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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 OSTI2014

CY2013 Annual Report for DOE-ITU INERI 2010-006-E

New concepts for nuclear energy development are considered in both the USA and Europe within the framework of the Generation-IV International Forum (GIF) as well as in various US-DOE programs (e.g. the Fuel Cycle Research and Development - FCRD) and as part of the European Sustainable Nuclear Energy Technology Platform (SNE-TP). Since most new fuel cycle concepts envisage the adoption of a closed nuclear fuel cycle employing fast reactors, the fuel behavior characteristics of the various proposed advanced fuel forms must be effectively investigated using state of the art experimental techniques before implementation. More rapid progress can be achieved if effective synergy with advanced (multi-scale) modeling efforts can be achieved. The fuel systems to be considered include minor actinide (MA) transmutation fuel types such as advanced MOX, advanced metal alloy, inert matrix fuel (IMF), and other ceramic fuels like nitrides, carbides, etc., for fast neutronic spectrum conditions. Most of the advanced fuel compounds have already been the object of past examination programs, which included irradiations in research reactors. The knowledge derived from previous experience constitutes a significant, albeit incomplete body of data. New or upgraded experimental tools are available today that can extend the scientific and technological knowledge towards achieving the objectives associated with the new generation of nuclear reactors and fuels. The objectives of this project will be three-fold: (1) to extend the available knowledge on properties and irradiation behavior of high burnup and minor actinide bearing advanced fuel systems; (2) to establish a synergy with multi-scale and code development efforts in which experimental data and expertise on the irradiation behavior of nuclear fuels is properly conveyed for the upgrade/development of advanced modeling tools; (3) to promote the effective use of international resources to the characterization of irradiated fuel through exchange of expertise and information among leading experimental facilities. The priorities in this project will be set according to the down selection procedure of U.S. and European development programs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Ultra-selective ligand-driven separation of strategic actinides

Abstract Metal ion separations are critical to numerous fields, including nuclear medicine, waste recycling, space exploration, and fundamental research. Nonetheless, operational conditions and performance are limited, imposing compromises between recovery, purity, and cost. Siderophore-inspired ligands show unprecedented charge-based selectivity and compatibility with harsh industry conditions, affording excellent separation efficiency, robustness and process control. Here, we successfully demonstrate a general separation strategy on three distinct systems, for Ac, Pu, and Bk purification. Separation factors (SF) obtained with model compound 3,4,3-LI(1,2-HOPO) are orders of magnitude higher than with any other ligand currently employed: 10 6 between Ac and relevant metal impurities, and over 10 8 for redox-free Pu purification against uranyl ions and trivalent actinides or fission products. Finally, a one-step separation method (SF > 3 × 10 6 and radiopurity > 99.999%) enables the isolation of Bk from adjacent actinides and fission products. The proposed approach offers a paradigm change for the production of strategic elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Thorium Oxo‐Clusters as Building Blocks for Open Frameworks

Abstract Fundamental understanding of tetravalent actinide chemistry is essential to optimize many steps of the nuclear fuel cycle, as well as to predict actinide speciation in the environment. Herein, we report synthesis and structure of three open inorganic frameworks composed of Th 4+ ‐oligomers and sulfate anions. The compounds [Th 10 O 4 (OH) 8 (SO 4 ) 12 (H 2 O) 18 ] ⋅ 28 H 2 O ( 1 ), [Th 9 O 4 (OH) 5 (SO 4 ) 12 (H 2 O) 18 ] ⋅ 1 TMA ⋅ 18 H 2 O ( 2 ), and [Th 8.5 O 4 (OH) 4 (SO 4 ) 12 (H 2 O) 18 ] ⋅ 2 TMA ⋅ n H 2 O ( 3 ) were obtained by slow evaporation of aqueous Th 4+ ‐SO 4 2− solutions, with variable SO 4 2− :Th 4+ ratios (SO 4 2− :Th 4+ =1:1, 1.5:1 and 2:1 for 1 , 2 , and 3 ; TMA=tetramethylammonium). The structure of 1 features a neutral open framework architecture with two interpenetrating networks, built from Th 6 O 4 (OH) 4 12+ hexamers and Th 2 (OH) 2 6+ dimers, linked by sulfate anions. The complex anionic framework of 2 is built from hexamers, dimers, and monomers, with charge‐balancing TMA cations. Compound 3 is very similar to 2 , but it is constructed only from hexamers and monomers. Small angle X‐ray scattering (SAXS) of the reaction solutions reveals pre‐assembled hexamer building units in the presence of sulfate, and underlines the key role of the sulfate‐oxoanion ligand on thorium polymerization processes.

