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At least 379 records · Page 21

Theory of electric, magnetic, and toroidal polarizations in crystalline solids with applications to hexagonal lonsdaleite and cubic diamond

Multipolar order in bulk crystalline solids is characterized by multipole densities-denoted as polarizations in this work-that cannot be cleanly defined using the concepts of classical electromagnetism. Here we use group theory to overcome this difficulty and present a systematic study of electric, magnetic, and toroidal multipolar order in crystalline solids. Based on our symmetry analysis, we identify five categories of polarized matter, each of which is characterized by distinct features in the electronic band structure. For example, Rashba spin splitting in electropolar bulk materials like wurtzite represents the electric dipolarization in these materials. We also develop a general formalism of indicators for individual multipole densities that provide a physical interpretation and quantification of multipolar order. Our work clarifies the relation between patterns of localized multipoles and macroscopic multipole densities they give rise to. To illustrate the general theory, we discuss its application to polarized variants of hexagonal lonsdaleite and cubic diamond structures. In conclusion, our work provides a general framework for classifying and expanding current understanding of multipolar order in complex materials.

36 MATERIALS SCIENCE↗

Tailored polyMOFs for ion transport in lithium-based battery electrolyte

Owing to their low flammability, solid-state and quasi-solid-state electrolytes are safer alternatives to liquid organic electrolytes for energy storage applications. Metal–organic frameworks (MOFs), with facile functional tunability, long-range order, and rich host–guest interactions, have been implemented as electrolyte materials in a wide range of energy storage applications. In this work, we investigate a class of MOFs called polyMOFs as quasi-solid-state electrolyte materials. Unlike MOF–polymer composites, which are physical mixtures of MOF particles and polymers, polyMOFs are composed of polymeric linkers and metal ion nodes that self-assembled into crystalline and porous framework materials. PolyMOFs thus marry the ionic transport properties of liquid electrolyte and polymers with the synthetic versatility and host–guest interactions of MOFs. We demonstrate that the functionality of the polymer backbone of the polyMOF linker can improve room-temperature ion transport in the material. The polyMOF based on poly(ethylene glycol) (PEG) exhibits greater ionic conductivity, lithium transference number, and lower activation energy than its polyethylene (PE) analog. Supported by solid-state 7 Li nuclear magnetic resonance spectroscopy, we propose these improvements are due to stronger coordination of Li + to oxide sites in PEG, allowing for dissociation of Li and its associated anion. DFT studies further reveal that the confined solvent molecule mediates Li + transport in PEG-functionalized UiO-66 via a metastable adsorption and hopping mechanism. This work lies at the interface of inorganic and polymer electrolytes, unveiling fundamental insights into the design of next-generation ion conductive materials for energy technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Neural Network Enhanced RKPM for Electrochemical-Mechanical Coupled Damage Modeling of Energy Storage Materials

Energy storage materials undergo significant charge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. For Li-ion batteries, for example, lithium moving between electrodes during charging and discharging process causes expansion and contraction of grains, and the strongly anisotropic and nonlinearly [Li]-dependent grain material properties can cause grains to expand into and contract away from each other, leading to chemo-mechanical cracking. In the first part of this work, a RKPM based computational framework for solving the coupled solid-phase lithium conservation with Fickian diffusion and the lithium concentration dependent anisotropic mechanical problem subjected to a highly nonlinear Butler-Volmer boundary condition is introduced. The choice of RKPM completeness conditions for lithium concentration and mechanical deformation fields, and the variational consistency condition for the domain integration of the coupled problem is first determined. In the second part of this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material, by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that is necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure.

damage modeling↗

Suspension electrolyte with modified Li + solvation environment for lithium metal batteries

Designing a stable solid–electrolyte interphase on a Li anode is imperative to developing reliable Li metal batteries. In this work, we report a suspension electrolyte design that modifies the Li + solvation environment in liquid electrolytes and creates inorganic-rich solid–electrolyte interphases on Li. Li 2 O nanoparticles suspended in liquid electrolytes were investigated as a proof of concept. Through theoretical and empirical analyses of Li 2 O suspension electrolytes, the roles played by Li 2 O in the liquid electrolyte and solid–electrolyte interphases of the Li anode are elucidated. Also, the suspension electrolyte design is applied in conventional and state-of-the-art high-performance electrolytes to demonstrate its applicability. Based on electrochemical analyses, improved Coulombic efficiency (up to ~99.7%), reduced Li nucleation overpotential, stabilized Li interphases and prolonged cycle life of anode-free cells (~70 cycles at 80% of initial capacity) were achieved with the suspension electrolytes. We expect this design principle and our findings to be expanded into developing electrolytes and solid–electrolyte interphases for Li metal batteries.

