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At least 1,279 records · Page 71

Inverse design of plasma metamaterial devices with realistic elements

In an expansion of a previous study, we apply inverse design methods to produce two-dimensional plasma metamaterial devices with realistic plasma elements which incorporate quartz envelopes, collisionality (loss), non-uniform density profiles, and resistance to experimental error/perturbation. Finite difference frequency domain simulations are used along with forward-mode differentiation to design waveguides and demultiplexers operating under the transverse magnetic polarization. Additionally, optimal devices with realistic elements are compared to previous devices with idealized elements, and several parameter initialization schemes for the optimization algorithm are explored, yielding a robust procedure for producing such devices. Demultiplexing and waveguiding are demonstrated for microwave-regime devices composed of plasma elements with reasonable space-averaged plasma frequencies ~10GHz and a collision frequency ~1 GHz, allowing for future in-situ training and experimental realization of these designs.

42 ENGINEERING↗

Analytical integration of the tractions induced by non-singular dislocations on an arbitrary shaped triangular quadratic element

Here, an analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. Phys. Solids 54 561–587). The nodal force expressions can be used when considering both a single convolution or double convolution of the Green's function with the core distribution. A solution is also proposed for the case of a semi-infinite segment through the study of the asymptotic behavior of the analytical expressions. The proposed approach is exact and very computationally efficient. The choice of an arbitrary shaped triangular element and quadratic shape functions allow the consideration of complex geometries and comply with automatic meshing procedures. These analytical expressions could also be employed to estimate dislocation interactions with interfaces.

42 ENGINEERING↗

Electromagnetic wave propagation based upon spectral-element methodology in dispersive and attenuating media

SUMMARY We build on mathematical equivalences between Maxwell’s wave equations for an electromagnetic medium and elastic seismic wave equations. This allows us to readily model Maxwell’s wave propagation in the spectral-element codes SPECFEM2D and SPECFEM3D, written for acoustic, viscoelastic and poroelastic seismic wave propagation, providing the ability to handle complex geometries, inherent to finite-element methods and retaining the strength of exponential convergence and accuracy due to the use of high-degree polynomials to interpolate field functions on the elements, characteristic to spectral-element methods (SEMs). Attenuation and dispersion processes related to the frequency dependence of dielectric permittivity and conductivity are also included using a Zener model, similar to shear attenuation in viscoelastic media or viscous diffusion in poroelastic media, and a Kelvin–Voigt model, respectively. Ability to account for anisotropic media is also discussed. Here, we limit ourselves to certain dielectric permittivity tensor geometries, in order to conserve a diagonal mass matrix after discretization of the system of equations. Doing so, simulation of Maxwell’s wave equations in the radar frequency range based on SEM can be solved using explicit time integration schemes well suited for parallel computation. We validate our formulation with analytical solutions. In 2-D, our implementation allows for the modelling of both a transverse magnetic (TM) mode, suitable for surface based reflection ground penetration radar type of applications, and a transverse electric (TE) mode more suitable for crosshole and vertical radar profiling setups. Two 2-D examples are designed to demonstrated the use of the TM and TE modes. A 3-D example is also presented, which allows for the full TEM solution, different antenna orientations, and out-of-plane variations in material properties.

58 GEOSCIENCES↗

Spitzer mid-infrared detections of neutron star merger GW170817 suggests synthesis of the heaviest elements

Abstract We report our Spitzer Space Telescope observations and detections of the binary neutron star merger GW170817. At 4.5 μm, GW170817 is detected at 21.9 mag AB at +43 days and 23.9 mag AB at +74 days after merger. At 3.6 μm, GW170817 is not detected to a limit of 23.2 mag AB at +43 days and 23.1 mag AB at +74 days. Our detections constitute the latest and reddest constraints on the kilonova/macronova emission and composition of heavy elements. The 4.5 μm luminosity at this late phase cannot be explained by elements exclusively from the first abundance peak of the r-process. Moreover, the steep decline in the Spitzer band, with a power-law index of 3.4 ± 0.2, can be explained by a few of the heaviest isotopes with half-life around 14 d dominating the luminosity (e.g. 140Ba, 143Pr, 147Nd, 156Eu, 191Os, 223Ra, 225Ra, 233Pa, 234Th) or a model with lower deposition efficiency. This data offers evidence that the heaviest elements in the second and third r-process abundance peak were indeed synthesized. Our conclusion is verified by both analytics and network simulations and robust despite intricacies and uncertainties in the nuclear physics. Future observations with Spitzer and James Webb Space Telescope will further illuminate the relative abundance of the synthesized heavy elements.

