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234 records · Page 5

Atomic faulting drives exceptional toughness in low thermal expansion chromium alloys

Endowing functional properties with mechanical responses in traditional metals has been a frontier topic, akin to transforming base metal into gold. Chromium and its alloys, with their functional deficiencies and limited ductility, serve as typical examples. Herein, we report a Cr96Fe4Ge1.3B1 alloy that unifies low thermal expansion (LTE, αl = 1.79 × 10-6 K-1, 200 − 315 K) with exceptional toughness (240.2 J·cm-3). The enhancement in mechanical responses is primarily attributed to layered Cr2B intermetallic precipitates, which ameliorate interfacial cohesion and simultaneously refine the grain structure. The weakened interlayer interactions within the Cr-B layers facilitate the nucleation and movement of numerous tiny stacking faults in precipitates, efficiently alleviating strain energy and resulting in marked work-hardening ability. Additionally, antiferromagnetic fluctuations in the BCC matrix contribute to the unique LTE behavior. This paves the way for the design of high-performance alloys featuring layered-symmetry precipitates.

Yu, Chengyi [University of Science and Technology

IUS materials outgassing condensation effects on sensitive spacecraft surfaces

Four materials used on the inertial upper state (IUS) were subjected to vacuum conditions and heated to near-operational temperatures (93 to 316 C), releasing volatile materials. A fraction of the volatile materials were collected on 25 C solar cells, optical solar reflectors (OSR's) or aluminized Mylar. The contaminated surfaces were exposed to 26 equivalent sun hours of simulated solar ultraviolet (UV) radiation. Measurements of contamination deposit mass, structure, reflectance and effects on solar cell power output were made before and after UV irradiation. Standard total mass loss - volatile condensible materials (TML - VCM) tests were also performed. A 2500 A thick contaminant layer produced by EPDM rubber motor-case insulation outgassing increased the solar absorptance of the OSR's from 0.07 to 0.14, and to 0.18 after UV exposure. An 83,000 A layer caused an increase from 0.07 to 0.21, and then the 0.46 after UV exposure. The Kevlar-epoxy motor-case material outgassing condensation raised the absorptance from 0.07 to 0.13, but UV had no effect. Outgassing from multilayer insulation and carbon-carbon nozzle materials did not affect the solar absorptance of the OSR's.

C. R. Mullen

Mitigating electrochemical degradation in CsPbBr{sub 3} gamma detectors by organic and inorganic encapsulation.

CsPbBr3 perovskite semiconductors have emerged as a leading candidate for nextgeneration radiation detectors because of their exceptional charge transport properties, defect tolerance, and record-breaking sensitivity and energy resolution. Their long-term stability, however, is hindered by electrode-driven electrochemical decomposition, which is accelerated by moisture- and oxygen-assisted ion migration during operation. Here, we investigated organic and inorganic encapsulation strategies as both environmental barriers and means to suppress interfacial degradation pathways. Atomic layer deposition (ALD) of Al2O3 provided a conformal passivation layer that blocked environmental ingress, suppressed ionic diffusion, reduced leakage current, enhanced energy resolution and expanded the operational electric-field window beyond 5 kV∙cm1 . By contrast, organic encapsulants such as paraffin wax and polystyrene slowed moisture diffusion but did not suppress interfacial reactions, with wax extending stability to over 90 days. These results show that ALD-Al2O3 suppresses dominant interfacial degradation pathways, enabling stable, high-field operation and advancing the practical deployment of CsPbBr3 γ-ray detectors.