25 ENERGY STORAGE↗

Electrified Operando -Freezing of Electrocatalytic CO 2 Reduction Cells for Cryogenic Electron Microscopy

The ability to freeze and stabilize reaction intermediates in their metastable states and obtain their structural and chemical information with high spatial resolution would be very powerful to unravel the fundamentals in many important materials technologies such as catalysis and batteries. Here, we develop an electrified operando-freezing methodology for the first time to preserve these metastable states under electrochemical reaction conditions for cryogenic electron microscopy (cryo-EM) imaging and spectroscopy. Using Cu catalysts for CO 2 reduction as a model system, we observe restructuring of the Cu catalyst in a CO 2 atmosphere while the same catalyst remains intact in an air atmosphere at the nanometer scale. Furthermore, we discover the existence of single valance Cu (1+) state and C-O bonding at the electrified liquid-solid interface of the operando-frozen samples, which are key reaction intermediates that traditional ex situ measurements fail to detect. Finally, this work highlights our novel technique to study the local structure and chemistry of electrified liquid-solid interfaces, which has broad impact for many electrochemical reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Demonstration of MgCr 2– x Mn x O 4 Spinel Oxide Cathodes in High-Voltage Mg Batteries

Solid-solution oxide spinels with high redox voltages and facile Mg 2+ mobility have been identified as promising candidates for practical, high-voltage cathodes in Mg batteries. In this work, we discuss the development of MgCr 2-x Mn x O 4 [x = 0.5, 1, 1.2] solid-solution spinel oxides as a cathode material and their electrochemical performance paired with an Mg anode in a full cell. This work presents the first demonstration of full cells with these materials. Mg-Cr-Mn spinel oxides with varying Cr and Mn contents were synthesized using alternative synthetic routes for optimal electrochemical performance. High-resolution synchrotron powder X-ray diffraction (PXRD), solid-state nuclear magnetic resonance (NMR) spectroscopy, and electron microscopy showed that these different synthetic routes resulted in changes in structures and particle morphologies, which in turn affect the electrochemical performance. Particularly, the urea coprecipitation synthetic route resulted in high-surface-area particles that enabled lower overpotentials and increased discharge capacity. The high surface area also resulted in expedited structural degradation caused by the irreversible migration of Mg 2+ into normally vacant 16c sites in the spinel lattice. This structural degradation was lessened by using a hydrosauna-urea synthesis method, which decreased the Mg/Mn inversion ratio while retaining high-surface-area particles with good cycling performance. Furthermore, our findings highlight the necessity for high surface area or nanostructured spinel oxide cathodes with minimized Mg-Mn inversion to enable spinel oxide cathodes in Mg full cells.

Mg anode↗

Identifying Bounds of Inorganic Content in Solventless Processing of Hybrid Solid Electrolytes

Solid-state lithium batteries require safe, robust electrolytes to enable higher energy densities and improved safety over conventional cells. Hybrid polymer–ceramic electrolytes are a promising solution, combining the processability of polymers with the high ionic conductivity and mechanical strength of inorganic fillers. In this work, we demonstrate a solventless, UV-curing method to produce hybrid solid electrolytes using a poly(ethylene glycol) dimethyl ether (PEGDME)-based photocurable matrix incorporating Li 1.5 Al 0.5 Ge 1.5 (PO 4 ) 3 (LAGP) or Li 7 La 3 Zr 2 O 12 (LLZO) ceramic electrolyte. Inorganic filler loadings up to ∼55 wt.% could be successfully incorporated via this process which was the highest inorganic content at which the slurry remains processable and cured into a uniform film. The resulting UV-cured composite electrolytes remain flexible and exhibit room-temperature ionic conductivities on the order of 10 −4 S·cm −1 , along with notably improved lithium-ion transference numbers compared to conventional polymer electrolytes. Similar performance and processing limits were observed for both LAGP and LLZO, indicating that ceramic filler chemistry does not significantly affect the UV-curing process or the electrolyte's ion transport properties in this regime. Eliminating solvents from fabrication not only simplifies processing and mitigates environmental concerns but also enables higher solid contents that enhance mechanical strength and help suppress lithium dendrite formation. In conclusion, this scalable approach thus paves the way for manufacturing robust composite solid electrolytes for next-generation solid-state batteries (SSBs).

