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DOE OSTI2026

Formation of Bimetallic Nanoparticles via Exsolution Using a Reducible Metal Oxide Capping Layer

Bimetallic nanoparticles are promising catalysts that can improve performance in heterogeneous catalysis and solid-state electrochemistry. Exsolution is a useful method for forming such nanoparticles; however, it is limited by the elements present within the host oxide lattice. Here, in this work, we develop and demonstrate a strategy to form bimetallic particles from La 0.5 Sr 0.5 Ti 0.94 Ni 0.06 O 3 (LSTN) exsolution and using a reducible SnO 2 capping layer, expanding the range of elements available for bimetallic nanoparticle formation. Using this capping layer strategy, we formed nickel–tin (Ni 0 –Sn 0 ) bimetallic nanoparticles via exsolution. We used in situ near-ambient pressure X-ray photoelectron spectroscopy to monitor surface chemical changes during exsolution, showing that first, SnO 2 volatilized. This SnO 2 loss exposed the perovskite surface of LSTN to reducing conditions, which induced Ni exsolution, and compounded with SnO 2 reduction led to the formation of bimetallic Ni 0 –Sn 0 particles. To evaluate the associated microstructural evolution, we measured grazing incidence small-angle X-ray scattering (GISAXS), which confirmed the loss of the SnO 2 capping layer, and scattering simulations suggested the formation of bimetallic particles. We confirmed the bimetallic nanoparticle composition and morphology by Auger spectroscopy and scanning transmission electron microscopy. The resulting bimetallic nanoparticles were smaller and more thermally stable than the monometallic Ni counterparts on LSTN. This capping layer and exsolution approach allow synthesizing multimetallic nanoparticles and can be applied to other reducible metal oxides and perovskite hosts, broadening the compositional space for advanced catalytic materials.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Design of monolithic piezoelectric bimorph mirrors made from lithium niobate

Recent advances in deformable mirrors based on monolithic piezoelectric substrates, such as lithium niobate, have the potential to improve the image quality of X-ray optical systems on synchrotron and free-electron laser beamlines and microscopes. However, the quantitative relationship between design parameters and the deformed shape has not been readily available in the literature. We present an analytical model, validated through finite element analysis, enabling calculation of tangential and sagittal curvatures based on mirror dimensions, crystallographic orientation, and applied voltage. We demonstrate that through the selection of material orientation, it is possible to achieve different deformed shapes (sphere, cylinder, or hyperbolic paraboloid). This methodology can be generalized to other piezoelectric materials and substrate-integrated actuator systems.

Marzari, Francesco [University of Trento (Italy); ↗

DOE OSTI2026

Synchrotron resolved microscale mineralogy and elemental composition of individual plinthic and manganiferous nodules from agricultural soils

Iron and manganese oxides are strong sorbents and elemental scavengers in the environment that can form macroscopic nodules in soils. Despite their importance in the geochemical cycling of nutrients and contaminants, nodules are rarely characterized. When analyzed, they are often combined into bulk samples, obscuring individual characteristics. This study investigates the composition and mineralogy of individual plinthic and manganiferous nodules in soil from cropping systems in the Farming Systems Project in Beltsville, Maryland. Elemental composition indicates the accumulation of contaminants and nutrients, including copper in all nodules and high levels of phosphorus in select nodules. Sequential extractions determine that highly crystalline minerals comprise the nodules, locking away these nutrients and contaminants. Bulk X-ray diffraction (XRD) demonstrated distinct mineralogies in the plinthic and manganiferous nodules, with the former comprised of quartz, goethite, and kaolinite, and the latter consisting of quartz, Mn 2 O 3 , and hematite. Synchrotron and laboratory-based X-ray fluorescence (XRF) mapping gives critical insight into the elemental distribution within the nodules and elucidates spatial elemental associations, including the coupling of manganese and iron in the manganiferous nodules. XRF maps paired with µXRD provide microscale spatial resolution in mineralogy, which resolved several phases not apparent in bulk XRD, manganese’s association with goethite, and minerals indicative of redox transformations, including magnetite and maghemite. These novel results provide critical insight into the microscale mineralogy and individual elemental composition of plinthic and manganiferous nodules, as well as how they alter bulk soil geochemistry in ways largely unaccounted for in research on soil systems.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Comparison of automated chemical-guided segmentation and human annotation of soil organic matter in X-ray microcomputed tomography imaging in contrasted soil types

