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At least 163 records · Page 9

Potential Control of Oxygen Non-Stoichiometry in Cerium Oxide and Phase Transition Away from Equilibrium

Cerium oxide (ceria, CeO 2 ) is a technologically important material for energy conversion applications. Its activities strongly depend on redox states and oxygen vacancy concentration. Understanding the functionality of chemical active species and behavior of oxygen vacancy during operation, especially in high-temperature solid-state electrochemical cells, is the key to advance future material design. Herein, the structure evolution of ceria is spatially resolved using bulk-sensitive operando X-ray diffraction and spectroscopy techniques. During water electrolysis, ceria undergoes reduction, and its oxygen non-stoichiometry shows a dependence on the electrochemical current. Cerium local bonding environments vary concurrently to accommodate oxygen vacancy formation, resulting in changes in Ce-O coordination number and Ce 3+ /Ce 4+ redox couple. When reduced enough, a crystallographic phase transition occurs from α to an α' phase with more oxygen vacancies. Nevertheless, the transition behavior is intriguingly different from the one predicted in the standard phase diagram of ceria. This work demonstrates a feasible means to control oxygen non-stoichiometry in ceria via electrochemical potential. It also sheds light on the mechanism of phase transitions induced by electrochemical potential. For electrochemical systems, effects from a large-scale electrical environment should be taken into consideration, besides effective oxygen partial pressure and temperature.

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Operando X-ray Absorption Spectroscopy Study of SnO 2 Nanoparticles for Electrochemical Reduction of CO 2 to Formate

Tin–based electrocatalysts exhibit a remarkable ability to catalyze CO 2 to formate selectively. Understanding the size-property relationships and exploring the evolutions of active size still lack complete understanding. Herein, we prepared SnO 2 nanoparticles (NPs) with controllable size supported on commercial carbon spheres (SnO 2 /C–n, n=1,2,3) by a simple low-temperature annealing method. The transmission electron microscopy(TEM)/scanning transmission electron microscope (STEM) images and fitting results of the small angle X-ray scattering (SAXS) profile confirm the increased size of SnO 2 NPs as the increase of SnO 2 loading. The catalytic performance of SnO 2 has proved the size-dependent effect during CO 2 reduction reaction process. The as-prepared SnO 2 /C–1 displayed the maximum Faradic efficiency of formate (FE HCOO– ) of 82.7% at –1.0 V vs. RHE. In contrast, SnO 2 /C–2 and SnO 2 /C–3 with larger particle sizes achieved lower maximum FE HCOO– and larger overpotential. Moreover, we employed operando XAS to study the evolution of the oxidation state and local coordination environment of SnO 2 under working conditions. In addition to the observed the shifts of rising edge of Sn K-edge X-ray absorption near edge structure (XANES) spectra to lower energy side as the applied voltage decreases, the decreased coordination number of Sn in the Sn-O scattering path and the presence of Sn mental contribution in extended X-ray absorption fine structure (EXAFS) spectra verify the reduction of SnO 2 to SnO x and metallic Sn.

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Z-Contrast Enhancement in Au–Pt Nanocatalysts by Correlative X-ray Absorption Spectroscopy and Electron Microscopy: Implications for Composition Determination

The properties of bimetallic nanoparticles (BNPs) vary widely as a function of their composition and size distributions. X-ray absorption fine structure analysis is commonly used to characterize their structure, but its application to elements that are close to each other in the periodic table is hampered by poor Z-contrast. For this study, we trained an artificial neural network to recognize the partial coordination numbers in AuPt NPs synthesized via peptide templating using their X-ray absorption near-edge structure spectra. This approach, combined with scanning transmission electron microscopy analysis, revealed unique details of this prototype catalytic system that has different forms of heterogeneities at both the intra- and inter-particle levels. Our method based on the enhancement of Z-contrast of metal species will have implications for compositional studies of BNPs.

