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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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533 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Anion-dependent phase behavior of methylimidazolium-based ionic liquids mixed with water: Correlation between local molecular structure and mesoscale behaviors

The mesoscopic phase behavior of decylmethylimidazolium (C 10 mim) ionic liquids (ILs) bearing three monovalent anions—thiocyanate (SCN − ), nitrate (NO 3 − ), and chloride (Cl − )—mixed with water at relatively high IL contents (50–95 wt%) was investigated. Small-angle and wide-angle X-ray scattering (SAXS/WAXS) were employed to follow the evolution of both local and mesoscale structures across this composition range. In the absence of water, C 10 mimSCN and C 10 mimCl behaved as disordered liquids, whereas C 10 mimNO 3 spontaneously formed a hexagonally ordered cylindrical mesophase and displayed a sticky-solid macroscopic appearance. Upon addition of water, C 10 mimSCN remained a viscous liquid and only weakly ordered lamellar domains were observed. This limited ordering is attributed to the lack of hydrogen bonding and weak interaction energy between SCN − anions and C 10 mim + cations. In contrast, the trigonal-planar NO 3 − and point-like Cl − anions promoted the formation of well-defined hexagonal mesophases up to 35–45 wt% water. The formation of hydrogen bonding of the two anions with imidazolium ring protons likely enabled the creation of compact ion clusters that effectively exclude water molecules from the immediate vicinity of the IL aggregates. These findings demonstrate that the interaction energy between ion pairs dictate IL-water interactions and therefore control the transition from disordered liquids to ordered mesophases in IL/water mixtures with high IL contents. In conclusion, the combined SAXS/WAXS analysis reveals a correlation between local intermolecular structure and the emergence of mesoscopic order, providing a systematic framework for tailoring mesoscale structures in alkylimidazolium-based IL/water systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Predicting microstructurally sensitive fatigue‐crack path in WE43 magnesium using high‐fidelity numerical modeling and three‐dimensional experimental characterization

Abstract Microstructurally small fatigue‐crack growth in polycrystalline materials is highly three‐dimensional due to sensitivity to local microstructural features (e.g., grains). One requirement for modeling microstructurally sensitive crack propagation is establishing the criteria that govern crack evolution, including crack deflection. Here, a high‐fidelity finite‐element modeling framework is used to assess the performance and validity of various crack‐growth criteria, including slip‐based metrics (e.g., fatigue‐indicator parameters), as potential criteria for predicting three‐dimensional crack paths in polycrystalline materials. The modeling framework represents cracks as geometrically explicit discontinuities and involves voxel‐based remeshing, mesh‐gradation control, and a crystal‐plasticity constitutive model. The predictions are compared to experimental measurements of WE43 magnesium samples subject to fatigue loading, for which three‐dimensional grain structures and fatigue‐crack surfaces were measured post‐mortem using near‐field high‐energy x‐ray diffraction microscopy and x‐ray computed tomography. Findings from this work are expected to improve the predictive capabilities of simulations involving microstructurally small fatigue‐crack growth in polycrystalline materials.

Engineering↗
DOE OSTI2024

Multiple Peaks and a Long Precursor in the Type IIn Supernova 2021qqp: An Energetic Explosion in a Complex Circumstellar Environment

Abstract We present optical photometry and spectroscopy of the Type IIn supernova (SN) 2021qqp. Its unusual light curve is marked by a long precursor for ≈300 days, a rapid increase in brightness for ≈60 days, and then a sharp increase of ≈1.6 mag in only a few days to a first peak ofM r ≈ −19.5 mag. The light curve then declines rapidly until it rebrightens to a second distinct peak ofM r ≈ −17.3 mag centered at ≈335 days after the first peak. The spectra are dominated by Balmer lines with a complex morphology, including a narrow component with a width of ≈1300 km s −1 (first peak) and ≈2500 km s −1 (second peak) that we associate with the circumstellar medium (CSM) and a P Cygni component with an absorption velocity of ≈8500 km s −1 (first peak) and ≈5600 km s −1 (second peak) that we associate with the SN–CSM interaction shell. Using the luminosity and velocity evolution, we construct a flexible analytical model, finding two significant mass-loss episodes with peak mass loss rates of ≈10 and ≈5M ⊙ yr −1 about 0.8 and 2 yr before explosion, respectively, with a total CSM mass of ≈2–4M ⊙ . We show that the most recent mass-loss episode could explain the precursor for the year preceding the explosion. The SN ejecta mass is constrained to be ≈5–30M ⊙ for an explosion energy of ≈(3–10) × 10 51 erg. We discuss eruptive massive stars (luminous blue variable, pulsational pair instability) and an extreme stellar merger with a compact object as possible progenitor channels.