Falaise, Clément↗
DOE OSTI2015

Sigma Team for Advanced Actinide Recycle FY2015 Accomplishments and Directions

The Sigma Team for Minor Actinide Recycle (STAAR) has made notable progress in FY 2015 toward the overarching goal to develop more efficient separation methods for actinides in support of the United States Department of Energy (USDOE) objective of sustainable fuel cycles. Research in STAAR has been emphasizing the separation of americium and other minor actinides (MAs) to enable closed nuclear fuel recycle options, mainly within the paradigm of aqueous reprocessing of used oxide nuclear fuel dissolved in nitric acid. Its major scientific challenge concerns achieving selectivity for trivalent actinides vs lanthanides. Not only is this challenge yielding to research advances, but technology concepts such as ALSEP (Actinide Lanthanide Separation) are maturing toward demonstration readiness. Efforts are organized in five task areas: 1) combining bifunctional neutral extractants with an acidic extractant to form a single process solvent, developing a process flowsheet, and demonstrating it at bench scale; 2) oxidation of Am(III) to Am(VI) and subsequent separation with other multivalent actinides; 3) developing an effective soft-donor solvent system for An(III) selective extraction using mixed N,O-donor or all-N donor extractants such as triazinyl pyridine compounds; 4) testing of inorganic and hybrid-type ion exchange materials for MA separations; and 5) computer-aided molecular design to identify altogether new extractants and complexants and theory-based experimental data interpretation. Within these tasks, two strategies are employed, one involving oxidation of americium to its pentavalent or hexavalent state and one that seeks to selectively complex trivalent americium either in the aqueous phase or the solvent phase. Solvent extraction represents the primary separation method employed, though ion exchange and crystallization play an important role. Highlights of accomplishments include: Confirmation of the first-ever electrolytic oxidation of Am(III) in a noncomplexing aqueous solution and submission of this scientific breakthrough as a paper in Science; The first-ever co-crystallization of Am(VI) with UO 2 (NO 3 ) 2 ∙ 6H 2 O, opening the door to a new approach for separating hexavalent actinides as a group; Results showing that three potentially problematic metals will not present risk in ALSEP; Improvement in ALSEP contactor stripping kinetics to acceptable performance; A comparison of centrifugal contactors vs mixer-settlers showing the former performs better in ALSEP stripping; Synthesis of new mixed N,O-donor extractants with enhanced solubility and strength for selective trivalent actinide extraction; Development of computational methods showing promise in prediction of the selectivity of new extractants for trivalent actinides vs lanthanides; An order-of-magnitude improvement in aqueous Am/Eu complexation selectivity of an alternative macrocyclic stripping agent for ALSEP, potentially enabling an option for an Am product stream free from both Ln and Cm. An alternative aqueous combination of dipicolinate complexant and malonate buffer that may present options for ALSEP and TALSPEAK (Trivalent Actinide-Lanthanide Separations by Phosphorus-reagent Extraction from Aqueous Komplexes) type separations. The ALSEP concept is advancing toward a benchtop flowsheet demonstration planned for FY 2016, and a bench-scale test bed at Idaho National Laboratory (INL) will be employed to demonstrate at least one tandem Am oxidation and separation concept. This report outlines the goals of the STAAR, significance of achieving these goals, STAAR organization around the above aims and questions, recent highlights, and future directions. The report also includes a listing of publications, reports, patents, and dissertations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Pressure modulated charge transfer and phonon interactions drive phase transitions in uranium–aluminum laves phases

