In addition, options for creating pre-cracked regions and particle boundary conditions are available. CabanaPD currently enables two common force models: prototype microelastic brittle (PMB) and linear peridynamic solid (LPS). For both of these models, versions with and without fracture as well as linearized model options are available. CabanaPD is designed to be extensible for addition of more complex force models, boundary conditions, etc.

Reeve, Sam↗

Damage Modeling of Solid Oxide Fuel Cells Accounting for Redox Effects

This work applies a multiscale mechanistic damage model developed for brittle ceramics and implemented in commercial finite element (FE) packages via user subroutines to study progressive damage in solid oxide fuel cells (SOFC) subjected to thermomechanical loading under normal operating and shutdown conditions including redox effects. The damage model captures the micromechanics of stiffness reduction due to material porosity change and microcracking and integrates the as-obtained stiffness reduction law into a continuum damage mechanics (CDM) formulation for the evolution of microcracks up to fracture. The volumetric “swelling” that occurs during redox is treated in constitutive modeling similarly to thermal expansion, but swelling strains are irreversible. Furthermore, this damage model was first validated through predictions of strength and stress-strain response for the SOFC electrode materials. Next, it has been applied to predict the potential for degradation in a generic planar SOFC stack with large active area cells. Multicell stack models were simulated in both co-flow and counter-flow configurations. In addition, a constant temperature redox cycle was also simulated to capture overall cell electrode damage due to volumetric swelling of the nickel (Ni)-based anode in the anode-supported cells.

25 ENERGY STORAGE↗

Creating Hydride Rim Structures in Zircaloy 4 Cladding Tubes to Mimic High Burnup

During their long service in commercial light water reactors, zirconium alloy cladding tubes are subject to oxidation and subsequent hydrogen pickup which can degrade the materials mechanical properties [1]. These degradations can lead to premature cladding ruptures during reactor power transients [2] as well as negatively impact the claddings post quench ductility following high temperature steam oxidation in thermal hydraulic transients [3]. Hydrogen has low solid solubility in zirconium and usually precipitates as brittle zirconium hydride platelets in the cladding metal matrix. Due to temperature driven diffusion (Soret effect) and the grain texture of stress relieved zirconium metal tubes, these hydrides precipitate with a circumferential orientation near the outer surface of the cladding tubes forming a hydride rim which can serve as a site for crack initiation during circumferential ‘hoop’ loading of the cladding [4rim formation][5]. In order to better understand the effect of hydride rims on the fracture behavior of stress relieved zirconium alloy cladding tubes a procedure to produce these rim-like structures is being developed at Idaho National Laboratory (INL).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Joining Dissimilar Materials via Rotational Hammer Riveting Technique

A mechanically robust joining method for Mg/Al and Mg/CFRP could enable multi-material assemblies that decrease vehicle weight while offering more flexibility for designers. However, certain challenges exist for joining Mg/Al and Mg/CFRP. Mechanical joining, such as conventional riveting, clinching and bolting do not form a metallurgical bond between the fastener and metal sheet being fastened. Large differences in physical and mechanical properties of metals and polymers make joining Al or Mg to CFRP challenging via various welding techniques. With solid-state and fusion based welding, rapid formation of brittle intermetallic compounds at the Mg/Al interface lead to interfacial fracture under mechanical loading. In this study, a Rotational Hammer Rivet (RHR) technique was developed to fabricate Mg/CFRP and Mg/Al joints. With RHR technique, direct joining between Mg/Al and Mg/CFRP were replaced by joining Mg rivet head and top Mg sheet. Through heat generated by plastic deformation of an Mg rivet, RHR creates a metallurgical bond between rivet head and Mg sheet which seals corrosive electrolyte from penetrating around the rivet head.

riveting, magnesium alloys, CFRP, Dissimilar Joini↗

Effects of cyclic plasma heating on surface damage of micro-porous tungsten

The operating temperature window of solid tungsten (W) is dictated by its Ductile to Brittle Transition Temperature (DBTT) and re-crystallization temperature; roughly between 300-1300 °C. The brittleness of W at lower temperatures is exasperated when it undergoes recrystallization. We investigate here the thermal shock resistance of micro-porous W as a meta-material fabricated in a 3D open-cell network structure. We present experimental results for the effects of cyclic high-enthalpy arc-jet plasma on surface damage in three testing categories. Observed damage includes surface ablation of asperities, melting and solidification of W-fuzz on samples that have been exposed to a prior helium plasma, and micro-cracks at ligament triple junctions. Scanning electron microscope (SEM) observations show more micro-cracking on 54% and 23% foams compared to the 43% ones. In all tested samples, thermal expansion/contraction displacements were accommodated by ligament rotation and a network of micro-cracks. Furthermore, no large through-thickness crack were observed.