Astronomy & Astrophysics↗
DOE OSTI2025

Surface deposition of nanometer scale carbon structures on Bi 2 Sr 2 CaCu 2 O 8+δ using a low-cost scanning electron microscope

In this work, we investigate optically active nanostructures on Bi 2 Sr 2 CaCu 2 O 8+δ (BSCCO). The nanostructures are constructed from carbon nanocrystals formed using the electron beam of a scanning electron microscope to locally decompose residual hydrocarbons at the BSCCO surface. Atomic force microscopy is used to characterize the dimensions of these structures as a function of beam exposure time. This technique has been used to induce localized intercalation to form carbon nanoparticles up to tens of nanometers into a variety of 2D materials. Cross-sectional scanning transmission electron microscopy in BSCCO shows the presence of these carbon deposits on the surface, but there is no evidence they penetrate into the BSCCO substrate. Therefore, this technique is not suitable for localized intercalation in BSCCO, and it does have promise as a cost-effective approach to pattern nanometer scale etch stops.

2D materials↗
DOE OSTI2024

Enhanced Hydrogen Evolution Catalysis of Pentlandite due to the Increases in Coordination Number and Sulfur Vacancy during Cubic‐Hexagonal Phase Transition

Abstract The search for new phases is an important direction in materials science. The phase transition of sulfides results in significant changes in catalytic performance, such as MoS 2 and WS 2 . Cubic pentlandite [cPn, (Fe, Ni) 9 S 8 ] can be a functional material in batteries, solar cells, and catalytic fields. However, no report about the material properties of other phases of pentlandite exists. In this study, the unit‐cell parameters of a new phase of pentlandite, sulfur‐vacancy enriched hexagonal pentlandite (hPn), and the phase boundary between cPn and hPn are determined for the first time. Compared to cPn, the hPn shows a high coordination number, more sulfur vacancies, and high conductivity, which result in significantly higher hydrogen evolution performance of hPn than that of cPn and make the non‐nano rock catalyst hPn superior to other most known nanosulfide catalysts. The increase of sulfur vacancies during phase transition provides a new approach to designing functional materials.

Chemistry↗
DOE OSTI2025

Structure–Property Linkage in Alloys Using Graph Neural Network and Explainable Artificial Intelligence

Deep learning tools have recently shown significant potential for accelerating the prediction of microstructure–property linkage in materials. While deep neural networks like convolution neural networks (CNNs) can extract physics information from 3D microstructure images, they often require a large network architecture and substantial training time. In this research, we trained a graph neural network (GNN) using phase field generated microstructures of Ni-Al alloys to predict the evolution of mechanical properties. We found that a single GNN is capable of accurately predicting the strengthening of Ni-Al alloys with microstructures of varying sizes and dimensions, which cannot otherwise be done with a CNN. Additionally, GNN requires significantly less GPU utilization than CNN and offers more interpretable explanation of predictions using saliency analysis as features are manually defined in the graph. We also utilize explainable artificial intelligence tool Bayesian Inference to determine the coefficients in the power law equation that governs coarsening of precipitates. Overall, our work demonstrates the ability of the GNN to accurately and efficiently extract relevant information from material microstructures without having restrictions on microstructure size or dimension and offers an interpretable explanation.

Chemistry↗
DOE OSTI2025

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗
DOE OSTI2026

Conformational Isomerization of Imide Anions Governs Solvation and Transport in Water-in-Salt Electrolytes

The behavior of highly concentrated electrolytes departs radically from the dilute-solution theory, yet the molecular origin of this transformation remains unresolved. Here, we identify the conformational isomerization of molecular ions as a decisive, previously unrecognized control parameter governing structure and transport in crowded aqueous electrolytes. Across a series of fluorosulfonimide anions, we show that increasing concentration drives a collective shift from extended transoid to compact cisoid conformers, revealed by small-angle X-ray scattering, vibrational spectroscopy, pulsed-field gradient NMR, and molecular dynamics simulations. This conformational transition triggers a collapse of the hydrogen-bonded water network and the emergence of densely packed ionic domains with confined water, producing a qualitative change in Li+ transport from solvent-mediated diffusion to network-confined hopping. Anion size and asymmetry systematically tune the onset of this transition, demonstrating that molecular geometry dictates mesoscale organization and dynamics in the ion-rich regime. Our results establish ion conformation, not merely composition or coordination, as a fundamental thermodynamic variable in concentrated solutions, providing a chemical framework that unifies solvation structure and transport in water-in-salt electrolytes and suggesting new principles for designing dense ionic media.

