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DOE OSTI2021

Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory

This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO 2 in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. Therefore, the first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO 2 is the C–C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO2 model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Feebly-interacting particles: FIPs 2020 workshop report

With the establishment and maturation of the experimental programs searching for new physics with sizeable couplings at the LHC, there is an increasing interest in the broader particle and astrophysics community for exploring the physics of light and feebly-interacting particles as a paradigm complementary to a New Physics sector at the TeV scale and beyond. FIPs 2020 has been the first workshop fully dedicated to the physics of feebly-interacting particles and was held virtually from 31 August to 4 September 2020. The workshop has gathered together experts from collider, beam dump, fixed target experiments, as well as from astrophysics, axions/ALPs searches, current/future neutrino experiments, and dark matter direct detection communities to discuss progress in experimental searches and underlying theory models for FIPs physics, and to enhance the cross-fertilisation across different fields. FIPs 2020 has been complemented by the topical workshop “Physics Beyond Colliders meets theory”, held at CERN from 7 June to 9 June 2020. This document presents the summary of the talks presented at the workshops and the outcome of the subsequent discussions held immediately after. It aims to provide a clear picture of this blooming field and proposes a few recommendations for the next round of experimental results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Spin dynamics of the antiferromagnetic Heisenberg model on a kagome bilayer

We research the spin dynamics of a classical Heisenberg antiferromagnet with nearest-neighbor interactions on a quasi-two-dimensional kagome bilayer. This geometrically frustrated lattice consists of two kagome layers connected by a triangular-lattice linking layer. By combining Monte Carlo with precessional spin dynamics simulations, we compute the dynamical structure factor of the classical spin liquid in the kagome bilayer and investigate the thermal and dilution effects. While the low-frequency and long-wavelength dynamics of the cooperative paramagnetic phase is dominated by spin diffusion, weak magnon excitations persist at higher energies, giving rise to the half-moon pattern in the dynamical structure factor. In the presence of spin vacancies, the dynamical properties of the diluted system can be understood within the two-population picture. The spin diffusion of the “correlated” spin clusters is mainly driven by the zero-energy weather-vane modes, giving rise to an autocorrelation function that decays exponentially with time. On the other hand, the diffusive dynamics of the quasifree “orphan” spins leads to a distinctive longer-time power-law tail in the autocorrelation function. We discuss the implications of our work for the glassy behaviors observed in the archetypal frustrated magnet SrCr 9p Ga 12-9 pO 19 (SCGO).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Validating a Dynamic PWR Safety and Security Model?

Nuclear power plants (NPPs) are assessed for safety and security using separate models that cannot capture how an attacker's decisions and a plant's response unfold together in real time, leaving regulators and operators without a complete picture of true plant vulnerability. Traditional probabilistic risk assessment (PRA) methods treat adversarial events as fixed initiators with predetermined outcomes, and are structurally incapable of representing the time-dependent interplay between physical security events, safety system response, and operator mitigative actions. At Idaho National Laboratory (INL), I contributed to the development and validation of Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF). Where static PRA relies on event-tree logic that cannot evolve mid-scenario, MASS-DEF couples a time-dependent dynamic PRA tool EMRALD (Event Modeling Risk Assessment using Linked Diagrams) with attack simulation software, allowing attacker behavior, plant system states, and operator actions to interact across time. My work focused on validating a general Pressurized Water Reactor (PWR) model. I traced model logic against PWR plant to identified errors in logic and confirm accuracy. I then built and tested attack scenarios against a general PWR model to verify that the model produced expected outcomes across all logical pathways. I also contributed a section to a related technical paper applying the same EMRALD platform to radiation dose modeling. Results show that MASS-DEF can quantitatively demonstrate that many plants exceed their regulatory security thresholds. This demonstrated margin provides a technically defensible basis for reducing the number of guards without compromising regulatory compliance. Physical security costs represent roughly 10% of annual operating budgets, making such reductions directly meaningful to INL's mission of sustaining existing commercial NPPs. This internship strengthened my understanding of nuclear systems, probabilistic modeling, and technical writing, and has solidified my pursuit of a career at a national laboratory.

