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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 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Nonempirical Range-Separated Hybrid Functional with Spatially Dependent Screened Exchange

Electronic structure calculations based on density functional theory (DFT) have successfully predicted numerous ground-state properties of a variety of molecules and materials. However, exchange and correlation functionals currently used in the literature, including semilocal and hybrid functionals, are often inaccurate to describe the electronic properties of heterogeneous solids, especially systems composed of building blocks with large dielectric mismatch. Here, in this study, we present a dielectric-dependent range-separated hybrid functional, screened-exchange range-separated hybrid (SE-RSH), for the investigation of heterogeneous materials. We define a spatially dependent fraction of exact exchange inspired by the static Coulomb-hole and screened-exchange (COHSEX) approximation used in many-body perturbation theory, and we show that the proposed functional accurately predicts the electronic structure of several nonmetallic interfaces, three- and two-dimensional, pristine, and defective solids and nanoparticles.

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

Point defects and impurities in fluorite PuO 2

The native surface oxide of plutonium plays a critical role in ensuring the stability and safe storage of the underlying metal; consequently, understanding the role of defects and impurities in determining the properties of the oxide layer is critical. Here, in this study, we use hybrid density-functional theory calculations to evaluate the electronic structure and defect chemistry of PuO 2 , the most stable of the native oxide phases, including both native and extrinsic defects. We find that oxygen vacancies (𝑉 O ) form readily in PuO 2 , as do polarons. Electron polarons (𝜂 − ) are the lowest-energy acceptor species in PuO 2 , while the charge compensating donor species will shift from 𝑉 O under O-poor conditions to hole polarons (𝜂 + ) under O-rich conditions. Nitrogen and fluorine can substitute readily for oxygen atoms under O-poor conditions, while fluorine can also incorporate in an interstitial configuration (F$^−_i$) under more O-rich conditions. Carbon and chlorine incorporation in PuO 2 will be very limited. We also evaluate the kinetic barriers for oxygen-related defects, which we find to diffuse readily when present. Our results provide valuable insights into the critical role and variable chemistry of point defects and impurities in PuO 2 , which in turn have important implications for the safe storage of the underlying metal layer. In short, exposure of freshly prepared plutonium to reactive nitrogen- and fluorine-containing contaminants should be avoided, while carbon- or chlorine-containing contaminants are less likely to incorporate readily into the oxide.

Materials science↗
DOE OSTI2021

Cathode pre-lithiation/sodiation for next-generation batteries

Electrochemical energy storage is playing a pivotal role in the global pursuit of a clean and sustainable energy future. Lithium-ion batteries (LIBs) are the state-of-the-art technology, but future energy requirements demand higher energy densities and a more diverse battery landscape to meet a wide variety of applications. Unfortunately, many next-generation LIB chemistries and beyond-LIB technologies suffer from large first-cycle irreversible capacity caused by active ion loss. The field of pre-lithiation/sodiation has recently emerged as researchers attempt to mitigate active ion loss and boost the energy density of next-generation LIBs and sodium-ion batteries. Herein, we highlight recent advances in cathode pre-lithiation/sodiation using sacrificial additives and pre-lithiation/sodiation of cathode active materials.

25 ENERGY STORAGE↗
DOE OSTI2023

Design principles for NASICON super-ionic conductors

Na Super Ionic Conductor (NASICON) materials are an important class of solid-state electrolytes owing to their high ionic conductivity and superior chemical and electrochemical stability. In this paper, we combine first-principles calculations, experimental synthesis and testing, and natural language-driven text-mined historical data on NASICON ionic conductivity to achieve clear insights into how chemical composition influences the Na-ion conductivity. These insights, together with a high-throughput first-principles analysis of the compositional space over which NASICONs are expected to be stable, lead to the successful synthesis and electrochemical investigation of several new NASICONs solid-state conductors. Among these, a high ionic conductivity of 1.2 mS cm ₋1 could be achieved at 25 °C. We find that the ionic conductivity increases with average metal size up to a certain value and that the substitution of PO 4 polyanions by SiO 4 also enhances the ionic conductivity. While optimal ionic conductivity is found near a Na content of 3 per formula unit, the exact optimum depends on other compositional variables. Surprisingly, the Na content enhances the ionic conductivity mostly through its effect on the activation barrier, rather than through the carrier concentration. These deconvoluted design criteria may provide guidelines for the design of optimized NASICON conductors.

