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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Understanding Electrochemical Reaction Mechanisms of Sulfur in All‐Solid‐State Batteries through Operando and Theoretical Studies **

Abstract Due to its outstanding safety and high energy density, all‐solid‐state lithium‐sulfur batteries (ASLSBs) are considered as a potential future energy storage technology. The electrochemical reaction pathway in ASLSBs with inorganic solid‐state electrolytes is different from Li‐S batteries with liquid electrolytes, but the mechanism remains unclear. By combining operando Raman spectroscopy and ex situ X‐ray absorption spectroscopy, we investigated the reaction mechanism of sulfur (S 8 ) in ASLSBs. Our results revealed that no Li 2 S 8, Li 2 S 6, and Li 2 S 4 were formed, yet Li 2 S 2 was detected. Furthermore, first‐principles structural calculations were employed to disclose the formation energy of solid state Li 2 S n (1≤ n ≤8), in which Li 2 S 2 was a metastable phase, consistent with experimental observations. Meanwhile, partial S 8 and Li 2 S 2 remained at the full lithiation stage, suggesting incomplete reaction due to sluggish reaction kinetics in ASLSBs.

25 ENERGY STORAGE↗
DOE OSTI2019

Effects of crystallization on mechanical behavior and corrosion performance of a ductile Zr 68 Al 8 Ni8Cu 16 bulk metallic glass

Here, we studied the effects of heat treatment on the microstructures, crystallization kinetics, mechanical performance, and anti-corrosion behavior of a hypoeutectic Zr 68 Al 8 Ni 8 Cu 16 bulk metallic glass (BMG). Through annealing, the precipitated phases were crystalline Zr 2 Cu and Zr 2 Ni. The total crystallinity was determined to be 10% and 77% for the samples annealed at 673 K and 713 K, respectively. The partial crystallization of the alloy leads to a dramatic deterioration in the ductility as compared to the as-cast BMG. Furthermore, the decrease in the ductility was accompanied by an increase in the crystallinity. The as-cast Zr-based BMG exhibited a greater corrosion resistance in the HCl solution than that of the annealed alloy. The depletion in the Zr and Al cation fractions of the surface oxidation film, which resulted from the precipitation of reactive nanocrystalline phases from the glassy matrix, is responsible for the reduced corrosion resistance.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Role of shell composition and morphology in achieving single-emitter photostability for green-emitting “giant” quantum dots

The use of the varied chemical reactivity of precursors to drive the production of a desired nanocrystal architecture has become a common method to grow thick-shell graded alloy quantum dots (QDs) with robust optical properties. Conclusions on their behavior assume the ideal chemical gradation and uniform particle composition. In this work, advanced analytical electron microscopy (high-resolution scanning transmission electron microscopy coupled with energy dispersive spectroscopy) is used to confirm the nature and extent of compositional gradation and these data are compared with performance behavior obtained from single-nanocrystal spectroscopy to elucidate structure, chemical-composition, and optical-property correlations. In particular, the evolution of the chemical structure and single-nanocrystal luminescence was determined for a time-series of graded-alloy “CdZnSSe/ZnS” core/shell QDs prepared in a single-pot reaction. In a separate step, thick (~6 monolayers) to giant (>14 monolayers) shells of ZnS were added to the alloyed QDs via a successive ionic layer adsorption and reaction (SILAR) process, and the impact of this shell on the optical performance was also assessed. By determining the degree of alloying for each component element on a per-particle basis, we observe that the actual product from the single-pot reaction is less “graded” in Cd and more so in Se than anticipated, with Se extending throughout the structure. The latter suggests much slower Se reaction kinetics than expected or an ability of Se to diffuse away from the initially nucleated core. It was also found that the subsequent growth of thick phase-pure ZnS shells by the SILAR method was required to significantly reduce blinking and photobleaching. However, correlated single-nanocrystal optical characterization and electron microscopy further revealed that these beneficial properties are only achieved if the thick ZnS shell is complete and without large lattice discontinuities. Thus, we identify the necessary structural design features that are required for ideal light emission properties in these green-visible emitting QDs.