Kasliwal, Mansi M. (ORCID:0000000256194938)↗

Critical-Element-Free Permanent-Magnet Materials Based on Ce 2 Fe 14 B

Developing a critical-element-free low-cost permanent magnet is an urgent necessity in view of rapidly developing technologies and the associated huge market demand for Nd 2 Fe 14 B-based magnets. Here, inspired by the abundant and low-cost nature of Ce and these high-performance Nd 2 Fe 14 B permanent magnets, we explore whether it is in fact possible to attain a useful performance in alloys based on the sister material Ce 2 Fe 14 B, employing both experimental and theoretical efforts. Experimentally, we study Ce 2 Fe 14 B with Co, La, and Zr substitutions. The Zr substitution is explored in view of Zr’s frequent role in enhancing magnetic anisotropy in permanent magnets, while the Co and La substitutions serve to remedy the too-low Curie point of 433 K in the base alloy. While we find no Zr-related anisotropy enhancement either experimentally or theoretically, the cosubstitution of La and Co indeed improves the Curie temperature as well as the magnetization, M s , with a potential energy product as high as 38 MG Oe. These properties together suggest optimization of the alloy LaCeFe 12.7 Co 1.3 B (with only 7 wt % cobalt) as a critical-element-free permanent magnet. While the substituted elements do not enhance magnetic anisotropy, from theory, we find a substantial increase, to a first anisotropy constant, K1, as high as 4.24 MJ/m 3 , associated with Bi substitution for Ce. In this paper, our experimental and theoretical results demonstrate the great potential of La, Co, and Bi substitutions in developing low-cost and critical-element-free Ce 2 Fe 14 B-based permanent magnets.

36 MATERIALS SCIENCE↗

Few-nucleon matrix elements in pionless effective field theory in a finite volume

Here, pionless effective field theory in a finite volume (FVEFT $\notπ$ ) is investigated as a framework for the analysis of multinucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT π with the stochastic variational method, the spectra of nuclei with atomic number A ∈ {2, 3} are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass m $\notπ$ = 806 MeV , thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wave functions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT $\notπ$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one- and two-body effective field theory counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, in addition to the magnetic moments and the isovector longitudinal momentum fraction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate that the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Lastly, we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements

In this paper, the Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on the $N_f=2+1+1$ MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of $g_A = 1.213(26)$ with a quark-mass-dependent renormalization coefficient.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Overview of design and analysis activities for the W7-X scraper element

The Wendelstein 7-X stellarator is in final stages of commissioning, and will begin operation in late 2015. In the first phase, the machine will operate with a limiter, and will be restricted to low power and short pulse. But in 2019, plans are for an actively cooled divertor to be installed, and the machine will operate in steady state at full power. Recently, plasma simulations have indicated that, in this final operational phase, a bootstrap current will evolve in certain scenarios. This will cause the sensitive ends of the divertor target to be overloaded beyond their qualified limit. A high heat flux scraper element (HHF-SE) has been proposed in order to take up some of the convective flux and reduce the load on the divertor. In order to examine whether the HHF-SE will be able to effectively reduce the plasma flux in the divertor region of concern, and to determine how the pumping effectiveness will be affected by such a component, it is planned to include a test divertor unit scraper element (TDU-SE) in 2017 during an earlier operational phase. Several U.S. fusion energy science laboratories have been involved in the design, analysis (structural and thermal finite element, as well as computational fluid dynamics), plasma simulation, planning, prototyping, and diagnostic development around the scraper element program (both TDU-SE and HHF-SE). As a result, this paper presents an overview of all of these activities and their current status.