Soil organic matter (OM) formation and persistence is strongly influenced by the spatial distribution of organic substrates and microscale soil heterogeneity by dictating OM accessibility to microorganisms. However, traditional size and/or density fractionation techniques disrupt aggregate architecture, eliminating spatial information needed to fully understand intra-aggregate OM distribution. To quantify three-dimensional OM spatial distribution and automate segmentation in X-ray microcomputed tomography (µCT) imaging without human annotation bias, we developed an iodine gas vapor (I2) based staining workflow that eliminates labor-intensive manual annotation while maintaining segmentation accuracy, using aggregates from four taxonomically diverse soils (Xerofluvent, Haploxeroll Sphagnofibrist, Palehumult) with an 8-fold range of soil organic carbon. Human annotation of 10 µCT slices by the experienced and inexperienced annotators resulted in variations up to 3% in the Dice similarity coefficient (DSC), reflecting a degree of inherent subjectivity of manual labeling. Such inconsistencies are expected to compound as the number of manually annotated slices increases. Dual-energy µCT imaging at 33.1 keV (below the iodine (I) K-edge) and 33.2 keV (above the I K-edge) was used to resolve aggregate microstructure following I2 staining. The automated image subtraction pipeline identified OM regions by the I Kedge induced brightness increases, achieving DSC values of 0.58–0.83 relative to an experienced annotator. Sensitivity analyses revealed that the reconstruction alpha value—optimized via the open-source tool TomocuPy—and the 3D registration slice count were the primary determinants of accuracy, providing a novel benchmark for dual-energy soil imaging. The pipeline without GPU acceleration achieved 9.6 to 43.2 times faster than manual annotation. Using GPU-accelerated image post-processing and affine transformation matrices, the pipeline successfully segmented OM elements for large-scale datasets (3232×3232 pixel, 2048 slices) within ~5200 s from raw file acquisition to segmented output. The high-throughput approach enables the quantification of OM spatial distribution across diverse and heterogeneous soil.

Soil microbial biomass↗

DOE OSTI2026

Magnetic structure of topological nodal-line semimetal EuSb 2

Here, we investigated the magnetic structure of the magnetic topological nodal-line semimetal EuSb 2 using x-ray resonant magnetic scattering at the Eu 𝐿 3 absorption edge. Forbidden magnetic reflections confirm antiferromagnetic ordering with propagation vector 𝐪 = (0.5,0,0) below 𝑇 N ≈ 27 K. Azimuthal-angle-dependent measurements reveal that the Eu moments are aligned along the monoclinic 𝑏 axis. Comparison between the measured 𝐐-dependent magnetic Bragg peak intensities and calculations based on representation analysis identifies the magnetic structure as the A-type antiferromagnetic 𝛤 4 representation with a (++−−) arrangement along the 𝑎 direction. These results establish the microscopic magnetic structure of EuSb 2 and provide a basis for understanding the interplay between antiferromagnetism and topological electronic states in this system.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Metal Identity and Coordination Environment Modulate Single-Atom Catalyst Stability During Electrocatalysis

A major hurdle to the implementation of single-atom catalysts (SACs) in real-world systems is a poor understanding of their stability under operating conditions, which is particularly relevant due to the high surface free energy of SACs. Here, we evaluated the aggregation behavior of a suite of SACs varied by metal identity (Fe, Co, Ni, and Cu) during electrocatalytic nitrate reduction using in situ X-ray absorption spectroscopy. The metal center had significant influence on reconstruction, where under identical applied reductive potentials, SACs underwent varying levels of reconstruction, ranging from no discernible change to complete reduction into metallic nanoparticles. Such in situ experiments revealed Cu SACs to be the most susceptible to aggregation, prompting a deeper investigation into how coordination environment (O-, B-, and N-graphene) affected Cu SAC aggregation. We further conducted density functional theory calculations to elucidate the relationship between Cu SAC structure and stability. This work deconvolutes the relationship between SAC architecture and stability, which is essential to evaluate and explain for the realization of SACs for electrocatalysis.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Comparison of the Arrhenius parameters between conventional hydrothermal and microwave-assisted synthesis methods for tin oxide nanoparticles