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

Solar neutrino measurements using the full data period of Super-Kamiokande-IV

An analysis of solar neutrino data from the fourth phase of Super-Kamiokande (SK-IV) from October 2008 to May 2018 is performed and the results are presented. The observation time of the dataset of SK-IV corresponds to 2970 days and the total live time for all four phases is 5805 days. For more precise solar neutrino measurements, several improvements are applied in this analysis: lowering the data acquisition threshold in May 2015, further reduction of the spallation background using neutron clustering events, precise energy reconstruction considering the time variation of the PMT gain. The observed number of solar neutrino events in 3.49–19.49 MeV electron kinetic energy region during SK-IV is 65,443 − 388 + 390 ( stat . ) ± 925 ( syst . ) events. Corresponding B 8 solar neutrino flux is ( 2.314 ± 0.014 ( stat . ) ± 0.040 ( syst . ) ) × 10 6 cm − 2 s − 1 , assuming a pure electron-neutrino flavor component without neutrino oscillations. The flux combined with all SK phases up to SK-IV is ( 2.336 ± 0.011 ( stat . ) ± 0.043 ( syst . ) ) × 10 6 cm − 2 s − 1 . Based on the neutrino oscillation analysis from all solar experiments, including the SK 5805 days dataset, the best-fit neutrino oscillation parameters are sin 2 θ 12 , solar = 0.306 ± 0.013 and Δ m 21 , solar 2 = ( 6.1 0 − 0.81 + 0.95 ) × 10 − 5 eV 2 , with a deviation of about 1.5 σ from the Δ m 21 2 parameter obtained by KamLAND. The best-fit neutrino oscillation parameters obtained from all solar experiments and KamLAND are sin 2 θ 12 , global = 0.307 ± 0.012 and Δ m 21 , global 2 = ( 7.5 0 − 0.18 + 0.19 ) × 10 − 5 eV 2 . Published by the American Physical Society 2024

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Kinetic model describing self-limiting CO 2 diffusion in supported amine adsorbents

A reaction–diffusion shrinking core model describing the decay in diffusivity of supported amine sorbents upon CO 2 sorption under both simulated direct air capture and point source capture conditions is described. The decay in CO 2 diffusivity is associated with crosslinking in the aminopolymer samples and general pore blockage in the amino-silane derived samples, which occurs as CO 2 is adsorbed. The model is used to extract four kinetic parameters that govern the CO 2 uptake kinetics and working capacity: an apparent reaction rate constant, an initial effective diffusivity, and two dimensionless decay parameters. Ideally, an initially reaction limited system would allow for direct determination of the intrinsic reaction rate constant; however, sorption experiments suggest mass transfer resistances related to gas mixing, external boundary layers and intraparticle diffusion are present. Reaction rate constants are determined and agree well with theoretical values predicted with the Eyring equation parameterized using density functional theory energies from literature sources. The kinetic performance is expressed as the average effective diffusivity as a function of average conversion, which can be correlated to the dispersion of sorption sites on the support and the morphology of the active sorbent phase. Four supports are impregnated or grafted with amines, SBA-15, single-walled zeolite nanotubes (ZNT), Syloid SiO 2 , and γ-Al 2 O 3 . Due to its pore structure, γ-Al 2 O 3 supported amines can be modeled at the μm scale or at the nm scale, where the shell balance is on the μm-sized macroporous particle aggregate or on the nm-sized amine film on the surface of the Al 2 O 3 nanoparticles, which comprise the spherical particle aggregates. Faster diffusion rates are maintained under 400 ppm rather than 10% CO 2 due to a slower reaction rate giving a slower decay in diffusivity. In conclusion, this work provides a first principles kinetic analysis of CO 2 sorption where previous models are semi-empirical and use arbitrary kinetic parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Kinetic Modeling of Secondary Organic Aerosol in a Weather-Chemistry Model: Parameterizations, Processes, and Predictions for GOAmazon