36 MATERIALS SCIENCE↗

A solid-state extrusion pathway extensible to upcycling aluminum scrap and end-of-life permanent magnets into ductile Al-6061/SmCo 5 structural magnetic composites

Permanent magnets offer strong potential for multifunctional structural components, but their inherent brittleness limits direct integration. Here, SolidStir® Extrusion (SSE) is used to embed SmCo5 powder into AA6061 in the solid state, and the resulting microstructure, interfacial chemistry, mechanical properties, and magnetic response are systematically characterized. SSE fragments the initial SmCo 5 powder into predominantly fine particles dispersed within an ultrafine Al matrix, with a volume fraction of ∼ 4–6 % in this proof-of-concept study. Interfacial reactions form a continuous Al–Co reaction layer, with local atomic-resolution indexing consistent with Al 13 Co 4 , together with Sm–Si-rich reaction products, while the matrix contains Sm–Co–Si-rich precipitates and Mg 2 Si, producing features from nanometers to micrometers. Compared with an Al extrudate, this architecture increases yield strength by ∼ 42 % and tensile strength by ∼ 31 %, while preserving uniform elongation, and it sustains work hardening in compression from 150 to 400 °C. The composite retained hard-magnetic behavior, with axial magnetization of 12.7 A·m 2 kg −1 at 6 T and intrinsic coercivity of 9.6 kOe. These findings demonstrate that SSE can produce Al-based load-bearing magnetic composites while preserving useful SmCo5 functionality.

36 MATERIALS SCIENCE↗

Phase Field Modeling of Corrosion for Design of Next-Generation Magnesium-Aluminum Vehicle Joints

In this study, WPI and its partners sought to understand galvanic corrosion in Mg-Al friction stir weld (FSW) joints. Unlike fusion welds, FSW is done in the solid state. This limits (but does not eliminate) the formation of brittle Al-Mg intermetallics, resulting in better joint strength and corrosion resistance. This study aimed to understand corrosion behavior of Mg-Al FSW joints by using a Cahn-Hilliard phase field electrochemistry model based on the work of Pongsaksawad et al. Its context challenge problem was an ultra-light door designed by Magna with 6061-Al sheet outer and ZEK100-Mg sheet inner panels, joined by an adhesive and FSW. Unlike most FSW joints, which weld through the softer material into the harder one, the Al sheet’s hem joint around Mg required the FSW tool to through the harder Al into the softer Mg, which was itself a challenge. Despite this challenge, PNNL succeeded in consistently making very strong FSW lap joints, by using a triflute tool and power control. Characterization showed mostly separate Al and Mg regions in the weld, usually with a hook protruding from Al into Mg, which likely contributed to high joint strength. Nanohardness mapping showed higher hardness in thin Mg swirls into the Al nugget, likely due to the intermetallics. The study used the industry standard SAE J2334 Cyclic Corrosion Test (CCT) to simulate corrosion conditions over the life of a vehicle, as well as linear polarization testing and ASTM G71 pitting corrosion testing. Corrosion reactions were: H 2 O + ½O 2 + 2e - → 2OH - at the Al cathode, and either Mg → Mg 2+ + 2e - or Mg + 2OH - → Mg(OH) 2 + 2e - at the Mg anode, with electron transfer through the joint. Mass loss increased with Al section length, supporting the hypothesis that galvanic corrosion in Al-Mg joints is limited by the cathodic reaction. Both pitting corrosion (first anode reaction) and hydroxide film formation (second reaction) were observed. The J2334 CCT test method was slightly modified, adding a chromium solution cleaning step after each week of corrosion testing, in order to remove Mg oxides and hydroxides and accurately measure mass loss over time. That said, FSW joints treated in this way did not did not exhibit significant reduction in lap shear strength of the joints vs. newly welded samples which had not undergone corrosion. Corrosion appeared to consist mainly of pitting in Mg in a way which did not directly affect the bond between the materials where the joints failed. A Cahn-Hilliard phase field model coupled with electrical potential described the electronically mediated galvanic corrosion electrochemical reactions described above in the four-component Al-Mg-H 2 O-(H 2 O+½O 2 ) system. This 2-D model successfully predicted Mg(OH)₂ formation at the anode in some circumstances, and Mg pitting corrosion in others, and showed the correct electric field directions in both cases. The model predicted Mg pit corrosion depth within a factor of two of measured pits.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Time-dependent THMC properties and microstructural evolution of damaged rocks in excavation damage zone