Microwave (MW) irradiation has emerged as a powerful tool for accelerating materials synthesis, yet the origins of its specific influence on reaction kinetics remain elusive. While multiple studies have attributed the observed enhancements in reaction rates under MW heating to reduced activation energies, other accounts have suggested modifications to the Arrhenius pre-exponential factor as the predominant cause. Distinguishing between these parameters in modern applications of MW processing in nanomaterials requires experimental approaches capable of resolving the dynamic and nuanced structural kinetics that govern MW-assisted chemistry. Here, we combine in-situ synchrotron X-ray total scattering with pair distribution function (PDF) analysis to track the structural evolution of SnO 2 nanoparticles synthesized via MW-assisted and conventional hydrothermal conditions. Avrami modeling and Arrhenius analysis suggest that although MW irradiation yields a higher apparent activation energy, the enhanced crystallization is better explained by a pre-exponential factor several orders of magnitude larger than that of conventional heating. These findings suggest that the MW field induces a higher frequency of successful molecular rearrangements rather than lowering the intrinsic activation barrier. The results contribute further insights clarifying the role of the applied MW field for materials design where MW-specific effects can be deliberately harnessed. Furthermore, this work presents a framework promoting the utility of in-situ PDF characterization coupled with kinetic analysis for developing more sophisticated descriptions of nanoscale transformations for MW-driven reaction kinetics.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Synthesis and Characterization of Layered Actinide (U, Np, Pu) Oxide and Hydroxide Phases

Systematic structural comparisons across the early actinides remain limited by the scarcity of well-defined transuranic layered oxide and oxyhydroxide phases. Here, we report the synthesis and single-crystal characterization of new layered actinide compounds spanning U, Np, and Pu obtained under mild hydrothermal conditions in concentrated alkali hydroxide media. These include hydrated oxides α-Cs 2 U 2 O 7 •0.5H 2 O and Rb 2 An 2 O 7 •0.5H 2 O (An = Np, Pu), oxy-hydroxides Rb 6 [(AnO 2 ) 6 O 8 (OH) 2 ]•xH 2 O x = 0, 0.5 (An = U, Np) and Rb 4 [(UO 2 ) 5 O 6 (OH) 2 ]•2H 2 O, as well as nitrate-intercalated compounds Cs 6 [(AnO 2 ) 3 O 4 (OH) 2 ](NO 3 ) 2 (An = Np, Pu). Single-crystal X-ray diffraction studies reveal extended two-dimensional architectures constructed from edge- and vertex-sharing actinyl polyhedra, with systematic evolution in equatorial coordination, hydration, and anionic sheet topology across the U–Np–Pu series. Incorporation of nitrate anions within the interlayer region of Cs 6 [(AnO 2 ) 3 O 4 (OH) 2 ](NO 3 ) 2 establishes a previously unobserved structural motif in layered transuranic oxyhydroxides, demonstrating an additional pathway for anion-mediated framework stabilization. Correlation of crystallographic metrics with single-crystal Raman spectroscopy provides new vibrational benchmarks linking differences in An═O yl bond lengths to the equatorial coordination and the interstitial cations. These findings expand the structural hierarchy of layered actinide materials and address clarifying periodic trends governing topology, bonding, and vibrational signatures in high-valent 5ƒ oxide systems.

actinides↗

DOE OSTI2026

Ca Metal Batteries and Sn Anode Alloying: Resolving Misconceptions in Ca–Sn Alloy Formation

Ca metal anode suffers from surface passivation and struggles to effectively plate and strip in conventional Ca electrolytes, making the development of alloy anode for calcium metal battery essential. This work systematically and carefully evaluates the electrochemical formation and feasibility of the Sn anode and its possibility of alloying with Ca using a combination of cyclic voltammetry, scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM/EDS), X-ray diffraction (XRD), and synchrotron transmission X-ray microscopy (TXM). Electrochemical measurements and SEM/EDS analyses indicate apparent Ca alloy formation. However, detailed XRD and TXM characterization reveal substantial lithium-ion involvement when lithium metal is employed as the reference electrode, even in electrolytes with high Ca salt concentrations. These findings highlight a significant risk of misinterpretation: Although limited Ca–Sn alloying may occur, the faster kinetics of Li + can dominate the alloying process, leading to a Li-driven reactions at the Sn anode. In contrast, cells constructed with Ca metal as both reference and counter electrodes exhibit distinct redox features only during the initial cycles, followed by rapid cell failure. The high oxidation currents induce severe Ca passivation, occurring nearly concurrently with Sn dealloying. Overall, this study provides critical insight into the practical limitations and common experimental artifacts associated with Ca metal battery systems and underscores the necessity for rigorous cell design and cautious interpretation when evaluating alloy chemistry in multivalent Ca-based batteries.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Evolution of charge density wave soft phonon modes in Pd 𝑥 ⁢ErTe 3