Nguyen, Huong TD↗
DOE OSTI2024

Autonomous phototaxis of hydrogel swimmers

The design of synthetic soft matter capable of emulating the complex behaviors of living organisms, such as sensing and adapting to their environment, remains an important challenge in developing biomimetic materials. Functionalized hydrogels are ideal candidates for such materials since they are highly responsive to their environment and can be operated in water. In this work, we investigate a hybrid bonding hydrogel composed of peptide amphiphile supramolecular nanofibers covalently attached to a photoresponsive network, in which high-aspect-ratio ferromagnetic nanowires are aligned along the length of the sample, designed to swim under oscillating magnetic fields. This hybrid hydrogel swimmer can autonomously swim toward a light source by utilizing photoinduced interactions between supramolecular and covalent networks reminiscent of phototactic swimming in living systems. Using a combination of experimental techniques and a continuum model incorporating photochemistry, magnetoelasticity, and hydrodynamics, we explain the swimming mechanism and predict phototactic behavior. Our work highlights the potential role of hybrid bonding polymers, which leverage the interplay between supramolecular assemblies and covalent networks. We demonstrate how these polymers can be tailored to react dynamically to their environment, paving the way for developing intelligent and autonomous robotic systems.

Science & Technology - Other Topics↗
DOE OSTI2026

SILICON CARBIDE THERMOMETRY USING RAMAN SPECTROSCOPY ON IRRADIATED TRISO PARTICLES

Silicon carbide (SiC) passive thermometry has emerged as a promising post-irradiation examination (PIE) technique for estimating irradiation temperature near the end of irradiation. While dilatometry techniques have been traditionally used to analyze prismatic samples after irradiation, Raman spectroscopy has recently been shown to provide comparable results by analyzing Raman-active phonon modes. In this work, Raman spectroscopy has been applied to the SiC layer of cross-sectioned irradiation tristructural isotropic (TRISO) particles from the AGR-5/6/7 experiment to evaluate the feasibility of particle-scale passive thermometry. Two-dimensional Raman mapping was used to measure the position of the SiC longitudinal optical (LO) phonon, which was then converted to an apparent irradiation temperature using a previously established empirical correlation. Particles from AGR-5/6/7 Compacts 2-2-1 and 5-1-3 were selected as their calculated time-averaged, volume-averaged (TAVA) temperatures (828°C and 706°C, respectively) fall within the range of the sensitivity of the experimental approach. The use of SiC thermometry was anticipated to confirm or highlight potential deviations from calculated end-of-life TAVA temperature across compacts. Four particles from Compact 2-2-1 and two particles from Compact 5-1-3 were selected based on 110mAg inventory (either some measurable activity or below the minimum detection limit) which is commonly used as an indicator of in-pile temperature variation of particles within the same compact. Across every particle selected it was determined that the average LO peak position was located around 968 cm-1 to 969 cm-1. Using the previously determined empirical correlation, this corresponds to an irradiation temperature around 950°C to 966°C, which does not align with the reported TAVA temperature values. This discrepancy in apparent irradiation temperatures likely reflects a combination of uncertainties in the calculated particle temperatures and differences in irradiation history between the present specimens and those used to establish the empirical Raman calibration such as neutron flux (damage rate) and SiC microstructure (as fabricated and irradiated).

Vawdrey, Josh [ORNL]↗
DOE OSTI2024

WRF-Comfort: simulating microscale variability in outdoor heat stress at the city scale with a mesoscale model

Abstract. Urban overheating and its ongoing exacerbation due to global warming and urban development lead to increased exposure to urban heat and increased thermal discomfort and heat stress. To quantify thermal stress, specific indices have been proposed that depend on air temperature, mean radiant temperature (MRT), wind speed, and relative humidity. While temperature and humidity vary on scales of hundreds of meters, MRT and wind speed are strongly affected by individual buildings and trees and vary on the meter scale. Therefore, most numerical thermal comfort studies apply microscale models to limited spatial domains (commonly representing urban neighborhoods with building blocks) with resolutions on the order of 1 m and a few hours of simulation. This prevents the analysis of the impact of city-scale adaptation and/or mitigation strategies on thermal stress and comfort. To solve this problem, we develop a methodology to estimate thermal stress indicators and their subgrid variability in mesoscale models – here applied to the multilayer urban canopy parameterization BEP-BEM within the Weather Research and Forecasting (WRF) model. The new scheme (consisting of three main steps) can readily assess intra-neighborhood-scale heat stress distributions across whole cities and for timescales of minutes to years. The first key component of the approach is the estimation of MRT in several locations within streets for different street orientations. Second, mean wind speed and its subgrid variability are downscaled as a function of the local urban morphology based on relations derived from a set of microscale LES and RANS simulations across a wide range of realistic and idealized urban morphologies. Lastly, we compute the distributions of two thermal stress indices for each grid square, combining all the subgrid values of MRT, wind speed, air temperature, and absolute humidity. From these distributions, we quantify the high and low tails of the heat stress distribution in each grid square across the city, representing the thermal diversity experienced in street canyons. In this contribution, we present the core methodology as well as simulation results for Madrid (Spain), which illustrate strong differences between heat stress indices and common heat metrics like air or surface temperature both across the city and over the diurnal cycle.