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

Probing Interactions between Adsorbed Polymers and γ-Al 2 O 3 Using Solid-State NMR

The interactions between polymers and metal oxide surfaces affect the physical properties of polymer composites and the selectivity of catalysts used for plastic conversion. Gauging the strengths of these interactions and how they depend on adsorption conformations and polymer structure is nevertheless quite challenging. Herein, we evaluate whether a recently introduced dynamic nuclear polarization-based surface-to-atom distance measurement method can be used to gauge the specific interactions between five vinyl polymers and an oxide support (alumina). The adsorption conformations of polymer monolayers were studied using site-specific 13 C{ 27 Al} rotational-echo saturation-pulse double-resonance (RESPDOR) experiments. The method is effective in revealing the average distance between the adsorbed polymer and the surface, as well as the fraction of the monomers that are adsorbed. Polymers that possess larger side chains are more weakly adsorbed, as evidenced by their formation of more numerous loop and tail structures. In conclusion, the measured RESPDOR dephasing data further reveals that polymer adsorption conformations are largely disordered and involve few hydrogen bonding interactions.

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

Underlying Roles of Polyol Additives in Promoting CO2 Capture in PEI/Silica Adsorbents

Solid-supported amines having low molecular weight branched poly(ethylenimine) (PEI) physically impregnated into porous solid supports are promising adsorbents for CO2 capture. Co-impregnating short-chain poly(ethylene glycol) (PEG) together with PEI alters the performance of the adsorbent, delivering improved amine efficiency (AE, mol CO2 sorbed / mol N) and faster CO2 uptake rates. To uncover the physical basis for this improved gas capture performance, we probed the distribution and mobility of the polymers in the pores via small angle neutron scattering (SANS), solid-state NMR, and molecular dynamic (MD) simulation studies. SANS and MD simulations reveal that PEG displaces wall-bound PEI, making amines more accessible for CO2 sorption. Solid-state NMR and MD simulation suggest intercalation of PEG into PEI domains, separating PEI domains and reducing amine-amine interactions, providing potential PEG-rich and amine-poor interfacial domains that bind CO2 weakly via physisorption while providing facile pathways for CO2 diffusion. Contrary to a prior literature hypothesis, no evidence is obtained for PEG facilitating PEI mobility in solid supports. Instead, the data suggest that PEG chains coordinate to PEI, form larger bodies with reduced mobility compared to PEI alone. We also demonstrate promising CO2 uptake and desorption kinetics at varied temperatures, given by favorable amine distribution.

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

Evidence for I 2 loss from the perovskite–gas interface upon light-induced halide segregation

Sunlight-induced halide segregation in (CH 3 NH 3 )Pb(Br x I 1−x ) 3 (1 > x > 0.2), which limits obtainable voltages from solar cells with these perovskite absorbers, reverses upon resting in the dark. However, sustained illumination at ca. 1 sun opens a new decomposition pathway, leading to irreversible I 2 loss in an open system. We conclusively show I 2 off-gassing from halide-segregated (CH 3 NH 3 )Pb(Br 0.75 I 0.25 ) 3 by trapping gaseous I 2 and tracking the electronic conductivity of the perovskite, which increases from electron-doping as iodides are oxidized to iodine. Importantly, we show that this reaction occurs across the perovskite-air solid–gas interface, without confounding effects from solvent or reactive solid interfaces. This characterization was conducted under a nitrogen atmosphere, avoiding vacuum- and oxygen-driven I 2 loss pathways. Consistent observations of I 2 loss upon light-soaking CsPb(Br 0.75 I 0.25 ) 3 films show that this reaction is intrinsic to the inorganic framework. We propose that the disruption of iodide-rich domains in the halide-segregated films through I 2 loss can masquerade as a light-induced healing or apparent remixing of the segregated film, when in fact it leads to irreversible decomposition. Although I 2 off-gassing is less likely in bromide-rich solid solutions, light-induced halide segregation brings the iodides into proximity and forms electronic states that are energetically poised to trap and accumulate holes, providing a driving force for I 2 loss. Thus, even bromide-rich mixed-halide perovskite absorbers will benefit from I 2 -impermeable encapsulation for long-term stability.

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

On the Impact of Mechanics on Electrochemistry of Lithium-Ion Battery Anodes

Abstract Models exploring electrochemistry-mechanics coupling in liquid electrolyte lithium-ion battery anodes have traditionally incorporated stress impact on thermodynamics, bulk diffusive transport, and fracture, while stress-kinetics coupling is more explored in the context of all solid-state batteries. Here, we showcase the existence of strong link between active particle surface pressure and reaction kinetics affecting performance even in liquid electrolyte systems. Traction-free and immobile particle surface mechanical boundary conditions are used to delineate the varying pressure magnitudes in graphite host during cycling. Both tensile and compressive stresses are generated in traction-free case, while a fixed surface subjects the entire particle to a compression state. Pressure magnitudes are nearly two to three orders of magnitude higher for the latter resulting in significant depression of open circuit potential and improvement of exchange current densities compared to stress-free state. The results demonstrate the need for incorporating stress-kinetics linkage in models and provide a rationale for putting battery electrodes under compression to improve kinetics.

