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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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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Foam Fracturing Study for Stimulation Development of Enhanced Geothermal Systems

The large thermal gradients and high subsurface temperatures of the western region of the U.S. hold great potential for the implementation of enhanced geothermal systems (EGS). The development of these potential EGS resources requires stimulation of the reservoir to enhance permeability and it has been widely reported that a substantial amount of water will be required should conventional hydraulic stimulation be used. This presents a huge challenge and a high risk to the geothermal development because the water stress1 in these areas is already high or extremely high. The use of foam, a gas/liquid mixture predominantly composed of gas, in fracturing is considered and explored in this project as a potential approach to address water concerns with hydraulic stimulation in the development of EGS. This project, led by Oak Ridge National Laboratory (ORNL) in collaboration with Temple University, was awarded in an open lab call in 2018, and was part of the DOE GTO waterless stimulation initiative. The goal of the project was to demonstrate the feasibility of foam fracturing for EGS development through two primary tasks: Task 1: Laboratory study of the effectiveness of foam fracturing for representative geological materials, including cyclic pressurization using foam (led by ORNL) and Task 2: High temperature foam material selection and characterization (led by Temple University). In FY19, ORNL finished the critical review on serval issues associated with foam fracturing and the implementation of the proposed tasks in a lab study (Wang, et al., 2019), and completed the foam fracturing testing using cement as a model material (Wang, et al, 2020a). The work at ORNL was geared up to develop a brand-new foam testing system in FY20. The purchase of main components for the new system was finished in the first half of the FY20. The assembly of the foam testing system and foam fracturing testing were completed in the second half of the FY20 (Wang, et al., 2021a). Task 1 required the development of a test system which can be used to perform hydraulic fracturing of geological specimens with both water and foamed liquids at pressure up to 6,000 psi (41.4 MPa). The system possesses several capabilities that conventional injection systems lack for hydraulic fracturing. In addition to its ability to generate foam with controlled quality, it is capable of cycling pressure levels between specified values up to frequencies of 50 Hz. The latter capability was developed to evaluate the hypothesis that cyclic loading of samples would produce enhanced fracturing. The system consists of two sections: one for foam generation and another for foam injection. The foam is generated through separate control and pressurization of liquid and gas phases with controlled flow rates. The injection section is equipped with a low-flow Coriolis flow that monitors the density of foam to ensure the injection is in the range of target foam quality2. Experimental results of foam fracturing are reported for cylindrical granite specimens using water and aqueous N2 foam as the fracturing fluids. All experiments were performed for unconfined conditions. The effects of injection mode (i.e., monotonic vs cyclic pressurization) on breakdown pressure and failure response sample were investigated using water alone as a fracturing fluid and foams with a range of compositions. It was found that in the case of monotonic injection, the breakdown pressure of granite specimens tended to be slightly higher when fracturing with foam. Additionally, with a foam quality of 90%, the water use can be reduced by 50 to 84%, depending on hole size. On the other hand, it was observed that the breakdown pressure can be brought down to 70% of the monotonic breakdown pressure by using low cycle fatigue. Finally, discussions are presented regarding injectivity and water use reduction.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Assessing entropy for catalytic processes at complex reactive interfaces

When chemical reactions are accelerated by a catalyst, entropy differences between reactants and their transient intermediates can be the driving force behind the promotion or inhibition of desired and parasitic chemical pathways. Understanding and controlling catalytic processes therefore requires both a fundamental and practicable understanding of entropy in addition to enthalpy. In unstructured media such as the vapor phase equilibrated with sparsely covered surfaces, entropy can be adequately accounted for by well-established approaches based on translational, rotational, and harmonic vibrational partition functions. However, these approximations become inadequate in more complex condensed phase environments, e.g., solid liquid interfaces of confined reaction spaces. In this chapter, we provide an overview of the state-of-art in the computational quantification of entropy and its known ramifications on catalysis. The fundamental roles of thermodynamics and kinetics in catalysis are covered in enough detail to appreciate and contextualize the computational methods employed to compute chemically accurate estimates of entropy. These methods are discussed in appropriate detail and range from the ubiquitous harmonic oscillator approximation where entropy unrelated to high frequency oscillations is typically underestimated, to enhanced free energy sampling with molecular dynamics where the desired accuracy must be weighed against the associated computational cost of obtaining it. The rising importance of machine learning and artificial intelligence in accelerating methodological progress in this field is touched upon, as well. Finally, applications, successes, and pitfalls of using these methods are provided to showcase past and present accomplishments while clarifying where improvements in both understanding and methodology are still needed.

