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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Markov gap for geometric reflected entropy

The reflected entropy S R (A : B) of a density matrix ρ AB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N 2 gap between S R and I. We provide an information-theoretic interpretation of this gap by observing that S R - I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity S R - I the Markov gap. We then prove that for time-symmetric states in pure AdS 3 gravity, the Markov gap is universally lower bounded by log(2)ℓ AdS /2G N times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling S R - I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Processes at lithium-hydride/deuteride surfaces upon low energy impact of H/D

Sputtering, reflection, and retention processes at amorphous and crystalline lithium hydride surfaces due to impact of low energy (1–100 eV) hydrogen and deuterium atoms over the range of 0 o −85 o angle of incidence at 300 K surface temperature were investigated by atomistic computational methods. Classical molecular dynamics simulations were performed with improved reactive bond-order force field (ReaxFF) potentials that include long-range polarization effects. In addition to probabilities of surface processes, the energy and angular spectra of ejected particles were obtained. Comparison of these results with those previously obtained on pristine lithium surfaces indicates the importance of saturation of the Li surface and near-surface region with hydrogen. We show that such saturation, which is typical in both laboratory and fusion device experiments with lithium coating of the plasma-facing surfaces, significantly changes the surface processes with hydrogen irradiation in the understudied low-energy region of impact energies.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

On transport of electrons in a magnetized plasma sheath

Electron trajectories are analyzed in the plasma sheath region in a magnetic field that intersects the surface at a shallow angle. Depending on the size of the Debye width relative to the electron gyroradius, λ D /ρ e , an electron either drifts in the sheath electric field or follows a sequence of reflections (“bouncing”) on the surface before reversing its parallel velocity. For thin sheath, λ D /ρ e ≪ 1, the conservation of the electron magnetic moment can be violated, depending on the ratio of the electron perpendicular and parallel velocities V ⊥ /V || and the magnetic field pitch angle with respect to the surface. Small-scale waviness of the surface can strongly amplify this effect, leading to violation of the magnetic moment conservation even for λ D /ρ e ≳ 1, which opens a channel of anomalous radial transport for electrons in plasma devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Accelerating laser ray tracing in high fidelity physics simulations of laser melting using squeeze U-net

Laser melting is a core component of the ongoing industrial revolution, dubbed Industry 4.0, as lasers facilitate fast and precise melting and fusion in advanced manufacturing. There is a strong need to optimize the laser process using simulations. However, this has proven challenging as high fidelity simulations are needed for predictive modeling and this is currently prohibitively expensive even when run on hundreds of processors on high performance computers. The challenge is capturing complex physics of laser material interaction, fluid dynamics, thermal physics and material phase transformations at various length and time scales. To close this technological gap, we modified a squeeze U-net to accelerate the laser ray tracing component of such high fidelity models by ~4x–40x while preserving the core physics principle of conservation of energy with 97% accuracy. This approach enables the accurate modeling of global laser energy absorption as a function of local surface temperatures and complex surface topologies, which govern the reflection directions and energy losses of laser rays upon interacting with the material surface.

Computer science↗
DOE OSTI2021

Chemical Passivation of Crystalline Si by Al 2 O 3 Deposited Using Atomic Layer Deposition: Implications for Solar Cells

The atomistic-level mechanism for the chemical passivation of the monocrystalline Si (c-Si) surface with thermally annealed Al 2 O 3 was studied using in situ infrared spectroscopy and photoconductance decay measurements. Al 2 O 3 was deposited on high-lifetime, float-zone c-Si substrates using atomic layer deposition (ALD) from trimethylaluminum (TMA), and H 2 O or O 3 . Surface-sensitive attenuated total reflection Fourier transform infrared spectroscopy was used to monitor the c-Si/Al 2 O 3 interface, as well as the bulk of the Al 2 O 3 film during the entire process. Our results show that some surface Si–H bonds are preserved after the ALD of Al 2 O 3 on H-terminated Si. During the annealing step at 400 °C, restructuring occurs at the c-Si/Al 2 O 3 interface to form interfacial SiO x . Isotope labeling was used to differentiate interfacial SiD bonds on the c-Si surface from H incorporated in Al 2 O 3 . Within the sensitivity of our infrared setup (~10 13 cm –2 ), we did not observe any net migration of atomic H or D from Al 2 O 3 to the c-Si/Al 2 O 3 interface. To isolate the effects of chemical and field-effect passivation of Al 2 O 3 thin films, we carried out surface passivation studies on c-Si/SiO 2 /Al 2 O 3 stacks. We also annealed these stacks in different atmospheres to test the influence of annealing atmospheres on the chemical passivation of c-Si by Al 2 O 3 and observed that O 2 -containing atmosphere led to the best surface chemical passivation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Geometric surprises in the Python's lunch conjecture

A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python’s lunch conjecture of Brown et al., the bulge’s area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; and they probe entanglement shadows, orbifold singularities, and compact spaces such as the sphere in AdS _p× S^q p × S q . These features imply, according to the python’s lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.

