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At least 253 records · Page 14

G EANT 4 atomic relaxation data for transfermium nuclei (Z = 101–104)

Advanced theoretical methods can accurately calculate various atomic observables and predict electronic structure. Still, systematic computations of the radiative and non-radiative transition probabilities and energies are missing for the actinides and all the transfermium elements. However, these compilations are needed for comprehensive Monte-Carlo simulations (such as GEANT4) of the radioactive decay of transfermium nuclei. These simulations can forma basis for data analysis of experiments, especially with complex detection setups. Investigation of the transfermium nuclei is crucial for understanding the nature of the nuclear force. In this study, simulations based on data from the Jena Atomic Calculator (JAC) and the data from the Evaluated Atomic Data Library (EADL) present in GEANT4 were found compatible for the three elements Ba(Z = 56), U(Z = 92), and Fm(Z = 100), thus, validating the JAC calculations. For Z> 100, we also found sound agreement between simulations that used data generated with JAC and experimental results involving No(Z = 102) and Rf(Z = 104) isotopes. In conclusion, these results demonstrate that JAC can produce reliable atomic data sets for transfermium elements, which will assist in analyzing nuclear-decay-spectroscopy experiments.

GEANT4↗

Distinguishing fissile uranium isotopes using an active well neutron coincidence counter

Proposed thorium-based nuclear fuel cycles are likely to require quantification and verification of 233 U within nuclear material. Because of their similar fission cross sections, active neutron nondestructive assay (NDA) systems may respond similarly to 233 U and 235 U. Traditional safeguards equipment has been optimized for 235 U and 238 U quantification associated with conventional uranium/plutonium fuel cycles and may not be directly applicable to 233 U quantification when mixed with other actinides. This work used models of the large volume active well coincidence counter (LV-AWCC) at Oak Ridge National Laboratory to evaluate the performance of this neutron NDA system to differentiate fissile uranium isotopes. The models were developed to simulate NDA system performance in response to a number of triangular radiation signature training device sources within the central cavity or well. This work predicted that the LV-AWCC can effectively differentiate 233 U from 235 U in certain modes of operation. In active mode, the LV-AWCC with the cadmium liner results in different doubles count rates between the fissile isotopes for a given fissile uranium mass. Without the cadmium liner, the uranium isotopes provide a statistically indistinguishable doubles count rate response for the fissile masses considered in this work (up to approximately 150 g). The cadmium liner serves to harden the neutron interrogation spectrum, which better exploits the notable difference in the 233 U and 235 U fission cross sections at approximately 1 eV. In passive mode, the two fissile isotopes exhibit different doubles and singles count rates regardless of liner presence because the passive source strength of 233 U is approximately 2 orders of magnitude stronger than that of 235 U due to the shorter half-life and correspondingly higher (α, n) yield. We conclude that using neutron interrogation in the LV-AWCC, two measurements are needed to quantify 233 U content in mixed uranium items. The first measurement is used to determine the total fissile uranium mass using a mode that cannot distinguish fissile isotopes (i.e., where a similar response is observed for both fissile uranium isotopes such as active doubles without cadmium or using a thermal neutron interrogation source). In conclusion, the second measurement is used to determine the 233 U content by using a differentiating technique (e.g., passive doubles, passive doubles to singles ratio, active doubles with cadmium).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Shell effects in quasi-fission for calcium induced reactions forming thorium isotopes

Quantum shell effects induce an asymmetric fission mode in actinides, which disappears in neutron deficient isotopes. Quasi-fission, characterized by a significant mass transfer in heavy ion collisions at low-energies, is expected to be affected by similar shell effects. This is studied in 40−56 Ca+176 reactions with the time-dependent Hartree-Fock approach. All reactions exhibit a mass equilibration process that stops when a heavy fragment with 𝑍 ≃ 54 protons is formed. Unlike the fission of thorium compound nuclei, quasi-fission does not exhibit a transition to symmetric modes in neutron deficient systems. This observation is interpreted in terms of potential energy surfaces that show a persistence of an asymmetric valley with an increasing barrier preventing its population in fission of the most neutron deficient thorium isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dynamic separation of gases using microsieves