25 ENERGY STORAGE↗
DOE OSTI2024

Structural Evolution and Photoluminescence Quenching across the FASnI 3– x Br x ( x = 0–3) Perovskites

One of the primary methods for band gap tuning in metal halide perovskites has been halide (I/Br) mixing. Despite widespread usage of this type of chemical substitution in perovskite photovoltaics, there is still little understanding of the structural impacts of halide alloying, with the assumption being the formation of ideal solid solutions. The FASnI 3–x Br x (x = 0–3) family of compounds provides the first example where the assumption breaks down, as the composition space is broken into two unique regimes (x = 0–2.9; x = 2.9–3) based on their average structure with the former having a 3D and the latter having an extended 3D (pseudo 0D) structure. Pair distribution function (PDF) analyses further suggest a dynamic 5s 2 lone pair expression resulting in increasing levels of off-centering of the central Sn as the Br concentration is increased. These antiferroelectric distortions indicate that even the x = 0–2.9 phase space behaves as a nonideal solid-solution on a more local scale. Solid-state NMR confirms the difference in local structure yielding greater insight into the chemical nature and local distributions of the FA + cation. In contrast to the FAPbI 3–x Br x series, a drastic photoluminescence (PL) quenching is observed with x ≥ 1.9 compounds having no observable PL. In conclusion, our detailed studies attribute this quenching to structural transitions induced by the distortions of the [SnBr 6 ] octahedra in response to stereochemically expressed lone pairs of electrons. This is confirmed through density functional theory, having a direct impact on the electronic structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Overcoming Metastable CO 2 Adsorption in a Bulky Diamine-Appended Metal-Organic Framework

We report carbon capture at fossil fuel-fired power plants is a critical strategy to mitigate anthropogenic contributions to global warming, but widespread deployment of this technology is hindered by a lack of energy-efficient materials that can be optimized for CO 2 capture from a specific flue gas. As a result of their tunable, step-shaped CO 2 adsorption profiles, diamine-functionalized metal-organic frameworks (MOFs) of the form diamine-Mg 2 (dobpdc) (dobpdc 4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) are among the most promising materials for carbon capture applications. Here, we present a detailed investigation of dmen-Mg 2 (dobpdc) (dmen = 1,2-diamino-2-methylpropane), one of only two MOFs with an adsorption step near the optimal pressure for CO 2 capture from coal flue gas. While prior characterization suggested that this material only adsorbs CO 2 to half capacity (0.5 CO 2 per diamine) at 1 bar, we show that the half-capacity state is actually a metastable intermediate. Under appropriate conditions, the MOF adsorbs CO 2 to full capacity, but conversion from the half-capacity structure happens on a very slow time scale, rendering it inaccessible in traditional adsorption measurements. Data from solid-state magic angle spinning nuclear magnetic resonance spectroscopy, coupled with van der Waals-corrected density functional theory, indicate that ammonium carbamate chains formed at half capacity and full capacity adopt opposing configurations, and the need to convert between these states likely dictates the sluggish post-half-capacity uptake. By use of the more symmetric parent framework Mg 2 (pc-dobpdc) (pc-dobpdc 4- = 3,3'-dioxidobiphenyl-4,4'-dicarboxylate), the metastable trap can be avoided and the full CO 2 capacity of dmen-Mg 2 (pc-dobpdc) accessed under conditions relevant for carbon capture from coal-fired power plants.

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

Heterolytic Scission of Hydrogen Within a Crystalline Frustrated Lewis Pair

We report the heterolysis of molecular hydrogen under ambient conditions by the crystalline frustrated Lewis pair (FLP) 1-{2-[bis(pentafluorophenyl)boryl]phenyl}-2,2,6,6-tetramethylpiperidine (KCAT). The gas–solid reaction provides an approach to prepare the solvent-free, polycrystalline ion pair KCATH2 through a single crystal to single crystal transformation. The crystal lattice of KCATH2 increases in size relative to the parent KCAT by approximately 2%. Microscopy was used to follow the transformation of the highly colored red/orange KCAT to the colorless KCATH2 over a period of 2 h at 300 K under a flow of H2 gas. There is no evidence of crystal decrepitation during hydrogen uptake. Inelastic neutron scattering employed over a temperature range from 4–200 K did not provide evidence for the formation of polarized H2 in a precursor complex within the crystal at low temperatures and high pressures. However, at 300 K, the INS spectrum of KCAT transformed to the INS spectrum of KCATH2. Calculations suggest that the driving force is more favorable in the solid state compared to the solution or gas phase, but the addition of H2 into the KCAT crystal is unfavorable. Ab Initio methods were used to calculate the INS spectra of KCAT, KCATH2, and a possible precursor complex of H2 in the pocket between the B and N of crystalline KCAT. Ex-situ NMR showed that the transformation from KCAT to KCATH2 is quantitative and our results suggest that the hydrogen heterolysis process occurs via H2 diffusion into the FLP crystal with a rate-limiting movement of H2 from inactive positions to reactive sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Characteristics of Non-Fullerene Acceptor-Based Organic Photovoltaic Active Layers Using X-ray Scattering and Solid-State NMR