42 ENGINEERING↗

Mantle–melt partitioning of the highly siderophile elements: New results and application to Mars

Trace elements and extant and extinct isotopic attributes in Martian meteorites have been used to argue that Mars accreted quickly, differentiated into core and mantle, and established several mantle reservoirs, possibly within 10 Ma of T0. The partitioning of trace elements in the deep mantle has been relatively unstudied, despite the need for such knowledge in understanding magma ocean crystallization and the origin of depleted and enriched mantle reservoirs. The siderophile element composition of the Martian mantle and lithophile isotopic systems such as Sr, Hf, and Nd are thought to record evidence for early metal–silicate equilibrium and deep magma ocean at an intermediate depth and pressure of 800 km or 14 GPa. We have carried out experiments across this pressure range to better understand the mineral/melt partitioning of a wide range of elements. These new data are used to evaluate differentiation models for Mars and to help interpret the available isotopic data. The relatively incompatible nature of Re compared to mildly compatible Os means that the crystallization of a deep magma ocean will lead to residual liquids with superchondritic Re/Os, and solids with subchondritic Re/Os. Such material available in the mantle could be the source of enriched isotopic reservoir that produced shergottites with +γOs values. Slightly subchondritic Re/Os ratios in the crystallizing solids would provide a reservoir that could produce -γOs values. Finally, melting of mixtures of these two enriched and depleted endmembers could explain the Nd-Os isotopic correlations and systematics of shergottites.

58 GEOSCIENCES↗

Side readout of long scintillation crystal elements with digital SiPM for TOF-DOI PET

Purpose: Side readout of scintillation light from crystal elements in positron emission tomography (PET) is an alternative to conventional end-readout configurations, with the benefit of being able to provide accurate depth-of-interaction (DOI) information and good energy resolution while achieving excellent timing resolution required for time-of-flight PET. This paper explores different readout geometries of scintillation crystal elements with the goal of achieving a detector that simultaneously achieves excellent timing resolution, energy resolution, spatial resolution, and photon sensitivity. Methods: The performance of discrete LYSO scintillation elements of different lengths read out from the end/side with digital silicon photomultipliers (dSiPMs) has been assessed. Results: Compared to 3 × 3 × 20 mm{sup 3} LYSO crystals read out from their ends with a coincidence resolving time (CRT) of 162 ± 6 ps FWHM and saturated energy spectra, a side-readout configuration achieved an excellent CRT of 144 ± 2 ps FWHM after correcting for timing skews within the dSiPM and an energy resolution of 11.8% ± 0.2% without requiring energy saturation correction. Using a maximum likelihood estimation method on individual dSiPM pixel response that corresponds to different 511 keV photon interaction positions, the DOI resolution of this 3 × 3 × 20 mm{sup 3} crystal side-readout configuration was computed to be 0.8 mm FWHM with negligible artifacts at the crystal ends. On the other hand, with smaller 3 × 3 × 5 mm{sup 3} LYSO crystals that can also be tiled/stacked to provide DOI information, a timing resolution of 134 ± 6 ps was attained but produced highly saturated energy spectra. Conclusions: The energy, timing, and DOI resolution information extracted from the side of long scintillation crystal elements coupled to dSiPM have been acquired for the first time. The authors conclude in this proof of concept study that such detector configuration has the potential to enable outstanding detector performance in terms of timing, energy, and DOI resolution.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Physics–Dynamics Coupling with Element-Based High-Order Galerkin Methods: Quasi-Equal-Area Physics Grid

Atmospheric modeling with element-based high-order Galerkin methods presents a unique challenge to the conventional physics–dynamics coupling paradigm, due to the highly irregular distribution of nodes within an element and the distinct numerical characteristics of the Galerkin method. The conventional coupling procedure is to evaluate the physical parameterizations ( physics) on the dynamical core grid. Evaluating the physics at the nodal points exacerbates numerical noise from the Galerkin method, enabling and amplifying local extrema at element boundaries. Grid imprinting may be substantially reduced through the introduction of an entirely separate, approximately isotropic finite-volume grid for evaluating the physics forcing. Integration of the spectral basis over the control volumes provides an area-average state to the physics, which is more representative of the state in the vicinity of the nodal points rather than the nodal point itself and is more consistent with the notion of a “large-scale state” required by conventional physics packages. This study documents the implementation of a quasi-equal-area physics grid into NCAR’s Community Atmosphere Model Spectral Element and is shown to be effective at mitigating grid imprinting in the solution. The physics grid is also appropriate for coupling to other components within the Community Earth System Model, since the coupler requires component fluxes to be defined on a finite-volume grid, and one can be certain that the fluxes on the physics grid are, indeed, volume averaged.