Physics↗
DOE OSTI2024

Vibrational study of CO, O 2 , and H 2 Adsorbed on the CoCrFeNi (110) High Entropy Alloy Surface

The vibrational properties of CO, O 2 , and H 2 molecularly or dissociatively adsorbed on a CoCrFeNi(110) surface have been probed using highresolution energy loss spectroscopy (HREELS) and modeled using density functional theory (DFT) calculations. Large (~20 mm3) single-crystal, quaternary face-centered cubic CoCrFeNi was synthesized via a modified Czochralski technique. We show strong evidence that CO adsorbs primarily on bridge and on-top sites in compositionally varied local environments, which reflect the random, multielemental surface composition inherent in a high entropy alloy. A variation of adsorption sites is also found with oxygen, which exhibits two broad groups of modes. Comparison to previous photoemission and theoretical studies suggests that the higher energy modes consist primarily of local CrO x species, while the lower energy modes are due to oxygen atoms adsorbed on other metal sites. Unlike CO and O 2 , HREELS upon H 2 adsorption shows only two much narrower modes and is consistent with atomic adsorption on 3-fold hollow sites. The hypothesized adsorption sites for all three species are directly corroborated by our DFT calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Effect of He seeding on hydrogen isotope permeation in tungsten by H-D mixed plasma exposure

Hydrogen (H) and deuterium (D) permeation fluxes for tungsten (W) by H-D mixed plasma were studied to clarify the hydrogen isotope effect on permeation by a newly designed plasma driven permeation (PDP) device at Shizuoka University. A mixed H-D plasma was produced by introducing H and D gasses with various ratios. The atomic ratio and permeation flux in the plasma were measured during the experiments. It was found that the H:D atomic ratio in the plasma was almost proportional to the introduced H:D gas ratio. When single species of H or D was irradiated, the H permeation rate showed approximately 1.6 times as high as that of D. Under H-D mixed plasma irradiation, the highest HD permeation rate was observed when the atomic ratio of H:D in the plasma was 50:50. In addition, the effect of He seeding on H-D mixed plasma driven permeation behavior was also evaluated. The recycling of hydrogen isotopes on the upstream side was enhanced due to the formation of He bubbles near the surface, which would prevent the dissolution of hydrogen isotopes into bulk W and enhance the reflection process during plasma exposure. H and D permeation fluxes were clearly reduced by seeding He in H-D mixed plasma. At lower temperature (~723 K), the ratio of steady permeation fluxes of H and D was about 75 : 25, confirming the high permeation flux of H . These results have demonstrated a significant hydrogen isotope effect, even if He was seeded or not. As the temperature increased, H and D permeation fluxes approached unity at 923 K. Therefore,this indicates that the hydrogen isotope effect was determined by the combination of recycling / reflection at or beneath the surface, which will be controlled by the temperature during plasma exposure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Complex Adsorption Behavior of Neodymium and Ytterbium on Structurally-Distinct Alumina Surfaces

New sources of rare earth elements (REEs) are needed to support a green energy transition. REEs adsorbed to aluminum-rich clays in weathering deposits represent important resources but the mechanisms responsible for their retention and ease of extraction are unresolved. Disordered coordination and co-occurrence of multiple species pose challenges to investigating REE adsorption processes via established spectroscopic methods. In this study, we applied element-specific surface crystallography methods to obtain a new perspective on the complexity of REE adsorption mechanisms and affinities. Alumina (001) and (012) crystal surfaces were utilized to evaluate surface-specific controls on Nd(III) and Yb(III) adsorption behavior. The REEs displayed similar total adsorption to alumina (001) as a mixture of inner- and outer-sphere complexes, but Nd displayed a greater proportion of inner-sphere binding. Adsorption of ordered inner- and outer-sphere REE species was substantially lower on alumina (012). These distinct behaviors reflect differences in the surface functional group charging and topography of the two surfaces. However, alumina (012) also hosted a substantial population of disordered adsorbed species, especially for Nd, potentially associated with Al vacancy surface defects. Here, the accumulation of light versus heavy REEs via adsorption in weathering deposits likely results from multiple, competing reactions affected by clay particle morphology. Leaching procedures for resource recovery should account for differential rates of desorption by coexisting inner- and outer-sphere REE surface complexes.