Geology↗
DOE OSTI2025

Dimensional Evolution Guides Property Control in the A n Cu 4– n TiS 4 Semiconductor Series

Through progressive reduction of the three-dimensional (3D) covalent network of Cu 4 TiS 4 , we isolate seven new members of the A n Cu 4–n TiS 4 family (A = alkali metal; n = 0–4), spanning 3D, 2D, 1D, and 0D structural fragments. The dimensional reduction is rational, as it preserves the edge-sharing connectivity between [CuS 4 ] 7– and [TiS 4 ] 4– tetrahedra across the series. This structural evolution is driven by the stepwise substitution of Cu with alkali metals, guiding the formation of fragments with reduced dimensionality. The effects of “n” and “A” on the crystal structures, stabilities, electronic structures, and optoelectronic properties are profound, demonstrating that the manipulation of alkali metal size and A n Cu 4–n TiS 4 stoichiometry enables predictable variations in structure and properties. For example, the n = 0 and n = 4 end members of the A n Cu 4–n TiS 4 family set the range of achievable band gaps with 2.00 eV for Cu 4 TiS 4 , 2.60 eV for Na 4 TiS 4 , and intermediate values for the n = 1–3 members. Notably, CsCu 3 TiS 4 exhibits exceptional air stability and congruent melting, with density functional theory (DFT) calculating moderate hole and electron effective masses in specific crystallographic directions (mh = 1.24m 0 , me = 0.87m 0 ). Additionally, A 3 CuTiS 4 (A = Na, K, Rb) displays direct band gap behavior and long photoluminescence lifetimes of 2.3–8.6 μs, and K 3 CuTiS 4 has a PLQY of 5.19%. These findings underscore the potential of the A n Cu 4–n TiS 4 family for applications in optoelectronics and demonstrate widely applicable design concepts that unveil rational stoichiometries within a given composition space to generate a series of crystal structures related through an evolving covalent dimensionality that corresponds to a predictable electronic structure and property progression.

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

Topological prethermal strong zero modes on superconducting processors

Abstract Symmetry-protected topological phases 1–4 cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model 5 . They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations 1–4,6–8 . In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay 9–11 . Here we report the observation of a distinct type of topological edge mode 12–14 , which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach 15–18 to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems.

Science & Technology - Other Topics↗
DOE OSTI2025

Gauge theory of giant phonon magnetic moment in doped Dirac semimetals

Here, we develop a quantitative theory of phonon magnetic moment in doped Dirac semimetals. Our theory is based on an emergent gauge field approach to the electron-phonon coupling, applicable to gapless systems. We find that the magnetic moment is directly proportional to the electrical Hall conductivity through the phonon Hall viscosity. Our theory is combined with the first-principles calculations, allowing us to quantitatively implement it to realistic materials. Magnetic moments are found to be of the order of a Bohr magneton for Raman-active phonon modes in graphene and Cd 3 ⁢As 2 . Our results provide practical guidance for the dynamical generation of large magnetization in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Reversible control over the distribution of chemical inhomogeneities in multiferroic BiFeO3

Abstract Despite the appeal of flawless order, semiconductor technology has demonstrated that implanting inhomogeneities into single-crystalline materials is pivotal for modern electronics. However, the influence of the local arrangement of chemical inhomogeneities on the material’s functionalities is underexplored. In this work, we control the distribution of chemical inhomogeneities in La 3+ -substituted ferroelectric BiFeO 3 thin films. By means of a stress- and composition-driven phase transition, we trigger the formation of a lattice of La 3+ -rich and La 3+ -poor layers. This ordering correlates with the emergence of an antipolar phase. An electric field restores the original ferroelectric phase and re-randomizes the distribution of the La 3+ inhomogeneities. Leveraging these insights, we tune the polar/antipolar phase coexistence to set the net polarization of La 0.15 Bi 0.85 FeO 3 to any desired value between its saturation limits. Finally, we control the net polarization response in device-compliant capacitor heterostructures to show that inhomogeneity-distribution control is a valuable tool in the design of functional oxide electronics.