Secondary organic aerosol (SOA) forms and evolves in the atmosphere through many pathways and processes, over diverse spatial and time scales. Hence, there is a need to represent these widely-varying kinetic processes in large-scale atmospheric models to allow for accurate predictions of the abundance, properties, and impacts of SOA. In this work, we integrated a kinetic, process-level model (simpleSOM-MOSAIC) into a weather-chemistry model (WRF-Chem) to simulate the oxidation chemistry and microphysics of atmospheric SOA. simpleSOM-MOSAIC simulates multigenerational gas-phase chemistry, autoxidation reactions, heterogeneous oxidation, oligomerization, and phase-state-influenced gas/particle partitioning of SOA. As a case study, the integrated WRF-Chem-simpleSOM-MOSAIC (WC-SSM) model was used to simulate the photochemical evolution downwind of a large city (Manaus, Brazil) in the Amazon and, in turn, study the anthropogenic and biogenic interactions in an otherwise pristine environment. Consistent with previous work, we found that OA was enhanced by up to a factor of four in the urban plume due to elevated hydroxyl radical (OH) concentrations, relative to the background, and that this OA was dominated by SOA from biogenic precursors (80%). Further, in addition to accurately simulating the OA enhancement in the urban plume, the model reproduced the magnitude of the OA oxygen-to-carbon (O:C) ratio and broadly tracked the evolution of the aerosol size distribution. Our work highlights the importance of including an integrated, kinetic representation of SOA processes in an atmospheric model

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Magnetic and singlet phases in the three-dimensional periodic Anderson Model

Heavy-fermion materials are compounds in which localized f orbitals hybridize with delocalized d ones, leading to quasiparticles with large renormalized masses. The presence of strongly correlated f electrons at the Fermi level may also lead to long-range order, such as magnetism, or unconventional superconductivity. From a theoretical point of view, the “standard model” for heavy-fermion compounds is the periodic Anderson model (PAM). Despite being extensively scrutinized, its thermodynamic properties in three-dimensional (3D) lattices have not been carefully addressed by unbiased methodologies. Here we investigate the 3D PAM employing state-of-the-art finite-temperature auxiliary-field quantum Monte Carlo simulations. Furthermore, we present the behavior of the kinetic energy, the entropy, the specific heat, and the double occupancy as functions of the temperature and the hybridization strength. From these quantities, and by the analysis of the spin-spin correlation functions, we investigate the occurrence of magnetic phase transitions at finite temperatures, and we determine the phase diagram of the model, including the behavior of the Néel temperature as a function of the external parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Alkali-silica reaction products and cracks: X-ray micro-tomography-based analysis of their spatial-temporal evolution at a mesoscale

In this study, we propose a laboratory-scale methodology, based on X-ray micro-tomography and caesium (Cs) as a contrast agent, to advance the understanding of cracking due to alkali-silica reaction (ASR) in concrete. The methodology allows achieving a completely non-destructive and time-lapse characterization of the spatial-temporal patterns of both the cracks and the ASR products. While Cs addition slightly accelerated the ASR kinetics, the crack patterns, with and without Cs addition, were statistically equivalent. Cracks with ASR products appeared first in the aggregates, close to the interface with the cement paste. They propagated afterwards towards the aggregates interior. Some products were then extruded for several mm into air voids and cracks in the cement paste. This process suggests that, in the early stage, the ASR products may be a low-viscosity gel that can flow away from the source aggregate and may settle later elsewhere as a rigid phase, upon calcium uptake.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Kinetics and evolution of solid-state metal dealloying in thin films with multimodal analysis