With the recent development of non-fullerene acceptors, power conversion efficiencies of bulk-heterojunction organic solar cells have exceeded 18%. The morphology of the BHJ active layer, including packing, ordering, orientation, and phase behavior of the donor(s) and acceptor(s), plays critical roles in determining the device performance. We characterized the morphology of active layers consisting of mixtures of a PTB7/PTB7-Th (donor) and ITIC (acceptor) using grazing incidence wide-angle X-ray scattering, resonant soft X-ray scattering, and solid-state nuclear magnetic resonance (ssNMR) to correlate the morphology with device performance. PTB7-Th/ITIC shows a better device performance than that of PTB7/ITIC due to a smaller π-πstacking distance and smaller domain size of the phase separated morphology. One of PTB7/ITIC samples, processed from mixed solvents (chlorobenzene/benzene = 1:1 by volume), shows a possible partial miscibility and smaller domain size as revealed by ssNMR T 1ρ relaxation times, which is detrimental to device performance. ssNMR results showed that ITIC could crystallize into different forms depending on processing conditions, which may have implications on the manufacturing of devices using it as an ingredient, as well as its long-term stability in service.

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

Synthesis, transport properties and electronic structure of p-type Cu 1+x Mn 2–x InTe 4 ( x = 0, 0.2, 0.3)

The synthesis, electronic structure and temperature dependent transport properties of polycrystalline Cu 1+x Mn 2–x InTe 4 (x = 0, 0.2, 0.3) are reported for the first time. These quaternary chalcogenides were synthesized by direct reaction of the elements, followed by solid state annealing and hot press densification. The thermal conductivity is low for all specimens and intrinsic to the material system. Furthermore, the off-stoichiometry specimens illustrate the sensitivity of the transport properties to stoichiometry, with a greater than two-orders-of magnitude increase in carrier concentration with increased Cu content. First principles calculations of the electronic structure are also reported, and are in agreement with the experimental data. Here, this fundamental investigation shows the potential towards further optimization of the electrical properties that, in addition to the intrinsically low thermal conductivity, provides a basis for further research into the viability of this material system for potential energy-related applications.

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

A molten carbonate shell modified perovskite redox catalyst for anaerobic oxidative dehydrogenation of ethane

Acceptor-doped, redox-active perovskite oxides such as La 0.8 Sr 0.2 FeO 3 (LSF) are active for ethane oxidation to CO x but show poor selectivity to ethylene. This article reports molten Li 2 CO 3 as an effective “promoter” to modify LSF for chemical looping–oxidative dehydrogenation (CL-ODH) of ethane. Under the working state, the redox catalyst is composed of a molten Li 2 CO 3 layer covering the solid LSF substrate. The molten layer facilitates the transport of active peroxide (O 2 2- ) species formed on LSF while blocking the nonselective sites. Spectroscopy measurements and density functional theory calculations indicate that Fe 4+ →Fe 3+ transition is responsible for the peroxide formation, which results in both exothermic ODH and air reoxidation steps. With >90% ethylene selectivity, up to 59% ethylene yield, and favorable heat of reactions, the core-shell redox catalyst has an excellent potential to be effective for intensified ethane conversion. The mechanistic findings also provide a generalized approach for designing CL-ODH redox catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

FY2020 Annual Report on Subcontract B631779 with UC Berkeley: Reactive Precursors Additive Manufacturing Report