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Isolated Metal Sites in Cu–Zn–Y/Beta for Direct and Selective Butene-Rich C 3+ Olefin Formation from Ethanol

Direct and selective production of C 3+ olefins from bioethanol remains a critical challenge and important for the production of renewable transportation fuels such as aviation biofuels. In this study, we report a Cu–Zn–Y/Beta catalyst for selective ethanol conversion to butene-rich C 3+ olefins (88% selectivity at 100% ethanol conversion, 623 K), where the Cu, Zn, and Y sites are all highly dispersed. The ethanol-to-butene reaction network includes ethanol dehydrogenation, aldol condensation to crotonaldehyde, and hydrogenation to butyraldehyde, followed by further hydrogenation and dehydration reactions to form butenes. Cu sites play a critical role in promoting hydrogenation of the crotonaldehyde C═C bond to form butyraldehyde in the presence of hydrogen, making this a distinctive pathway from crotyl alcohol-based ethanol-to-butadiene reaction. Reaction rate measurements in the presence of ethanol and acetaldehyde (543 K, 12 kPa ethanol, 1.2 kPa acetaldehyde, 101.9 kPa H 2 ) over monometallic Zn/Beta and Y/Beta catalysts indicate that Y sites have higher C–C coupling rates than over Zn sites (initial C–C coupling rate, 6.1 × 10 –3 mol mol Y –1 s –1 vs 1.2 × 10 –3 mol mol Zn –1 s –1 ). Further, Lewis-acidic Y-site densities over Cu–Zn–Y/Beta with varied Y loadings are linearly correlated with the initial C–C coupling rates, suggesting that Lewis-acidic Y sites are the predominant sites that catalyze C–C coupling in Cu–Zn–Y/Beta catalysts. Control experiments show that the dealuminated Beta support is important to form higher density of Lewis-acidic Y sites in comparison with other supports such as silica, or deboronated MWW despite similar atomic dispersion of Y sites and Y–O coordination numbers over these supports, leading to more than 9 times higher C–C coupling rate per mole Y over dealuminated Beta relative to other supports. This study highlights the significance of unique combination of metal sites in contributing to the selective valorization of ethanol to C 3+ olefins, motivating for exploring multifunctional zeolite catalysts, where the presence of multiple sites with varying reactivities and functions allows for controlling the predominant molecular fluxes toward the desired products in complex reactions.

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Metal–Oxide Interface Sites Created Using Atomic Layer Deposition and Tested for CO Oxidation

The performance of catalysts made out of Pt supported on TiO 2 thin films grown on SBA-15 (a silica mesoporous material) by atomic layer deposition (ALD) was characterized systematically by combining in situ infrared absorption spectroscopy (IR) with other techniques including electron microscopy and adsorption−desorption isothermal measurements. The titania films in the resulting high-surface-area catalysts were evenly distributed throughout the inner surface of the SBA-15 mesopores, and their thickness could be controlled at a submonolayer level, with 3 to 4 TiO 2 ALD cycles needed for the complete coverage of the silica sites. The titania films could be deposited either before or after adding the metal (Pt), which was dispersed in the form of small nanoparticles (NPs) approximately 4−6 nm in diameter, in order to exert some control on the density and nature of the Pt/TiO 2 interface sites. One important lesson deriving from this work is that such an order of deposition leads to significantly different catalysts in spite of the fact that most of their structural properties are similar. If the Pt is deposited on the titania films, the resulting metal NPs are slightly smaller than those grown on silica and display CO adsorption sites with lower surface Pt coordination numbers. On the other hand, when TiO 2 is deposited on the Pt/SBA-15 starting material, some titania grows on the metal and partially blocks its surface while also creating new interface sites where CO binds more weakly and displays lower C−O stretching frequencies. In terms of catalytic performance, the results from in situ IR CO site titration and kinetic measurements combined suggest a mechanism where CO first adsorbs on Pt atop sites and then migrates to Pt/TiO 2 interface sites, where oxidation takes place. Both types of sites appear to be similar in all the catalysts tested, but catalytic performance could be optimized by tuning their surface densities. Maximum catalytic activity was obtained when the TiO2 films were deposited first and with TiO 2 coverages of at least half a monolayer, that is, after at least 2 ALD cycles.