Unal, Mustafa

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING

Smart Process Planning for Automated Fiber Placement

Many industries, including aerospace, automotive, wind energy, maritime, and sporting goods, rely on strong, lightweight materials called composites. These materials are made by layering fibers, which can come in the form of narrow strips or wider sheets, and setting them in a polymer matrix. One of the most advanced ways to make these parts is through automated fiber placement, where a machine lays down the fibers in precise patterns. This method can create very efficient and strong designs, but it is complex, expensive, and often depends heavily on the experience of skilled engineers. Today, the design, manufacturing, and inspection stages of composite production are usually handled separately. This separation means that important information, such as how a part will be built or what defects might occur, is not always shared between stages. As a result, parts may not be as lightweight, strong, or defect-free as possible, and the process can take longer and cost more. This research develops a smart process planning system that connects design, manufacturing, and inspection into one continuous process. Built as software that works with existing tools, the system can automatically plan how the fibers are placed, predicting and reducing defects while improving both manufacturability and strength. The system optimizes not only individual layers but also how defects are distributed across all layers, preventing them from stacking up in ways that weaken the final part. It also uses inspection results from completed parts to improve future designs, creating a feedback loop where each stage informs the others. The system was tested by designing a composite panel using this new approach and comparing it to a panel made with state-of-the-art manual planning methods. The results showed that the system could intentionally control where defects appeared and increase the efficiency of the planning process. By unifying design, manufacturing, and inspection, this research shows a way to make advanced composite manufacturing more efficient, consistent, and cost-effective. This approach lowers the barrier to using automated fiber placement and opens the door for its wider adoption not only in aerospace but also in industries such as automotive, wind energy, maritime, and sporting goods, where strong and lightweight structures are essential.

Computer-Aided Process Planning

All-Polyester Multilayer Plastics (‘All-Polyester MLPs’): A Redesign for Inherently Recyclable Plastics

Multilayer plastics (MLPs) are widely used in modern packaging because they combine multiple functions such as oxygen and moisture barriers, mechanical strength, puncture resistance, and heat sealability into lightweight and cost-effective packaging solutions. These attributes are essential for food, beverage, pharmaceutical, and consumer goods packaging. However, conventional commercial MLPs typically consist of five to twelve layers made from chemically incompatible materials, including polyolefins, polyethylene terephthalate, nylon, ethylene-vinyl alcohol (EVOH), adhesives, and tie layers. This complexity makes MLPs extremely difficult to recycle. As a result, the vast majority of multilayer plastics (MLPs) are disposed of through landfilling or incineration. This disposal pathway perpetuates demand for virgin material production, thereby driving high industrial energy consumption, increasing greenhouse gas (GHG) emissions, and contributing to the long-term accumulation of plastic waste. The scope of work included: (1) Design and fabrication of all-polyester multilayer structures using commercially relevant processing methods; (2) Experimental validation of barrier, mechanical, and sealing performance; (3) Demonstration of both mechanical and chemical recycling pathways; and (4) Comprehensive techno-economic analysis (TEA) and life-cycle assessment (LCA) to quantify cost, energy, and environmental impacts.

36 MATERIALS SCIENCE

An Overview of Experiments and Modeling of Polysiloxane-Coated Thermal Protection Systems for Missions to Mars, Titan, and Beyond.