Separation of light weight molecules, such as nitrogen, argon, and oxygen, from heavier compounds can have significant impacts on energy capture, environmental monitoring, or isotopic applications. Large-scale gas separation techniques, like gas centrifugation and membrane mitigation, can be problematic as they impart tremendous energy and induce high mechanical stress onto the instrumentation. Microsieves, also known as micronozzles or microfunnels, are developed to create physical barriers to separate specific isotopes and gases. Separation is achieved using a converging and diverging micronozzle to impose supersonic gas flow around a curved wall, and it has been used for the separation of heavy actinide isotopes in low weight gas as well as separation of low weight gas compositions of nitrogen and argon back in 1900s. However, systematic reviews of this unique technology are lacking. The application of the Laval style nozzle, which has a converging/diverging entrance fundamental to the micronozzle, is included in this review due to its importance in industrial applications in uranium (U) isotope refinement. Using advanced computational fluid dynamic (CFD) simulations, the extent of gas separation can be modelled. Herein, we first examine the literature and survey recent advances on fabrication techniques for creating curved micronozzles, methods and separation principles used to design devices. Furthermore, we then follow with highlights of CFD simulations applied to evaluate the separation effects using microsieves. Finally, identification of the gap and recommendation for future development and applications are suggested for using intrinsic molecular features and fluidic dynamics in formulating separation strategies.

30 Microfluidics↗

Rapid analysis of 237 Np and Pu isotopes in unseparated sample matrices using ICP-MS/MS

Inductively coupled plasma tandem mass spectrometry (ICP-MS/MS) is an emerging technique for measuring actinide isotopes when assessing pre- and post- detonation nuclear material. In this study, ICP-MS/MS was investigated for direct Np and Pu quantitation in unseparated, dissolved bulk soil matrices. To achieve this, purified nitric oxide (NO) was investigated for the reactivity of Th, Np, U, Pu, Am, and Cm. Purifying NO prior to the collision reaction cell (CRC) results in increased sensitivity and allows for higher gas flows to be utilized for the removal of interferences. Here, the interference from uranium hydrides was mitigated to less than 3.85 x 10 -11 . This method was demonstrated on standard reference materials which were measured for 237 Np and 238,239,240 Pu in dilute sample digestions. The 238 Pu measurement was validated by spiking into a standard reference material and was accurately measured with an excess of 85000 of 238 U.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

147 Nd Quantification Using HSCCC-Purified Samples

Quantifying the fission product 147 Nd in nuclear debris samples is an important component of post-detonation nuclear forensics. The most accurate quantifications are obtained when Nd is purified from all other fission products, actinides, activation products, and environmental matrix contained within the debris. In this study, a recently developed method for Nd purification was tested, purifying 147 Nd from solutions of mixed fission products using high-speed counter-current chromatography (HSCCC). Importantly, the new method allowed for faster elution of Nd from the column as compared with established high performance liquid chromatography (HPLC) methods, and resulted in accurate/precise 147 Nd quantification by gamma-ray spectrometry. While the up-front equipment costs associated with HSCCC may be higher, its operational costs are on par with those of HPLC (solvents, extractants, power). Gas-flow proportional beta decay counting revealed contamination from the nearest neighbor lanthanide 143 Pr (a gamma-silent radioisotope) in the HSCCC-purified samples, but the activity contribution from 147 Nd could still be quantified. Remarkably consistent elution profiles were observed for the HSCCC method, spanning rare earth element (REE) loadings of more than 10 orders of magnitude (tracer to mmol quantities). In conclusion, the reliability and speed of the new method suggest utility for the rapid separation and quantification of 147 Nd in unknown samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Crystallographic Evidence for Formation of M 6 O 8 /M 6 O 9 f-Element Clusters in Hydrolysis Reactions