Kollias, Loukas↗
DOE OSTI2025

An epitaxial surface heterostructure anchoring approach for high-performance Ni-rich layered cathodes

Nickel-rich (Ni≥90%) layered oxides materials have emerged as a promising candidate for next-generation high-energy-density lithium-ion batteries (LIBs). However, their widespread application is hindered by structural fatigue and lattice oxygen loss. In this work, an epitaxial surface rock-salt nanolayer is successfully developed on the LiNi 0.9 Co 0.1 O 2 sub-surface via heteroatom anchoring utilizing high-valence element molybdenum modification. This in-situ formed conformal buffer phase with a thickness of 1.2nm effectively suppresses the continuous interphase side-reactions, and thus maintains the excellent structure integrity at high voltage. Furthermore, theoretical calculations indicate that the lattice oxygen reversibility in the anion framework of the optimized sample is obviously enhanced due to the higher content of O 2p states near the Fermi level than that of the pristine one. Meanwhile, the stronger Mo–O bond further reduces cell volume alteration, which improves the bulk structure stability of modified materials. Besides, the detailed charge compensation mechanism suggests that the average oxidation state of Ni is reduced, which induces more active Li + participating in the redox reactions, boosting the cell energy density. As a result, the uniquely designed cathode materials exhibit an extraordinary discharge capacity of 245.4 mAh g −1 at 0.1 C, remarkable rate performance of 169.3 mAh g −1 at 10 C at 4.5V, and a high capacity retention of 70.5% after 1000 cycles in full cells at a high cut-off voltage of 4.4V. Further, this strategy provides an valuable insight into constructing distinctive heterostructure on high-performance Ni-rich layered cathodes for LIBs.

25 ENERGY STORAGE↗
DOE OSTI2025

Exploring Cs 2 AgIn x Bi 1− x Cl 6 double perovskites for optoelectronics: insights from theoretical and photophysical approaches

Lead-free halide double perovskites (HDPs) have become attractive materials for optoelectronic applications owing to their nontoxicity, structural stability, and germane photoelectric properties. In this work, we report the synthesis of high-quality In-alloyed Cs 2 AgIn x Bi (1−x) Cl 6 nanocrystals (NCs) using the antisolvent recrystallization method and comprehensively investigate the effects of In alloying on the structural, morphological, optoelectronic, and temperature-dependent photoluminescence (TDPL) properties using the state-of-the-art experimental and computational tools. Both XRD and Raman spectroscopy analyses confirmed the synthesis of highly crystalline Cs 2 AgIn x Bi (1−x) Cl 6 materials, which exhibited cubic morphology, as confirmed by TEM analysis. Room-temperature photoluminescence (PL) measurements revealed a drastic increase in the intensity above 75% In concentration with dual emission, whereas the time-resolved PL (TR-PL) results show an increase in the average lifetime values with an increase in In content, suggesting that the materials have excellent optical properties and hence are suitable candidates for optoelectronics. The TDPL measurements revealed the smallest Huang–Rhys factor (18.6) for the Cs 2 AgIn x Bi (1−x) Cl 6 (x = 0.9) sample, indicating weak exciton–phonon coupling in this composition. When deployed in the fabrication of a photodetector device, the Cs 2 AgIn x Bi (1−x) Cl 6 (x = 0.9) sample exhibited significantly enhanced photoresponsivity and a faster response time, confirming its potential for photodetector applications. Complementary DFT calculations showed that In alloying modifies the band structure of Cs 2 AgIn x Bi (1−x) Cl 6 . Our results provide valuable insights for designing multifunctional Cs 2 AgIn x Bi (1−x) Cl 6 -based materials for next-generation energy and optoelectronic devices.