Phenolic Impregnated Carbon Ablator (PICA) gained heritage during the historic Stardust mission, where it successfully returned samples from a comet’s tail and has since been instrumental in delivering payloads to the surface of Mars [1-3]. Most recently, PICA enabled the safe return of samples collected from asteroid Bennu as part of the OSIRIS-REx mission. This rich legacy underscores PICA’s critical role in allowing NASA’s most ambitious exploration missions. However, the friable nature of its phenolic phase presents challenges during handling and pre-launch activities. To mitigate this issue, PICA is coated with a polysiloxane resin system, which serves to suppress particulate dispersion and thereby safeguard spacecraft components. A comprehensive understanding of the polysiloxane resin’s behavior is imperative, as it profoundly shapes the material response of PICA during atmospheric entry by influencing its thermal and oxidative stability. This influence extends to thermocouple plugs embedded within thermal protection systems. These plugs have demonstrated their significance in missions such as Mars Science Laboratory (MSL) and Mars 2020, where the MEDLI and MEDLI2 instrumentation suites delivered in-valuable insights into the performance of thermal protection systems during entry into the Martian atmosphere [4]. Looking ahead, missions such as Dragonfly, set to descend into Titan’s dense atmosphere, aim to leverage advanced sensor technologies to further refine our understanding of thermal protection response [5]. Moreover, thermocouple plugs play an essential role in validating cutting-edge material response models, such as those pioneered under NASA’s Entry Systems Modeling Project (ESM), designed, in-part, to predict the operational integrity of thermal protection systems under the extreme stresses of atmospheric entry. To achieve these modeling goals, ground-based experiments are crucial to provide the foundational data necessary for developing and refining these predictive tools. To this end, an extensive test campaign was conducted at the Hypersonic Materials Environmental Test System (HyMETS) to investigate the high-temperature behavior of the polysiloxane resin in an air environment [6]. These experiments revealed critical phenomena, including the formation of a silicon oxycarbide layer that enhances oxidation resistance, moderates surface temperatures, and alters in-depth thermal response. Building on these findings, subsequent tests were designed to simulate atmospheric entry conditions in reactive gases, such as CO2 and N2, to mimic the environments of Mars and Titan, respectively, as well as non-reactive gases representing the atmospheres of the Ice Giants (Neptune and Uranus). A heating rate dependent decomposition mechanism has been identified for the polysiloxane resin under oxidizing conditions (Fig. 1). In the initial stage, the resin and the underlying thermal protection system undergo pyrolysis, rapidly generating a thin amorphous silicon oxycarbide interwoven with carbonaceous char and residual fibers from PICA. During the second stage, the nascent oxide layer establishes a robust, oxidation-resistant thermal barrier coating, which significantly impedes heat transfer to the underlying carbonaceous char, resulting in a stagnation of the surface temperature. A key factor contributing to this thermal resistance is the low recombination efficiency of atomic oxygen (γ), which further diminishes the heat load on the material’s interior layers [7]. Moreover, as the surface temperature stagnates, the silicon oxycarbide phase separates into distinct regions of silica and free graphite. Ultimately, when the heat flux reaches a critical threshold, a third stage is triggered, leading to the breakdown of the coating through carbothermal reduction, exposing the underlying char layer. This exposure leads to a dramatic surface temperature spike, driven by highly exothermic reactions between atomic oxygen and the char layer, further accelerating material degradation. A detailed mass and heat transfer model of PICA coated with polysiloxane resin was implemented in the Porous material Analysis Toolbox based on OpenFOAM, PATO [8]. The initial stage was considered negligible in this model because the resin decomposition occurs rapidly within a thin surface layer. Instead, the coating was directly considered as an oxygen-resistant thermal barrier coating. For the second stage, the thin amorphous silicon oxycarbide was treated as a pure silica surface to simplify the thermochemical behavior. The model ac-counts for surface equilibrium processes using representative elements of the coating-environment system. For the third stage, specific boundary conditions were developed to estimate the onset and progression of the coating removal. Two-dimensional material response simulations were conducted to compare uncoated and coated PICA using boundary conditions calibrated with HyMETS data. Fig. 2 illustrates that the simulations closely align with experimental data, successfully reproducing measured temperature profiles. This work will include the latest advancements in the coating model, including the calibration of recombination of atomic oxygen at the surface during the second phase. These simulated results will be further validated against additional CO2 data points from HyMETS, reinforcing the models’ predictive capabilities. These mechanisms and their effects on thermal protection systems, including thermochemical behavior and thermocouple probe performance in extreme environments, provide crucial insights for optimizing spacecraft designs that safeguard scientific payload and ensure mission success in future planetary exploration endeavors.