Science & Technology - Other Topics↗
DOE OSTI2026

Direct Observation of Elusive (DTBM‐SEGPHOS)CuH Monomer Enables Mechanistic Insights Into Hydrocupration, Aggregation, and Dynamics of Alkene Functionalization Catalysis

The bulky diphosphine DTBM-SEGPHOS is widely employed in CuH-catalyzed transformations as it provides remarkably active catalyst systems. The transient (DTBM-SEGPHOS)CuH monomer (LCuH) is the often-invoked active species. However, its instability has prevented spectroscopic characterization and mechanistic elucidation, hindering mechanistic understanding. We report low-temperature NMR spectroscopic characterization of LCuH, enabling quantitative kinetic analysis of the stoichiometric hydrocupration and catalytic hydroboration of cyclopentene, as well as the structural identification of two CuH clusters. LCuH inserts cyclopentene at −43°C, reaffirming its high reactivity toward olefins. LCuH deactivates to form L 2 Cu 3 H 3 and L 2 Cu 4 H 4 clusters, in which LCuH dimerization initiates aggregation. Kinetic analysis of reactions of unactivated alkenes indicates that competing on-cycle alkene hydrocupration and LCuH dimerization impact performance, as catalyst deactivation and turnover occur on comparable timescales. Structure–activity analysis using atomistic simulations shows that the steric profile of DTBM-SEGPHOS increases the CuH dimerization barrier by ∼7.7 kcal mol−1 compared to that of SEGPHOS, rationalizing the unique ability of DTBM-SEGPHOS to stabilize a reactive monomer for hydrocupration of broader alkene substrates. These findings illustrate the fundamental design principle that steric control of aggregation governs CuH catalyst performance, explaining both the exceptional activity of (DTBM-SEGPHOS)CuH and the limitations imposed by competing deactivation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Understanding Photovoltage Deficits in Electrochemically Grown Tin Sulfide (SnS) Thin-Film Photovoltaic Devices

Tin­(II) sulfide (SnS) is an earth-abundant semiconductor with a direct optical bandgap of ca. 1.1 eV, which makes it a promising absorber material for thin-film photovoltaic (PV) devices. However, existing devices have significant photovoltage deficits, which may be related to the anisotropic structure of the layered Herzenbergite SnS crystal structure. Here, we explore electrochemical deposition as a near room temperature path to oriented SnS crystal films on Mo and FTO substrates and employ vibrating Kelvin probe surface photovoltage (SPV) spectroscopy and J–V measurements to identify conversion losses in them. According to grazing-incidence X-ray diffraction and SEM, the SnS films consist of crystalline microplates with preferred orientation in the [111] and [001] directions. The bare SnS films produce only small and irreversible surface photovoltage signals, due charge trapping and recombination at the SnS surfaces, but addition of a CdS buffer layer lowers the charge recombination rate by 2 orders of magnitude and increases both the photovoltage and its reversibility due to the formation of a p-SnS/n-CdS junction. According to SPV, the FTO/SnS back interface (but not the Mo/SnS interface) forms a detrimental p–n junction that hinders hole transfer. Additional shunting through the relatively open microcrystal SnS layers and a lower conductivity of the FTO substrate explain the low power conversion efficiencies of the final devices (0.18 and 0.10% for the Mo and FTO substrates). Altogether, this work establishes a low-temperature path for the fabrication of crystalline SnS film-based solar cells and identifies the bottlenecks that limit high photoconversion efficiency.

deposition↗
DOE OSTI2026

Electronic glasses from a broken gauge symmetry in disorder-free systems

Glass phases can be stabilized by quenched disorders, as in most spin-glass materials, or self-generated through kinetic freezing in disorder-free systems. A canonical example of the latter is structural glasses, which have been extensively studied for many decades. Yet, how the rugged energy landscape of a glass phase is spontaneously generated in disorder-free systems remains one of the key questions in glass physics. Here, in this work, we present a general electronic mechanism for the emergence of glassy phase using the example of itinerant electrons coupled to XY spins on a lattice. This model can also be viewed as the mean-field theory of a superconducting system with attractive density-density interactions. Intriguingly, the electron gauge symmetry in the strong pairing limit gives rise to a macroscopic degeneracy of XY spins. In the presence of electron hopping that breaks the gauge symmetry, the lifting of the extensive degeneracy leads to a glass phase with disordered pairings. Our findings highlight a scenario in which a glassy state originates from the breaking of quantum gauge symmetry without quenched disorders.

XY model↗