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At least 559 records · Page 31

Metal-insulator and magnetic phase diagram of Ca 2 RuO 4 from auxiliary field quantum Monte Carlo and dynamical mean field theory

Layered perovskite ruthenium oxides exhibit a striking series of metal-insulator and magnetic-nonmagnetic phase transitions easily tuned by temperature, pressure, epitaxy, and nonlinear drive. In this work, we combine results from two complementary state-of-the-art many-body methods, auxiliary field quantum Monte Carlo and dynamical mean field theory, to determine the low-temperature phase diagram of Ca 2 RuO 4 . Both methods predict a low-temperature, pressure-driven metal-insulator transition accompanied by a ferromagnetic-antiferromagnetic transition. Further, the properties of the ferromagnetic state vary nonmonotonically with pressure and are dominated by the ruthenium $d_{xy}$ orbital, while the properties of the antiferromagnetic state are dominated by the $d_{xz}$ and $d_{yz}$ orbitals. Differences in the details of the predictions of the two methods are analyzed. This work is theoretically important as it presents the first application of the auxiliary field quantum Monte Carlo method to an orbitally degenerate system with both Mott and Hunds physics and provides an important comparison of the dynamical mean field and auxiliary field quantum Monte Carlo methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Transducer Resolution Effect on Pressure Fluctuations Beneath Hypersonic Turbulent Boundary Layers

The size of a pressure transducer is known to affect the accuracy of measurements of wall-pressure fluctuations beneath a turbulent boundary layer because of spatial averaging over the sensing area of the transducer. In this paper, the effect of finite transducer size is investigated by applying spatial averaging or wavenumber filters to a database of hypersonic wall pressure generated from a direct numerical simulation (DNS) that simulates the turbulent portion of the boundary layer over a sharp 7° half-angle cone at nominally Mach 8. Here, a good comparison between the DNS and the experiment in the Sandia Hypersonic Wind Tunnel at Mach 8 is achieved after spatial averaging is applied to the DNS data over an area similar to the sensing area of the transducer. The study shows that a finite sensor size similar to that of the PCB132 transducer can cause significant attenuation in the root-mean-square and power spectral density (PSD) of wall-pressure fluctuations, and the attenuation effect is identical between cone and flat plate configurations at the same friction Reynolds number. The Corcos theory is found to successfully compensate for the attenuated high-frequency components of the wall-pressure PSD.

42 ENGINEERING↗

Pressure feedback control of electro-hydraulic actuators using fixed displacement hydraulic machines

This paper presents the development of a control strategy for Electro-Hydraulic Actuator (EHA) systems based on fixed displacement hydraulic machines. Although some previous studies on EHAs show benefits in terms of energy efficiency and regeneration capability compared to conventional hydraulic systems, few studies focus on the dynamic performance of EHAs. Unlike traditional valve-controlled systems, an EHA based on a fixed displacement pump typically relies on variation of the electric motor shaft speed to control the actuator velocity. This study shows that pressure feedback can be used to control the speed of the electric machine, thus achieving the required actuator/machine dynamic response. A simulation model is developed by including the EM, the hydraulic system, and the actuation system, which can give a realistic prediction of the EHA performance for a typical duty cycle. An open-circuit EHA previously proposed by the authors is used to validate the control strategy, and the simulation results show superior dynamic performance, exhibiting a reduction in response time and oscillatory behavior, compared to a feedforward EHA controller. Following the method presented in this study, it is possible to design a controller with a pressure feedback strategy for EHA systems with different size and actuation requirements

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Structure and dynamics of ethane confined in silica nanopores in the presence of CO 2