In this contribution, we have conducted an examination of crystallographic data which includes 184 4f- and 5f-structures containing the M 6 O 8 or M 6 O 9 moiety. Since much of the work in this field has actually been done to explore the formation and properties of metal organic frameworks (MOFs), we hope that this collection can be used by actinide scientists to further investigate structural and mechanistic trends and gain insight into the formation of these compounds. Here we discuss the general trends in coordination, ligands used, and bonding within the M 6 O 8 or M 6 O 9 core in the hope that further computational work can benefit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reactions of Studtite UO 4 ·4H 2 O in Alkali Hydroxides: Isolation of Single-Crystal Uranate Phases under Mild Hydrothermal Conditions

Uranyl peroxide complexes, particularly studtite (UO 4 ·4H 2 O), are important phases within the nuclear fuel cycle, forming through radiolysis-induced reactions on the surfaces of spent fuel and in waste environments. Studtite has been identified in Hanford’s irradiated fuel storage basins, Chornobyl’s corium lavas, and is anticipated on Fukushima’s fuel debris. While its formation and stability have been extensively studied, the reactivity of UO 4 ·4H 2 O in highly alkaline environments such as those encountered in high-level nuclear waste remains underexplored. These environments contain molar concentrations of [OH - ] and present a chemically dynamic and reactive environment where actinide behavior is not well understood. Reported here are investigations of uranium reactions in concentrated alkali hydroxides under mild hydrothermal conditions (<200 °C) that have resulted in the isolation of the alkali metal uranates Li 2 UO 4 , α-Na 2 UO 4 , γ-Na 2 U 2 O 7 , and K 2 U 2 O 7 . In contrast to conventional solid-state methods (>800 °C) that typically yield polycrystalline powders, our approach enables the isolation of these uranates as single crystals, allowing us to provide single-crystal structure solutions of certain uranates for the first time. Our findings match the results of high-level waste tank sampling, confirming that sodium diuranate (Na 2 U 2 O 7 ) is the most persistent uranium phase, potentially forming through reactions of uranyl peroxide intermediates with NaOH under radiolytic and highly alkaline conditions.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Enhancing f -Element Separations with ADAAM-EH: The Impact of Phase Modifiers and a DGA Aqueous Complexant

Recent investigations have used a 2-ethylhexyl diamide amine (ADAAM-EH) for Am/Cm separations in combination with N,N,N ',N '-tetraethyldiglycolamide as an aqueous complexant to achieve an unprecedented separation factor of 41. The aim of this research effort is to understand the speciation of trivalent lanthanide (Ln) and actinide (An) ions in the organic phase of an ADAAM-EH extraction system, both with and without phase modifiers (PM) (1-octanol and tri-n-butyl phosphate (TBP)). Leveraging spectroscopic techniques in combination with distribution ratio measurements provides an understanding of organic phase f-element ligand complexation. In the absence of PM, Ln is extracted in a stoichiometric 1:1 [M(ADAAM-EH) 1 (NO 3 ) x (H 2 O) 1 ](NO 3 ) 3-x complex. The addition of 1-octanol at 20 vol % results in multiple species present. One of the species is the same as the no PM case, and the other species results in an increased -OH coordination to the inner sphere, potentially displacing some NO 3 . In the case of TBP, increasing concentration results in additional red-shifted bands in the UV-visible spectra, suggesting the complexation of additional ligands of either ADAAM-EH or TBP. Finally, the new system knowledge obtained by and spectroscopic experiments will provide benchmarking information for computational studies of the inner- and outer-sphere coordination environments of f-element cations and insights into ADAAM-EH adduct formation with PM, like 1-octanol and TBP.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kinetics and Mechanism of Ce(IV) Phase Transfer by the Neutral Extractants Tributyl Phosphate and N,N -Di(2-ethylhexyl)isobutyramide