Thin-film solid-state metal dealloying (thin-film SSMD) is an emerging technique that uses self-organization to design nanostructured thin films. The resulting 3D bicontinuous nanostructures are promising for a wide range of applications, such as catalysis and energy storage. In this work, we prepared thin films by SSMD using Ti-Cu as the parent alloy and Mg as the solvent. Using a multimodal approach, we combined synchrotron X-ray spectroscopy, diffraction, and high-resolution electron-based spectroscopy and imaging to study their morphological, structural, and chemical evolution. The processing-structure relationship was analyzed as a function of parent alloy composition and dealloying temperature and time. Morphological transitions from globular, to lamellar, to bicontinuous structures, in conjunction with a ligament size evolution, were identified as functions of the parent alloy composition. The dealloying rate increased with increasing concentration of interdiffusing elements (dissolving component) in the parent alloy. The parting limit, a dealloying compositional threshold, was systematically analyzed and determined to be 30%–40%. The order of crystalline phase formation is CuMg 2 , Cu 2 Mg, and Ti; the Ti phase first shows self-reorganization during dealloying, separate from the crystallization process. The coarsening in thin-film SSMD was identified and not entirely self-similar; in addition to the increase of ligament size over time, the formation of larger globular ligaments were also observed. This work furthers our fundamental understanding of thin-film SSMD and nanostructured thin-film design, where the thermodynamic and kinetic effects differ from the bulk counterparts. The fact that dealloying and diffusion outpaces the crystallization and new phase formation also offers opportunities to utilize thin-film SSMD in certain alloy systems in which deleterious intermetallic phases need to be suppressed, that may not be possible in the bulk geometry.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Spin alignment of vector mesons by glasma fields

We explain how spin alignment of vector mesons can be induced by background fields, such as electromagnetic fields or soft gluon fields. Our study is based on the quantum kinetic theory of spinning quarks and antiquarks and incorporates the relaxation of the dynamically generated spin polarization. The spin density matrix of vector mesons is obtained by quark coalescence via the Wigner function and kinetic equation. Our approach predicts a local spin correlation that is distinct from the nonlocal expressions previously obtained in phenomenological derivations. We estimate the magnitude of such local correlations in the glasma model of the preequilibrium phase of relativistic heavy ion collisions. It is found that the resulting spin alignment could be greatly enhanced and may be comparable to the experimental measurement in order of magnitude. We further propose new phenomenological scenarios to qualitatively explain the transverse-momentum and centrality dependence of spin alignment in a self-consistent framework.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Kinetics of Shear-Induced Structural Ordering in Dense Colloids

The macroscopic rheological response of a colloidal solution is highly correlated with the local microscopic structure, as revealed by an in situ Rheo-SAXS experiment with a high temporal resolution. Oscillatory shear can induce a strain-controlled ordering-to-disorder transition, resulting in a shear-thickening process that is different from the normal shear-thickening behavior that is driven by hydrodynamics and particle friction. Here, we reveal that there is a complex time-dependent kinetics toward structural ordering under different applied strains. When the strain amplitude reaches a critical value that starts to induce disordering in the system, the pathway toward the dynamic equilibrium can also become highly non-monotonic. Within the same oscillatory cycle, there is a strong correlation of ordering with different phases of the oscillation, with the system oscillating between two dynamic metastable states.

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

A Nanoscale Ternary Amide‐rGO Composite with Boosted Kinetics for Reversible H 2 Storage

Abstract Metal amides are attractive candidates for hydrogen storage due to their high volumetric and gravimetric hydrogen densities. However, the sluggish kinetics and competing side reactions during hydrogen uptake and release limit their practical use. Here, a novel nanoconfined Li 2 Mg(NH) 2 @reduced graphene oxide (rGO) composite is presented, which is fabricated using a melt‐infiltration method with a minimum weight penalty of only 2 wt.%. The presence of rGO ensures close contact between the active phases, effectively preventing aggregation during cycling process. As a result, the reversible capacity of Li 2 Mg(NH) 2 @rGO reaches 4.42 wt.%, with no capacity degradation observed after multiple cycling. Theoretical calculations show that rGO catalyzes the hydrogen bond cleavage at the Mg‐amide/Li hydride interface, leading to local dehydrogenation hotspots and significantly improves kinetics of dehydrogenation compared to the bulk counterpart. This study provides a promising strategy for designing metal imide‐based composites to overcome the kinetic limitations and improve their reversible hydrogen storage performance.