This work succeeded in reaching each of the stated milestones for developing, printing, reacting, and characterizing the uranium carbide final products. Leveraging experience gained from creating magnesium oxide inks (milestone #1) and prior reactive precursor work with boron carbide (milestone #2) a uranium carbide reactive precursor ink was developed. The chosen composition of ink utilized a mixture of wax, petrolatum, and stearic acid as the binder. The reactive precursor portion of the ink was comprised of uranium oxide and nano particle activated carbon for production of uranium carbide via carbothermal reduction. Following an in-air burnout of the binder at 160C the printed samples were reacted and sintered at 1750C in an argon environment induction furnace. The resulting product has an open porosity dense, foam-like internal structure with a calculated density of 89% in the solid fraction.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Data for Stetten et al. (2025), "Biogeochemical controls on iron speciation and cycling across upland to shoreline gradients in freshwater and estuarine coastal soils (Lake Erie and Chesapeake Bay, United States)"

Coastal environments are dynamic interfaces that mediate carbon and nutrient exchanges between terrestrial landscapes and open waters, but it is unclear how biogeochemical reactions, in particular iron (Fe) redox transformations, affect the understanding and prediction of coastal ecosystem functions. This dataset includes measurements from two freshwater sites in the Western and Central basins of Lake Erie (Ohio, United States) and two estuarine sites in the Chesapeake Bay (Maryland, United States); the analytical results were reported by Stetten et al. (2025) in Science of the Total Environment. It was produced as part of the COMPASS-FME project, which seeks to advance a scalable, predictive understanding of the fundamental biogeochemical processes, ecological structure, and ecosystem dynamics that distinguish coastal terrestrial-aquatic interfaces from the purely terrestrial or aquatic systems to which they are coupled. The sites were sampled in November 2022 (CRC), December 2022 (MSM), February 2023 (GCW), and March 2023 (OWC); site codes follow those used by Pennington et al. (2025).The dataset consists of the following soil data:- Solid data (Fe concentration, etc.)- Porewater data (sulfate, sulfide, etc.)- Linear combination fitting results of X-ray absorption near edge structure (XANES) spectra; i.e., quantitative results of the oxidation state of Fe, indicated as a proportion of pure Fe(III) and Fe(II) model compounds- Linear combination fitting results of EXAFS (extended X-ray absorption fine structure) spectra, indicated as proportion of of Fe-model compounds (illite, smectite, etc.)Each data type has a single file in comma-separated value (CSV) format. No special software is required to read it.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A large enhancement of ionic conductivity in SrCoO 2.5 controlled by isostructural phase transition and negative linear compressibility

The exploration of next-generation materials and the underlying mechanisms for high ionic conductivity have been the mainstay of the study in the solid state ionic field, but with limited success. Here, we performed closely integrated in situ high-pressure structural and electronic characterizations on SrCoO 2.5 , a typical material for solid fuel cell application. We discovered that the activation energy for ionic transport decreased by approximately 47% at 13.6 GPa upon compression, demonstrating a large enhancement of conductivity. Such a desired functional behavior is strongly interlinked with the pressure-driven isostructural phase transition at which negative linear compressibility occurs along c-lattice, weakening the interaction between Co and O atoms and then enhancing the ionic diffusion. Our results provide fundamental insight of the solid ionic mechanism and materials-by-design for future high-performance oxides.

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

Two-Dimensional Uranyl Borates: From Conventional to Extreme Synthetic Conditions: Two-Dimensional Uranyl Borates: From Conventional to Extreme Synthetic Conditions

A systematic investigation of uranyl borates under different synthetic conditions resulted in five new 2D compounds, namely, (H 3 O)[(UO 2 )(BO 3 )], Li[(UO 2 )(BO 3 )] · (H 2 O), α-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ], β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] and K 2.5 [(UO 2 ) 5 (BO 3 ) 2 O 2.5 (OH) 1.5 ] · (H 2 O) 2.5 . (H 3 O)[(UO 2 )(BO 3 )] and Li[(UO 2 )(BO 3 )] · (H 2 O) were obtained from hydrothermal reactions at 220 °C using the same mineralizer. Both materials possess the uranophane sheet topology with different symmetry of the unit cells. In the structure of (H 3 O)[(UO 2 )(BO 3 )] and Li[(UO 2 )(BO 3 )] · (H 2 O), UO 7 pentagonal bipyramids share edges and vertexes with four BO 3 planar triangles. α-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] and β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] are polytypes. α-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] was synthesized from a high-temperature solid-state reaction under ambient pressure; whereas β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] was obtained from a high-temperature/high-pressure (HT/HP) reaction. Both structures have an identical anion topology, but β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] crystallizes in space group with higher symmetry. In K 2.5 [(UO 2 ) 5 (BO 3 ) 2 O 2.5 (OH) 1.5 ] · (H 2 O) 2.5 , which was obtained from a hydrothermal reaction, UO 7 polyhedra share vertexes and edges with two independent BO 3 triangles, forming the most complex uranyl borate layers among all five compounds. The different synthetic routes, novel topologies, thermal behavior and Raman spectra are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