54 ENVIRONMENTAL SCIENCES↗

Ultra-high-precision alignment of the elastomerically mounted elements of the science camera lenses for the Mars Science Laboratory (MSL) rover

Cameras built for space exploration are required to meet stringent environmental conditions, such as thermal and dynamic loads for both the optics (camera lens) and imaging electronics. On a multitude of spaceborne imaging instruments, optical elements are supported in their mounts via an elastomeric bonding approach using a room temperature vulcanizing silicone as the bonding agent. Employing this integration method, we achieved element-to-element alignment, measured as the total indicated runout, using a high-precision contact probe to be on the order of half a wavelength of He-Ne laser light, or 0.3 {mu}m, on the Malin Space Science Systems lenses for the Mars Science Laboratory (MSL) cameras. This is a higher precision than the current industry state-of-the-art, and it was achieved for the very challenging small diameter lens elements. This paper describes the design philosophy, implementation, and integration method that resulted in achieving this level of precision for interelement alignment. The results are based on actual measurements that were made during the process of building the MSL rover's science camera lenses, namely Mastcams, the Mars Hand Lens Imager, and the Mars Descent Imager. The optical designs of these cameras lenses are described in detail in [Opt. Eng.48, 103002 (2009)10.1117/1.3251343], while further information on the four science cameras can be found at http://www.msss.com.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Elemental Concentrations in the Seed of Mutants and Natural Variants of Arabidopsis thaliana Grown under Varying Soil Conditions

The concentrations of mineral nutrients in seeds are critical to both the life cycle of plants as well as human nutrition. These concentrations are strongly influenced by soil conditions, as shown here by quantifying the concentration of 14 elements in seeds from Arabidopsis thaliana plants grown under four different soil conditions: standard, or modified with NaCl, heavy metals, or alkali. Each of the modified soils resulted in a unique change to the seed ionome (the mineral nutrient content of the seeds). To help identify the genetic networks regulating the seed ionome, changes in elemental concentrations were evaluated using mutants corresponding to 760 genes as well as 10 naturally occurring accessions. The frequency of ionomic phenotypes supports an estimate that as much as 11% of the A. thaliana genome encodes proteins of functional relevance to ion homeostasis in seeds. A subset of mutants were analyzed with two independent alleles, providing five examples of genes important for regulation of the seed ionome: SOS2, ABH1, CCC, At3g14280 and CNGC2. In a comparison of nine different accessions to a Col-0 reference, eight accessions were observed to have reproducible differences in elemental concentrations, seven of which were dependent on specific soil conditions. These results indicate that the A. thaliana seed ionome is distinct from the vegetative ionome, and that elemental analysis is a sensitive approach to identify genes controlling ion homeostasis, including those that regulate gene expression, phospho-regulation, and ion transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Standard atomic weights of the elements 2021 (IUPAC Technical Report)

Following the reviews of atomic-weight determinations and other cognate data in 2015, 2017, 2019 and 2021, the IUPAC (International Union of Pure and Applied Chemistry) Commission on Isotopic Abundances and Atomic Weights (CIAAW) reports changes of standard atomic weights. The symbol A r°(E) was selected for standard atomic weight of an element to distinguish it from the atomic weight of an element E in a specific substance P, designated A r(E, P). The CIAAW has changed the values of the standard atomic weights of five elements based on recent determinations of terrestrial isotopic abundances. The standard atomic weight of argon and lead have changed to an interval to reflect that the natural variation in isotopic composition exceeds the measurement uncertainty of A r(Ar) and A r(Pb) in a specific substance. The standard atomic weights and/or the uncertainties of fourteen elements have been changed based on the Atomic Mass Evaluations 2016 and 2020 accomplished under the auspices of the International Union of Pure and Applied Physics (IUPAP). A r° of Ho, Tb, Tm and Y were changed in 2017 and again updated in 2021.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Discrete Element Modeling Results of Proppant Rearrangement in the Cooke Conductivity Cell