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Unraveling Adsorbate-Induced Structural Evolution of Iron Carbide Nanoparticles

Iron carbide (Fe x C y ) nanoparticles (NPs) are promising candidates for replacing platinum group metals in industrial applications, such as high-temperature Fischer–Tropsch synthesis. However, due to their amorphous nature, characterization of the active sites has been challenging experimentally and computationally. Here, using a combined density functional theory (DFT), neural network interatomic potential-assisted global optimization, and ensemble learning study, we evaluate dynamic surface changes associated with syngas (H and CO) interactions. For this purpose, we have developed a general procedure that we use to model an experimentally relevant 270-atom Fe 182 C 88 NP using the neural network-assisted stochastic surface walk global optimization algorithm (SSW-NN). Once generated, the Fe 182 C 88 NP active sites and particle morphology are thoroughly characterized before the effects of syngas adsorbate interactions are explored by using DFT and molecular dynamics simulations. Lastly, we explore correlations between geometric and electronic features of the active sites and the adsorption of H (H ads ), using a regularized random forest machine learning algorithm. In doing so, we identified the Fe–C coordination number and p orbital occupancy as the most important descriptors affecting H ads . Furthermore, using a combined ML and quantum chemistry approach, our work demonstrates a general and efficient procedure for generating and probing complex surface phenomena on binary nanoparticles.

Adsorption↗

Small- and Wide-Angle X-ray Scattering Studies of Liquid–Liquid Phase Separation in Silicate Melts

Incongruent liquid-liquid phase separation is a common phenomenon in molten oxides, but there are few structural studies due to the high temperatures involved ca. >1600oC. In this work, we present a high-energy x-ray combined small/wide angle scattering (SAXS/WAXS) method that can directly probe non-equilibrium phase diagrams. The Porod exponent in the SAXS signal is extracted, which measures the roughness of the interface formed between different phases. Problematic volatilization of silica in Al 2 O 3 -, CaO-, and MgO-bearing silica-rich liquids were minimized using levitation, laser heating and rapid time-resolved measurements (lasting tens of seconds), to probe the kinetics of the phase separation process. The WAXS measurement simultaneously probes the local atomic structure of the liquid state and shows that the primary structural changes are associated with the SiO 2 network. Cation coordination numbers extracted from pair distribution functions support the model that the origin of phase separation in binary silicate systems is due to Coulombic repulsions between poorly screened cations. For CaO-SiO 2 , the liquid-liquid phase separation is found to correlate with a pause in the temperature dependent atomic disorder associated with SiO4 tetrahedra.

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The Stability of Nd Hydroxyl Complexes at Near Neutral to Alkaline pH from 25 to 75 °C: Implications for Monazite Solubility in Hydrothermal Aqueous Fluids

Speciation of rare earth elements (REE) in aqueous fluids controls their mobilization during fluid-rock interaction. Thermodynamic modeling provides important insights into the factors controlling REE mobility and fractionation in aqueous fluids, in which aqueous REE hydroxyl complexes are particularly important across a broad pH range. However, the stability of these REE hydroxyl complexes remains poorly determined due to limited experimental data above ambient temperature. In this work, UV–vis spectrophotometry experiments were conducted to determine the cumulative hydrolysis constants for neodymium (Nd) from 25 to 75 °C in near-neutral to alkaline solutions. The color indicator m -cresol purple was used to determine in situ pH. Alkaline NaOH-bearing aqueous solutions were doped with varying initial Nd concentrations (0 to ∼0.155 mmol/kg), which resulted in the release of protons (H + ) and pH decrease during hydrolysis of Nd 3+ according to Nd 3+ + n H 2 O = Nd(OH) n 3– n + H + . The average OH – ligand number coordinated to Nd 3+ was found to increase from 1.0 to 1.6 at 25 °C and from 1.2 to 2.8 at 75 °C over a pH range from 6.3 to 9.0. The measured speciation shows an increased predominance of Nd(OH) 3 0 over the Nd(OH) 2 + and Nd(OH) 2+ species with increased temperature and pH. The increasing cumulative formation constants (log*β° n , n = 1 to 3) retrieved from 25 to 75 °C differ by 0.1 to 1.9 logarithmic units in comparison to existing thermodynamic databases. These updated thermodynamic data have important implications for geochemical modeling of the speciation of Nd hydroxyl complexes and the solubility of monazite as a function of pH.