Tributyl phosphate and N,N-di(2-ethylhexyl)isobutyramide (DEHiBA) are uranium-selective extractants that could be used to recover low-enriched uranium from commercial used nuclear fuel. The economic viability of liquid-liquid extraction processes for chemical separations depends on both thermodynamic and kinetic considerations. Here we used microfluidic droplet extraction to measure interfacial phase transfer rate constants for the extraction and stripping of Ce(IV), a non-radioactive actinide surrogate. The Damkohler numbers for each system were calculated and the phase transfer processes were determined to be diffusion-limited under all conditions, contrary to prior studies using constant interface stirred cells and single drop methods. A well-extracted 2:1 DEHiBA/Ce(IV) complex in the organic phase was determined from batch distribution studies, suggesting a different extraction mechanism for Ce(IV) compared with poorly extracted Pu(IV). Finally, phase disengagement rates were found to be rapid in both systems, in agreement with other studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Determining the Effects of Zero-Field Splitting and Magnetic Exchange in Dimeric Europium(II) Complexes

Related BAP [BAP = bis(acyl)phosphide] and Acac (Acac = β-diketonate) molecules perform as robust supports for both lanthanide and actinide metals. Here, a molecular bimetallic Eu 2+ complex was successfully targeted and isolated by employing sodium bis(mesitoyl)phosphide [Na( mes BAP)] in a salt metathesis with EuI 2 , producing [Eu( mes BAP) 2 (et 2 o)] 2 (et 2 o = metal-coordinated diethyl ether). The corresponding Acac-Eu 2+ complex was targeted using mes Acac– (1,3-dimesityl-1,3-propanedione), generating [Eu( mes Acac) 2 (et 2 o)] 2 . Both complexes were characterized by single-crystal X-ray diffraction, UV–vis, IR, and NMR spectroscopies, and variable-temperature magnetic susceptibility. [Eu( mes BAP) 2 (et 2 o)] 2 was persistent under anaerobic, anhydrous conditions, whereas the analogous [Eu( mes Acac) 2 (et 2 o)] 2 showed evidence of decomposition under identical conditions. Finally, variable-temperature magnetic susceptibility and magnetization studies of [Eu( mes BAP) 2 (et 2 o)] 2 and [Eu( mes Acac) 2 (et 2 o)] 2 were performed, resulting in similar magnetic exchange coupling values of J ex = –0.018 and –0.023 cm –1 and axial zero-field-splitting D values of –0.38 and –0.51 cm –1 , respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparison of Americium(III) and Neodymium(III) Monothiophosphate Complexes

Mixed-donor ligands, such as those containing a combination of O/N or O/S, have been studied extensively for the selective extraction of trivalent actinides, especially Am 3+ and Cm3+, from lanthanides during the recycling of used nuclear fuel. Oxygen/sulfur donor ligand combinations also result from the hydrolytic and/or radiolytic degradation of dithiophosphates, such as the Cyanex® class of extractants, that are initially converted to monothiophosphates. To understand potential differences between the binding of such degraded ligands to Nd 3+ and Am 3+ , the monothiophosphate complexes [M(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- (M 3+ = Nd 3+ , Am 3+ ) were prepared and characterized by single crystal X-ray diffraction and optical spectroscopy and studied as a function of pressure up ca. 14 GPa using diamond-anvil techniques. Although Nd 3+ and Am 3+ have nearly identical eight-coordinated ionic radii, these structures reveal that while the M-O bond distances in these complexes are nearly equal that the M-S distances are statistically different. Moreover, for [Nd(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- , the hypersensitive 4 I 9/2 → 4 G 5 / 2 transition shifts as a function of pressure by -11 cm -1 /GPa. Whereas for [Am(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- , the 7 F 0 → 7 F 6 transition shows a slightly stronger pressure dependence with a shift of -13 cm -1 /GPa and also exhibits broadening of the 5f →5f transitions at high pressures. This data likely indicates an increased involvement of the 5f orbitals in bonding to Am 3+ relative to that of Nd 3+ in these complexes.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Uranium Chemistry: Identifying the Next Frontiers