Lanthanide AB 2 intermetallic compounds known as Laves phases have itinerant 3d and localized 4f electrons, which lead to interesting physical properties such as magnetic anisotropy and high Curie temperatures. Actinide Laves phases can display physical properties that are similarly intriguing. However, at reduced A–A spacing the C14 and C15 polytypes may exhibit larger wavefunction overlap for their 5f electron states and distinct characteristics for phases with more delocalized chemical bonding. The C36 polytype, on the other hand, is extraordinarily rare (<5% of known Laves phases). UAl 2 is the only known actinide Laves phase to show a pressure-controllable C15 → C36 transition. Here, we apply first principles calculations to determine the origin of the C15 → C36 phase transition and reveal the differences between the corresponding properties of each phase. Pressure increases lead to bond compression–induced electron transfer from Al to U, which drives dynamic instability in the C15 phonon modes because of the uniform U–U bonding environment. Further, the opposite phenomena is observed in C36: varied U–U bonding environments are vibronically more stable after charge transfer. We find that the interplay between charge transfer, chemical bonding, and phononic stability are central to predicting phase transitions and corresponding changes in physical properties for both C15 and C36 UAl 2 .

36 MATERIALS SCIENCE↗
DOE OSTI2019

Development of a CALPHAD Thermodynamic Database for Pu-U-Fe-Ga Alloys

The interaction of actinides and actinide alloys such as the δ-stabilized Pu-Ga alloy with iron is of interest to understand the impurity effects on phase stability. A newly developed and self-consistent CALPHAD thermodynamic database is presented which covers the elements: Pu, U, Fe, Ga across their whole composition and temperature ranges. The phase diagram and thermodynamic properties of plutonium-iron (Pu-Fe) and uranium-iron (U-Fe) systems are successfully reassessed, with emphasis on the actinide rich side. Density functional theory (DFT) calculations are performed to validate the stability of the stoichiometric (Pu,U) 6 Fe and (Pu,U)Fe 2 compounds by computing their formation enthalpies. These data are combined to construct the Pu-U-Fe ternary phase diagram. The thermodynamic assessment of Fe-Ga is presented for the first time and application to the quaternary Pu-U-Fe-Ga system is discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The crystal and coordination chemistry of neptunium in all its oxidation states: An expanded structural hierarchy of neptunium compounds

We report structures of 388 neptunium-bearing crystal structures are sorted into an expanded structural hierarchy and examined. The majority of structures contain Np(V) (149), Np(VI) (99), or Np(IV) (91) whereas structures containing Np(II), Np(III), Np(VII), or more than one oxidation state are rare. Coordination geometry of Np(V) and Np(VI) compounds is dominated by the approximately linear neptunyl cation. Actinyl–actinyl interactions (AAIs) are most prevalent in Np(V) compounds and are observed in 48% of these extended structures. Prismatic coordination geometries are commonly observed in Np(IV) compounds. Np(III) organometallic complexes display a variety of coordination modes. Coordination chemistry of Np(VII) compounds is dominated by the tetra-oxido core. Updated average bond length values are provided for Np(IV), Np(V), Np(VI), and Np(VII) compounds and updated bond valence parameters for Np(IV) are reported. A graphical notation system for neptunyl structures coordinated by organic ligands was developed to facilitate discussion and identify similarities between neptunyl compounds coordinated by oxyanions and neptunyl compounds coordinated by organic ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Cluster-Expanded Solids: A Strategy for Assembling Functional Porous Materials