98 - NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL↗

DOE OSTI2026

Mechanistic insight into the effects of A-site doping in perovskite nanorods on interfacial Li-ion and Na-ion transport in polymer–perovskite composite electrolytes

Composite polymer electrolytes (CPEs) offer a promising pathway to safer and higher energy density electrochemical energy storage yet optimizing interfacial ion transport remains a critical challenge due to high resistances and a lack of understanding of the complex interfacial electrostatic interactions. This work investigates the mechanistic origins of the interfacial ion transport enhancement in single-ion conducting (SIC) polymer electrolytes filled with A-site disordered perovskite LaxMyTiOz (LMTO) (M = Li, Na, K) nanorods. By integrating Density Functional Theory (DFT) with broadband dielectric spectroscopy (BDS) and pulsed-field-gradient NMR (PFG-NMR), we analyze the ion transport behavior in Li-based and Na-based SIC systems containing compositionally distinct LMTO fillers (LMTO800 and LMTO900). Specifically, we introduce the site-to-site energy difference (ΔE) descriptor, which extends beyond single-site descriptors such as adsorption energy and ion binding energies. We demonstrate that ΔE together with ion binding energies provide a more comprehensive picture of the energy landscape at the polymer–ceramic interface. The combined DFT and experimental results show that A-site doping in the ceramic filler can effectively modulate ΔE and ion binding energies, creating a favorable potential energy landscape that promotes enhanced ion transport along the interface. This comprehensive study illustrates the impact of ceramic compositional tuning on interfacial ion transport and provides materials design rules towards real-world applications.

B shepard, Lauren [Pennsylvania State University]↗

NASA NTRS1984

A consistent picture of coronal and chromospheric processes in a well-observed solar flare

The solar flare of 15:22 UT on June 24, 1980 is analyzed using simultaneous observations in hard X-rays, soft X-rays, and H-alpha line profiles obtained from instruments aboard the Solar Maximum Mission and ground-based instruments. The theoretical H-alpha profiles of Canfield, Gunkler, and Ricchiazzi (1984) are used to analyze the H-alpha data, and the work of Hummer and Rybicki (1968) is used to provide qualitative velocity information. The soft X-ray data are employed to obtain coronal measurements of parameters of interest, while the flux and spectrum of the hard X-rays are used to calculate the peak power of nonthermal electrons. Various flare phenomena are studied, including heating of the chromosphere by nonthermal electrons, enhanced coronal pressure, enhanced thermal conduction, chromospheric evaporation and mass motion. It is shown that the observations strongly suggest a scenario in which two large magnetic loop systems interact to provide the flare energy.

Gunkler, T. A.↗

NASA NTRS1998

Droplet Combustion Experiment

Liquid fuel combustion provides a major portion of the world's energy supply. In most practical combustion devices, liquid burns after being separated into a droplet spray. Essential to the design of efficient combustion systems is a knowledge of droplet combustion behavior. The microgravity environment aboard spacecraft provides an opportunity to investigate the complex interactions between the physical and chemical combustion processes involved in droplet combustion without the complications of natural buoyancy. Launched on STS-83 and STS-94 (April 4 and July 1, 1997), the Droplet Combustion Experiment (DCE) investigated the fundamentals of droplet combustion under a range of pressures (0.25 to 1 atm), oxygen mole fractions (<0.5), and droplet sizes (1.5 to 5 mm). Principal DCE flight hardware features were a chamber to supply selected test environments, the use of crew-inserted bottles, and a vent system to remove unwanted gaseous combustion products. The internal apparatus contained the droplet deployment and ignition mechanisms to burn single, freely deployed droplets in microgravity. Diagnostics systems included a 35-mm high-speed motion picture camera (see the following sequence of photos) with a backlight to photograph burning droplets and a camcorder to monitor experiment operations. Additional diagnostics included an ultraviolet-light-sensitive CCD (charge couple discharge) camera to obtain flame radiation from hydroxyl radicals (see the final figure) and a 35-mm SLR (single-lens-reflex) camera to obtain color still photographs of the flames.

Nayagam, Vedha↗

DOE OSTI2026

SALSAA: a statistical approach to line shapes from an average atom

Ion-Stark line broadening is a key density diagnostic for hot dense plasmas relevant to inertial fusion and astrophysics. It is caused by interactions of a radiating ion with nearby perturbing ions, whose electric microfields lead to changes in bound-bound transition energies. Ion-Stark broadening becomes increasingly difficult to compute for complex, many-electron ions with myriad transitions. In this paper, we propose a simplified approach to ion-Stark broadening based on self-consistent ion distributions and electronic structure from an average-atom model. We find that this approach reproduces the line shape predictions of one traditional method for high-n K-shell emission lines in aluminum ions with accuracy sufficient for density diagnostics in thermal plasmas with equal ion and electron temperatures. We expect that this approach can be extended to provide a reasonable picture of ion-Stark broadening in many-electron ions, enabling rapid calculations of line profiles in complex spectra.