Here, we investigated the lattice dynamics of quasi-two-dimensional Pd-intercalated ErTe 3 in relation to its charge-density-wave (CDW) transitions by means of x-ray diffuse and meV-resolution inelastic x-ray scattering. In pristine ErTe 3 , CDW order develops at orthogonal in-plane wave vectors q$^𝑐_1$ =(0,0,0.29) (the 𝑐−CDW ) and q$^𝑎_2 $= (0.31,0,0) (the 𝑎−CDW ), with transition temperatures $𝑇^𝑐_1$ = 270K and $𝑇^𝑎_2$ = 160K, respectively. Remarkably, we observe diffuse x-ray scattering already near the higher transition temperature $𝑇^𝑐_1$ along 𝑎−CDW but at a slightly different wave vector q$^𝑎_1$ = (0.29,0,0). Inelastic x-ray scattering for Pd 0.01 ⁢ErTe 3 shows that a partial phonon softening at q$^𝑎_1$, underscoring the strong competition between ordering tendencies along the nearly equivalent in-plane axes of the orthorhombic lattice. For intercalation levels 𝑥 ≥ 0.02, the 𝑎−CDW state is suppressed. Nevertheless, a similar correlation between phonon softening and diffuse scattering persists along the [100] direction, again observed at q$^𝑎_1$ = (0.29,0,0) and $𝑇^𝑐_1$. These findings suggest that the 𝑎−CDW is fully suppressed for 𝑥 ≥ 0.02, and that the residual diffuse scattering at originates from the partial phonon softening associated with the 𝑐−CDW, reflected by the near equality of the absolute size of q$^𝑐_1$ and q$^𝑎_1$.

Maity, Avishek [Technische Univ. München, Garching↗

DOE OSTI2026

Thermal cycling-driven microstructural changes of eutectic Al–Si phase change materials in SS304 containers revealed by multi-modal imaging

Aluminum-based Al–Si alloys are widely used as phase change materials (PCMs) in thermal energy storage (TES) systems owing to their high volumetric latent heat and superior thermal conductivity. However, their long-term reliability is limited by degradation processes that remain insufficiently understood. In this work, we employ a multimodal, correlative characterization framework to systematically resolve the degradation behavior of eutectic Al–Si PCMs in contact with SS304 containers under repeated thermal cycling. By integrating high-resolution electron microscopy, three-dimensional X-ray fluorescence (3D XRF) imaging, and differential scanning calorimetry (DSC), we directly link spatially resolved compositional and microstructural evolution to changes in thermophysical properties. The correlative analysis reveals that elemental leaching of Fe, Cr, and Ni from the stainless-steel container into the PCM drives the formation of intermetallic compounds (IMCs) both at the interface and within the bulk PCM, leading to pronounced compositional heterogeneity. These interfacial reactions and diffusion-induced transformations progressively destabilize the Al–Si eutectic, reducing the effective phase-transforming fraction. Consistent with these observations, DSC measurements show a decrease in melting temperature and latent heat of fusion with thermal cycling. These results underscore the critical influence of interfacial reactions and material compatibility on the stability, durability, and overall performance of Al–Si-based TES systems.