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Thermodynamics of MgO Atomic Layer Deposition Surface Reactions

The realities of atomic layer deposition (ALD) surface reactions often deviate from the simple ligand exchange frequently used to illustrate the technique. A detailed understanding of these reactions is necessary to develop greater surface synthetic control including chemical selectivity for patterning or to target defects. Here, the thermodynamics of surface reactions relevant to MgO ALD were investigated using pyroelectric calorimetry to measure the time-resolved heat generation. These reactions show exothermic heat generation of 0.12 mJ/cm 2 and 0.15 mJ/cm 2 for alternating Mg(CpEt) 2 and H 2 O reactions, respectively. The total reaction heat closely matches the standard reaction enthalpy for bulk MgO, supplemented with first-principles molecular calculations. First-principles models further reveal that while simple ligand exchange is favorable during surface reactions, the required increase in Mg-coordination number from two in the precursor to six in bulk MgO requires additional coverage-dependent surface reactions, which depend on the availability and stability of proximal surface hydroxyls.

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Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low energy structures of Pd n (n = 1-21) clusters supported on CeO 2 (111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pdn clusters of any structure. Low energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters and large cluster isomers share similarities in both shape and energy, and elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

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Low-Temperature Activation and Coupling of Methane on MgO Nanostructures Embedded in Cu 2 O/Cu(111)

Here, the efficient conversion of methane into valuable hydrocarbons such as ethane and ethylene at relatively low temperatures without deactivation issues is crucial for advancing sustainable energy solutions. Herein, AP-XPS and STM studies show that MgO nanostructures (0.2-0.5 nm wide, 0.4-0.6 Å high) embedded in a Cu 2 O/Cu(111) substrate activate methane at room temperature, mainly dissociating it into CH x (x = 2 or 3) and H adatoms, with minimal conversion to C adatoms. These MgO nanostructures in contact with Cu 2 O/Cu(111) exhibit unique reactivity, enabling C-C coupling into ethane and ethylene at 500 K, a significantly lower temperature than that required for bulk MgO catalysts (>700 K), with negligible carbon deposition and no deactivation. DFT calculations corroborate these experimental findings. The CH 4,gas → *CH 3 +*H reaction is a downhill process on MgO/Cu 2 O/Cu(111) surfaces. The activation of methane is facilitated by an electron transfer from copper to MgO and the existence of Mg and O atoms with a low coordination number in the oxide nanostructures. The formation of O-CH 3 and O-H bonds overcomes the energy necessary for the cleavage of a C-H bond in methane. DFT studies reveal that smaller Mg 2 O 2 model clusters provide stronger binding and lower activation barriers for C-H dissociation in CH 4 , while larger Mg 3 O 3 clusters promote C-C coupling due to weaker *CH 3 binding. All these results emphasize the importance of size when optimizing the catalytic performance of MgO nanostructures in the selective conversion of methane.

36 MATERIALS SCIENCE↗

Temperature-Dependent Properties of Molten Li 2 BeF 4 Salt Using Ab Initio Molecular Dynamics

Molten lithium tetrafluoroberyllate (Li 2 BeF 4 ) salt, also known as FLiBe, with a 2:1 mixture of LiF and BeF 2 is being proposed as a coolant and solvent in advanced nuclear reactor designs, such as the molten salt reactor or the fluoride salt cooled high-temperature reactor. We present the results on the structure and properties of FLiBe over a wide range of temperatures, 0–2000 K, from high-throughput ab initio molecular dynamics simulation using a supercell model of 504 atoms. The variations in the local structures of solid and liquid FLiBe with temperature are discussed in terms of a pair distribution function, coordination number, and bond angle distribution. The temperature-dependent electronic structure and optical and mechanical properties of FLiBe are calculated. The optical and mechanical property results are reported for the first time. The results above and below the melting temperature (~732 K) are compared with the experimental data and with data for crystalline FLiBe. The electronic structure and interatomic bonding results are discussed in correlation with the mechanical strength. A novel concept of total bond order density (TBOD), an important quantum mechanical parameter, is used to characterize the internal cohesion and strength in the simulated models. The results show a variation in the rate of change in properties in solid and liquid phases with anomalous behavior across the melting region. The observed trend is the decrease in mechanical strength, band gap, and TBOD in a nonlinear fashion as a function of temperature. The refractive index shows a surprising minimum at 850 K, among the tested temperatures, which lies above the melting point. These findings provide a new platform to understand the interplay between the temperature-dependent structures and properties of FLiBe salt.