average-atom↗

NASA NTRS2004

Arctic Strato-Mesospheric Temperature and Wind Variations

Upper stratosphere and mesosphere rocket measurements are actively used to investigate interaction between the neutral, electrical, and chemical atmospheres and between lower and upper layers of these regions. Satellite temperature measurements from HALOE and from inflatable falling spheres complement each other and allow illustrations of the annual cycle to 85 km altitude. Falling sphere wind and temperature measurements reveal variability that differs as a function of altitude, location, and time. We discuss the state of the Arctic atmosphere during the summer 2002 (Andoya, Norway) and winter 2003 (ESRANGE, Sweden) campaigns of MaCWAVE. Balloon-borne profiles to 30 km altitude and sphere profiles between 50 and 90 km show unique small-scale structure. Nonetheless, there are practical implications that additional measurements are very much needed to complete the full vertical profile picture. Our discussion concentrates on the distribution of temperature and wind and their variability. However, reliable measurements from other high latitude NASA programs over a number of years are available to help properly calculate mean values and the distribution of the individual measurements. Since the available rocket data in the Arctic's upper atmosphere are sparse the results we present are basically a snapshot of atmospheric structure.

Schmidlin, F. J.↗

DOE OSTI2025

Separate, separated, and together: the transcriptional program of the Clostridium acetobutylicum-Clostridium ljungdahlii syntrophy leading to interspecies cell fusion

ABSTRACT Syntrophic cocultures (hitherto assumed to be commensalistic) of Clostridium acetobutylicum and Clostridium ljungdahlii , whereby CO 2 and H 2 produced by the former feed the latter, result in interspecies cell fusion involving large-scale exchange of protein, RNA, and DNA between the two organisms. Although mammalian cell fusion is mechanistically dissected, the mechanism for such microbial-cell fusions is unknown. To start exploring this mechanism, we used RNA sequencing to identify genes differentially expressed in this coculture using two types of comparisons. One type compared coculture to the two monocultures, capturing the combined impact of interactions through soluble signals in the medium and through direct cell-to-cell interactions. The second type compared membrane-separated versus -unseparated cocultures, isolating the impact of interspecies physical contact. While we could not firmly identify specific genes that might drive cell fusion, consistent with our hypothesized model for this interspecies microbial cell fusion, we observed differential regulation of genes involved in C. ljungdahlii’s autotrophic Wood-Ljungdahl pathway metabolism and genes of the motility machinery. Unexpectedly, we also identified differential regulation of biosynthetic genes of several amino acids, and notably of arginine and histidine. We verified that they are produced by C. acetobutylicum and are metabolized by C. ljungdahlii to its growth advantage. These and other findings, and notably upregulation of C. acetobutylicum ribosomal-protein genes, paint a more complex syntrophic picture and suggest a mutualistic relationship, whereby beyond CO 2 and H 2 , C. acetobutylicum feeds C. ljungdahlii with growth-boosting amino acids, while benefiting from the H 2 utilization by C. ljungdahlii . IMPORTANCE The construction and study of synthetic microbial cocultures is a growing research area due to the untapped potential of defined multi-species industrial bioprocesses and the utility of defined cocultures for generating insight into complex, undefined, natural microbial consortia. Our previous work showed that coculturing C. acetobutylicum and C. ljungdahlii leads to a unique metabolic phenotype (production of isopropanol) and heterologous cell fusion events. Here, we used RNAseq to explore genes involved in and impacted by these fusions. First, we compared gene expression in coculture to each monoculture. Second, we utilized a transwell system to compare gene expression in mixed cocultures to cocultures with both species physically separated by a permeable membrane, isolating the impact of interspecies “touching” on the transcriptome. This study deepens our mechanistic understanding of the C. acetobutylicum-C. ljungdahlii coculture phenotype, laying the groundwork for reverse genetic studies of heterologous cell fusion in Clostridium cocultures.