08 HYDROGEN↗
DOE OSTI2022

Effects of oxygen on the adsorption/oxidation of aqueous Sb(III) by Fe-loaded biochar: An X-ray absorption spectroscopy study

Fe-loaded biochar (FeBC) has been considered for Sb(III) adsorption, but the effects of oxygen (O 2 ) on the adsorption need further investigation. Liquid-/solid-phase analyses were conducted to investigate the role of O 2 in the Sb(III) adsorption by FeBC. The adsorption was best described by the pseudo-second-order (PSO) model for kinetic results and by the Langmuir model for thermodynamic results. More than 96.8 % of Sb(III) was adsorbed by FeBC, and available O 2 increased the liquid-phase Sb(III) oxidation efficiency by 2.1–7.5 times. The peak changes at ~1640 and 3450 cm -1 in FTIR spectra indicated the occurrence of inner-sphere complexation between Sb(III)/Sb(V) and hydroxyl (–OH)/carboxyl (–COOH) groups in FeBC under aerobic and anaerobic conditions. Fe/Sb X-ray absorption spectroscopy (XAS) analysis results showed aqueous Sb(III) complexed to the edge-sharing Fe(III)-O-Fe(III) in FeBC. Regardless of whether O 2 was available or not, solid-phase edge-sharing Fe(III)-O-Sb(V) complexes (~3.05 Å), which had lower toxicity and migration ability than aqueous Sb(III), formed through a ligand-to-metal charge-transfer (LMCT) process. More than 91 % of adsorbed Sb(III) was oxidized to edge-sharing Fe(III)-O-Sb(V) complexes in 3 h. Additionally, the Sb(V) from liquid-phase oxidation could also directly complex to the Fe(III)-O-Fe(III) and form edge-sharing Fe(III)-O-Sb(V) complexes. Here these results provide evidence to inform further FeBC application for the Sb-contaminated water treatment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Efficient Low-Temperature Direct Lithium Extraction from Chloride Brines Enabled by High-Capacity Sorbent

The demand for lithium, a key component in rechargeable batteries for electric vehicles and renewable energy storage systems, has surged in recent years. Meeting this demand requires efficient extraction methods that are both environmentally friendly and economically viable. This study investigates the utilization of the high-capacity sorbent amorphous aluminum hydroxide for enabling efficient direct lithium extraction at low temperatures. Traditional extraction methods often involve acid-leaching and energy-intensive processes that are not only expensive but also environmentally taxing. In contrast, our approach leverages the exceptional sorption properties of amorphous aluminum hydroxide to facilitate lithium extraction directly from brine, achieving extraction efficiencies of 94.4% in case 1 and 96.2% in case 2 at low temperatures. Kinetic modeling using the Avrami–Erofe’ev framework reveals a nucleation-growth mechanism ( n = 0.71, k = 0.131 h –1 ), providing quantitative insights into the solid-state phase transformation process. This method significantly reduces energy consumption and minimizes the environmental footprint. Through systematic experimentation and optimization, we demonstrate the effectiveness and scalability of our approach, highlighting its potential to revolutionize lithium extraction processes. Our findings highlight the potential of high-capacity sorbents, particularly amorphous aluminum hydroxide toward sustainable lithium production, contributing to the advancement of clean-energy technologies.

anions↗
DOE OSTI2021

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s -1 , agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Mathematical Modeling of Hydroxide-Exchange-Membrane Water Electrolyzer