Fundamental understanding of the subcritical/supercritical behavior of key hydrocarbon species inside nano-porous matrices at elevated pressure and temperature is less developed compared to bulk fluids, but this knowledge is of great importance for chemical and energy engineering industries. This study explores in detail the structure and dynamics of ethane (C 2 H 6 ) fluid confined in silica nanopores, with a focus on the effects of pressure and different ratios of C 2 H 6 and CO 2 at non-ambient temperature. Quasi-elastic neutron scattering (QENS) experiments were carried out for the pure C 2 H 6 , C 2 H 6 :CO 2 = 3:1, and 1:3 mixed fluids confined in 4-nm cylindrical silica pores at three different pressures (30 bars, 65 bars, and 100 bars) at 323 K. Two Lorentzian functions were required to fit the spectra, corresponding to fast and slow translational motions. No localized motions (rotations and vibrations) were detected. Higher pressures resulted in hindrances of the diffusivity of C 2 H 6 molecules in all systems investigated. Pore size was found to be an important factor, i.e., the dynamics of confined C 2 H 6 is more restricted in smaller pores compared to the larger pores used in previous studies. Molecular dynamics simulations were performed to complement the QENS experiment at 65 bars, providing supportive structure information and comparable dynamic information. The simulations indicate that CO 2 molecules are more strongly attracted to the pore surface compared to C 2 H 6 . The C 2 H 6 molecules interacting with or near the pore surface form a dense first layer (L1) close to the pore surface and a second less dense layer (L2) extending into the pore center. Both the experiments and simulations revealed the role that CO 2 molecules play in enhancing C 2 H 6 diffusion (“molecular lubrication”) at high CO 2 :C 2 H 6 ratios. The energy scales of the two dynamic components, fast and slow, quantified by both techniques, are in very good agreement. Herein, the simulations identified the fast component as the main contributor to the dynamics. Molecule motions in the L2 region are mostly responsible for the dynamics (fast and slow) that can be detected by the instrument.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Raman studies of hydrogen trapped in As 4 O 6 ·2H 2 at high pressure and low temperature

In this work, Raman spectroscopic measurements of the arsenolite–hydrogen inclusion compound As 4 O 6 ·2H 2 were performed in diamond anvil cells at high pressure and variable temperature down to 80 K. The experimental results were complemented by ab initio molecular dynamics simulations and phonon calculations. Observation of three hydrogen vibrons in As 4 O 6 ·2H 2 is reported in the entire temperature and pressure range studied (up to 24 GPa). While the experiments performed with protium and deuterium at variable temperatures allowed for the assignment of two vibrons as Q 1 (1) and Q 1 (0) transitions of ortho and para spin isomers of hydrogen trapped in the inclusion compound, the origin of the third vibron could not be unequivocally established. Low-temperature spectra revealed that the lowest-frequency vibron is actually composed of two overlapping bands of A g and T 2g symmetries dominated by H 2 stretching modes as predicted by our previous density functional theory calculations. We observed low-frequency modes of As 4 O 6 ·2H 2 vibrations dominated by H 2 “librations,” which were missed in a previous study. A low-temperature fine structure was observed for the J = 0 → 2 and J = 1 → 3 manifolds of hydrogen trapped in As 4 O 6 ·2H 2 , indicating the lifting of degeneracy due to an anisotropic environment. A non-spherical distribution was captured by molecular dynamics simulations, which revealed that the trajectory of H 2 molecules is skewed along the crystallographic $\langle$111$\rangle$ direction. Last but not least, low-temperature synchrotron powder x-ray diffraction measurements on As 4 O 6 ·2H 2 revealed that the bulk structure of the compound is preserved down to 5 K at 1.6 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Isostructural Phase Transition of Fe 2 ⁢O 3 under Laser Shock Compression

We present in situ x-ray diffraction and velocity measurements of Fe 2⁢ O 3 under laser shock compression at pressures between 38–122 GPa. None of the high-pressure phases reported by static compression studies were observed. Instead, we observed an isostructural phase transition from 𝛼−Fe 2⁢ O 3 to a new 𝛼′−Fe 2 ⁢O 3 phase at a pressure of 50–62 GPa. The 𝛼′−Fe 2⁢ O 3 phase differs from 𝛼−Fe 2 ⁢O 3 by an 11% volume drop and a different unit cell compressibility. We further observed a two-wave structure in the velocity profile, which can be related to an intermediate regime where both 𝛼 and 𝛼′ phases coexist. Furthermore, density functional theory calculations with a Hubbard parameter indicate that the observed unit cell volume drop can be associated with a spin transition following a magnetic collapse.