Willis, Noah B. (ORCID:0009000689365955)↗

NASA NTRS2013

High Energy Interactions in Massive Binaries: An Application to a Most Mysterious Binary

Extremely massive stars (50M and above) are exceedingly rare in the local Universe but are believed to have composed the entire first generation of stars, which lived fast, died young and left behind the first generation of black holes and set the stage for the formation of lower mass stars suitable to support life. There are significant uncertainties about how this happened (and how it still happens), mostly due to our poor knowledge of how stars change mass as they evolve. Extremely massive stars give mass back to the ISM via strong radiatively-driven winds and sometimes through sporadic eruptions of the most massive and brightest stars. Such mass loss plays an important role in the chemical and dynamical evolution of the local interstellar medium prior to the supernova explosion. Below we discuss how high energy thermal (and, in some cases, non-thermal) emission, along with modern simulations in 2 and 3 dimensions, can be used to help determine a physically realistic picture of mass loss in a well-studied, mysterious system.

Corcoran, Michael↗

DOE OSTI2020

Conversion between triplet pair states is controlled by molecular coupling in pentadithiophene thin films

In singlet fission (SF) the initially formed correlated triplet pair state, 1 (TT), may evolve toward independent triplet excitons or higher spin states of the (TT) species. The latter result is often considered undesirable from a light harvesting perspective but may be attractive for quantum information sciences (QIS) applications, as the final exciton pair can be spin-entangled and magnetically active with relatively long room temperature decoherence times. In this study we use ultrafast transient absorption (TA) and time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy to monitor SF and triplet pair evolution in a series of alkyl silyl-functionalized pentadithiophene (PDT) thin films designed with systematically varying pairwise and long-range molecular interactions between PDT chromophores. The lifetime of the (TT) species varies from 40 ns to 1.5 μs, the latter of which is associated with extremely weak intermolecular coupling, sharp optical spectroscopic features, and complex TR-EPR spectra that are composed of a mixture of triplet and quintet-like features. On the other hand, more tightly coupled films produce broader transient optical spectra but simpler TR-EPR spectra consistent with significant population in 5 (TT) 0 . These distinctions are rationalized through the role of exciton diffusion and predictions of TT state mixing with low exchange coupling J versus pure spin substate population with larger J. The connection between population evolution using electronic and spin spectroscopies enables assignments that provide a more detailed picture of triplet pair evolution than previously presented and provides critical guidance for designing molecular QIS systems based on light-induced spin coherence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Anomalous lattice thermal conductivity increase with temperature in cubic GeTe correlated with strengthening of second-nearest neighbor bonds

Understanding thermal transport mechanisms in phase change materials is critical to elucidating the microscopic picture of phase transitions and advancing thermal energy conversion and storage. Experiments consistently show that cubic phase germanium telluride (GeTe) has an unexpected increase in lattice thermal conductivity with rising temperature. Despite its ubiquity, resolving its origin has remained elusive. In this work, we carry out temperature-dependent lattice thermal conductivity calculations for cubic GeTe through efficient, high-order machine-learned models and additional corrections for coherence effects. We corroborate the calculated phonon properties with our inelastic X-ray scattering measurements. Our calculated lattice thermal conductivity values agree well with experiments and show a similar increasing trend. Through additional bonding strength calculations, we propose that a major contributor to the increasing lattice thermal conductivity is the strengthening of second-nearest neighbor interactions. The findings herein serve to deepen our understanding of thermal transport in phase-change materials.

36 MATERIALS SCIENCE↗

DOE OSTI2023

The Present and Future of QCD: QCD Town Meeting White Paper – An Input to the 2023 NSAC Long Range Plan

It is currently understood that there are four fundamental forces in nature: gravitational, electromagnetic, weak and strong forces. The strong force governs the interactions between quarks and gluons, elementary particles whose interactions give rise to the vast majority of visible mass in the universe. The mathematical description of the strong force is provided by the non-Abelian gauge theory Quantum Chromodynamics (QCD). While QCD is an exquisite theory, constructing the nucleons and nuclei from quarks, and furthermore explaining the behavior of quarks and gluons at all energies, remain to be complex and challenging problems. Such challenges, along with the desire to understand all visible matter at the most fundamental level, position the study of QCD as a central thrust of research in nuclear science. Experimental insight into the strong force can be gained using large particle accelerator facilities, which are necessary to probe the very short distance scales over which quarks and gluons interact. The Long Range Plans (LRPs) exercise of 1989 and 1996 led directly to the construction of two world-class facilities: the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) that is focused on studying how the structure of hadrons emerges from QCD (cold QCD research), and the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab (BNL) that aims at the discovery and study of a new state of matter, the quark-gluon plasma (QGP), at extremely high temperatures (hot QCD research). These past investments have produced major advances. Nucleons and nuclei are being studied with increasing precision with a unified description of the partonic structure utilizing multi-dimensional imaging. Significant progress has been made, paving the way towards a complete picture of how quarks and gluons give rise to the mass, spin, and momentum of the nucleon. In hot QCD, the QGP is created in the collisions of nuclei at RHIC and the Large Hadron Collider (LHC) and is observed to behave like a fluid with very low specific shear viscosity; the current goals are to understand how the fluid behavior emerges from QCD and to characterize the temperature (and chemical potential) dependence of the properties of the QGP. As this White Paper is written, current experimental programs at CEBAF, RHIC and the LHC continue to provide exciting near term opportunities to capitalize on the investments in experimental equipment and accelerator operations. Most importantly, the QCD community looks forward to the construction of the Electron Ion Collider (EIC) as a major new facility to push forward QCD research in the next decades, with significant focus on exploring the properties of gluons, the mediators of the strong force.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. Furthermore, the theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate and illustrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf’s ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed in parallel for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. However, when the observations are not so normalized, the sheaf model still remains valid.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