Batteries↗

Accelerating Laboratory-Based, All-Solid-State Battery Research and Development: Industrially Relevant Small-Batch Dry-Processing, Small and Low-Cost Test Fixtures, and Short-Tolerant Separators

This work presents improvements to mixing (for dry-processed electrodes), separator robustness, and cell testing jigs for all-solid-state batteries (ASSBs). These developments combine synergistically to enable rapid research and development of ASSB catholytes. A mechanical "kneader" is designed and built which emulates the mixing and fibrillation of poly-tetrafluoroethylene binder that occurs in industrially relevant twin-screw extruders. A modest improvement in the mixing and dispersion catholyte materials is observed using micro-resolution X-ray computed tomography (X-ray CT). Catholytes are paired with an In-metal anode and separated by a novel, dual-layer, polyaramid-fiber-supported, sulfide-solid electrolyte (Li6 PS5 Cl) separator. This separator achieves high short tolerance which enabled a 95% success rate across 20 attempted cells and to date over 100 successful cells have been built. ASSBs were tested in a 2032 coin-cell format. Simultaneous cycling of a large number of cells is further enabled by a compact and low cost (~ 38 USD per jig) pressure application jig of which 100 have been constructed to date. The utility of these advances is demonstrated through a brief study on the effect cathode-side conductive carbon and current collector type has on capacity and rate performance.

25 ENERGY STORAGE↗

Boron Nitride Solid-State Neutron Detectors

The goal of this project is to build upon the work performed under the Texas Tech IDEAS project (DE-AR0000964 monitored by Dr. Isik Kizilyalli) to bring the developed B-10 enriched hexagonal boron nitride (h- 10 BN or 10 BN or BN) semiconductor neutron detector technology to the next level of maturity. In comparison to He-3 ( 3 He) gas detectors, BN neutron detectors possess all the intrinsic advantages of semiconductor devices: light weight, compact size, fast response speed, high spatial resolution, high temperature and low voltage operation capability, ease of mass production via existing semiconductor infrastructures, low cost of operation and maintenance, flexible form factors, and durability. The project will develop a prototype h- 10 BN neutron detector as a potential replacement for the 3 He gas neutron detectors (LND 25185 or equivalent) used in various neutron survey meters currently produced and commercialized by Ludlum Measurements, Inc. (LMI). To increase the overall detection efficiency, it is essential to maximize the collection efficiency of charge carriers (electrons and holes) generated by the nuclear reaction, which demands a further push to achieve 10 BN epilayers with improved material quality. The material growth processes will be guided by characterization of structural, optical, and electrical properties of h-BN. Selective devices will be calibrated at LMI. During ARPA-E supporting period, the key material parameters of h-BN produced by metal organic chemical vapor deposition (MOCVD), including the layer thickness, mobility-lifetime product, surface recombination field and detector size for maintaining a high charge collection efficiency all have been improved by several orders of magnitude. These improvements have enabled the realization of high-performance h 10BN semiconductor thermal neutron detectors. Presently, h- 10 BN thermal neutron detectors developed under ARPA-E’s support hold the record high detection efficiency among all solid-state detectors at 59%. With further development in manufacturing, there is no question that h-BN detectors will replace the traditional He-3 gas detectors in certain application areas by offering obvious advantages of semiconductor technologies over gas detectors and opportunities for users to dedicate the scarce and expensive supply of He-3 gas to other application areas where substitutes of He-3 gas are not possible.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Self‐Templated 3D Sulfide‐Based Solid Composite Electrolyte for Solid‐State Sodium Metal Batteries