14 SOLAR ENERGY↗
DOE OSTI2020

Cooperative response of magnetism and superconductivity in the magnetic superconductor RbEuFe 4 As 4

Herein, we present a study of the magnetic-flux evolution in the magnetic superconductor RbEuFe 4 As 4 performed using magneto-optical imaging and magnetization measurements during field cooling and warming and magnetic field cycling at temperatures above and below the magnetic transition point, T$_m$. The vortex patterns emerging at T ≲ T$_m$ reveal that the Eu-spin subsystem serves as an internal pump of the magnetic flux while the superconducting critical current controls the delivery of magnetic-flux quanta into the bulk. The interplay of magnetic susceptibility amplifying the magnetic induction and vortex pinning attenuating the magnetic-flux entry results in a field- and temperature-dependent critical state that emulates a paramagnetic Meissner effect. The observed vortex dynamics corresponds to a nontrivial spatial current distribution and yields a self-consistent inhomogeneous enhancement of the sample magnetization.

36 MATERIALS SCIENCE↗
DOE OSTI2024

PPI DataHub Project Data Package: S. elongatus PCC 7942 Circadian Control Bioproduction Metabolomics (PB-DP5)

The purpose of this experiment was to evaluate how circadian clock regulation impacts carbon partitioning between storage, growth, and product synthesis in Synechococcus elongatus PCC 7942 in providing insights to strategies for enhanced bioproduction. Culture samples were collected at 0, 0.5, 1, 2, 4, 6, and 8 hours for extracellular sucrose analysis. Circadian metabolomics data was acquired using a Agilent single quadrupole gas chromatography-mass spectrometer and processed using Agilent Mass Hunter for targeted sucrose quantification. Metabolomic analysis of PCC 7942 light-dark cycle cultures transitioned to constant light revealed distinct temporal patterns in sucrose production. Processed metabolomic datasets are openly accessible from the PNNL DataHub project dataset download page and contain secondary processed GC-MS results files and supporting metadata materials linked to relevant source code information supporting data transparency and reuse.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

An IFU View of the Active Galactic Nuclei in MaNGA Galaxy Pairs

The role of active galactic nuclei (AGNs) during galaxy interactions and how they influence the star formation in the system are still under debate. We use a sample of 1156 galaxies in galaxy pairs or mergers (hereafter "pairs") from the MaNGA survey. This pair sample is selected by the velocity offset, projected separation, and morphology, and is further classified into four cases along the merger sequence based on morphological signatures. We then identify a total of 61 (5.5%) AGNs in pairs based on the emission-line diagnostics. No evolution of the AGN fraction is found, either along the merger sequence or compared to isolated galaxies (5.0%). We observe a higher fraction of passive galaxies in galaxy pairs, especially in the pre-merging cases, and associate the higher fraction to their environmental dependence. The isolated AGN and AGNs in pairs show similar distributions in their global stellar mass, star-formation rate (SFR), and central [O iii] surface brightness. AGNs in pairs show radial profiles of increasing specific SFR and declining Dn4000 from center to outskirts, and no significant difference from the isolated AGNs. This is clearly different from star-forming galaxies (SFGs) in our pair sample, which show enhanced central star formation, as reported before. AGNs in pairs have lower Balmer decrements at outer regions, possibly indicating less dust attenuation. Our findings suggest that AGNs are likely follow an inside-out quenching and the merger impact on the star formation in AGNs is less prominent than in SFGs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Dimuon production in the MicroBooNE detector

This analysis studies the production of the rare signal with two muons (dimuon) in the finalstate at µB using the Booster Neutrino Beam (BNB) as source of neutrino interactions. Themain background source for the dimuon signal are pions. Differentiating muons and pions hasbeen challenging at µB because the tracks left by these particles are almost identical. Thisanalysis faces this problem using a supervised classifier algorithm called boosted decisiontree (BDT). A Monte Carlo simulation (MC) enhanced dimuon signal sample was producedto train a BDT capable of recognizing this signal. A set of variables that show somediscrimination characteristics was used to perform the training. A MC neutrino interactionsimulation sample was used to estimate the background. Estimations of dimuon productionin real data samples were made for different cases. Additionally, an analysis of the systematicuncertainties, fake data studies, and BDT performance checks were obtained.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Cyclic moisture reactivation of calcium sorbents for long duration thermochemical energy storage