While uranium is the most extensively studied actinide in terms of chemical properties, there remains much to be explored about its fundamental chemistry. Organometallic and organoactinide chemistry first emerged in the 1950s with research that found inspiration from transition-metal chemistry with the synthesis and characterization of uranocene, expanding new opportunities for organoactinide chemistry. Since then, a significant amount of research has pursued many avenues characterizing the fundamental nature of the f orbitals and their modes of bonding as well as their potential in catalysis. Uranium(III/IV) arene complexes dominate much of uranium organometallic chemistry, with bonding interactions stabilized by δ-back-bonding. Recent additions to this area of chemistry include the first UI and new additions of U II organouranium compounds. Uranium–transition metal complexes are still rare and maintain U IV oxidation states, with variable bond lengths determining the transition-metal oxidation state. Resultant reactivities are discussed as synthetic complexes, and unique bonding and coordination motifs are highlighted. In conclusion, this Viewpoint will focus on significant developments in uranium chemistry from the last 15 years while considering key areas for future research.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Computational Investigation of the Chemical Bond between An(III) Ions and Soft-Donor Ligands

The chemical bonding of actinide ions with arene and borohydride ligands is explored via quantum chemical methods to understand how the transuranium elements interact with softdonor ligands. Specifically, the [An(C 6 Me 6 )(BH 4 ) 3 ] complexes (An = U, Np, and Pu) and their reduced congeners are studied. Density functional theory (DFT) shows that the metal–ligand interactions in the neutral complexes are governed by electrostatic interactions. Both DFT and complete active space (CASSCF) results show that as one moves from U to Pu, the 5f-orbitals are stabilized leading to a poorer energy match with the ligand orbitals. This contributes to progressively weaker metal-arene and metal-borohydride interactions across the series due to a decrease in energy-driven covalency. A reduction in orbital contributions to bonding is obtained for the transuranium-arene interactions as well. Upon reduction, the arene is reduced, forming a δ-bond. This causes the An–arene distances to contract by 0.1–0.2 Å compared to the neutral complexes. The ground state is assigned as the intermediate-spin state where the arene radical is antiferromagnetically coupled to the metal-centered f-electrons in Np and Pu. On the other hand, the ferromagnetically and antiferromagnetically coupled states are close in energy in the uranium complex, but do not mix when spin– orbit coupling is included using a state-interaction approach (SO-CASPT2). The population of the CASSCF δ*-antibonding natural orbital increases from U to Pu consistent with the increased An–arene distances, weaker interactions, and decreasing covalency across the series. Although the An–B distance increases by ca. 0.06 Å upon reduction, both the neutral and reduced species involve an An(III)–borohydride bond and as such are qualitatively similar. The Np complexes can be assigned to have slightly weaker bonding than the uranium analogs but are overall “uranium-like”. The Pu complexes are predicted to have less covalent contributions to bonding in both the Pu–arene and Pu–borohydride interactions; however, the Pu–arene interaction is predicted to be particularly weak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

U 4+/5+/6+ in a Conserved Pseudotetrahedral Imidophosphorane Coordination Sphere

While several ligand systems support uranium across a range of oxidation states, spanning more than two oxidation states in a conserved coordination geometry is uncommon among structurally authenticated complexes. Imidophosphorane ligands significantly stabilize high-valent lanthanide and actinide complexes. Here, we report a series of homoleptic uranium imidophosphorane complexes, spanning the +4, +5 and +6 oxidation states in a four-coordinate pseudotetrahedral ligand field. The +6 oxidation state is accessible using a mild ferrocenium oxidant, yielding a rare example of U6+ in a pseudotetrahedral coordination environment. As the formal oxidation state increases, the U–N distances gradually contract, consistent with the Shannon ionic radii of U 4+/5+/6+ . Compared to reported complexes, the short U–N distances observed in the U 6+ complex are more comparable to dianionic imido ligands than monoanionic amido ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural and Spectroscopic Characterization of Plutonium and Other Tetravalent Metals Complexed to a Keggin Ion