The study of propped fracture conductivity began in earnest with the development of the Cooke cell which later became part of the initial API standard. Subsequent developments included a patented multicell design to conduct 4 tests in a press at the same time. Other modifications have been used by various investigators. Recent studies by the Stim-Lab proppant consortium have indicated that the flow field across a Cooke proppant conductivity testing cell may not be uniform as initially believed which resulted is significantly different conductivity results. Post test analysis of low temperature metal alloy injections at the termination of proppant testing prior to the release of the applied stress suggest that higher flow is to be expected along the sides and top of the proppant pack than compared to the middle of the pack. To evaluate these experimental findings, a physics-based two-dimensional (2-D) discrete element model (DEM) was developed and applied to simulate proppant rearrangement during stress loading in the Cooke conductivity cell and the resulting porosity field. Analysis of these simulations are critical to understanding the impact of modification to the testing cell as well as understanding key proppant conductivity issues such as how these effects are manifested in proppant concentration testing results. The 2-D DEM model was constructed to represent a realistic cross section of the Cooke cell with a distribution of four material properties, three that represented the Cooke cell (steel, sandstone,square rings), and one representing the proppant. In principle, Cooke cell materials can be approximated as assemblies of independent discrete elements (particles) of various sizes and material properties that interact via cohesive interactions, repulsive forces, and frictional forces. The macroscopic behavior can then be modeled as the collective behavior of many interacting discrete elements. This DEM model is particularly suitable for modeling proppant mechanical interactions subjected to an applied stress, where the experimental cell is represented as a cohesive body composed of a large number of discrete elements, and proppants can be modeled as the individual discrete particles with various sizes (following the proppant size distribution-density function used in the test) that exhibit no cohesive strength between the particles. Initial 2-D DEM modeling results suggest that proppant rearrangement and non-uniform stress distribution across the proppant pack results in significant non-uniform porosity distribution across the Cooke cell. Larger porosities develop along the edge of the proppant pack beneath the square ring seal and would result in a disproportionate higher flow field along these edges as compared to the middle of the proppant pack. These results suggest that reported conductivity values determined by the Cooke cell may be biased to overestimate the actual conductivity of the proppant at high stresses and that modifications to the standard Cooke cell will affect the magnitude of this bias.

03 NATURAL GAS↗

Intelligent Integrated Machining: Handheld XRF for Mapping Zr Coating and Al-6061 Cladding Thickness in RERTR Fuel Elements

An inexpensive commercially available handheld energy dispersive x‐ray fluorescence spectrometer is used to provide a rapid non‐destructive estimate of coating and/or cladding thickness in situ . The portable XRF instrument contains a battery‐operated low‐power polychromatic source coupled with a Peltier‐cooled silicon drift detector; built‐in analysis software based upon the Method of Fundamental Parameters converts measured spectral intensities to elemental concentrations, reported as normalized weight percentages. Using detected signals from elements unique to the base material and coating or cladding materials, calibration curves and associated empirical algorithms for determining the thickness of the high‐purity zirconium coating on an RERTR fuel element prior to cladding with aluminum, and for determining the thickness of the Al‐6061 cladding after HIP for a known zirconium layer thickness, are constructed. For Zr over bare DU‐10Mo, agreement between the measured and the calculated thickness is ± 5% or better. For the multilayer system consisting of Al‐6061 over Zr over Du‐10Mo, agreement between calculated and measured thickness is ± 10‐15% over the thickness range of interest. Simultaneous estimates for the Al cladding and underlying Zr coating can be made using the elemental composition output only when the Mo signal is in the quasi‐static range (corresponding to Al thicknesses of ~15 mils (0.381 mm) and greater) and not so low that measurement error is greater than the signal itself; under these conditions, accuracy is on the order of ±15 – 20%. More accurate determination of both Zr and Al thickness simultaneously may be possible if the count‐rates associated with individual fluorescent lines in the multilayer sample are available rather than just the weight percent composition currently output by the XRF analyzer software.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Prioritization Study of Elements Relevant to RIMS Counter-WMD

A systematic study of the priority in which elements should be investigated in order to maximize the possible impact on RIMS Counter-WMD research has been carried out. Candidate elements included U, Th, transuranic elements, and select fission products such as Tc and Eu. This list has been updated to reflect assessments based on potential utility to debris diagnostics as well as the degree of complexity required to develop the RIMS method for the measurement of expected isotope abundances. Factors considered in this study include production of actinides in a fission environment, the existence of available resonance ionization-specific spectroscopic work, as well as practical experimental considerations (sample synthesis for research and activity/safety considerations). The resultant prioritized list of additional elements (beyond U) to be carried forward in this study are, in order of interest, Pu, Am, and Np. If resources and time lines permit, we would also like to investigate Th and Eu. Cm would be a final choice due to the logistics of creating and handling higher activity, short-lived materials, and the paucity of pre-existing spectroscopic studies.

36 MATERIALS SCIENCE↗