58 GEOSCIENCES↗
DOE OSTI2020

The Magnitude and Waveform of Shock Waves Induced by X-ray Lasers in Water

The high energy densities deposited in materials by focused X-ray laser pulses generate shock waves which travel away from the irradiated region, and can generate complex wave patterns or induce phase changes. We determined the time-pressure histories of shocks induced by X-ray laser pulses in liquid water microdrops, by measuring the surface velocity of the microdrops from images recorded during the reflection of the shock at the surface. Measurements were made with ~30 µm diameter droplets using 10 keV X-rays, for X-ray pulse energies that deposited linear energy densities from 3.5 to 120 mJ/m; measurements were also made with ~60 µm diameter drops for a narrower energy range. At a distance of 15 µm from the X-ray beam, the peak shock pressures ranged from 44 to 472 MPa, and the corresponding time-pressure histories of the shocks had a fast quasi-exponential decay with positive pressure durations estimated to range from 2 to 5 ns. Knowledge of the amplitude and waveform of the shock waves enables accurate modeling of shock propagation and experiment designs that either maximize or minimize the effect of shocks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Demonstration and Automation of Reflected Target Optical Measurement for Heliostats

Accurate optical surfaces are a primary driver of concentrated solar power plant performance. Errors in pointing and tracking mirrors, the canting of individual mirror facets, and the surface slope of the mirror itself can be caused by errors during assembly, transportation, wind loading, gravity, and many other sources. The tools that exist to measure these error sources today largely rely on fringe deflectometry (SOFAST, QDec, others), or photogrammetry with targets attached to the mirror surface. Since 2022, NREL has been developing a measurement method called the Reflected Target Non-intrusive Assessment (ReTNA) system. This system differs from most established methods in that we perform deflectometry with a pattern of coded targets, identified in space with photogrammetry. Reflected target systems have several advantages over traditional fringe deflectometry systems. Firstly, they can be operated in bright or ambient lighting, a challenge for fringe systems that use a projector and screen. Reflected target systems also can use a much lighter and less expensive target than projector-based systems. Lastly, 2D slope measurement can be solved from a single image, which leads to several advantages for accommodating faster measurements and smaller sized targets. These advantages make ReTNA particularly well-suited for applications where there are space or lighting constraints, like performing heliostat quality assurance on an assembly line. It's also useful when a lightweight, flexible system is needed, like for heliostat developers to quickly measure a new heliostat design at different orientations, to observe gravitational effects on the mirror surface shape. In the last year, significant improvements were made to this tool to make it more useful for these applications. These improvements were focused around validation of the ReTNA measurement system, and automation of the setup and measurement process. First, we present an improved ReTNA layout, for use on the heliostat assembly line. Next, we detail the various changes to the ReTNA software and computer vision methods to automate data collection in this new setup, and lessons learned from this process. The goal with this new setup is to perform a full heliostat surface characterization without removing the mirror from the assembly line. Lastly, we share results from several ReTNA validation studies undertaken over the last year. These include repeated ReTNA measurement on demonstration mirror facets, comparisons with other optical measurement tools, and some studies aimed at quantifying the uncertainty of ReTNA measurement under various constraints (mirror-target spacing, camera resolution, etc.). These results are compared with 2024 HelioCon performance targets, and our planned next steps for the ReTNA measurement system are presented.

CSP↗
DOE OSTI2024

Daytime cooling efficiencies of urban trees derived from land surface temperature are much higher than those for air temperature

Accurately capturing the impact of urban trees on temperature can help optimize urban heat mitigation strategies. Recently, there has been widespread use of remotely sensed land surface temperature (T s ) to quantify the cooling efficiency (CE) of urban trees. However, remotely sensed T s reflects emitted radiation from the surface of an object seen from the point of view of the thermal sensor, which is not a good proxy for the air temperature (T a ) perceived by humans. The extent to which the CEs derived from T s reflect the true experiences of urban residents is debatable. Therefore, this study systematically compared the T s -based CE (CE T s ) with the T a -based CE (CE T a ) in 392 European urban clusters. CE T s and CE T a were defined as the reductions in T s and T a , respectively, for every 1% increase in fractional tree cover (FTC). The results show that the increase in FTC has a substantial impact on reducing T s and T a in most cities during daytime. However, at night, the response of T s and T a to increased FTC appears to be much weaker and ambiguous. On average, for European cities, daytime CE T s reaches 0.075 °C % -1 , which is significantly higher (by an order of magnitude) than the corresponding CE T a of 0.006 °C % -1 . In contrast, the average nighttime CE T s and CE T a for European cities are similar, both approximating zero. Overall, urban trees can lower daytime temperatures, but the magnitude of their cooling effect is notably amplified when using remotely sensed T s estimates compared to in situ T a measurements, which is important to consider for accurately constraining public health benefits. Our findings provide critical insights into the realistic efficiencies of alleviating urban heat through tree planting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Relativistic flying laser focus by a laser-produced parabolic plasma mirror