This grant provided (partial) support for the research efforts of three graduate students and two undergraduate students. The intention of the program was to explore the use of molecular precursors in generating functional porous materials with precisely tailored structures and properties. Prior work in our laboratory had demonstrated the feasibility of employing face-capped octahedral clusters of the type [Re 6 Q 8 (CN) 6 ] 3-/4- (Q = S, Se, Te) in the expansion of known metal-cyanide frameworks. For example, the use of [Re 6 Se 8 (CN) 6 ] 4- as a reactant in place of [Fe(CN) 6 ] 4- resulted in formation of Fe 4 [Re 6 Se 8 (CN) 6 ] 3 ·36H 2 O, featuring an expanded form of the porous three-dimensional framework of Prussian blue (Fe 4 [Fe(CN) 6 ] 3 ·14H 2 O). This compound could be dehydrated without loss of integrity, and the increase in void volume significantly enhances its capacity as a molecular sieve, enabling absorption of larger molecules. For this project, we continued with our efforts to devise new routes to microporous coordination solids that function as molecular sieves, sensors, or catalysts. In particular, our focus was on: (i) the synthesis of new molecular precursors of specific utility for such purposes, and (ii) attempts to incorporate these and existing molecular precursors into new coordination solids. Investigations of the terminal ligand substitution chemistry of the carbon-centered, trigonal prismatic cluster [W 6 CCl 18 ] 2- generated the solvated species [W 6 CCl 12 (DMF) 6 ] 2+ and [W 6 CCl 12 (py) 6 ] 2+ , as well as the potential framework building units [W 6 C(CN) 18 ] 3- , [W 6 CCl 12 (pyrazine) 6 ] 2+ , [W 6 CCl 12 (4-cyanopyridine) 6 ] 2+ , and [W 6 CCl 12 (4,4'-bipyridine) 6 ] 2+ . Efforts to produce microporous magnets capable of performing magnetic separations led to characterization of the microporous Prussian blue analogues CsNi[Cr(CN) 6 ] and Cr 3 [Cr(CN) 6 ] 2 ·6H 2 O. With BET surface areas of 370 m 2 /g and 390 m 2 /g, respectively, these compounds exhibit show ferrimagnetic ordering at temperatures of 65 and 220 K, respectively, the highest ordering temperatures yet observed for any microporous magnet. Efforts to produce actinide-based cluster building units were also undertaken, as were experiments probing the reactivity of new metal-organic frameworks possessing coordinatively-unsaturated metal centers. This research further provided an excellent opportunity for training graduate and undergraduate students in the synthesis and characterization of inorganic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bonding and reactivity of isostructural uranyl and neptunyl peroxide phases

Understanding the reactivity of actinide peroxides is critical for predicting the behavior of spent nuclear fuel in radiolytic environments. Herein, we report the synthesis and characterization of a lithium neptunyl(VI) hydroxo peroxo compound (LiNp), which is isostructural to the uranyl analogue (LiU). Single-crystal X-ray diffraction reveals that LiNp contains both [NpO 2 (O 2 ) 3 ] 4- and [NpO 2 (OH) 4 ] 2- units stabilized by Li + and hydrogen bonding and Raman spectroscopy shows systematic redshifts in neptunyl vibrational modes relative to uranyl. DFT calculations highlight the importance of secondary coordination in reproducing vibrational and structural features, but challenges remain with correctly modeling strong sigma donors. Solid-state EPR spectroscopy and DFT confirm superoxide stabilization within LiU and calculations suggest favorability of the analogous radical species in LiNp. Solution state EPR spectroscopy with the radical spin trap 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide (BMPO) reveal evidence of superoxide in the LiU and LiNp phases and suggests stabilization of superoxide within actinyl triperoxide complexes, forming [AnO 2 (O 2 ) 2 (O) 2 • ] 3- .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Orbital-Selective Kondo Entanglement and Antiferromagnetic Order in USb 2