Water electrolyzers can transform intermittent renewable energy like solar energy and wind energy into the chemical energy of hydrogen with zero greenhouse-gas emissions. The hydroxide-exchange membrane electrolyzer (HEME) combines the capability to produce pressurized hydrogen with the advantage of being able to use low or non-platinum group metal (PGM) electrocatalysts in the alkaline environment.1 Hydroxide salts, for example, KOH, are added to the HEME water feed on both anode and cathode to improve its performance. However, the specific mechanism of performance improvement still needs to be further understood. In addition, at high current densities, bubble evolution can result in mass-transport limitations, a less well studied phenomena. Mathematical modeling is ideal to explore these issues as it is cost and time efficient and can deconvolute the physics, processes, and observed phenomena and study the applied-voltage breakdown. In this work, we extend our previously developed 1D two-phase continuum model2 to study the varies processes in the HEME and provide insights on performance optimizations. First, the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER) kinetics at different hydroxide concentrations have been studied by rotating disk electrodes (RDE) and implemented in the model. Then, the model is calibrated and validated against experimental HEME polarization curves for different KOH concentrations as a liquid electrolyte. The model clearly shows a performance increase with increasing KOH concentrations, which is consistent with the experimental results. The reduced ohmic resistance and increased electrochemical active surface area (ECSA) are the two main reasons for performance increase. The large amount of hydroxide in the liquid electrolyte not only helps to distribute the reactant hydroxide throughout the catalyst layer (CL), which reduces ohmic loss, but also enables reaction at the interface between the liquid electrolyte and electrocatalyst, which increases the ECSA. Applied-voltage breakdown demonstrates that the electrolyzer performance is dominated by anode kinetics and ohmic loss. A comparison with the DI water feed shows a more uniform current distribution in the anode CL when KOH is added, which indicates a higher utilization of the CL. Second, we present modeling on the effects of bubble coverage. As gas evolves, part of the ECSA is minimized due to bubble coverage. To account for this effect, an empirical relationship between the fractional bubble coverage and the current density is implemented in the model.3 The model shows this bubble coverage effect is more pronounced at large current densities with DI water feed. Acknowledgements This work was funded under the HydroGEN Consortium by the Energy Efficiency and Renewable Energy, Hydrogen and Fuel Cell Technologies Office, of the U. S. Department of Energy under contract number DE-AC02-05CH11231. References R. Abbasi, B. P. Setzler, S. Lin, J. Wang, Y. Zhao, H. Xu, B. Pivovar, B. Tian, X. Chen, G. Wu and Y. Yan, 31, 1805876 (2019). L. N. Stanislaw, M. R. Gerhardt and A. Z. Weber, ECS Transactions, 92, 767 (2019). H. Vogt and R. J. Balzer, Electrochimica Acta, 50, 2073 (2005).

Liu, Jiangjin↗
DOE OSTI2024

Microwave and rf Spectroscopy of 2D Carrier Systems and Bilayers (Final Technical Report)

We performed microwave spectroscopic studies of two dimensional electron systems (2DES) exhibiting the quantum Hall effect (QHE) in GaAs/Al${_x}$Ga$_{1-x}$As heterostructures. A common theme of the proposed work is electron solids, of which the simplest is the Wigner crystal, a triangular lattice of individual carriers. The solids are stabilized by carrier-carrier interaction and occur under conditions when the kinetic energy of the system is "frozen out" by high magnetic field, $B$. One of the main reasons for microwave spectroscopic study of 2DES is that the solid phases have striking microwave or rf spectra. In the low wave vector ($q$) limit these spectra exhibit a resonance that is understood as a pinning mode, a small collective oscillation of pieces of the solid within the disorder potential. Pinning modes can be very sharp, with quality factors up to around 30, and are valuable as signatures of the electron solids, and can reveal a solid even when standard dc transport shows an insulator, an integer QHE, or even a fractional QHE The pinning mode also is sensitive to the solid properties, and can reveal transitions between solids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