25 ENERGY STORAGE↗

DOE OSTI2026

Learning neural representations for X-ray ptychography reconstruction with unknown probes

X-ray ptychography provides exceptional nanoscale resolution and is widely applied in materials science, biology, and nanotechnology. However, its full potential is constrained by the critical challenge of accurately reconstructing images when the illuminating probe is unknown. Conventional iterative methods and deep learning approaches are often suboptimal, particularly under the low-signal conditions inherent to low-dose and high-speed experiments. These limitations compromise reconstruction fidelity and restrict the broader adoption of the technique. In this work, we introduce the Ptychographic Implicit Neural Representation (PtyINR), a self-supervised framework that simultaneously addresses the object- and probe-recovery problem. By parameterizing both as continuous neural representations, PtyINR performs end-to-end reconstruction directly from raw diffraction patterns without requiring any pre-characterization of the probe. Extensive evaluations demonstrate that PtyINR achieves superior reconstruction quality on both simulated and experimental data, with remarkable robustness under challenging low-signal conditions. Furthermore, PtyINR offers a generalizable, physics-informed framework for addressing probe-dependent inverse problems, making it applicable to a wide range of computational microscopy problems.

36 MATERIALS SCIENCE↗

DOE OSTI2026

High Pressure Synthesis of Ultrasmall Nanodiamonds with Nitrogen Vacancy Centers

C–H terminated nanometer scale diamonds ( d = 1 to 15 nm) are synthesized from 1-fluoroadamantane at high pressure (6–8 GPa) and high temperature (500–1500 °C) in a multianvil press. High resolution transmission electron microscopy, X-ray diffraction, Raman, diffuse reflectance Fourier transform infrared, and X-ray absorption spectroscopies demonstrate the excellent crystallinity and atomically flat C–H terminated surfaces of nanodiamonds with (111) and (110) facets. The importance of hydrogen to the synthesis of nanodiamond and its faceting is discussed. Following vacancy generation, annealing and oxidation of the nanodiamonds, optically detected magnetic resonance and electron spin resonance coherence times ( T 2 = 0.9 and 2.1 μs) of nitrogen vacancy (NV) centers are measured. Finally, the obtained T 2 values are equivalent to the shallow NV centers (depth <10 nm) in bulk diamond crystals and larger nanocrystals prepared by mechanical milling.

36 MATERIALS SCIENCE↗

DOE OSTI2026

How Does Metal Spin State Affect Electronic Communication in Mixed-Valence Dimers? Insights from Ultrafast Near-Infrared and Soft X-ray Transient Absorption Spectroscopy

Recent advancements in photocatalysis, photovoltaics, and quantum information science take advantage of electron spin, and determining how spin multiplicity affects electron transfer is key to understanding these phenomena. Here, in this study, we examine how metal spin state affects electronic communication in an organometallic mixed-valence dimer, ferrocenyl cobaltocenium ([Fe II Cp 2 Co III Cp 2 ] + ). This complex can be photoexcited from its low-spin singlet Fe II ground state to form intermediate-spin triplet Fe II and high-spin quintet Fe II excited states. Using femtosecond optical transient absorption (OTA) spectroscopy with visible (vis), near-infrared (NIR), and short-wave IR (SWIR) probes, supported by time-dependent density functional theory (TD-DFT) calculations, we measure Fe II Co III →Fe III Co II intervalence charge transfer (IVCT) bands in each of the Fe II spin states. Mulliken–Hush analysis of the excited-state IVCT bands was used to compute the electronic coupling between the metal centers in all three spin states, which increased as quintet < triplet < singlet. Meanwhile, the peak energy of the bands, and thus the ΔG of the IVCT transition, increased as triplet < quintet < singlet. Then, to directly probe the electronic structure at each metal center, we employed picosecond soft X-ray transient absorption (XTA) spectroscopy at the Fe and Co L 3 edges. Our results show that the low-spin and high-spin states of [Fe II Cp 2 Co III Cp 2 ] + are valence-localized, while the intermediate-spin state is partially delocalized. The differences in charge delocalization are attributed to differences in orbital occupation and geometry that affect the free energy and superexchange coupling.

Burke, John H. [Univ. of Illinois at Urbana-Champa↗

DOE OSTI2026

Ground calibration plan for the Athena/X-IFU microcalorimeter spectrometer

The X-ray Integral Field Unit is the X-ray imaging spectrometer on board one of ESA’s next large missions, Athena. Athena is set to investigate the theme of the Hot and Energetic Universe, with a launch planned in the late-2030s. Based on a high-sensitivity transition edge sensor (TES) detector array operated at very low temperature (50 mK), X-IFU will provide spatially resolved high-resolution spectroscopy of the X-ray sky in the 0.2 to 12 keV energy band, with an energy resolution goal of 4 eV up to 7 keV [3 eV design goal]. This work presents the current calibration plan of the X-IFU. It provides the requirements applicable to the X-IFU calibration, describes the overall calibration strategy, and details the procedure and sources needed for the ground calibration of each parameter or characteristics of the X-IFU.