In heavy-fermion compounds, the dual character of f electrons underlies their rich and often exotic properties like fragile heavy quasiparticles, a variety of magnetic orders and unconventional superconductivity. 5f-electron actinide materials provide a rich setting to elucidate the larger and outstanding issue of the competition between magnetic order and Kondo entanglement and, more generally, the interplay among different channels of interactions in correlated electron systems. Here, by using angle-resolved photoemission spectroscopy, we present the detailed electronic structure of USb 2 and observe two different kinds of nearly flat bands in the antiferromagnetic state of USb 2 . Polarization-dependent measurements show that these electronic states are derived from 5f orbitals with different characters; in addition, further temperature-dependent measurements reveal that one of them is driven by the Kondo correlations between the 5f electrons and conduction electrons, while the other reflects the dominant role of the magnetic order. Furthermore, our results on the low-energy electronic excitations of USb 2 implicate orbital selectivity as an important new ingredient for the competition between Kondo correlations and magnetic order and, by extension, in the rich landscape of quantum phases for strongly correlated f electron systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Polymorphic Transitions in Cerium-Substituted Zirconolite (CaZrTi 2 O 7 )

Compounds with the formulae CaZr 1–x Ce x Ti 2 O 7 with x = 0.1–0.5 were synthesized by solid state reaction. Cerium was used as a surrogate for actinide elements. A transition from the 2M polymorph to the 4M polymorph (expanded unit cell due to cation ordering) in zirconolite was observed with increasing cerium content. The presence of both tri- and tetravalent Ce, contrary to formulation, was confirmed using X-ray absorption near edge spectroscopy, suggesting substitution on both Ca and Zr sites. Sintering was carried out via spark plasma sintering, during which the perovskite phase (Ca 0.4 Ce 0.4 TiO 3 ) was stabilized due to the reducing conditions of this technique. Scanning electron microscopy and energy dispersive spectrometry revealed that the 2M polymorph was dilute in Ce content in comparison to the 4M-zirconolite. High temperature X-ray diffraction was used to detail the kinetics of perovskite to zirconolite transition. It was found that CaCeTi 2 O 7 (cubic pyrochlore) formed as an intermediate phase during the transition. Lastly, our results show that a transition from 2M- to 4M-zirconolite occurs with increasing Ce content and can be controlled by adjusting the P O2 and the heat treatment temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Estimation of M 1 scissors mode strength for deformed nuclei in the medium- to heavy-mass region by statistical Hauser-Feshbach model calculations

Radiative neutron capture is an important nuclear reaction whose accurate description is needed for many applications ranging from nuclear technology to nuclear astrophysics. The description of such a process relies on the Hauser-Feshbach theory which requires the nuclear optical potential, level density, and γ-strength function as model inputs. It has recently been suggested that the M 1 scissors mode may explain discrepancies between theoretical calculations and evaluated data. We explore statistical model calculations with the strength of the M 1 scissors mode estimated to be dependent on the nuclear deformation of the compound system. We show that the form of the M 1 scissors mode improves the theoretical description of evaluated data and the match to experiment in both the fission product and actinide regions. Since the scissors mode occurs in the range of a few keV to a few MeV, it may also impact the neutron capture cross sections of neutron-rich nuclei that participate in the rapid neutron capture process of nucleosynthesis. As a result, we comment on the possible impact to nucleosynthesis by evaluating neutron capture rates for neutron-rich nuclei with the M 1 scissors mode active.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Friends or Foes: Fundamental Principles of Th-Organic Scaffold Chemistry Using Zr-Analogs as a Guide

The fundamental interest in actinide chemistry, particularly for the development of thorium-based materials, is experiencing a renaissance owing to the recent and rapidly growing attention to fuel cycle reactors, radiological daughters for nuclear medicine, and efficient nuclear stockpile development. Herein, we uncover fundamental principles of thorium chemistry on the example of Th-based extended structures such as metal–organic frameworks in comparison with the discrete systems and zirconium extended analogs, demonstrating remarkable over two-and-half-year chemical stability of Th-based frameworks as a function of metal node connectivity, amount of defects, and conformational linker rigidity through comprehensive spectroscopic and crystallographic analysis as well as theoretical modeling. Despite exceptional chemical stability, we report the first example of studies focusing on the reactivity of the most chemically stable Th-based frameworks in comparison with the discrete Th-based systems such as metal–organic complexes and a cage, contrasting multicycle recyclability and selectivity (>97%) of the extended structures in comparison with the molecular compounds. Altogether, the presented work not only establishes the conceptual foundation for evaluating the capabilities of Th-based materials but also represents a milestone for their multifaceted future and foreshadows their potential to shape the next era of actinide chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Selectivity in Ligand Binding to Uranyl Compounds: A Synthetic, Structural, Thermodynamic and Computational Study