Active Oxidation

High‐Loading Lithium‐Sulfur Batteries with Solvent‐Free Dry‐Electrode Processing

Abstract Lithium‐sulfur (Li‐S) batteries, with their high energy density, nontoxicity, and the natural abundance of sulfur, hold immense potential as the next‐generation energy storage technology. To maximize the actual energy density of the Li‐S batteries for practical applications, it is crucial to escalate the areal capacity of the sulfur cathode by fabricating an electrode with high sulfur loading. Herein, ultra‐high sulfur loading (up to 12 mg cm −2 ) cathodes are fabricated through an industrially viable and sustainable solvent‐free dry‐processing method that utilizes a polytetrafluoroethylene binder fibrillation. Due to its low porosity cathode architecture formed by the binder fibrillation process, the dry‐processed electrodes exhibit a relatively lower initial capacity compared to the slurry‐processed electrode. However, its mechanical stability is well maintained throughout the cycling without the formation of electrode cracking, demonstrating significantly superior cycling stability. Additionally, through the optimization of the dry‐processing, a single‐layer pouch cell with a loading of 9 mg cm −2 and a novel multi‐layer pouch cell that uses an aluminum mesh as its current collector with a total loading of 14 mg cm −2 are introduced. To address the reduced initial capacity of dry‐processed electrodes, strategies such as incorporating electrocatalysts or employing prelithiated active materials are suggested.

Chemistry

Developing a Pyrolysis Gas Thermal Blocking Model for Reentry Demise

In NASA’s Object Reentry Survival Analysis Tool (ORSAT), aerodynamic drag and aerothermal heating coefficients are computed for each of the free-molecular, continuum, and transitional flow regimes using analytical and semi-analytical methods. These heating coefficients were derived for typical metallic materials that melt and do not have a strong gas-phase contribution to the flow in the boundary layer. Modern satellites typically feature fiber-reinforced polymer (FRP) components, such as solar array booms, facesheets of sandwich panels, or overwraps for composite-overwrapped pressure vessels (COPV). These FRP materials do not behave the same as metals in the reentry environment, but instead will pyrolyze and develop significant volumes of gas into the boundary layer. Accurately predicting the reentry demise of FRP components is critical to assessing the reentry casualty risk for modern spacecraft. Research in recent years has shown that this demisability can depend heavily on how the expulsion of gaseous pyrolysis products through the outer surface of the material affects the heat flux at the surface. The ODPO has been developing a reduced-order model of the effect of pyrolysis gas blowing on the heat flux based on correlations between a blowing factor and a non-dimensional heat flux to be incorporated in the upcoming version 7.3 of the Object Reentry Survivability Analysis Tool (ORSAT). This presentation discusses the progress of this development project and the challenges remaining for generalizing the model across families of FRP materials.

Benton Greene

Ultrafast low-temperature metal–insulator interface phonon dynamics and heat transport in a Pt/Gd 3 Fe 5 O 12 heterostructure

Interfacial thermal and acoustic phenomena have an important role in quantum science and technology, including in spintronic and spincaloritronic materials and devices. Simultaneous measurements of the low-temperature thermal and acoustic properties of a metal/insulator heterostructure reveal distinct dynamics in the characteristic phonon frequency ranges of acoustic and thermal transport. The measurements probed a heterostructure consisting of a thin film of Pt on the ferrimagnetic insulator gadolinium iron garnet (Gd 3 Fe 5 O 12 , GdIG) grown epitaxially on a gadolinium gallium garnet substrate. Ultrafast structural dynamics within the Pt layer were tracked using time-resolved ultrafast x-ray diffraction and analyzed to probe interfacial acoustic and thermal properties. The rapid heating of the Pt layer by a 400 nm wavelength femtosecond-duration optical pulse produced transient structural changes that provided the stimulus for these measurements. Rapid heating produced a broadband acoustic pulse that was partially reflected by the Pt/GdIG interface. Temporal frequencies up to 740 GHz, corresponding to angular frequencies of several THz, were detected in a wavelet analysis of the acoustic oscillations of the strain in the Pt layer. The structural results were analyzed to determine (i) the acoustic damping coefficient and phonon mean free path in Pt at frequencies of hundreds of GHz and (ii) the Grüneisen anharmonicity parameter. The thermal conductance of the Pt/GdIG interface was tracked using the slower, tens-of-picosecond-scale, dynamics of the initial cooling of the heated Pt layer. Analysis using a model based on the Boltzmann transport equation shows that the phonon transmission is lower at the phonon frequencies relevant to thermal transport than for subterahertz regime acoustics.