Here, the question of electromagnetic field intensification towards the values typical for strong field quantum electrodynamics is of fundamental importance. One of the most promising intensification schemes is based on the relativistic-flying mirror concept, which shows that the electromagnetic radiation reflected by the mirror will be frequency upshifted by a factor of 4γ 2 (γ is the Lorentz factor of the mirror). In laser-plasma interactions, such a mirror travels with relativistic velocities through plasma and typically has a parabolic form, which is advantageous for light intensification. Thus, a relativistic-flying parabolic mirror reflects the counterpropagating radiation in the form of a focused and flying electromagnetic wave with a high frequency. The relativistic-flying motion of the laser focus makes the electric and magnetic field distributions of the focus complicated, and the mathematical expressions describing the field distributions of the focus become of fundamental interest. We present analytical expressions describing the field distribution formed by an ideal flying mirror which has a perfect reflectance over the entire surface and wavelength range. The peak field strength of an incident laser pulse with a center wavelength of λ 0 and an effective beam radius of w e is enhanced by a factor proportional to γ 3 (w e /λ 0 ) in the relativistic limit. Electron-positron pair production is investigated in the context of invariant fields based on the enhanced electromagnetic field. The pair production rate under the relativistic-flying laser focus is modified by the Lorentz γ-factor and the beam radius-wavelength ratio (w e /λ 0 ). We show that the electron-positron pairs can be created by colliding two counterpropagating relativistic-flying laser focuses in vacuum, each of which is formed when a 180 TW laser pulse is reflected by a relativistic-flying parabolic mirror with γ=12.2.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Characteristics of Future Warmer Base States in CESM2

Abstract Simulations of 21st century climate with Community Earth System Model version 2 (CESM2) using the standard atmosphere (CAM6), denoted CESM2(CAM6), and the latest generation of the Whole Atmosphere Community Climate Model (WACCM6), denoted CESM2(WACCM6), are presented, and a survey of general results is described. The equilibrium climate sensitivity (ECS) of CESM2(CAM6) is 5.3°C, and CESM2(WACCM6) is 4.8°C, while the transient climate response (TCR) is 2.1°C in CESM2(CAM6) and 2.0°C in CESM2(WACCM6). Thus, these two CESM2 model versions have higher values of ECS than the previous generation of model, the CESM (CAM5) (hereafter CESM1), that had an ECS of 4.1°C, though the CESM2 versions have lower values of TCR compared to the CESM1 with a somewhat higher value of 2.3°C. All model versions produce credible simulations of the time evolution of historical global surface temperature. The higher ECS values for the CESM2 versions are reflected in higher values of global surface temperature increase by 2,100 in CESM2(CAM6) and CESM2(WACCM6) compared to CESM1 between comparable emission scenarios for the high forcing scenario. Future warming among CESM2 model versions and scenarios diverges around 2050. The larger values of TCR and ECS in CESM2(CAM6) compared to CESM1 are manifested by greater warming in the tropics. Associated with a higher climate sensitivity, for CESM2(CAM6) the first instance of an ice‐free Arctic in September occurs for all scenarios and ensemble members in the 2030–2050 time frame, but about a decade later in CESM2(WACCM6), occurring around 2040–2060.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Correlation between infrared spectra features and coverage of different adsorption sites for the NO/Pd(111) system

This study investigates the adsorption of nitric oxide (NO) on Pd(111) surfaces at 200 K using infrared reflection absorption spectroscopy (IRRAS). Peak positions and areas are used as proxies for tracking coverage of different species, serving as groundwork for in-situ experiments that need real-time tracking of surface species. Here, we derived a mathematical model correlating NO coverage with dose, consistent with the Molecular Langmuir Model. Distinct correlations are observed between coverage and spectral features (peak position and peak area for the NO vibration): at lower coverages (θ<0.6), the total integrated peak areas are linearly corelated to coverage; at higher coverages (θ>0.6), the peak center for a compressed-hollow site becomes the primary coverage indicator, showing a linear relationship between wavenumber and coverage. Note that this study addresses coverages below saturation. These findings refine our understanding of NO adsorption and establish a foundation for real-time in situ transient kinetics studies of chemical reactions involving NO on Pd(111).