47 OTHER INSTRUMENTATION↗

DOE OSTI2026

Nanoscale strain wave generation by a piezoelectric grating from polar vortices

Nanostructures formed by spontaneously broken symmetry have provided new ways to manipulate quantum states. Specifically, topological structures with periodic spatial ordering, such as polar vortices and skyrmions, can be ideal hosts for creating engineered responses in both spatial and frequency domains. So far, however, only a few examples of such hierarchical engineering have been reported in the literature. Here we demonstrate that the spatially modulated piezoelectric response of a polar vortex structure can create strain waves with a characteristic nanoscale wavefront. Using time-resolved pump–probe resonant X-ray scattering and diffraction measurements, coupled with dynamical phase-field simulations, we show that the piezoelectric modulation of the spontaneously formed polar vortex crystal functions as an acoustic diffraction grating. This system converts incoming laterally uniform strain waves into outgoing waves with a characteristic sub-terahertz frequency, driven by an intrinsic excitation of the polar vortex crystal. Moreover, our phase-field simulations suggest that the dynamic mechanical displacements exhibiting vortex textures are generated from both space- and time-varying piezoelectric responses. Our findings illustrate a new method for generating nanoscale strain waves with unique spatial textures by tuning the hierarchical order of polar topologies to engineer new collective modes, allowing for a wide range of control through the topological lattice.

ferroelectrics↗

DOE OSTI2026

First use of an InSb crystal for x-ray imaging spectroscopy of highly ionized tungsten in the Wendelstein 7-X stellarator

Advances in time and space resolved measurements of highly charged states of tungsten (W) through x-ray imaging spectroscopy have enabled investigation of impurity transport in the Wendelstein 7-X (W7-X) stellarator. The high-resolution x-ray imaging spectrometer (HR-XIS) system on W7-X utilizes the Bragg diffraction properties of a set of multiple crystals to measure a range of impurity emission lines within sections of the 1–7 Å wavelength range, including transitions of W. A new indium–antimonide crystal has been installed on the HR-XIS system to allow viewing of the 5.5–6.2 Å region focusing on emissions of W. Consequently, many bright W emission lines from W 40+ to W 47+ were observed in this wavelength range, both in plasmas with injected W and in those with only intrinsic W impurity sources, showing the high sensitivity of the diagnostic. Three W 46+ emissions correspond in wavelength and intensity with calculated photon emissivity coefficients and can be exploited for W transport and concentration applications in plasmas with T e ≳ 2.1 keV. Here, an estimate of the core W density behavior in two separate turbulence-reduced ‘high-performance’ (HP) discharges on W7-X is done using the 5.6893 Å W 46+ line. The n W behavior in HP scenarios can be explained by previous experimental results and neoclassical predictions.

XICS↗

DOE OSTI2026

Astrophysical Neutrino Sources as Colliders

High-energy neutrinos arise from processes at large center-of-mass energies, offering a window to test physics at comparable scales or beyond those accessible in collider experiments on Earth. Here, we present a recipe for extracting two-sided bounds on the inelastic $pp$ and $pγ$ cross sections from neutrino point-source data, by independently constraining every astrophysical input (cosmic-ray luminosities and target densities) through electromagnetic observations or theoretical arguments. The cross section is then the only remaining free parameter. Applying this framework to the IceCube associations with TXS~0506+056, NGC~1068, and the Galactic Plane, to a stacked population of eleven X-ray bright Seyfert galaxies, to the ultra-high-energy KM3NeT event KM3-230213A, and to projected observations of ultra-high-energy neutrinos, we obtain constraints that span center-of-mass energies from $\sqrt{s}\sim 1$ GeV to $\sim 10^{5}$ GeV, some of which are well beyond the reach of the LHC and, for the $pγ$ channel, beyond HERA. Several of these bounds are more stringent than unitarity limits.

Argüelles, Carlos A. [Harvard U.]↗