The transition to a flexible and reliable energy infrastructure, using electro-thermal energy generation technologies such as geothermal, concentrated solar power, and nuclear, usually demands simultaneous advancement of thermal energy storage (TES) to support on-demand electricity generation and industrial applications while mitigating the inherent intermittency of renewable energy sources and power outages from direct energy generation. Among TES technologies, thermochemical energy storage (TCES) based on calcium looping emerges as a compelling high-power energy storage candidate due to its high reaction enthalpy, compatibility with elevated operating temperatures, and abundance of low-cost materials. However, the long-term durability of calcium-based sorbents for TCES is hindered by surface sintering and particle aggregation, leading to performance degradation over repeated thermal cycles. This study explores a moisture hydration-based strategy to regenerate a degraded calcium sorbent and mitigate performance degradation for long duration TCES. The addition of moisture transforms calcium oxide into calcium hydroxide and produces intercalation water layers, associated with a regenerated surface area and reduced calcium oxide crystallite size. Both these effects are beneficial in restoring the sorbents' reactivity for carbonization. Additionally, an optimized hydration-assisted reactivation protocol balances the recovered energy storage capacity with heating penalty required for moisture removal from hydrated samples, resulting in an enhanced energy storage capacity up to 176% compared to benchmark sorbents that undergo cycling without reactivation after 60 cycles. In conclusion, these results highlight the potential of hydration-assisted reactivation to enhance the long-term performance of TCES, providing an effective pathway to advancing electro-thermal storage technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Path Sampling for Rare Events Boosted by Machine Learning

The study by Jung et al. introduced Artificial Intelligence for Molecular Mechanism Discovery (AIMMD), a novel sampling algorithm that integrates machine learning to enhance the efficiency of transition path sampling (TPS). By enabling on-the-fly estimation of the committor probability and simultaneously deriving a human-interpretable reaction coordinate, AIMMD offers a robust framework for elucidating the mechanistic pathways of complex molecular processes. Here, this commentary provides a discussion and critical analysis of the core AIMMD framework, explores its recent extensions, and offers an assessment of the method’s potential impact and limitations.

Minh, Porhouy [Univ. of Minnesota, Minneapolis, MN↗
DOE OSTI2026

Purcell enhancement of directional edge photocurrent in a van der Waals self-cavity

Cavities provide a means to manipulate the optical and electronic responses of quantum materials by selectively enhancing light-matter interaction at specific frequencies and momenta. While cavities typically involve external structures, exfoliated flakes of van der Waals (vdW) materials can form intrinsic self-cavities due to their small finite dimensions, confining electromagnetic fields into plasmonic cavity modes, characterized by standing-wave current distributions. While cavity-enhanced phenomena are well-studied at optical frequencies, the impact of self-cavities on nonlinear electronic responses—such as directional photocurrent—remains largely unexplored, particularly in the terahertz regime, critical for emerging ultrafast optoelectronic technologies. Here, we report a self-cavity-induced Purcell enhancement of directional photocurrents in the vdW semimetal WTe 2 . Using ultrafast optoelectronic circuitry, we measured coherent near-field THz emission resulting from nonlinear photocurrents excited at the sample edges. We observed enhanced emission at finite frequencies, tunable via excitation fluence and sample geometry, which we attribute to plasmonic interference effects controlled by the cavity boundaries. We developed an analytical theory that captures the cavity resonance conditions and spectral response across multiple devices. Our findings establish WTe 2 as a bias-free, geometry-tunable THz emitter and demonstrate the potential of self-cavity engineering for controlling nonlinear, nonequilibrium dynamics in quantum materials.