25 ENERGY STORAGE↗
DOE OSTI2022

Smooth Modified Surfaces of Silicon for the Study of Ionic Liquid Interfaces by Neutron Reflectometry

Silicon surfaces with termination of hydrogen (H–Si), quartz, native silicon (native-Si), and chemically deposited (Au–Si) cd and sputtered gold (Au–Si) s were fabricated with roughness less than 6 Å to study the solid–liquid interface of the ionic liquid (IL) methyltrioctylammonium bis(trifluoromethylsulfonyl)imide, [N 1888 ][TFSI], by neutron reflectometry (NR). The modifications made to the silicon surface were to obtain a native positive or negative charge similar to a charged surface in electrochemical systems. The differences in scattering length density (SLD) based on mass density and composition of IL were examined. Perpendicular to the substrate surface, a distinct transition between the first ion layer and the bulk liquid is resolved out of the reflectivity data for the gold surfaces and in particular the chemically deposited Au–Si. Other interfaces are best described by a diffuse transition between regions of different SLDs. The diffuse transitions between SLDs observed here suggest that the interfacial structure of IL, while ordered, is best described by a continuous variation in composition as opposed to distinct layers of ions.

25 ENERGY STORAGE↗
DOE OSTI2023

THz Plasmonics and Topological Optics of Weyl Semimetals

THz magneto-optical properties of 3D topological Weyl semimetals were investigated with both THz spectroscopy and THz pump-probe measurements. The unique THz effects predicted in these materials may have important applications in THz technology. The electronic band structure was characterized spectroscopically through THz zero-field reflectance and/or cyclotron resonance measurements. The studies included the dynamic chiral pumping and the study of the predicted novel magneto-electric effects arising from the underlying Berry curvature and magneto plasmonic-like effects in the absence of an applied magnetic field. Chiral pumping in the extreme quantum limit was studied on Weyl semimetals to directly probe the chiral N=0 Landau level. Non-linear pump-probe measurements were used to measure the chiral pumping lifetime. Solids with topologically robust electronic states exhibit unusual electronic and optical transport properties that do not exist in other materials. A particularly interesting example is chiral charge pumping, the so-called chiral anomaly, in recently discovered topological Weyl and Dirac semimetals, where simultaneous application of parallel DC electric and magnetic fields creates an imbalance in the number of carriers of opposite topological charge (chirality). In an earlier study we investigated the Weyl metals Na 3 Bi and Cd 3 As 2 . In this grant we followed up with magneto-optical studies of TaAs, another Weyl semimetal. More recently, we have also characterized other Weyl and Dirac systems that have come on line. The Physics community is still looking for the “hydrogen atom” of the Weyl semimetal. CoSi is one promising new system which features Weyl node spacing comparable to the Brillouin zone size. This system may be suitable for study of the predicted chiral plasmons that arise from the Berry curvature in Weyl materials. In other experiments gates can be applied to the samples in order to study the Fermi arc surface states by modulation reflectance spectroscopy at THz frequencies.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A spall and diffraction study of nanosecond pressure release across the iron ε-α phase boundary

The extreme response of polycrystalline iron at high pressures and high strain rates is revealed by means of high-power laser pulses. The compression portion of the pulse coupled with x-ray diffraction identifies the expected body-centered cubic (α) to hexagonal close packed (ε) displacive transformation. Upon release, observation shows that the complete reverse transformation takes approximately 8 ns and that the structure returns to its initial microstructural configuration, in a reversible transformation path. This is in good agreement with molecular dynamics (MD) simulations which predict an inverse dependence between transformation time and strain rate. The grain size is reduced from μm to nm range during compression and begins increasing back to the original grain size on decompression. The kinetics of the transition is dictated by heterogenous nucleation as it follows the Johnson-Mehl-Avrami-Kolmogorov equation with the appropriate time exponent of ~1. This is confirmed by MD simulations which also identify profuse twinning and dislocation generation. Here, the tensile pulse generated upon reflection at the free surface is captured by time-resolved free surface velocity measurements from which a peak tensile stress of 7 GPa is obtained, in stark contrast with its quasi-static value of ~200 MPa. At these strain rates, the strength of grain interiors, which is determined by twinning and slip exceeds the strength of the boundaries, and failure initiates preferentially in the latter.

36 MATERIALS SCIENCE↗