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Computational and Experimental Characterization of the Ligand Environment of a Ni-Oxo Catalyst Supported in the Metal–Organic Framework NU-1000

Heterogeneous catalysts exhibit significant changes in composition due to the influence of operating conditions, and these compositional changes can have dramatic effects on catalytic performance. For traditional bulk metal heterogeneous catalysts, relationships between composition and catalytic operating conditions are well documented. However, the influence of operating conditions on the compositions of single-site heterogeneous catalysts remains largely unresolved. To address this, we report a combined computational and experimental characterization of a Ni oxo catalyst under catalytic hydrogenation conditions. Specifically, pair distribution function (PDF) analysis is combined with ab initio thermodynamic modeling to investigate ligand environments present on a Ni oxo cluster supported in the metal–organic framework NU-1000. Comparisons of the experimentally observed and simulated Ni–O coordination numbers and Ni–O, Ni···Ni, and Ni···Zr distances provide insight into the Ni ligand environment under H 2 (g). These comparisons suggest significant OH and H 2 O content and, further, that different Ni ions within the cluster and/or NU-1000 structure may comprise subtly different numbers of these ligands. Further, the observation of significant H 2 O content under H 2 (g) suggests that the NU-1000 support supplies H 2 O to the cluster. Examples of ligand environments that could lead to the observed PDFs are provided. Furthermore, the combination of simulations and experiments provides new insights into the ligand environment for Ni-NU-1000 catalysts that will be useful for understanding the ligand environments of other single-site Ni catalysts as well.

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Operando High-Energy-Resolution X-ray Spectroscopy of Evolving Cu Nanoparticle Electrocatalysts for CO 2 Reduction

Advances in electrocatalysis research rely heavily on building a thorough mechanistic understanding of catalyst active sites under realistic operating conditions. Only recently have techniques emerged that enable sensitive spectroscopic data collection to distinguish catalytically relevant surface sites from the underlying bulk material under applied potential in the presence of an electrolyte layer. Here, we demonstrate that operando high-energy-resolution fluorescence detected X-ray absorption spectroscopy (HERFD-XAS) is a powerful spectroscopic method which offers critical surface chemistry insights in CO 2 electroreduction with sub-electronvolt energy resolution using hard X-rays. Combined with the high surface area-to-volume ratio of 5 nm copper nanoparticles, operando HERFD-XAS allows us to observe with clear evidence the breaking of chemical bonds between the ligands and the Cu surface as part of the ligand desorption process occurring under electrochemical potentials relevant for the CO 2 reduction reaction (CO 2 RR). In addition, the dynamic evolution of oxidation state and coordination number throughout the operation of the nanocatalyst was continuously tracked. With these results in hand, undercoordinated metallic copper nanograins are proposed to be the real active sites in the CO 2 RR. In conclusion, this work emphasizes the importance of HERFD-XAS compared to routine XAS in catalyst characterization and mechanism exploration, especially in the complicated electrochemical CO 2 RR.