condensed-matter physics↗
DOE OSTI2020

Smart Scattering Scanning Near-Field Optical Microscopy

Scattering scanning near-field optical microscopy (s-SNOM) provides spectroscopic imaging from molecular to quantum materials with few nanometer deep subdiffraction limited spatial resolution. However, in its conventional implementation s-SNOM is slow to effectively acquire a series of spatio-spectral images, especially with large fields of view. This problem is further exacerbated for weak resonance contrast or when using light sources with limited spectral irradiance. Indeed, the generally limited signal-to-noise ratio prevents sampling a weak signal at the Nyquist sampling rate. Here, we demonstrate how acquisition time and sampling rate can be significantly reduced by using compressed sampling, matrix completion, and adaptive random sampling, while maintaining or even enhancing the physical or chemical image content. We use fully sampled real data sets of molecular, biological, and quantum materials as ground-truth physical data and show how deep under-sampling with a corresponding reduction of acquisition time by 1 order of magnitude or more retains the core s-SNOM image information. We demonstrate that a sampling rate of up to 6× smaller than the Nyquist criterion can be applied, which would provide a 30-fold reduction in the data required under typical experimental conditions. Furthermore, our smart s-SNOM approach is generally applicable and provides systematic full spatio-spectral s-SNOM imaging with a large field of view at high spectral resolution and reduced acquisition time.

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

Distinct Composition‐Dependent Topological Hall Effect in Mn 2‐x Zn x Sb

Abstract Spintronics, an evolving interdisciplinary field at the intersection of magnetism and electronics, explores innovative applications of electron charge and spin properties for advanced electronic devices. The topological Hall effect (THE), a key component in spintronics, has gained significance due to emerging theories surrounding noncoplanar chiral spin textures. This study focuses on Mn 2‐x Zn x Sb, a material crystalizing in centrosymmetric space group with rich magnetic phases tunable by Zn contents. Through comprehensive magnetic and transport characterizations, we found that the high‐Zn ( x > 0.6) samples display THE which is enhanced with decreasing temperature, while THE in the low‐Zn ( x < 0.6) samples show an opposite trend. The coexistence of those distinct temperature dependencies for THE suggests very different magnetic interactions/structures for different compositions and underscores the strong coupling between magnetism and transport in Mn 2‐x Zn x Sb. The findings contribute to understanding topological magnetism in centrosymmetric tetragonal lattices, establishing Mn 2‐x Zn x Sb as a unique platform for exploring tunable transport effects and opening avenues for further exploration in the realm of spintronics.

Nabi, Md Rafique Un↗
DOE OSTI2026

Machine Learning–Augmented Laser-Induced Breakdown Spectroscopy for Spectral Discrimination of Iron Oxalates

Enhanced characterization and phase identification of post-PUREX Pu Oxalates (PuOXA) are pivotal for nonproliferation and pre-detonation nuclear forensics. Despite significant advances in the characterization of PuO 2 samples, little is known about the impact of both the chemical structure and oxidation states of PuOXA (i.e., Pu(III) and Pu(IV)) have on optical emission signatures. Here, we demonstrate the analytical capabilities of laser-induced breakdown spectroscopy (LIBS) applied to Fe(II) and Fe(III) oxalate samples as surrogates for PuOXA, highlighting the discriminating features in the LIBS emission spectra arising from differences in the oxidation states within mixed FeOXA samples. We report the enhancement of spectral feature selection using Principal Component Analysis (PCA), which enables the analytical superiority of machine learning algorithms such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Partial Least Squares Regression (PLSR), Support Vector Regression (SVR), and Random Forest Regression (RFR) over conventional univariate techniques for phase discrimination and chemometric analysis. Cluster analysis revealed how both matrix effects and laser ablation influence cluster separability by introducing spectral artifacts that misdirect the maximization of variance. PCA-selected emission lines were used in the regression models, demonstrating that both univariate and multivariate linear regression models (i.e., PLSR and SVR) can achieve acceptable performance, with machine learning models outperforming conventional calibration regressions. Furthermore, the application of non-linearly activated PCA-selected emission lines illustrates how simplifying the data while retaining captured variance enables the use of less complex and more computationally efficient models. Furthermore, this is particularly evident in the underperformance of RFR, which suffers from increased computational costs and overfitting owing to its high complexity.