36 MATERIALS SCIENCE↗

Fuel Stratification Influence on NO x Emission in a Premixed Axial Reacting Jet-in-Crossflow at High Pressure

Three reacting jet-in-crossflow (JiC) methane/air flames were numerically investigated in a lean axially staged combustor at a pressure of five atmospheres. A detailed chemistry Star-CCM+ computational fluid dynamics (CFD) model was used with 53 species considered and the result of turbulence-governed finite-rate modeling was validated with in-house experimental data. An optically accessible test section features three side windows, allowing local flow and flame analysis with particle image velocimetry (PIV) and CH* chemiluminescence as well as pressure, temperature, and species exit measurements. The research objective was to predict and verify NO x formation of the premixed 12.7 mm axial jet. Three headend temperature levels were investigated along with three premixed jets at lean (φ Jet = 0.75), near-stoichiometric (φ Jet = 1.07), and rich (φ Jet = 1.78) axial fuel line equivalence ratio. Based on the matching exit emission concentration, global emission benefits were investigated by adjustment of the fuel stratification. The perfectly premixed methane/air flames of this study were shown to ignite at the lee-side of the jet. For the elevated headend temperature level T = 1800 K, the flame extended beyond the windward jet trajectory and caused high axial NO production. For industry application, a firing temperature of 1920 K was achieved with a NO x optimized fuel split of 25%, combining a lean headend (φ Headend = 0.61) with a rich (φ Jet = 1.78) jet equivalence ratio. As a result, this operating point allowed minimization of the combustor residence time at temperatures above 1700 K as well as combustion in a compact flame at the jet lee-side along the counter rotating vortex pair.

03 NATURAL GAS↗

Shock-induced twinning/detwinning and spall failure in Cu–Ta nanolaminates at atomic scales

Here, this study provides new insights into the role of interfaces on the deformation and failure mechanisms in shock-loaded Cu–Ta–Cu trilayer system. The thickness of the Ta layer, piston velocities, and shock pulse durations were varied to explore the impact of impedance mismatch and loading conditions on spallation behavior and twin formation. It was found that the interfaces play a crucial role in the dynamic response of these multilayered systems since secondary reflection waves generated at the interfaces significantly affected the peak stress and pressure profiles, influencing void nucleation and failure modes. In the trilayer systems, failure predominantly occurred at interfaces and within the Ta layer, with void nucleation sites and twinning behavior being markedly different compared to single-crystal Cu and Ta. Increasing the Ta layer thickness modified the wave interactions, leading to different failure locations. Higher piston velocities were associated with increased spall strength by enhancing wave interactions and void formation, particularly at the interfaces and within the Ta layer, under specific configurations. Additionally, shorter shock pulse durations facilitated earlier initiation of the release fan, reducing twin formation and altering the failure dynamics by accelerating twin annihilation and pressure release.

36 MATERIALS SCIENCE↗

Effect of helium bubbles on the mobility of edge dislocations in copper

Abstract Helium bubbles can form in materials upon exposure to irradiation. It is well known that the presence of helium bubbles can cause changes in the mechanical behavior of materials. To improve the lifetime of nuclear components, it is important to understand deformation mechanisms in helium-containing materials. In this work, we investigate the interactions between edge dislocations and helium bubbles in copper using molecular dynamics (MD) simulations. We focus on the effect of helium bubble pressure (equivalently, the helium-to-vacancy ratio) on the obstacle strength of helium bubbles and their interaction with dislocations. Our simulations predict significant differences in the interaction mechanisms as a function of helium bubble pressure. Specifically, bubbles with high internal pressure are found to exhibit weaker obstacle strength as compared to low-pressure bubbles of the same size due to the formation of super-jogs in the dislocation. Activation energies and rate constants extracted from the MD data confirm this transition in mechanism and enable upscaling of these phenomena to higher length-scale models.