Here, we report the isolation of the first plutonium(IV) complex with a Keggin ion chelator: Cs 20 [Pu(PW 11 O 39 ) 2 ] 2 ·13H 2 O. Single crystal XRD and solid-state UV–vis absorbance analysis demonstrate the stabilization of Pu 4+ by the Keggin ligand. The unit cell contains two [Pu(PW 11 O 39 ) 2 ] 10– complexes (Pu(PW 11 ) 2 ) bridged by Cs + . Raman and 31 P NMR spectra of Pu(PW 11 ) 2 are consistent with the analogous Zr 4+ , Hf 4+ , Ce 4+ , and Th 4+ complexes. The Pu–O bond distances at the two Pu sites are 2.35(3) and 2.34(3) Å, matching the value extrapolated from the bonding trend built with the other 8-coordinated tetravalent cations. However, the long-range arrangement of the Pu(PW 11 ) 2 complexes within the lattice is unique in the series of M IV (PW 11 ) 2 compounds: pairs of Pu(PW 11 ) 2 are organized perpendicular to each other. Based on solution-state UV–visible absorbance, small-angle X-ray scattering (SAXS), and 31 P NMR, the tetravalent cations quantitatively form the 1:2 species in solution ([Pu(PW 11 O 39 ) 2 ] 10– (aq) ) and no 1:1 species ([Pu(PW 11 O 39 )(H 2 O) x ] 3– (aq) ). Finally, a linear correlation exists between the metal–oxygen distances in the M IV (PW 11 ) 2 compounds and the corresponding metal dioxides, allowing for extrapolation for Pa 4+ , Am 4+ , and Bk 4+ . The results indicate that our microscale POM approach represents a viable pathway to probe properties of rare actinide ions in discrete molecules, beyond the traditional oxide extended solids.

and nuclear chemistry↗

Structural Analysis of Curium, Promethium, and Early Lanthanides Using 2,2′:6′,2″-Terpyridine in the Presence of Acid

Trivalent lanthanides and actinides are difficult to separate, often relying on subtle differences in bonding between the 4f– and 5f–orbitals. However, trivalent Cm poses additional complexity owing to its half-filled 5f 7 shell. This configuration causes Cm to have very similar properties to several of the early lanthanides, more specifically, similarly sized Pm. In this study, similarities were probed through isolating an isostructural series between the early lanthanides (La–Eu) and Cm with the oligoamine 2,2′:6′2″-terpyridine in the presence of acid. Single-crystal X-ray diffraction studies highlighted the similarities of Pm and Cm under these conditions and further demonstrated the difficulty in separating these elements. Despite the similarities, differences exist between interactions of Pm and Cm with terpyridine in the solid state. Interestingly, Cm appears to be more similar to Sm than to Pm. Furthermore, this study continues to probe the fundamental chemistry of Pm and Cm with respect to slight differences that can be leveraged in their separation from each other.

Vogt, Trenton B. [Michigan State Univ., East Lansi↗

Data-Driven Kinetic Reaction Networks for Separation Chemistry

Understanding complex, multistep chemical reactions at the molecular level is a major challenge whose solution would greatly benefit the design and optimization of numerous chemical processes. The separation of rare-earth (4f) and actinide (5f) elements is an example where improving our chemical understanding is important for designing and optimizing new chemistries, even with a limited number of observations. Here, in this work, we leverage data-driven artificial intelligence and machine-learning approaches to develop kinetic reaction networks that describe the liquid–liquid extraction mechanism of uranium using N,N-di-2-ethylhexyl-isobutyramide (DEHiBA). Specifically, we compare and contrast the properties of two classes of models: (1) purely data-driven models that are regularized using chemistry-agnostic, L1 regression and (2) chemistry-informed models that are regularized using relative reaction energies provided by quantum mechanical calculations. We observe that purely data-driven models are unbiased, simple, and accurate in their predictions of experimental measurements when provided with sufficient data but are difficult to fully constrain and interpret. In contrast, chemistry-informed models exhibit significantly improved chemical interpretability and consistency, providing a detailed description of the separation process while achieving high accuracy through ensemble averaging. Overall, the dominant species predicted to be extracted into the organic phase is UO 2 (NO 3 ) 2 (DEHiBA) 2 , agreeing with experimental slope analysis, thermodynamic modeling, EXAFS, and crystal structures. This work demonstrates that leveraging the fundamental structure of the problem can lead to efficient learning schemes that provide both accurate predictions and chemical insights at a low computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