Acoustic phenomena

Numerical simulation of frost formation and heat transfer on fin-and-tube heat exchangers in turbulent cross-flow

Frost formation in fin-and-tube heat exchangers in turbulent cross-flow presents significant challenges in industrial refrigeration applications, affecting heat transfer efficiency and operational reliability. The purpose of this work is to investigate frost deposition and growth on a staggered bank of a fin-and-tube freezer coil under turbulent forced convection conditions. The focus here is on investigating conditions that closely replicate real-world scenarios in large walk-in industrial freezers. Using a direct numerical simulation approach, we examine the flow dynamics and thermal behaviour in the presence of frost, considering turbulent regimes characterized by a Reynolds number in the range 1050 ≤ R e D , avg ≤ 4800 , with the characteristic length being the outer diameter of the tube and the velocity being the bulk fluid velocity between the plates (fins). Computational fluid dynamics simulations are employed to resolve the interactions between turbulent airflow and the frost layer. Our approach incorporates a modified immersed boundary method and a slow-time acceleration technique to address the complex dynamic interface between the continuously evolving frost layer and the flowing air stream. Our findings indicate that frost forms more on the sides of the finned surfaces (plates) and less on the tubes themselves. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.

Science & Technology - Other Topics

Aerodynamic Performance and Acoustic Impacts of Varying Tip Speeds and Tripping Conditions on Small Rotors in an Anechoic Hover Chamber

Performance and acoustic measurements were taken in a hover chamber for various optimum hovering rotors (OPT2) and a commercial-off-the-shelf (COTS) rotor. A total of 10 rotors are included in this report, all of which have two blades and a tip radius of 0.1905 m (7.5 in.). For the OPT2, results for three additive manufacturing methods of fabrication are presented: stereolithography(SLA) using Accura Xtreme, SLA using FormLabs 10K resin, and selective laser sintering (SLS) using mineral-filled PA12 nylon material. All but one set of rotors were designed with a trailing edge bluntness that is 3% of the chord length, and one set was designed with a bluntness that is 1% of the chord length. Spanwise boundary layer trips were applied to the SLA, FormLabs and COTS rotors. Performance comparisons between untripped and tripped configurations demonstrate the impact of boundary layer state on rotor efficiency. Acoustic results, including periodic and broadband noise components, are presented. The effects of tripping these rotors near the leading edge are also presented. For some of the rotors, acoustic spectra of tip speed sweeps are presented to show how the frequency content changes with tip speed. Amplitude and frequency scaling methods are used to collapse broadband spectra at various tip speeds towards a unified curve. These findings contribute to the understanding of small rotor aeroacoustics and provide valuable datasets for computational model validation in urban air mobility applications.

eVTOL

Iron surface corrosion in supercritical CO2 at atomic scale investigated by molecular dynamics simulations

Understanding the corrosion behavior of steels in supercritical carbon dioxide (S-CO2) is essential for ensuring the safe application of S-CO2 as a heat-transfer fluid in high-temperature energy systems, including advanced nuclear reactors. In this work, molecular dynamics (MD) simulations using ReaxFF potential are performed to explore the atomic-scale corrosion mechanisms of body-centered cubic iron (BCC-Fe) in S-CO2. The results show that CO2 molecules in S-CO2 decompose at the Fe surface, generating free C and O atoms that form Fe-C and Fe-O bonds and subsequently produce oxides and carbides. Concurrently, Fe atoms dissolve from the surface and diffuse into the S-CO2 region, resulting in interdiffusion of Fe, C and O atoms at the interface. The corrosion-layer thickness calculations show that high pressure and temperature induced by S-CO2 have stronger effects than surface orientation on the corrosion process. In addition, surface Fe atoms undergo substantial displacement under S-CO2 exposure, further accelerating corrosion. When a radiation-induced void is introduced near the Fe surface, the corrosion is enhanced. The void-matrix interface expands the reaction surface area and simultaneously induces corrosion reactions inside the bulk, resulting in a deeper penetration of C and O and thicker corrosion layers. All these results indicate that high-temperature, high-pressure and radiation-induced voids can seriously affect the corrosion of Fe in S-CO2, and must be considered to better use S-CO2 in nuclear facilities.

