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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Multioutput Convolutional Neural Network for Improved Parameter Extraction in Time-Resolved Electrostatic Force Microscopy Data

Time-resolved scanning probe microscopy methods, like time-resolved electrostatic force microscopy (trEFM), enable imaging of dynamic processes ranging from ion motion in batteries to electronic dynamics in microstructured thin film semiconductors for solar cells. Reconstructing the underlying physical dynamics from these techniques can be challenging due to the interplay of cantilever physics with the actual transient kinetics of interest in the resulting signal. Previously, quantitative trEFM used empirical calibration of the cantilever or feed-forward neural networks trained on simulated data to extract the physical dynamics of interest. Both these approaches are limited by interpreting the underlying signal as a single exponential function, which serves as an approximation but does not adequately reflect many realistic systems. Here, we present a multi-branched, multi-output convolutional neural network (CNN) that uses the trEFM signal in addition to the physical cantilever parameters as input. The trained CNN accurately extracts parameters describing both single-exponential and bi-exponential underlying functions, and more accurately reconstructs real experimental data in the presence of noise. This article demonstrates an application of physics-informed machine learning to complex signal processing tasks, enabling more efficient and accurate analysis of trEFM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Local structure, bonding, and asymmetry of $\mathrm{((NH_2)_2CH)PbBr_3}$, $\mathrm{CsPbBr_3}$, and $\mathrm{(CH_3MH_3)PbBr_3}$

Here we report local structure measurements for CsPbBr 3 and ((NH 2 ) 2 CH)PbBr 3 (FAPbBr 3 ) and compare them with recent results for (CH 3 NH 3 )PbBr 3 (MAPbBr 3 ). The Pb-Br bonding is similar for all three systems; the effective spring constants, κ, are comparable (ranging from 1.20 to 1.95 eV/Å 2 ), but small in magnitude indicating very soft materials. However, there are also important differences between the three systems. Static disorder is very small for CsPbBr3 but increases somewhat with the size of the organic molecular ions MA + and FA + . At room temperature, dynamic disorder dominates in all compounds. The thermal disorder of the Pb-Br pair distribution function (PDF), i.e., the Debye-Waller factor σ 2 follows a correlated Debye or Einstein model up to 300 K in CsPbBr 3 (orthorhombic phase), but for FAPbBr 3 and MAPbBr 3 , there is a break in the σ 2 (T) curve at the orthorhombic-tetragonal transition (o-t) near 150 K, indicating a small change in the spring constant κ. κ increases for MAPbBr 3 but decreases in FAPbBr 3 at this transition. These changes are attributed to changes in the H-bonding between Br - and MA + or FA + at this transition, as a result of librations or rotations of these molecular cations. In addition, the Pb-Br PDF becomes asymmetric at a relatively low temperature for FAPbBr 3 and MAPbBr 3 , while this effect is significantly smaller for CsPbBr 3 . Finally, we address the question of a model to explain the asymmetric PDF. Two main models are discussed in the literature, an anharmonic pair potential and a split-pair distribution, possibly driven by the presence of a lone pair on the Pb ion. We show that the fourth cumulant C 4 can differentiate between these two models and other possible models. Experimentally C 4 is positive at 250 K and above, for all three systems and that is inconsistent with a split-peak model, for which C 4 is negative for splittings larger than 0.12 Å.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Memory and rejuvenation in glassy systems

Here, the memory effect in a single crystal spin glass (Cu 0.92 Mn 0.08 ) has been measured using 1 Hz ac susceptibility measurements over a reduced temperature range of 0.4 - 0.7 T g and a model of the memory effect has been developed. A double-waiting-time protocol is carried out where the spin glass is first allowed to age at a temperature below T g , T w$_{1}$ , followed by a second aging 4 K lower, T w$_{2}$ . The 4 K separation is sufficient to ensure rejuvenation has occurred. The model is based on calculating overlaps between the growth of the correlation lengths at the two temperatures. It accounts for the absolute magnitude of the memory effect as a function of both waiting times and temperatures. The data can be explained by the memory loss being a function of the relative change in the correlated volume at the first waiting temperature due to growth in the correlations at the second waiting temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Origins of magnetic memory and strong exchange bias bordering magnetic compensation in mixed-lanthanide systems

Here, the unexpected physical phenomena resulting from the seemingly inconsequential substitutions of chemically similar lanthanide elements in the Pr 1-x Gd x ScGe system are exploited to further the understanding of rare-earth magnetism and inform materials design. By directly probing magnetic moments of crystallographically indistinguishable Pr and Gd we solve the puzzles of how an unusual magnetic memory and strong exchange bias emerge at specific, easily predictable chemistries. Both effects are rooted in a robust antiparallel arrangement of large 4f magnetic moments of light and heavy lanthanides. This enables precise control of nearly zero net magnetization either opposed to, or aligned with, the external magnetic field that persists over a wide range of temperatures and fields. Further, spontaneous perturbations in the random distribution of lanthanide ions makes strong exchange bias possible in bulk single-phase compounds bordering magnetic compensation, consequently expanding the materials base beyond artificial magnetic multilayers and broadening the range of potential applications of the phenomenon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Chirality reversal at finite magnetic impurity strength and local signatures of a topological phase transition

Here, we study the honeycomb lattice with a single magnetic impurity modeled by adding imaginary next-nearest-neighbor hopping 𝑖⁢ℎ on a single hexagon. This Haldane defect gives a topological mass term to the gapless Dirac cones and generates chirality. For a small density of defects, Neehus et al. [Phys. Rev. Lett. 135, 126604 (2025)] found that the system's chirality reverses at a critical ℎ 𝑐 ≈ 0.95 associated with an unexpected tricritical point of Dirac fermions at zero defect density. We investigate this zero-density limit by analyzing a single defect and computing two experimentally relevant measures of chirality: (1) orbital magnetization via local Chern marker, a bulk probe of all occupied states; and (2) electronic currents of low-energy states. Both probes show a chirality reversal at a critical ℎ 𝑐 ≈ 0.9–1.0. Motivated by this consistency, we propose a defect-scale toy model whose low-energy states reverse their chirality at ℎ$^{'}_{c}$ ≈ 0.87. Remarkably, the same pair of zero-energy bound states also generates the critical point ℎ 𝑐 in the full impurity projected T-matrix. Our results show how the chirality reversal produced by an impurity can be observed either in local probes or in the global topology, and suggest a possible role of the microscopic defect structure at the critical point.

Chern insulators↗
DOE OSTI2021

From Anderson localization on random regular graphs to many-body localization

Highlights: • Anderson transition from ergodicity to localization on random regular graphs (RRG). • Analytical, pool method, and exact-diagonalization study of correlations on RRG. • Many-body localization (MBL) to ergodicity transition: quantum dots and spin chains. • Dynamical eigenstate correlation functions in RRG and MBL problems. • Anderson localization on RRG as a toy model for MBL. The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the “most long-range” interaction. Central themes – which are common to the RRG and MBL problems – include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Multisublattice cluster expansion study of short-range ordering in iron-substituted strontium titanate

Owing to the challenges in obtaining realistic atomic configurations in large chemical phase spaces, it is not straightforward to describe structure–property relations in materials exhibiting configurational disorder. One example is iron-substituted strontium titanate (SrTi 1–x Fe x O 3–d , STF), a promising perovskite-derivative cathode material in solid oxide fuel cells that exhibits full solid solubility 0 ≤ x ≤ 1 and a tendency to exhibit short-range order. Here we demonstrate a multisublattice cluster expansion (CE) framework and apply it to STF across the full composition range. The CE approach is distinct from more traditional CE formulations in that clusters are defined explicitly by the chemical species distributed among multiple sublattices, rather than via cluster functions of occupation variables with decoration. The modified CE approach makes it easy to distinguish meaningful chemical interactions that are harder to extract from conventional CE, since for the latter chemical identity in a cluster is expressed as a product of site occupations. The least absolute shrinkage and selection operator (LASSO) is implemented as a regression analysis tool to select key clusters and avoid overfitting. We demonstrate this formulation on STF, and show that it can accurately predict configurational energies in comparison to conventional CE. From the key clusters, we identify that short-range ordering between substitutional Fe and oxygen vacancies (V O ) results in the formation of Fe–VO strings. In addition, we consider the stability of STF through CE-based Monte Carlo (MC) simulations and confirm the presence of superstructures that were previously observed in transmission electron microscopy. In this work, analysis of atomic configurations from MC samples reveals variations in the oxidation state of Fe atoms, which can be explained by the ordering tendency of Fe and V O . The cluster description and selection formalism described here may be applied to other disordered multisublattice systems for accurate and efficient material modeling.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Ironing out the transition metal contribution to the magnetism of the n = 3 members of the homologous series Pr n +1 M n Ge 3 n +1 (M = Fe, Co): Pr 4 Fe 3 Ge 10 vs. Pr 4 Co 3 Ge 10

The Ln n+1 M n X 3n+1 (Ln = lanthanide, M = transition metal, and X = tetrel) homologous series provides a platform to study collective phenomena in quantum materials. Here, in this work, we compare the crystal growth, structure, and magnetic properties of the n = 3 members of the Pr n+1 M n Ge 3n+1 (M = Fe, Co) analogues, Pr 4 Fe 3 Ge 10 (a = 4.3207 (10) Å, b = 35.523 (8) Å, c = 4.2982 (15) Å, and V = 659.7 (3) Å 3 ) and Pr 4 Co 3 Ge 10 (a = 4.3091 (12) Å, b = 35.750 (9) Å, c = 4.2807 (11) Å, and V = 659.4 (3) Å 3 ). We determined that the ideal flux growth conditions for each compound are highly dependent on the concentration of Sn flux and quench temperature. Pr 4 Fe 3 Ge 10 orders ferromagnetically at 10 K along the c-direction while Pr 4 Co 3 Ge 10 orders antiferromagnetically at 16 K along the b-direction. For both compounds, we observed a magnetic moment higher than that expected for only Pr 3+ ions (3.58 µ B /Pr), implying that the transition metal ions contribute to magnetic ordering (3.91, 3.48, and 3.69 µ B /Pr for Pr 4 Fe 3 Ge 10 , and 3.76, 4.04, and 3.83 µ B /Pr for Pr 4 Co 3 Ge 10 measured along the a-, b-, and c-directions, respectively). Moreover, the zero-field Mössbauer spectrum obtained at 4.2 K for Pr 4 Fe 3 Ge 10 demonstrates that the iron sites participate in magnetic ordering.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Co 3 Ga 2 Ge 5 : Probing site mixing of the Ru 3 Sn 7 structure type with elements difficult to distinguish by diffraction

Co 3 Ga 2 Ge 5 was synthesized through arc-melting stoichiometric ratios of the elements, and a Ru 3 Sn 7 -type structure was confirmed by X-ray diffraction. Because Co 3 Ga 2 Ge 5 contains Ga and Ge, which have very similar X-ray and neutron scattering factors, any Ga/Ge crystallographic site preference cannot be determined with diffraction alone. The purpose of this study is to highlight the importance of using multiple techniques to characterize otherwise structurally ambiguous intermetallic compounds. Here, we utilize 71 Ga nuclear magnetic resonance spectroscopy and an analysis of the X-ray absorption fine structure to clarify the amount of Ga/Ge site mixing. Our combined use of X-ray diffraction and spectroscopy provides a comprehensive structural analysis of Ga site mixing across the Ge crystallographic sites, enhancing the understanding of the structure and properties of Co 3 Ga 2 Ge 5 .

36 MATERIALS SCIENCE↗
DOE OSTI2025

Mesoporous Thin Film Architectures: Addressing Material Demands through Molecular Self-Assembly

Mesoporous thin films spark interest across a wide range of disciplines due to their tunable nanostructures, large internal surface areas, and strong compatibility with planar optical, electronic, and microfluidic devices. While attention in the porous materials community has shifted toward macroporous or disordered nanoporous systems, a resurgence in mesoporous thin film research is underway, driven by new molecular self-assembly methods, advanced materials chemistry, and improved characterization techniques. The integration of high-χN block copolymer design, kinetically persistent micelle templating, and postdeposition processing protocols now allows control over structural parameters such as pore size, wall thickness, porosity, and connectivity. These advances have overcome many of the thermodynamic and processing constraints that previously limited widespread adoption. Rather than serving only as high-surface-area supports, mesoporous thin films are engineered as active interfaces where responsive chemistries and nanoscale confinement act in tandem. Embedding switchable ligands, thermoresponsive polymers, redox mediators, or ion-selective groups directly within the pore walls enables real-time control over transport, optical, and electrochemical properties. These capabilities open up new directions in adaptive coatings, gated membranes, and fast-response biosensors. To further expand their functional scope, mesoporous films are integrated into hierarchical and multicomponent architectures. Techniques such as triblock terpolymer templating, crack-directed assembly, and nanoimprint lithography allow for control over spatial organization on the micron and submicron scale and pore system orientation. This enables programmable anisotropy, enhanced molecular diffusion, and wavelength-selective photonic behavior, essential for next-generation sensing, catalysis, and energy applications. Such structural and functional complexity requires equally sophisticated characterization. Multimodal and in situ techniques can track material dynamics under operational conditions. Recent progress includes extended-range ellipsometric porosimetry (EP) for hierarchical architectures, vacuum EP for interface energetics, time-resolved EP for diffusion kinetics, and correlative AFM-SAXS mapping. The introduction of advanced neutron-based spectroscopies, particularly quasielastic neutron scattering (QENS), promises to provide real-time access to ion transport dynamics and segmental motion under nanoscale confinement, offering a path toward deeper mechanistic understanding of structure-performance correlations in mesoporous systems. This Account reflects the technical advances made and the interdisciplinary collaborations that have shaped our collective vision. The particular dimensions of mesopores enable us to subtly tune interactions at the molecular, interfacial, and mesoscopic levels that permit us to harness nanoconfinement. What emerges is a versatile, modular platform capable of chemical gating, energy transduction, and sensing with a level of tunability unmatched by other porous materials. We highlight critical challenges including the need for more robust large-area processing, a deeper understanding of dynamic behavior under cycling, and better integration with device-level architectures. Our strategies support the transition of mesoporous thin films into active high-performance components in next-generation energy, environmental, and biomedical systems.

oxides↗
DOE OSTI2021

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales-picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure–function relationships require atomistic knowledge of the populated states in the ensemble. Here, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

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

Deciphering the Solvation Structure of Aqueous ZnCl 2 Solutions from X-ray Absorption Spectra Using the Interpretable Graph Neural Network

Machine learning (ML) provides powerful pathways for predicting spectroscopic observables from atomic structures, but its broader impact depends on making model predictions interpretable in terms of physical and chemical principles. Here, we introduce a physics-guided graph neural network (GNN) model that predicts Zn K-edge X-ray spectroscopy (XAS) spectra of aqueous ZnCl 2 solutions. Training data are generated from ab initio XAS calculations on molecular dynamics snapshots obtained using a machine learning interatomic potential. The GNN reproduces experimental spectra across concentrations from dilute (<0.1 m) to highly concentrated (30 m, “water-in-salt”) regimes and scales efficiently to large, disordered liquid systems beyond the reach of conventional ab initio approaches. Gradient-based attribution analysis reveals that the model learns physically meaningful structure-spectrum relationships. Ligand-specific attributions reflect orbital hybridization patterns and the origin of the excitations derived from the density functional theory. Bond-length attributions recover spectral shifts consistent with multiple-scattering theory. Finally, this work bridges data-driven prediction with electronic-structure theory, establishing a general paradigm for interpretable ML that links atomic structure, electronic structure, and spectroscopic observables.

25 ENERGY STORAGE↗
DOE OSTI2026

Pressure-Stabilized MnSb2 with Complex Incommensurate Magnetic Order

Marcasite-type compounds have been proposed as promising hosts of exotic magnetic quantum states, yet experimental realizations in stoichiometric, disorder-free systems remain limited. Here, we report the high-pressure stabilization and magnetic characterization of MnSb2, a marcasite-type compound that is thermodynamically metastable under ambient pressure. Single crystals were synthesized using a cubic multianvil press at 3.3 GPa and 490 °C for 24 h, and powder and single-crystal X-ray diffraction confirm the orthorhombic Pnnm structure. These crystals are stable at ambient pressure for a long time up to between 450 and 500 K. Heat-capacity measurements reveal phase transitions at approximately T0 ∼ 118 K and T1 ∼ 220 K. Neutron diffraction uncovers an unconventional magnetic state below T1 ∼ 220 K. Magnetic powder neutron diffraction refinements reveal possible multiple magnetic configurations that provide comparably acceptable fits to the experimental data. While most solutions are consistent with a spin-density-wave (SDW) description, helical models systematically yield inferior agreement factors. Across a broad range of models, the Mn ordered moment reaches a maximum value of approximately 2 μB and remains predominantly collinear, with minimal canting along the c-axis. At 200 K, the magnetic propagation vector is q = (0, 0.3975, 0.3783); upon cooling, the b component increases toward 0.5, reflecting a temperature-dependent evolution of the modulation. The need for modification of the magnetic model between high and low temperatures further highlights the complex and strongly temperature-dependent nature of the magnetic order in this system. These results establish MnSb2 as a pressure-stabilized marcasite magnet with a tunable, complex magnetic state and a compelling stoichiometric platform for exploring unconventional magnetic behavior, including potential altermagnetism.

Xu, Mingyu [Michigan State University , , , ,; Iow↗
DOE OSTI2024

High Entropy Protected Sharp Magnetic Transitions in Highly Disordered Spinel Ferrites

How disorder affects magnetic ordering is always an intriguing question, and it becomes even more interesting in the recently rising high entropy oxides due to the extremely high disorder density. However, due to the lack of high-quality single crystal samples, the strong compositional disorder effect on magnetic transition has not been deeply investigated. In this work, we have successfully synthesized high-quality single crystalline high entropy spinel ferrites (Mg 0.2 Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 ) x Fe 3-x O 4 . Our findings from high-temperature magnetization and neutron diffraction experiments showed ferrimagnetic transitions at 748, 694, and 674 K for x values of 1, 1.5, and 1.8, respectively. Notably, the magnetic transition almost showed no broadening for x values of 1 and 1.5, compared to Fe 3 O 4 . Extended X-ray absorption fine structure measurements provided insights into the elemental distribution among the octahedral and tetrahedral sites. The random distribution of elements across these sites reduced the formation of local clusters and short-range orders, enhancing sample homogeneity and preserving the sharpness of the magnetic transition, despite bond length variation. Here, our study not only marks the first successful synthesis of an HEO bulk single crystal exhibiting long-range magnetic order but also sheds light on the interaction between high configurational entropy and magnetic orderings. This opens new avenues for future research and applications of magnetic high entropy oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Universality and quantum criticality in quasiperiodic spin chains

Abstract Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Extracting structural motifs from pair distribution function data of nanostructures using explainable machine learning

Characterization of material structure with X-ray or neutron scattering using e.g. Pair Distribution Function (PDF) analysis most often rely on refining a structure model against an experimental dataset. However, identifying a suitable model is often a bottleneck. Recently, automated approaches have made it possible to test thousands of models for each dataset, but these methods are computationally expensive and analysing the output, i.e. extracting structural information from the resulting fits in a meaningful way, is challenging. Our Machine Learning based Motif Extractor (ML-MotEx) trains an ML algorithm on thousands of fits, and uses SHAP (SHapley Additive exPlanation) values to identify which model features are important for the fit quality. We use the method for 4 different chemical systems, including disordered nanomaterials and clusters. ML-MotEx opens for a type of modelling where each feature in a model is assigned an importance value for the fit quality based on explainable ML.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Transition of a network of nonlinear interactions into a regime of strong nonlinear fluctuations: A paradigm for the edge localized mode onset

We study how a network of nonlinear oscillators transits into a regime of strong nonlinear fluctuations when perturbed by a triad. In this regime, most of the potential energy contained in the waves is made available to the system through strong nonlinear fluctuations. This analysis is motivated by recent experimental observations [Dominski and Diallo, Plasma Phys. Control. Fusion 62, 095011 (2020)] where it was found that magnetic fluctuations trigger the onset of edge localized modes by suddenly exciting a network of nonlinear interactions. In our study, we consider the simplest system of many harmonic oscillators that are organized in a network of nonlinear triads. We model and simulate the sudden transition of this network of triads into a regime of strong nonlinear fluctuations—reminiscent of the onset of edge localized modes in tokamaks. This transition is triggered by the activation of a nonlinear perturbation. An abrupt rise of the system's disorder (an entropy-like quantity) is measured during the transition. This transition from weak to strong nonlinear fluctuations is even more abrupt when these fluctuations are chaotic, i.e., when the timescale of the nonlinear interaction is comparable to the timescale of the wave oscillations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Extracting the excitonic Hamiltonian of a chlorophyll dimer from broadband two-dimensional electronic spectroscopy

We apply Frenkel exciton theory to model the entire Q-band of a tightly bound chlorophyll dimer inspired by the photosynthetic reaction center of photosystem II. The potential of broadband two-dimensional electronic spectroscopy experiment spanning the Qx and Qy regions to extract the parameters of the model dimer Hamiltonian is examined through theoretical simulations of the experiment. We find that the local nature of Qx excitation enables identification of molecular properties of the delocalized Qy excitons. Specifically, we demonstrate that the cross-peak region, where excitation energy is resonant with Qy while detection is at Qx, contains specific spectral signatures that can reveal the full real-space molecular Hamiltonian, a task that is impossible by considering the Qy transitions alone. System–bath coupling and site energy disorder in realistic systems may limit the resolution of these spectral signatures due to spectral congestion.

Chemistry↗