Modeling coupled thermo-hydro-mechanical-chemical (THMC) processes in host rocks near high-level nuclear waste (HLW) repositories at various time scales is an extremely challenging task. The current study integrates experimental, theoretical, and numerical methods in assessing the evolution of excavation damage zone (EDZ) over time and its implication on the long-term migration of hazardous species. Argillite and rock salt and are the focus of this study. The first part of the report presents a novel time-dependent directional microcrack damage theory for generic brittle rocks. It features detailed statistical description of the microcracks within a damaged solid, permitting a direct upscaling of microscale processes such as crack growth kinetics, crack closure/opening, sliding friction to explain the macroscopic creep, nonlinear elasticity, shear dilation, and loading-unloading hysteresis. This provides a basic platform for describing the anisotropic mechanical and transport properties of damaged rocks during excavation and subsequent THMC loadings. The model is validated and numerically implemented to Finite Element (FE) package ABAQUS through the user-defined material (UMAT) interface and have demonstrated great potential in resolving the time-dependent and anisotropic evolution of damage in the EDZ. The second part of the report presents a multi-scale experimental effort in characterizing the thermal, hydraulic, and mechanical properties of Mancos shale and Avery Island salt. For the Mancos shale, triaxial compression tests are performed at different confining pressures and temperatures to probe its thermomechanical properties relevant to HLW repositories. The obtained stress-strain data are interpreted using the proposed directional damage theory. Post-test specimens are subjected to gas permeability tests to reveal the correlation between permeability and the degree of microcracking. At microscale, temperature-controlled nanoindentation tests are performed and found a linear correlation between fracture toughness and elastic modulus from 25°C to 300°C. For Avery Island salt, we have designed and manufactured a novel relative-humidity controlled uniaxial creep device. Long-term creep tests at low stresses (< 5 MPa) are performed at different levels of relative humidity (RH). Besides confirming the much higher creep rates as one would expect through extrapolating the high-stress creep data, the results reveal that the steady-state creep rate of rock salt is strongly dependent on the ambient RH, an aspect that is often neglected in the literature. Both behaviors can be attributed to the pressure-solution creep mechanism which dominates at low stress and high RH levels. The third part of the report explores a set of numerical strategies in modeling the THMC behavior of porous geomaterials. A fully implicit, monolithic FE solution that can flexibly interface with different material models and coupling mechanisms for THMC problems is developed and verified through the ABAQUS user-defined element (UEL) interface. The scheme is used to study the THM response of a hypothetical HLW storage site with reference to an existing in-situ heater test. Strategies for integrating the UEL and the microcrack UMAT are suggested. Another numerical endeavor of this study is to implement a higher-order asymptotic homogenization method to account for the heterogeneous porous structures. The same method is then extended to perform microstructure-informed thermo-mechanical modeling of generalized continua. The above outcomes of this project provide a strong thrust towards enhancing the fundamental understanding and modeling capability of the long-term evolution of host rocks in EDZ, thus helping achieve the design goal of 1-million-year isolation of high-level nuclear wastes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Assessment of binary eutectic Ni alloys for high-temperature applications via laser remelting

It has been recently demonstrated that eutectic alloys processed by additive manufacturing have excellent high-temperature mechanical properties. We suggest that nickel-base eutectic alloys may enable new combinations of structural and functional properties. To this end, we investigate the processability, microstructure, and thermal stability of five, binary near-eutectic Ni-X (X = B, Ce, La, Y, and Zr) alloys processed via surface laser-remelting. The microstructure of all alloys contain a two-phase lamellar eutectic microstructure consisting of γ-Ni and intermetallic phases; this microstructure is significantly finer (100–200 nm lamellar spacing) in the laser-remelted alloys than in the cast substrate (0.5–1.0 µm lamellar spacing). The microhardness of the laser-remelted alloys (550–770 HV) is 35–50% higher than that of the cast alloys (370–570 HV) due to this finer eutectic spacing. An anomalous eutectic microstructure appears at the meltpool boundaries, containing globular and lamellar γ-Ni phases. The alloys contain a high volume fraction (>50 vol%) of intermetallic phase which forms a continuous network, causing brittleness. Following laser-remelting trials, the alloys showed a high density of solid-state cracks, except for the Ni-Zr alloy which processed well. During thermal exposure at 700 and 900°C for up to 500 h, the eutectic microstructure coarsens. Coarsening occurs heterogeneously and initiates at the meltpool boundaries. This process occurs more slowly in the Ni-Zr and Ni-Y alloys, and more rapidly in the remaining alloys, resulting in greater microhardness retention in the Ni-Zr and Ni-Y alloys following thermal exposure at 700°C. Thus, among the five alloys, the Ni-Zr system exhibits a good combination of high-temperature mechanical properties and processability. Here, we conclude with recommendations for future work on designing additively manufactured alloys based on these eutectic Ni systems.