Abstract Rechargeable solid‐state sodium metal batteries (SSMBs) experience growing attention owing to the increased energy density (vs Na‐ion batteries) and cost‐effective materials. Inorganic sulfide‐based Na‐ion conductors also possess significant potential as promising solid electrolytes (SEs) in SSMBs. Nevertheless, due to the highly reactive Na metal, poor interface compatibility is the biggest obstacle for inorganic sulfide solid electrolytes such as Na 3 SbS 4 to achieve high performance in SSMBs. To address such electrochemical instability at the interface, new design of sulfide SE nanostructures and interface engineering are highly essential. In this work, a facile and straightforward approach is reported to prepare 3D sulfide‐based solid composite electrolytes (SCEs), which utilize porous Na 3 SbS 4 (NSS) as a self‐templated framework and fill with a phase transition polymer. The 3D structured SCEs display obviously improved interface stability toward Na metal than pristine sulfide. The assembled SSMBs (with TiS 2 or FeS 2 as cathodes) deliver outstanding electrochemical cycling performance. Moreover, the cycling of high‐voltage oxide cathode Na 0.67 Ni 0.33 Mn 0.67 O 2 (NNMO) is also demonstrated in SSMBs using 3D sulfide‐based SCEs. This study presents a novel design on the self‐templated nanostructure of SCEs, paving the way for the advancement of high‐energy sodium metal batteries.

Guo, Xiaolin↗

Solid-state platform for cooperative quantum dynamics driven by correlated emission

While traditionally regarded as an obstacle to quantum coherence, recent breakthroughs in quantum optics have shown that the dissipative interaction of a qubit with its environment can be leveraged to protect quantum states and synthesize many-body entanglement. Inspired by this progress, here we set the stage for the—as yet uncharted—exploration of analogous cooperative phenomena in hybrid solid-state platforms. We develop a comprehensive formalism for the quantum many-body dynamics of an ensemble of solid-state spin defects interacting with the magnetic field fluctuations of a common solid-state reservoir. Our framework applies to any solid-state reservoir whose fluctuating spin, pseudospin, or charge degrees of freedom generate magnetic fields. To understand whether correlations induced by dissipative processes can play a relevant role in a realistic experimental setup, we apply our model to a qubit array interacting via the spin fluctuations of a ferromagnetic bath. Our results show that the low-temperature collective relaxation rates of the qubit ensemble can display clear signatures of super- and subradiance, i.e., forms of cooperative dynamics traditionally achieved in atomic ensembles. We find that the solid-state analog of these cooperative phenomena is robust against spatial disorder in the qubit ensemble and thermal fluctuations of the magnetic reservoir, providing a route for their feasibility in near-term experiments. Finally, our work lays the foundation for a multiqubit approach to quantum sensing of solid-state systems and the direct generation of many-body entanglement in spin-defect ensembles. Furthermore, we discuss how the tunability of solid-state reservoirs opens up novel pathways for exploring cooperative phenomena in regimes beyond the reach of conventional quantum optics setups.

NV centers↗

Origin of rate limitations in solid-state polymer batteries from constrained segmental dynamics within the cathode

Currently, one of the key challenges preventing the wide commercialization of polymer-based solid-state batteries is achieving high-rate capabilities. This work unravels chain structure and segmental dynamics in a polymer-based composite cathode consisting of LiFePO 4 (LFP), carbon, and poly(ethylene oxide) (PEO) with lithium bis(trifluoromethanesulfonyl)imide. Small-angle neutron scattering (SANS) data reveal that PEO chains are adsorbed on the surface of LFP particles during slurry processing to make the composite electrode. The strong interaction between LFP and PEO chains leads to greatly reduced segmental dynamics of PEO, as discovered by quasi-elastic neutron scattering (QENS). The reduced segmental dynamics results in 70% decreased Li + mobility of the polymer electrolyte in the composite cathode. The combined SANS and QENS study indicates that one of the key bottlenecks that limits the rate performance of PEO-based polymer batteries originates from molecular interactions within the cathode.

25 ENERGY STORAGE↗

Solid-State, Single-Ion Conducting, Polymer Blend Electrolytes with Enhanced Li + Conduction, Electrochemical Stability, and Limiting Current Density