Oxalates↗
DOE OSTI2024

Impact of fused silica debris shields and enhanced mitigation techniques on large-aperture beam-sampling optics for the National Ignition Facility

Here, we show that the large-scale routine use of the fused silica debris shield (FSDS) maintains the ∼100× reduction in damage initiation rate and 70% increase in the install lifetime of a new grating debris shield (GDS) observed during pilot operations. Furthermore, we show that the install lifetimes of recycled GDS optics are nearly tripled using additional mitigation strategies such as expanding mitigation processing to include all damage sites larger than 10 μm (LT10) rather than just larger than 50 μm (LT50) and FSDS. We note that there is still a 50% difference between new and recycled optic installation lifetimes. We show that recycled optics have a 3.5× higher apparent initiation rate than new optics when exposed to nominally identical laser conditions.

FSDS↗
DOE OSTI2025

Role of Intersections in Fracture Connectivity

Networks of intersecting fractures often provide the flow paths through subsurface reservoirs. Assessing network connectivity is challenging because fracture intersections compose a vanishingly small fraction of the network void volume. In this paper, motivated by 3D X-ray imaging of the simplest element of fracture network, that is, two orthogonal fractures, we perform a percolation and finite-size scaling analysis to study the connectivity provided by fracture intersections. The conditions when an intersection enhances connectivity across a sample depend on spatial correlations in the fracture aperture distributions, on the stress state, and on the direction of flow. Here we consider three flow directions: (a) across intersections, (b) parallel to intersections and (c) around corners. For (a), intersections provide minimal enhancement of connectivity because they contribute little additional void area. For (b), intersections increase the probability of a connected path near threshold by enabling 3D connected pathways that are not possible in parallel fractures. Flow around corners, (c), is fundamentally the result of the intersection connecting two fractures in series and spatial correlations are broken around corners, suppressing the connectivity relative to (a). When the connected fractures are stressed equally, a joint percolation threshold emerges that continues to have scale invariance. However, when the fractures are stressed unequally, the system has mixed percolation without clearly defined percolation thresholds. In all cases, percolation probabilities are found to be scale dependent which has important consequences for the connectivity of larger fracture networks composed of the fundamental element studied here.

02 PETROLEUM↗
DOE OSTI2024

Enhancing high-fidelity neural network potentials through low-fidelity sampling

The efficacy of neural network potentials (NNPs) critically depends on the quality of the configurational datasets used for training. Prior research using empirical potentials has shown that well-selected liquid–solid transitional configurations of a metallic system can be translated to other metallic systems. This study demonstrates that such validated configurations can be relabeled using density functional theory (DFT) calculations, thereby enhancing the development of high-fidelity NNPs. Training strategies and sampling approaches are efficiently assessed using empirical potentials and subsequently relabeled via DFT in a highly parallelized fashion for high-fidelity NNP training. Our results reveal that relying solely on energy and force for NNP training is inadequate to prevent overfitting, highlighting the necessity of incorporating stress terms into the loss functions. To optimize training involving force and stress terms, we propose employing transfer learning to fine-tune the weights, ensuring that the potential surface is smooth for these quantities composed of energy derivatives. This approach markedly improves the accuracy of elastic constants derived from simulations in both empirical potential-based NNPs and relabeled DFT-based NNPs. Overall, this study offers significant insights into leveraging empirical potentials to expedite the development of reliable and robust NNPs at the DFT level.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Stimulated resonant inelastic X-ray scattering in a solid

Abstract When materials are exposed to X-ray pulses with sufficiently high intensity, various nonlinear effects can occur. The most fundamental one consists of stimulated electronic decays after resonant absorption of X-rays. Such stimulated decays enhance the number of emitted photons and the emission direction is confined to that of the stimulating incident photons which clone themselves in the process. Here we report the observation of stimulated resonant elastic (REXS) and inelastic (RIXS) X-ray scattering near the cobalt L 3 edge in solid Co/Pd multilayer samples. We observe an enhancement of order 10 6 of the stimulated over the conventional spontaneous RIXS signal into the small acceptance angle of the RIXS spectrometer. We also find that in solids both stimulated REXS and RIXS spectra contain contributions from inelastic electron scattering processes, even for ultrashort 5 fs pulses. Our results reveal the potential and caveats of the development of stimulated RIXS in condensed matter.

36 MATERIALS SCIENCE↗