36 MATERIALS SCIENCE↗

From atomistic models to machine learning: Predictive design of nanocarbons under extreme conditions

The formation of technologically valuable nanocarbon structures under extreme conditions, such as those produced during high-explosive detonations, remains poorly understood but holds significant potential for the development of controlled synthesis pathways. While detonation shockwaves provide the high-pressure, high-temperature environment required for nanodiamond formation, subsequent cooling and decompression dictate whether the diamond phase is preserved or transformed into other nanocarbon structures. Here, in this study, we employ GPU-accelerated reactive molecular dynamics (ReaxFF) simulations to investigate the graphitization and structural remodeling of detonation nanodiamond under nonlinear quench and pressure-release trajectories. We further investigate how the initial nanodiamond morphology; cuboctahedral, octahedral, or hexagonal prism influences the resulting transformation products. Evolution of nanostructure, allotrope (via simulated x-ray diffraction), carbon hybridization, and ring statistics are tracked during a two-stage quench from 5000 K to 60 GPa. Rapid cooling combined with slow decompression optimizes cubic diamond retention, whereas slow cooling with rapid pressure release promotes surface-to-core graphitization, producing concentric sp 2 -hybridized layers and hollowed inner shells. Octahedral nanodiamonds evolve into carbon nano-onions, initially forming bucky diamonds that progressively transform into fully sp 2 -hybridized structures, while hexagonal prisms preferentially form parallel-stacked graphite layers resembling carbon dots. Transient hexagonal diamond (lonsdaleite) emerges as an interfacial phase, suggesting potential reversibility in the shock-induced graphite-to-diamond transformation pathway transformation route. To extend predictive capabilities, we trained machine learning (ML) regressors on over 10 5 node-hours of molecular dynamics (MD) trajectories. A multilayer perceptron (MLP) model reliably predicts the number of graphitized layers from temperature–pressure trajectories with a coefficient of determination (R 2 ) exceeding 0.90. This high predictive fidelity enables efficient, high-throughput mapping of the synthesis parameter space for optimized graphitization outcomes. Collectively, morphological control combined with optimized quench–decompression conditions promote the selective synthesis of nanocarbon allotropes. This work establishes a data-driven framework for the rational, a priori design of carbon nanomaterials for applications in energy storage, sensing, and biomedicine.

Detonation nanodiamond remodeling↗

Preliminary modeling of triply periodic minimal surface (TPMS) structures using RELAP5-3D

With the United States Department of Energy (DOE)’s goal of quadrupling the nation’s nuclear energy supply by 2050, and with the Advanced Fuels Campaign pushing for new types of advanced reactor fuels and geometries, the need has arisen for new nuclear fuel designs. One such design is to swap out current nuclear fuel geometries in exchange for another type of geometry, called a Triply Periodic Minimal Surface (TPMS). TPMSs are self-supporting, infinitely repeating lattices—attributes that lend themselves well to additive manufacturing. These surfaces also possess enhanced heat transfer properties thanks to their internal area changes and large surface-area-to-volume ratios. Their drawback, however, is an increased pressure drop. Given the small amount of correlations and data (Reynolds numbers in the 2,000–8,000 range), and the minimal amount of experience so far obtained by modeling TPMS structures using 1D systems codes such as the Reactor Excursion and Leak Analysis Program (RELAP5-3D), further research into this topic was needed. Using data from the University of Wisconsin - Madison (UW), curve fits were created for both a Heat Transfer Coefficient (HTC) correlation and a Darcy friction factor empirical coefficient correlation. The curves’ coefficients and multipliers were then output and utilized in RELAP5-3D models of two upcoming experiments—Flow Loop for INFLUX Pressure drop (FLIP) and Microreactor Agile Non-nuclear Experimental Test (MAGNET)—aimed at increasing the available data for Reynolds numbers to the 16,000–36,000 range for TPMS structures. The models were run under the conditions utilized by a Computational Fluid Dynamics (CFD) analysis performed by another group at Idaho National Laboratory. Only CFD pressure drop values were obtained from the FLIP test, and those values showed that the RELAP5-3D models had a lower rate of pressure increase in comparison to the CFD values. In addition, there seemed to be a vertical shift upward in the pressure drop for both models whenever the TPMS porosity decreased, and the RELAP5-3D models showed a higher vertical shift in comparison to the CFD values. The MAGNET results did not correspond to any CFD or experimental results against which they could be compared, so they were instead compared against the proposed CFD input conditions. These values were then compared with each other to make sure the model seemed to be performing as expected, paving the way for future tests that can be run for the purpose of further analyses and comparisons. The pressure drop increased with temperature and mass flow rate independently. The temperature change would decrease with increasing mass flow rate and temperature, which was just as we expected based on the fact that the lower viscosity and decreased density would result in higher friction and churning losses. The last metric that was assessed was the enthalpy flow change, which increased with increasing mass flow rate and decreasing temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Ammonia Synthesis under Ambient Conditions: Insights into Water–Nitrogen–Magnetite Interfaces