Li, Wenhua

Method of making thin films of sodium fluorides and their derivatives by ALD

A method of making thin films of sodium fluorides and their derivatives by atomic layer deposition (“ALD”). A sodium precursor is exposed to a substrate in an ALD reactor. The sodium precursor is purged, leaving the substrate with a sodium intermediate bound thereon. A fluorine precursor is exposed to the bound sodium intermediate in the ALD reactor. The fluorine precursor is purged and a sodium fluoride film is formed on the substrate.

Mane, Anil U.

Robust and tunable oxide nanoscrolls for solar-driven H 2 generation and storage

Hydrogen gas is a promising alternative to fossil fuels due to its high energy output and environmentally safe byproducts. Various morphologies of photocatalytic materials have been explored for high-efficiency H 2 production, for instance, quasi-1D nanoscroll structures that provide a larger surface-to-volume ratio. Recently, we predicted layer-by-layer formation of stable oxide nanoscrolls directly from dichalcogenide precursors, eliminating the need for costly formation of two-dimensional oxides for a roll-up synthesis of nanoscrolls. Here, in this study, we evaluate the suitability of those oxide nanoscroll materials—MoO 3 , WO 3 , PdO 2 , HfO 2 , and GeO 2 —for solar-driven photocatalytic H 2 production and storage. Using excited state theory coupled with Bethe–Salpeter equation simulations, we discern their electronic and optical properties as a function of interlayer scroll spacing and find them to be highly conducive for solar-driven photocatalysis. Additionally, using ab initio molecular dynamics simulations, we show that they are also suitable for H 2 storage as the nanoscrolls exhibit an effective trapping of hydrogen, even in the presence of defects and vacancies in the oxides. This work thus demonstrates the discovery of robust and tunable oxide nanoscrolls as materials for advancing solar-driven hydrogen technologies.

Chemical compounds

Effect of Oxidizing Impurities on the Corrosion Behavior of Structural Alloys Exposed to MgCl 2 Molten Salt Vapor

The corrosion behavior of structural alloys SS304 and IN617 when exposed to vapors of MgCl 2 molten salt at 764 °C for 100 h in an argon atmosphere was investigated as a function of the level of oxidizing impurities (e.g., NaOH) present in the salt. Increasing the concentration of oxidizing impurities in the salt caused an increase in corrosion in both structural alloys, as measured by Cr depletion layers. A poorly adhered oxide scale layer containing Mg, Al, and Cr was observed on the surface of the metals, and local attack was observed as well. The Ni-based IN617 showed lower Cr depletion and less scale formation than the Fe-based SS304. These results demonstrate that oxidizing impurities in the molten salt will impact the vapor phase corrosion for structural members exposed to the molten salt headspace. This finding is highly relevant for understanding the effects of the vapor phase in molten salt applications, including molten salt thermal energy storage, molten salt nuclear reactors, and molten salt electrochemistry.

25 ENERGY STORAGE

Imaging a terahertz superfluid plasmon in a two-dimensional superconductor

The superconducting gap defines the fundamental energy scale for the emergence of dissipationless transport and collective phenomena in a superconductor. In layered high-temperature cuprate superconductors, in which the Cooper pairs are confined to weakly coupled two-dimensional (2D) copper–oxygen (CuO 2 ) planes, terahertz (THz) spectroscopy at subgap millielectronvolt (meV) energies has provided crucial insights into the collective superfluid response perpendicular to the superconducting layers. However, within the CuO 2 planes, the collective superfluid response manifests as plasmonic charge oscillations at energies far exceeding the superconducting gap, obscured by strong dissipation. Here, in this study, we present spectroscopic evidence of a below-gap, 2D superfluid plasmon in few-layer Bi 2 Sr 2 CaCu 2 O 8+x and spatially resolve its deeply subdiffractive THz electrodynamics. By placing the superconductor in the near field of a spintronic THz emitter, we reveal this distinct resonance—absent in bulk samples and observed only in the superconducting phase—and determine its plasmonic nature by mapping the geometric anisotropy and dispersion. Crucially, these measurements offer a direct view of the momentum-dependent and frequency-dependent superconducting transition in two dimensions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND