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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Layer-by-Layer-Processed Organic Solar Cells with 18.02% Efficiency Enabled by Regulating the Aggregation of Bottom Polymers

The fabrication of organic solar cells (OSCs) by a layer-by-layer (LBL) method has attracted growing attention in recent years. As already known, the pre-aggregates of conjugated polymers in solution have a profound impact on their microstructure morphology in films. Herein, by simply controlling the solution temperature and annealing processes, the pre-aggregation behavior of D18 polymer in solution can be fine-tuned and the microstructure of D18 bottom layer is well manipulated. The optimized D18 bottom layer can effectively regulate L8-BO upper-layer-forming suitable networks for efficient charge transportation. In addition, a vertical phase separation with a special D/D:A/A structure (P-i-N-type component distribution) is also formed. As a result, compared to the 16.43% power conversion efficiency (PCE) of the bulk heterojunction devices, such control enables bilayer OSC devices based on the polymer D18 and L8-BO to deliver an enhanced PCE of 18.02% with simultaneously improved short-circuit current density, open-circuit voltage, and fill factor. Importantly, it is also demonstrated in these results that the LBL deposition process utilizing the pre-aggregation of polymer and its fiber-network-forming ability is a very promising approach to improve charge dynamics, suppress carrier recombination, and fabricate highly efficient OSCs.

14 SOLAR ENERGY↗
DOE OSTI2026

Effects of gas purity on backgrounds of collision reaction cell-equipped MC-ICP-MS

The advent of multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) instruments equipped with collision reaction cells (CRCs) facilitates interference removal/mitigation via online gas phase separations. This approach has proven effective for high intensity ion beams measured on Faraday collectors; however, it has been observed that introduction of gas in the CRC can result in significant background signals relative to the more sensitive ion counters. These backgrounds hinder use of these instruments for low level concentration and isotopic ratio measurements when employing a reaction gas. Here, this work directly evaluates the effect of gas purity on backgrounds of CRC-MC-ICP-MS instruments. Introducing high-purity research grade O 2 (99.999%) into the CRC produces complex background spectra with intensities >10 4 cps observed at most masses across the measured mass range (7-300 m / z ). Some features of the observed spectra (i.e., positive mass defects) can be attributed to molecular compounds comprised of significant hydrogen. Additionally, some specific molecular species can be identified (i.e., MoO x H y + ) and appear to be derived from molybdenum rods comprising the CRC. Further purifying the gas reduces the intensity of these backgrounds by several orders of magnitude, to <10 2 cps in many cases, and reduces complexity of the resulting spectra. This reduction in background appears to be in part driven by removal of impurities (i.e., H 2 O) from the gas. This work demonstrates that additional purification of reaction gases prior to introduction into the CRC significantly reduces backgrounds detected, potentially expanding the utility of CRC-MC-ICP-MS for making low level measurements using inline gas phase ion separations.

Schlieder, Tyler D. [Pacific Northwest National La↗
DOE OSTI2022

Bicontinuous substrates with reduced pore restriction for CO 2 -selective composite membranes

A substrate with bicontinuous structure is attractive for thin-film composite (TFC) membrane synthesis due to its high surface porosity and well-interconnected bulk morphology. In this study, the vapor-induced phase separation (VIPS) of the casting solution comprising water, 2-pyrrolidone, and polyethersulfone (PES) was studied. By tuning the water addition in the casting solution and water vapor exposure time, the optimized substrate exhibited a bicontinuous surface with a high porosity of 24.2% (or 216/µm 2 pore density), thereby mitigating pore restriction and showing a high CO 2 permeance of 2.94×10 5 GPU. Compared to the benchmark PES substrate with cellular surface pores and lower gas permeance, the use of the bicontinuous substrate led to a 12% increase in the CO 2 permeance of the TFC membrane. The mitigated pore restriction was further rationalized by a resistance-in-series model. The analysis of the lateral diffusion and substrate resistances indicates that an even higher surface pore density of the substrate is required to fully realize the potential of ultra-permeable, CO 2 -selective polymers in the TFC configuration. As a result, the scalability of the VIPS process was demonstrated by the roll-to-roll fabrication of the optimized bicontinuous substrate with a width of 21" and a length of >100'.

42 ENGINEERING↗
DOE OSTI2021

High Miscibility Compatible with Ordered Molecular Packing Enables an Excellent Efficiency of 16.2% in All-Small-Molecule Organic Solar Cells

In all-small-molecule organic solar cells (ASM-OSCs), a high short-circuit current (Jsc) usually needs a small phase separation, while a high fill factor (FF) is generally realized in a highly ordered packing system. However, small domain and ordered packing always conflicted each other in ASM-OSCs, leading to a mutually restricted J sc and FF. Here, in this study, alleviation of the previous dilemma by the strategy of obtaining simultaneous good miscibility and ordered packing through modulating homo- and heteromolecular interactions is proposed. By moving the alkyl-thiolation side chains from the para- to the meta-position in the small-molecule donor, the surface tension and molecular planarity are synchronously enhanced, resulting in compatible properties of good miscibility with acceptor BTP-eC9 and strong self-assembly ability. As a result, an optimized morphology with multi-length-scale domains and highly ordered packing is realized. The device exhibits a long carrier lifetime (39.8 μs) and fast charge collection (15.5 ns). A record efficiency of 16.2% with a high FF of 75.6% and a J sc of 25.4 mA cm –2 in the ASM-OSCs is obtained. These results demonstrate that the strategy of simultaneously obtaining good miscibility with high crystallinity could be an efficient photovoltaic material design principle for high-performance ASM-OSCs.

14 SOLAR ENERGY↗
DOE OSTI2025

Strange quark matter as dark matter: 40 yr later, a reappraisal

ABSTRACT Forty years ago Witten suggested that dark matter could be composed of macroscopic clusters of strange quark matter. This idea was very popular for several years, but it dropped out of fashion once lattice quantum chromodynamics calculations indicated that the confinement/deconfinement transition, at small baryonic chemical potential, is not first order, which seemed to be a crucial requirement in order to produce large clusters of quarks. Here, we revisit the conditions under which strangelets can be produced in the Early Universe. We discuss the impact of an instability in the hadronic phase separating a low density, positive-strange-charge phase from a high-density phase with a negative strange charge. This second phase can rapidly stabilize by forming colour-superconducting gaps. The strangelets then undergo partial evaporation. In this way, we obtain distributions of their sizes in agreement with the observational constraints and we discuss the many astrophysical and cosmological implications of these objects. Finally, we examine the most promising techniques to detect this type of strangelets. We also show that strangelets can exist with masses $\lesssim $1017 g, while primordial black holes are ruled out in that mass range, allowing us to distinguish between these two dark matter candidates.

Clemente, Francesco Di (ORCID:0000000282573819)↗
DOE OSTI2020

Gas-phase molybdenum-99 separation from uranium dioxide by fluoride volatility using nitrogen trifluoride

Production of the important 99m Tc medical isotope parent, molybdenum-99 ( 99 Mo), via the fissioning of high- and low-enriched uranium (HEU/LEU) targets followed by target dissolution in acid and solution-phase purification of 99 Mo is time-consuming, generates quantities of corrosive radioactive waste, and can result in the release of an array of radionuclides to the atmosphere. An alternative 99 Mo purification method has been devised that has the potential to alleviate many of these issues. Herein, we demonstrate the feasibility of a rapid Mo/Tc gas-phase separation from UO 2 . The results indicate that volatile [ 99 Mo]Mo can be captured downstream of the reacted solid mixture on a column bed (trap) of alumina; the majority of the captured [ 99 Mo]Mo can be subsequently eluted from the alumina trap with a few milliliters of water. >1.0 × 10 5 single pass decontamination of U and the collected [ 99 Mo]Mo product is demonstrated. This simple thermo-fluorination technique has the potential to provide a rapid methodology for routine 99 Mo production.

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

Unveiling the Morphological and Physical Mechanism of Burn–in Loss Alleviation by Ternary Matrix Toward Stable and Efficient All–Polymer Solar Cells

All–polymer solar cells (All–PSCs) are considered the most promising candidate in achieving both efficient and stable organic photovoltaic devices, yet the field has rarely presented an in–depth understanding of corresponding device stability while efficiency is continuously boosted via the innovation of polymer acceptors. Herein, a ternary matrix is built for all–PSCs with optimized morphology, improved film ductility and importantly, boosted efficiency and better operational stability than its parental binary counterparts, as a platform to study the underlying mechanism. The target system PQM–Cl:PTQ10:PY–IT (0.8:0.2:1.2) exhibits an alleviated burn–in loss of morphology and efficiency under light soaking, which supports its promoted device lifetime. The comprehensive characterizations of fresh and light–soaked active layers lead to a clear illustration of opposite morphological and physical degradation direction of PQM–Cl and PTQ10, thus resulting in a delicate balance at the optimal ternary system. Specifically, the enlarging tendency of PQM–Cl and shrinking preference of PTQ10 in terms of phase separation leads to a stable morphology in their mixing phase; the hole transfer kinetics of PQM–Cl:PY–IT host is stabilized by incorporating PTQ10. Finally, this work succeeds in reaching a deep insight into all–PSC's stability promotion by a rational ternary design, which booms the prospect of gaining high–performance all–PSCs.

14 SOLAR ENERGY↗
DOE OSTI2025

First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

ABSTRACT We present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.

Nguyen, Ngoc Cuong [Center for Computational Engin↗
DOE OSTI2022

Phase Stability and Kinetics of Topotactic Dual Ca 2+ –Na + Ion Electrochemistry in NaSICON NaV 2 (PO 4 ) 3

Recent reports of reversible calcium plating and stripping have rekindled interest in the development of Ca-ion batteries (CIBs) as next-generation energy storage devices. This technology has the potential to overcome the limitations of conventional Li-ion batteries, but CIBs are plagued by a paucity of suitable cathode materials. To date, NaSICON-structured NaV 2 (PO 4 ) 3 has been demonstrated as a successful cathode candidate, exhibiting reversible (de)intercalation of 0.6 mol Ca 2+ along with stable cycling performance. However, a complex multiphase mixture forms on discharge so the Ca-ion charge storage mechanism in the NaSICON framework is poorly understood. Here in this work, we report on an investigation of the structure and/or Na + /Ca 2+ environment(s) of a variety of chemically prepared NaSICON Ca x Na y V 2 (PO 4 ) 3 phases which were characterized using synchrotron XRD, SEM-EDS, 23 Na NMR, and TEM. Highly calciated CaV 2 (PO 4 ) 3 , Ca 1.5 V 2 (PO 4 ) 3 , and CaNaV 2 (PO 4 ) 3 phases can be prepared at high temperature, but -unlike Ca 0.6 NaV 2 (PO 4 ) 3 -these materials are electrochemically inactive. To better understand the fundamental factors impacting successful Ca 2+ electrochemistry in this system, DFT was employed to examine the Ca x Na y V 2 (PO 4 ) 3 phase diagram and Ca 2+ diffusion mechanism. Theoretical insights show that phase separation into Na-rich and Ca-rich phases is a reason for the capacity limitation and demonstrate that Na + ions in the host materials assist the migration of neighboring Ca 2+ ions, enabling reversible electrochemistry in Ca x Na y V 2 (PO 4 ) 3 . This investigation of fundamental principles affecting reversible Ca 2+ (de)intercalation in Ca x Na y V 2 (PO 4 ) 3 allows for the development of design principles to enable the discovery of a variety of successful cathodes for CIBs.

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

Learning stochastic dynamics and predicting emergent behavior using transformers

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior under conditions not observed during training. We consider a lattice model of active matter undergoing continuous-time Monte Carlo dynamics, simulated at a density at which its steady state comprises small, dispersed clusters. We train a neural network called a transformer on a single trajectory of the model. The transformer, which we show has the capacity to represent dynamical rules that are numerous and nonlocal, learns that the dynamics of this model consists of a small number of processes. Forward-propagated trajectories of the trained transformer, at densities not encountered during training, exhibit motility-induced phase separation and so predict the existence of a nonequilibrium phase transition. Transformers have the flexibility to learn dynamical rules from observation without explicit enumeration of rates or coarse-graining of configuration space, and so the procedure used here can be applied to a wide range of physical systems, including those with large and complex dynamical generators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Exploration of lattice Hamiltonians for functional and structural discovery via Gaussian process-based exploration–exploitation

Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics that have allowed both decades of scientific discovery and provided a universal framework to understand a broad range of phenomena from alloying to frustrated and phase separated materials to quantum systems. Traditionally, exploration of the phase diagrams corresponding to multidimensional parameter spaces of Hamiltonians was performed using a combination of basic physical principles, analytical approximations, and extensive numerical modeling. However, exploration of complex multidimensional parameter spaces is subject to the classic dimensionality problem, and the behaviors of interest concentrated on low dimensional manifolds remain undiscovered. Here, we demonstrate that a combination of exploration and exploration–exploitation with Gaussian process modeling and Bayesian optimization allows effective exploration of the parameter space for lattice Hamiltonians and effectively maps the regions at which specific macroscopic functionalities or local structures are maximized. We argue that this approach is general and can be further extended well beyond the lattice Hamiltonians to effectively explore the parameter space of more complex off-lattice and dynamic models.

42 ENGINEERING↗
DOE OSTI2022

Challenges to magnetic doping of thin films of the Dirac semimetal Cd 3 As 2

Magnetic doping of topological quantum materials provides an attractive route for studying the effects of time-reversal symmetry breaking. Thus motivated, we explore the introduction of the transition metal Mn into thin films of the Dirac semimetal Cd 3 A s2 during growth by molecular beam epitaxy. Scanning transmission electron microscopy measurements show the formation of a Mn-rich phase at the top surface of Mn-doped Cd 3 A s2 thin films grown using both uniform doping and delta doping. This suggests that Mn acts as a surfactant during epitaxial growth of Cd 3 A s2 , resulting in phase separation. Magnetometry measurements of such samples indicate a ferromagnetic phase with out-of-plane magnetic anisotropy. Electrical magneto-transport measurements of these films as a function of temperature, magnetic field, and chemical potential reveal a lower carrier density and higher electron mobility compared with pristine Cd 3 A s2 films grown under similar conditions. This suggests that the surfactant effect might also serve to remove impurities from the bulk of the film. Further, we observe robust quantum transport (Shubnikov-de Haas oscillations and an incipient integer quantum Hall effect) in very thin (7 nm) Cd 3 A s2 films despite being in direct contact with a structurally disordered surface ferromagnetic overlayer.

36 MATERIALS SCIENCE↗
DOE OSTI2024

On interpretation of fluctuations of conserved charges at high T

Abstract Fluctuations of conserved charges calculated on the lattice which can be measured experimentally, are well reproduced by a hadron resonanse gas model at temperatures below$$T_{ch} \sim 155$$ T ch ∼ 155 MeV and radically deviate from the hadron resonance gas predictions above the chiral restoration crossover. This behaviour is typically interpreted as an indication of deconfinement in the quark-gluon plasma regime. We present an argument that this interpretation may be too simple. The argument is based on the scaling of quantities with the number of colors: demonstration of deconfinement and QGP requires observable that is sensitive to$$\sim N_c^2$$ ∼ N c 2 gluons while the conserved charges are sensitive only to quarks and above$$T_{ch}$$ T ch scale as$$N_c^1$$ N c 1 . The latter scaling is consistent with the existence of an intermediate regime characterized by restored chiral symmetry and by approximate chiral spin symmetry which is a symmetry of confining interaction. In this regime the energy density, pressure and entropy density scale as$$N_c^1$$ N c 1 . In the large$$N_c$$ N c limit this regime might become a distinct phase separated from the hadron gas and from QGP by phase transitions. A natural observable that associates with deconfinement and is directly sensitive to deconfined$$N_c^2-1$$ N c 2 - 1 gluons is the Polyakov loop; in the$$N_c=3$$ N c = 3 world it remains very close to 0 at temperatures well above chiral crossover, reaches the value$$\sim 0.5$$ ∼ 0.5 around$$\sim 3T_{ch}$$ ∼ 3 T ch and the value close to 1 at temperatures$$\sim 1$$ ∼ 1 GeV.

Physics↗
DOE OSTI2021

Modeling, Design, and Testing of a Novel Biphasic Solvent-Enabled Absorption System for Post-Combustion Carbon Capture

A novel absorption process enabled by a new class of biphasic solvents for post-combustion carbon capture (BiCAP) is presently being developed at the University of Illinois at Urbana-Champaign. The new biphasic solvents are water-lean solvent blends that develop dual liquid phases with the absorbed CO2 highly enriched in one of the phases. These solvents are superior in CO2 capacity and have high thermal and oxidative stability compared to MEA. The BiCAP technology features a unique process configuration of multi-stage CO2 absorption and liquid–liquid phase separation during CO2 absorption, allowing continual separation and removal of the CO2-enriched liquid phase for maintaining low solvent viscosity and a fast absorption rate. A 40 kWe-scale skid has recently been constructed at the Abbott Power Plant in Champaign, IL, to test the BiCAP solvent in continuous operation with a slipstream of real post-combustion flue gas. Along with improvements in the stripping configuration including cold feed bypass, the process is expected to achieve a minimum reboiler duty of 2,210 kJ/kg CO2 captured at a stripper operating pressure of 6 bar.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2026

Structural Heterogeneity and Hydrodynamics of an Intrinsically Disordered Protein Condensate

Biology demonstrates precise control over the free-energy landscape through the selective partitioning of biomacromolecules into membraneless organelles, enabling essential functions such as biochemical transformations, signaling cascades, and mechanical reinforcement. Although the function of these condensates depends on their underlying structure and hydrodynamics, molecular-scale information on these systems remains sparse. Here, in this study, neutron scattering is used to probe the organization and dynamics of the intrinsically disordered N-terminal domain of Galectin-3, an extracellular lectin responsible for facilitating liquid–liquid phase separation on the cellular surface, in both dilute and condensed phases. Dilute solutions contain isolated protein chains in equilibrium with mesoscopic clusters, whereas the condensed phase adopts a bicontinuous, microemulsion-like morphology. The dilute phase behavior is quantitatively described by coarse-grained polymer models from soft-matter physics, demonstrating their predictive power for complex biological proteins. At elevated concentrations, the proteins self-assemble akin to block copolymers, microphase separating through the aggregation of hydrophobic domains along the protein contour. The resulting condensate remains fluid-like despite a 25-fold increase in concentration; its internal hydrodynamics slow by only a factor of 3 relative to dilute protein chains. These results provide a molecular-level framework for how disordered proteins achieve both the structural complexity and dynamic fluidity of biomolecular condensates.

Carrick, Brian R. [Massachusetts Inst. of Technolo↗
DOE OSTI2025

Multiphase Processing of the Water-Soluble and Insoluble Phases of Biomass Burning Organic Aerosol

Biomass burning is one of the most significant sources of organic aerosol in the atmosphere. Biomass burning organic aerosol (BBOA) has been observed to undergo liquid– liquid phase separation (LLPS) to give core–shell morphology with the hydrophobic phase encapsulating the hydrophilic phase, potentially impacting the evolution of light-absorbing components, i.e., brown carbon (BrC), through multiphase processes. Here, we demonstrate how multiphase processing differs between the watersoluble (i.e., hydrophilic) and insoluble (i.e., hydrophobic) phases of BBOA in terms of reactive uptake of ozone in a coated-wall flow tube. Effects of relative humidity (RH) and ultraviolet (UV) irradiation were investigated. Experimental timeseries were used to inform simulations using multilayer kinetic modeling. Among non-irradiated thin films, the uptake coefficient was greatest for the water-soluble phase at 75% RH (3 × 10 –5 , corresponding to a diffusion coefficient of BrC, D BrC , of 3 × 10 –9 cm 2 s –1 ) and least for the same phase at 0% RH (1 × 10 –5 , corresponding to D BrC of 1 × 10 –10 cm 2 s –1 ). The uptake coefficient for the water-insoluble phase fell between these two (about 1.5 × 10 –5 ), regardless of RH, and the corresponding D BrC increased only slightly (8 × 10 –10 cm 2 s –1 at 0% RH to 9 × 10 –10 cm 2 s –1 at 75% RH). The uptake coefficients of both phases at 0% RH decreased significantly after UV irradiation, consistent with a transition from viscous liquid to solid and supported by qualitative microscopy observations. Modeling multiphase ozone oxidation of primary BrC components in the atmosphere demonstrated, first, that LLPS may extend the lifetime of water-soluble BBOA encapsulated by water-insoluble species by a factor of 1.5 at moderate to high RH and, also, that UV irradiation may extend the lifetime of both phases by more than a factor of 2.5.

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

Comparative study of helium bubbles in a Ti-Ta alloy and a Ti/Ta nanocomposite

Here, we investigated the size, density, and distribution of helium (He) bubbles in a Ti-Ta single-phase alloy and a Ti/Ta dual-phase nanocomposite using transmission electron microscopy. The Ti/Ta nanocomposite was fabricated via phase separation during high-temperature annealing of the single-phase Ti-Ta alloy. He ion implantation in the Ti-Ta single-phase alloy leads to the formation of nano-scale He bubbles (~1.7 nm in size, ~2.6×10 5 /μm 3 in volumetric density). He bubbles were found to segregate to grain boundaries. Under identical implantation conditions, numerous He bubbles also formed in the Ti/Ta nanocomposite. Closer inspection revealed that He bubbles in the Ti-rich phase are smaller and of higher volumetric density (~1.2 nm, ~8.4×10 5 /μm 3 ) than those in the Tarich phase (~3 nm, ~1.8×10 5 /μm 3 ) and the single-phase alloy. He bubbles were also observed to decorate phase boundaries, but they were generally smaller than those on grain boundaries. These results suggest that Ti/Ta phase boundaries are less conducive to the growth of large He bubbles than grain boundaries in the Ti-Ta single phase alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microphase Separation in Polyelectrolyte Blends: Weak Segregation Theory and Relation to Nuclear "Pasta".

We develop the weak segregation theory of micro phase separation in stoichiometric blends of oppositely and weakly charged polyelectrolytes, which would be immiscible in the absence of charged units. Short-range repulsions between polycation and polyanion monomers induce the formation of oppositely charged domains, the size of which is controlled by their excess Coulomb energy. The diagram of blend morphologies is constructed in the framework of Leibler's mean-field approach and to account for fluctuations within the Brazovskii-Fredrickson-Helfand approximation. Phase behavior of the polyelectrolyte blends is fully analogous to that of neutral diblock copolymers. The mean-field analysis predicts that the order-disorder transition (ODT) is second order for the symmetric blend. In asymmetric mixtures, an increasing incompatibility between polyelectrolytes triggers the usual cascade of first-order phase transitions, dis -> bcc -> hex -> lam. Fluctuations alter the phase diagram topology and allow the direct transitions from the disordered state (dis) to hex and lam microphases; for the symmetric blend, ODT becomes weakly first order. We also discuss that both microphase separation in polyelectrolyte blends and the formation of nuclear "pasta" phases within neutron stars are governed by similar physical principles, despite the 6 orders of magnitude difference in the periods of these structures.

Rumyantsev, Artem M.↗