New routes for transforming nitrogen into ammonia at ambient conditions would be a milestone toward an energy efficient and economically attractive production route in comparison to the traditional Haber-Bosch process. Recently, the synthesis of ammonia from water and nitrogen at room temperature and atmospheric pressure has been reported to be catalyzed by Fe 3 O 4 at the air-water interface. By integrating ambient pressure X-ray photoelectron spectroscopy and ab initio molecular dynamics and free energy calculations, we investigate the underlying thermodynamic mechanisms governing ammonia and hydrazine formation at the water-Fe 3 O 4 -nanoparticle interface. Here, we find that, unlike pure Fe 3 O 4 where N 2 can only interact with a limited number of Fe sites, hydroxylated species introduce large and diverse adsorption geometries where N 2 can bind through either Fe sites or Fe-OH groups, each of which are capable of independently facilitating proton-coupled electron transfer.

Chandy, Sruthy K. [University of California, Berke↗

Irradiation-induced reactions at the CeO 2 /SiO 2 /Si interface

The influence of high-energy (1.6 MeV) Ar 2+ irradiation on the interfacial interaction between cerium oxide thin films (~15 nm) with a SiO 2 /Si substrate is investigated using transmission electron microscopy, ultrahigh vacuum x-ray photoelectron spectroscopy (XPS), and a carbon monoxide (CO) oxidation catalytic reaction using ambient pressure XPS. The combination of these methods allows probing the dynamics of vacancy generation and its relation to chemical interactions at the CeO 2 /SiO 2 /Si interface. The results suggest that irradiation causes amorphization of some portion of CeO 2 at the CeO 2 /SiO 2 /Si interface and creates oxygen vacancies due to the formation of Ce 2 O 3 at room temperature. The subsequent ultra-high-vacuum annealing of irradiated films increases the concentration of Ce 2 O 3 with the simultaneous growth of the SiO 2 layer. Interactions with CO molecules result in an additional reduction of cerium and promote the transition of Ce 2 O 3 to a silicate compound. Furthermore, thermal annealing of thin films exposed to oxygen or carbon monoxide shows that the silicate phase is highly stabile even at 450 °C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polyamorphism in a solute-lean Al–Ce metallic glass

Polyamorphism discovered in lanthanide-rich metallic glasses (MGs) has been attributed to the electronic transition of the lanthanide element as a solvent element. In this work, we report that pressure-induced polyamorphism still exists in a Ce-poor Al 93 Ce 7 binary MG where the 4f electron element serves as a solute and solute–solute avoidance is expected. The polyamorphic transition, observed by in situ high-pressure synchrotron x-ray diffraction, is accompanied by a volume collapse of ~0.78% and occurs over a narrow pressure range from ~0.8 to ~1.8 GPa. Further synchrotron Ce L 3 -edge x-ray absorption spectroscopy measurements reveal that pressure-induced 4f electron delocalization underlies the polyamorphic transition. Molecular dynamics simulations confirm that the Ce atoms in the MG are completely isolated by the solvent Al atoms. This result demonstrates that 4f element-bearing alloys with extremely dilute concentrations can also exhibit polyamorphic states originating from electronic transitions, extending the compositional space of polyamorphism of MGs into very dilute regions. Our work suggests that tunable properties under compressive stress could be achieved in MGs by even minor doping of elements prone to electronic transitions.