The uranyl cation (UO 2 2+ ) is the most abundant form of uranium on the planet. It is estimated that 4.5 billion tons of uranium in this form exist in sea water. The ability to bind and extract the uranyl cation from aqueous solution while separating it from other elements would provide a limitless source of nuclear fuel. A large body of research concerns the selective recognition and extraction of uranyl. A stable molecule, the cation has a linear O=U=O geometry. The short U-O bonds (1.78 Å) arise from the combination of uranium 5f/6d and oxygen 2p orbitals. Due to the oxygen moieties being multiply bonded, these sites were not thought to be basic enough for Lewis acidic coordination to be a viable approach to sequestration. We believe that the goal of developing a practical system for uranium separation from seawater will not be attained without new insights into our existing fundamental knowledge of actinide chemistry. We posit that detailed studies of the kinetic and thermodynamic factors that influence interactions between f-elements and ligands with a range of donor atoms is essential to any major advance in this important area. The goal of this research is thus to broaden the coordination chemistry of the uranyl ion by studying new ligand systems via synthetic, structural, thermodynamic and computational methods. We anticipate that this fundamental science will find use beyond actinide separation technologies in areas such as nuclear waste remediation and nuclear materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Predictive Capability for Strongly Correlated Systems: Mott Transition in MnO, Multielectron Magnetic Moments, and Dynamics Effects in Correlated Materials

There are classes of materials that are important to DOE and to the science and technology community, generically referred to as strongly correlated electron systems (SCES), which have proven very difficult to understand and to simulate in a material-specific manner. These range from actinides, which are central to the DOE mission, to transition metal oxides, which include the most promising components of new spin electronics applications as well as the high temperature superconductors, to intermetallic compounds whose heavy fermion characteristics and quantum critical behavior has given rise to some of the most active areas in condensed matter theory. The objective of the CMSN cooperative research team was to focus on the application of these new methodologies to the specific issue of Mott transitions, multi-electron magnetic moments, and dynamical properties correlated materials. Working towards this goal, the W&M team extended its first-principles phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to accurately calculate structural phase transitions and excited states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Impact Of Sodium Oxalate, Sodium Aluminosilicate, and Gibbsite/Boehmite on ARP Filter Performance

The Savannah River Site (SRS) is currently treating radioactive liquid waste with the Actinide Removal Process (ARP) and the Modular Caustic Side Solvent Extraction Unit (MCU). Recently, the low filter flux through the ARP of approximately 5 gallons per minute has limited the rate at which radioactive liquid waste can be treated. Salt Batch 6 had a lower processing rate and required frequent filter cleaning. Savannah River Remediation (SRR) has a desire to understand the causes of the low filter flux and to increase ARP/MCU throughput. SRR requested SRNL to conduct bench-scale filter tests to evaluate whether sodium oxalate, sodium aluminosilicate, or aluminum solids (i.e., gibbsite and boehmite) could be the cause of excessive fouling of the crossflow or secondary filter at ARP. The authors conducted the tests by preparing slurries containing 6.6 M sodium Salt Batch 6 supernate, 2.5 g MST/L slurry, and varying concentrations of sodium oxalate, sodium aluminosilicate, and aluminum solids, processing the slurry through a bench-scale filter unit that contains a crossflow primary filter and a dead-end secondary filter, and measuring filter flux and transmembrane pressure as a function of time. Among the conclusions drwn from this work are the following: (1) All of the tests showed some evidence of fouling the secondary filter. This fouling could be from fine particles passing through the crossflow filter. (2) The sodium oxalate-containing feeds behaved differently from the sodium aluminosilicate- and gibbsite/boehmite-containing feeds.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