Additive manufacturing↗

Effects of Recovery Conditions and Aggregation Mechanisms on the Chemical and Physical Properties of Hybrid Poplar and Corn Stover Lignins

Heterogeneity in the physical properties and processing behavior of lignins recovered from biorefining process streams can hinder their effective utilization and industrial valorization. This work investigates lignin recovery by acidification from alkaline pretreatment liquors of varying sources (corn stover and hybrid poplar), compositions, solid contents, and incubation temperatures prior to filtration. Recovered lignins were characterized for filtration performance, mass yield, chemical composition, particle size and morphology, and color. A transition temperature was identified corresponding to marked shifts in lignin physical properties and was a function of the solid content and liquor source. Filtration below this temperature yielded slow-filtering, dark, brittle lignins with smoother particle surfaces, whereas precipitation above this threshold yielded fast-filtering, lighter, powdery lignins with rougher particle surfaces. The impact of temperature and concentration on universal cluster aggregation mechanisms was proposed to explain the differences between lignin particle properties and filtration behavior.

Aggregation↗

A Solution-Processable High-Modulus Crystalline Artificial Solid Electrolyte Interphase for Practical Lithium Metal Batteries

The solid electrolyte interphase (SEI) has been identified as a key challenge for Li metal anodes. The brittle and inhomogeneous native SEI generated by parasitic reactions between Li and liquid electrolytes can devastate battery performance; therefore, artificial SEIs (ASEIs) have been proposed as an effective strategy to replace native SEIs. Herein, as a collaboration between academia and industrial R&D teams, a multifunctional (crystalline, high modulus, and robust, Li + ion conductive, electrolyte-blocking, and solution processable) ASEI material, LiAl-FBD (where “FBD” refers to 2,2,3,3-tetra-fluoro-1,4-butanediol), for improving Li metal battery performance is designed and synthesized. The LiAl-FBD crystal structure consists of Al 3+ ions bridged by FBD 2– ligands to form anion clusters while Li + ions are loosely bound at the periphery, enabling an Li + ion conductivity of 9.4 × 10 –6 S cm –1 . Further, the fluorinated, short ligands endow LiAl-FBD with electrolyte phobicity and high modulus. The ASEI is found to prevent side reactions and extend the cycle life of Li metal electrodes. Specifically, pairing LiAl-FBD coated 50 μm thick Li with industrial 3.5 mAh cm –2 NMC811 cathode and 2.8 μL mAh –1 lean elec-trolyte, the Li metal full cells show superior cycle life compared to bare ones, achieving 250 cycles at 1 mA cm –2 .

25 ENERGY STORAGE↗

Why Firn Quakes

Snow dampens sounds, but anecdotal reports concisely describe audible propagating collapse events—firnquakes—in Antarctic and Arctic snowfields. We propose combining granular and continuum mechanics to form a testable theory for conditioning, triggering, and propagation of firnquakes consistent with scarce data. A central condition for collapse events is unconsolidated firn at depth. As firn grains compact, stresses are transmitted along force chains which carry the overburden and transition into a continuous medium by pressure sintering. This granular legacy creates solid-like supports of denser layers that keep the material below unconsolidated. Dynamic amplification triggers local brittle failure of the supports, which induces a cascade of collapse propagation. Using bulk density from ice cores as proxy for stiffness, we find the flexural wave speed by collapsing supports matches the recorded firnquake velocities on the order of 100 m/s. Our theory is to be tested in firn sheets and other compacting granular materials.

Voigtländer, A. [Lawrence Berkeley National Labora↗

Low viscosity of solid MgO at high pressures and strain rates measured using the laser-driven Richtmyer-Meshkov instability

Solids are often assumed to behave as viscous fluids under high-strain rates. This behavior has been studied experimentally in metals but largely unexplored in brittle ceramic materials. Here, in this study, we present a technique for measuring the viscosity of MgO using time-resolved velocimetry to track the growth rate of a perturbation caused by the Richtmyer-Meshkov instability at the OMEGA EP laser facility. To interpret the results, we use an in-house Eulerian hydrocode to simulate our experiments and model the plastic deformation of solid MgO as a viscous fluid. Results indicate that MgO has a surprisingly low upper bound to its effective viscosity of ∼10 2 ⁢ Pa s at 175 ± 15⁢ GPa, ∼3500⁢K, and 10 6 −10 7 s −1 strain rate.

Perez, Tyler M. [Johns Hopkins Univ., Baltimore, M↗