36 MATERIALS SCIENCE↗

Phase transitions and dimensional cross-over in layered confined solids

The nature of solid phases and cross-over of order–disorder phase transitions from two-dimensional (2D) layers to three-dimensional (3D) bulk in confined atomic systems remain largely unexplained. To this end, we consider noble gases and aluminum confined between graphene sheets at different pressures and temperatures. Using crystal structure search methods and molecular dynamics based on machine-learned potentials with quantum-mechanical accuracy, we identify structures of multilayer confined solids that deviate from simple close packing. Upon heating, we find that confined 2D monolayers melt according to the two-step continuous Kosterlitz–Thouless–Halperin–Nelson–Young theory. However, multilayer solids transition continuously into an intermediate layered-hexatic phase before melting discontinuously into an isotropic liquid. This intermediate phase persists at least up to 12 layers studied here. This change can be qualitatively understood based on the cross-over from 2D topological defects toward 3D ones during melting as the number of layers increases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonsuperconducting electronic ground state in pressurized BaFe 2 S 3 and BaFe 2 S 2.5 Se 0.5

In this work, we report a comprehensive study of the spin ladder compound BaFe 2 S 2.5 Se 0.5 using neutron diffraction, inelastic neutron scattering, high pressure synchrotron diffraction, and high pressure transport techniques. We find that BaFe 2 S 2.5 Se 0.5 possesses the same C m c m structure and stripe antiferromagnetic order as does BaFe 2 S 3 , but with a reduced Néel temperature of T N = 98 K compared to 120 K for the undoped system, and a slightly increased ordered moment of 1.40 μ B per iron. Additionally, the low-energy spin excitations in BaFe 2 S 2.5 Se 0.5 are likewise similar to those observed in BaFe 2 S 3 . However, unlike the reports of superconductivity in BaFe 2 S 3 below T c ~ 14 K under pressures of 10 GPa or more, we observe no superconductivity in BaFe 2 S 2.5 Se 0.5 at any pressure up to 19.7 GPa. In contrast, the resistivity exhibits an upturn at low temperature under pressure. Furthermore, we show that additional high-quality samples of BaFe 2 S 3 synthesized for this study likewise fail to become superconducting under pressure, instead displaying a similar upturn in resistivity at low temperature. These results demonstrate that microscopic, sample-specific details play an important role in determining the ultimate electronic ground state in this spin ladder system. We suggest that the upturn in resistivity at low temperature in both BaFe 2 S 3 and BaFe 2 S 2.5 Se 0.5 may result from Anderson localization induced by S vacancies and random Se substitutions, enhanced by the quasi-one-dimensional ladder structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Improved modeling of the solid-to-plasma transition of polystyrene ablator for laser direct-drive inertial confinement fusion hydrocodes

We report that the target performance of laser direct-drive inertial confinement fusion (ICF) can be limited by the development of hydrodynamic instabilities resulting from the nonhomegeneous laser absorption at the target surface, i.e., the laser imprint on the ablator. To understand and describe the formation of these instabilities, the early ablator evolution during the laser irradiation should be considered. In this work, an improved modeling of the solid-to-plasma transition of a polystyrene ablator for laser direct-drive ICF is proposed. This model is devoted to be implemented in hydrocodes dedicated to ICF which generally assume an initial plasma state. The present approach consists of the two-temperature model coupled to the electron, ion and neutral dynamics including the chemical fragmentation of polystyrene. The solid-to-plasma transition is shown to significantly influence the temporal evolution of both free electron density and temperatures, which can lead to different shock formation and propagation compared with an initial plasma state. The influence of the solid-to-plasma transition on the shock dynamics is evidenced by considering the scaling law of the pressure with respect to the laser intensity. The ablator transition is shown to modify the scaling law exponent compared with an initial plasma state.

36 MATERIALS SCIENCE↗

Nucleation of Dislocations in 3.9 nm Nanocrystals at High Pressure

As circuitry approaches single nanometer length scales, it has become important to predict the stability of single nanometer-sized metals. The behavior of metals at larger scales can be predicted based on the behavior of dislocations, but it is unclear if dislocations can form and be sustained at single nanometer dimensions. Here, we report the formation of dislocations within individual 3.9 nm Au nanocrystals under nonhydrostatic pressure in a diamond anvil cell. We used a combination of x-ray diffraction, optical absorbance spectroscopy, and molecular dynamics simulation to characterize the defects that are formed, which were found to be surface-nucleated partial dislocations. These results indicate that dislocations are still active at single nanometer length scales and can lead to permanent plasticity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