An interstellar cloud density from Copernicus observations of CO in the spectrum of Zeta Ophiuchi

Interstellar CO absorption bands in Copernicus spectra of Zeta Oph have been studied. Absorption profiles, computed under the assumption that excitation is due to collisions with H2 molecules and interaction with the 3-K background radiation field, were fitted to the reduced data of nine bands. When a gas kinetic temperature of 56 K is assumed, the best-fit condition implies a hydrogen-nucleus density of 120 per cu cm, a CO column density of 1.2 by 10 to the 15th power per sq cm, and a radial-velocity dispersion of 0.9 km/s. The relevance of these results to existing ideas concerning the Zeta Oph interstellar clouds is discussed. It is suggested that the strongest interstellar component is not circumstellar in origin but is instead part of a supernova remnant. Simple calculations are made to establish the plausibility of the supernova-remnant identification. This suggestion is also supported by Heiles's (1976) 21-cm pictures.

Smith, A. M.↗

NASA NTRS1985

Seasonal variation of the stratospheric circulation

An extensive analysis is made of the extratropical stratospheric circulation in terms of the seasonal variation of large-scale motion fields, with the aid of height and temperature data obtained from the TIROS satellite. Special attention is paid to a comparison of climatological aspects between the Northern Hemisphere (NH) and the Southern Hemisphere (SH). In order to see the general picture of the annual mach of the upper stratosphere, the zonal mean values of geopotential height of the 1 mb level at 70 deg N and 70 deg S were plotted on the daily basis throughout a year. It is observed that, during the winter, the zonal mean 1 mb height in the NH is much more variable than that in the SH. It is also notable that the SH height is rather oscillatory throughout the longer period from midwinter to early summer. Since the zonal mean height in the polar latitude is a rough measure of the mean zonal flow in extratropical latitudes, the difference of the seasonal variation between the two hemispheres mentioned above is considered to be due mainly to the planetary wave-mean flow interaction in the middle atmosphere. The wave activity in the middle atmosphere is represented more rigorously by the Eliassen-Palm flux associated with vertically propagating planetary waves forced from below. The day-to-day variation of the EP flux in the upper stratosphere shows that the wave activity varies intermittently with a characteristic time scale of about two weeks.

Hirota, I.↗

DOE OSTI2022

Access to Ru(IV)–Ru(V) and Ru(V)–Ru(VI) Redox in Layered Li 7 RuO 6 via Intercalation Reactions

The push to increase the capacity of oxides to store charge as Li-ion battery cathodes has challenged our knowledge of the boundaries of redox chemistry and its relationship to the atomic structure. Layered phases with Ru are now classical models in the quest for refined theories. Current understanding dictates that the highest formal state that can be reached in them is Ru(V), after which activity centered at the oxide anions is triggered. Yet, this picture is challenged by this investigation of the intercalation chemistry of Li 7 RuO 6 . Coupling structural and spectroscopic analysis with computational simulations, we show that Li 7 RuO 6 is capable of highly reversible lithiation to Li 8 RuO 6 through the Ru(V)/Ru(IV) redox couple. Further, Li 7 RuO 6 can also undergo anodic Li deintercalation, showing clear evidence of the reversible formation of Ru(VI) with octahedral coordination, an unusual state that is not accessible in other layered oxides. The results highlight the versatility of the Ru-O bond to undergo distinct redox transitions depending on the specific layered arrangements. They enrich our understanding of redox chemistry in solids while underscoring the need for descriptions of charge compensation that reflect the nuance of covalent interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