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Atomically Precise Single-Site Catalysts via Exsolution in a Polyoxometalate–Metal–Organic-Framework Architecture

Single-site catalysts (SSCs) achieve a high catalytic performance through atomically dispersed active sites. A challenge facing the development of SSCs is aggregation of active catalytic species. Reducing the loading of these sites to very low levels is a common strategy to mitigate aggregation and sintering; however, this limits the tools that can be used to characterize the SSCs. Here we report a sintering-resistant SSC with high loading that is achieved by incorporating Anderson–Evans polyoxometalate clusters (POMs, MMo 6 O 24 , M = Rh/Pt) within NU-1000, a Zr-based metal–organic framework (MOF). The dual confinement provided by isolating the active site within the POM, then isolating the POMs within the MOF, facilitates the formation of isolated noble metal sites with low coordination numbers via exsolution from the POM during activation. The high loading (up to 3.2 wt %) that can be achieved without sintering allowed the local structure transformation in the POM cluster and the surrounding MOF to be evaluated using in situ X-ray scattering with pair distribution function (PDF) analysis. Notably, the Rh/Pt···Mo distance in the active catalyst is shorter than the M···M bond lengths in the respective bulk metals. Furthermore, models of the active cluster structure were identified based on the PDF data with complementary computation and X-ray absorption spectroscopy analysis.

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Nucleophilic Displacement Reactions of Silver-Based Metal–Organic Chalcogenolates

Here, we report nucleophilic displacement reactions that can increase the dimensionality or coordination number of silver-based metal–organic chalcogenolates (MOChas). MOChas are crystalline ensembles containing one-dimensional (1D) or two-dimensional (2D) inorganic topologies with structures and properties defined by the choice of metal, chalcogen, and ligand. MOChas can be readily prepared from a variety of small-molecule ligands and metals or metal ions. Although MOChas offer ligand diversity, most reported examples use relatively small ligands, typically involving short alkyl chains, aryl rings, or molecular cages. This is because larger, more complex molecules often yield poor product morphologies with indeterminate structures. In this study, we overcame this limitation by employing a ligand exchange strategy whereby a 1D MOCha, silver(I) methyl 2-mercaptobenzoate (2MMB), is used as a silver source for preparing 2D examples. The reaction proceeds generally toward products composed of the stronger nucleophile. We show that the reaction prefers displacing 1D topologies to yield 2D ones and replacing thiolates with selenolates. We performed a study to characterize the mechanism by which organic chalcogenols and dichalcogenides exchange with MOChas. The collected data and product analysis support a proposed mechanism of nucleophilic substitution, explaining how both organic chalcogenols and dichalcogenides can displace ligands in MOChas. This work provides a new synthetic route that will enable the preparation of more elaborate MOChas and heterostructures thereof. This approach enabled the preparation of previously inaccessible oligophenyl MOChas, which were successfully solved via small-molecule serial femtosecond crystallography (smSFX) at the SPring-8 Ångström Compact Free Electron LAser (SACLA) facility.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation of Americium-Containing Phosphates, Silicates, Borates, Molybdates, and Fluorides Synthesized via High-Temperature Flux Crystal Growth

The crystal chemistry of americium-containing extended structures was investigated, and several classes of americium-containing solid-state oxide materials were obtained in single-crystal form via high-temperature flux crystal growth. This enabled the structural characterization of rare examples of ternary, quaternary, and penternary americium-containing silicates K 3 Am (Si 2 O 7 ) and Cs 6 Am 2 Si 21 O 48 , phosphates Na 3 Am (PO 4 ) 2 and K 3 Am (PO 4 ) 2 , borates Ba 3 Am 2 (BO 3 ) 4 and AmBO 3 , borate halides Ca 5 Am(BO 3 ) 4 Cl, molybdates Li 0.5 Am 0.5 MoO 4 , and fluorides CsAm 2 F 7 . Using these crystallographic data, the ionic radii of Am 3+ with coordination numbers of six (0.975 Å), seven (1.052 Å), and nine (1.162 Å) were established. A maximum entropy method (MEM) analysis was performed on the single-crystal X-ray diffraction data that were collected for K 3 Nd(PO 4 ) 2 /K 3 Am(PO 4 ) 2 , K 3 NdSi 2 O 7 /K 3 AmSi 2 O 7 , and NdBO 3 /AmBO 3 , to qualitatively compare the ionicities of the Nd–O and Am–O bonds. In conclusion, Raman spectroscopy data were collected on single crystals of K 3 Am(PO 4 ) 2 and compared to the calculated Raman spectrum of K 3 Am(PO 4 ) 2 obtained from DFT calculations.

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