The development of solid-state polymer electrolytes with high lithium conductivity is crucial to improve lithium-ion battery performance and ameliorate the safety challenges associated with current solvent-based electrolytes. Unfortunately, sluggish polymer segmental dynamics are known to constrain conductivity enhancements in solid-state polymer electrolyte systems, limiting overall performance. In this work, a glassy single-ion-conducting polymer, poly[lithium sulfonyl(trifluoromethane sulfonyl)imide methacrylate] (PLiMTFSI), was blended with a flexible polymer, poly(oligo-oxyethylene methyl ether methacrylate) (POEM), and the impact of PLiMTFSI molecular weight and ion concentration on the thermal and ion-conducting behavior of blend electrolytes was investigated. High ionic conductivities approaching 1 × 10 -2 S/cm at 150 °C were realized in this polymer blend electrolyte system as a result of decoupling Li + transport from polymer segmental dynamics. The decoupled ion transport was attributed to the packing frustration of the glassy PLiMTFSI – sufficient percolating free volume was generated to produce effective ion diffusion pathways. This decoupling was tunable as the ion transport could be altered from being closely coupled to the polymer segmental dynamics (Vogel–Tammann–Fulcher-like) to hopping (Arrhenius-like) by increasing the PLiMTFSI molecular weight and ion concentration. Moreover, the immobilized TFSI anion resulted in high Li + selectivity (Li + transference number = 0.9), high electrochemical stability (up to 4.7 V against Li + / Li), and limiting current density of 1.8 mA/cm 2 (electrolyte thickness = 0.05 cm). These features suggest that this single-ion-conducting, polymer blend electrolyte might be a promising alternative to a benchmark system – salt-doped polyethylene oxide. Moreover, the above characteristics can support the battery operation at higher voltages using energy-dense Li metal anodes, with faster charging rates and enhanced energy/power densities. Altogether, the results suggest that polymer chain packing frustration can be exploited to overcome the constraints of slow polymer segmental relaxations to achieve rapid and highly selective ion transport and enhanced performance in solid-state polymer electrolytes.

36 MATERIALS SCIENCE↗

Crystal engineering of heterocyclic arylene(ethynylene) oligomers through programmed aromatic stacking

Conjugated oligomers and polymers consisting of aromatic heterocycles are examples of next-generation organic electronic materials. However, control and optimization of the self-assembly of these materials in the solid-state, which is a crucial parameter for high efficiency performance, remains an unsolved challenge in materials development. In this work, we provide valuable insight into aromatic stacking interactions between fluorinated arene rings (ArF) and heterocycles with different electronic character (Het), and elaborate on the prospect of using these interactions to control the solid-state configurations of three-ring phenyleneethynylene oligomers (PEs). Oligomers possessing heterocycles typically thought of as electron-rich (ER) show blue-shifted optical spectra in the solid-state, while those incorporating heterocycles typically thought of us electron deficient (ED) show red-shifted solid-state optical spectra. Crystal structures show ArF-Het stacking interactions between the fluorinated side-chains and ER units, which twist the backbone out of planarity and prevent chromophore aggregation. Further, the interactions are absent in ED oligomers, highlighting cofacial incompatibility between ArF rings and ED units. A combination of TD-DFT computations and novel heterocycle descriptors reinforce our assignment of the oligomers as ED or ER, while exhaustive conformer analysis shows ArF-Het stacking interactions are a significant contributor to compound stability. Overall, this work describes the importance of heterocycle electronics in conformational control in the solid state, understanding of which can be a valuable asset in the development of novel optoelectronic materials.

36 MATERIALS SCIENCE↗

Tackling issues of lithium metal anodes with a novel polymeric lithicone coating

Lithium metal (Li) has been hindered from as anodes in commercial batteries for over 50 years, due to two main issues: continuous formation of solid electrolyte interphase (SEI) and lithium dendritic growth. In this work, we report a new strategy to tackle these issues, i.e., using molecular layer deposition (MLD) to grow an ionically conducting but electrically insulating polymeric lithicone coating, an Li-containing triethanolamine (LiTEA). Our electrochemical tests revealed that this LiTEA coating could serve as an exceptional protection layer over Li anodes. Consequently, the LiTEA-coated Li electrodes could achieve a superior cyclability of > 10000 Li stripping/plating cycles at a current density of 5 mA cm -2 and a long cyclability of > 5500 cycles at 2 mA cm -2 in Li||Li symmetric cells without failures, under a fixed areal capacity of 1 mAh cm -2 . Characterizations using scanning electron microscopy and X-ray photoelectron microscopy verified that Li + ions could be easily extracted through and deposited under the LiTEA coating during the stripping/plating processes. Consequently, this LiTEA coating significantly inhibited the formation of SEI and Li dendrites. This underlies the long cycling lifetime of the LiTEA-coated Li||Li cells. Coupling with the nickel-rich LiNi 0.8 Mn 0.1 Co 0.1 O 2 (NMC811) cathodes, more encouragingly, the LiTEA-coated Li anodes could remarkably extend the cyclability and sustainable capacity of the resultant Li||NMC full cells. Finally, we also demonstrated that the performance of Li||NMC cells could be further improved through combining an LiTEA-coated Li anode with an Li 2 S-modified NMC811 via atomic layer deposition (ALD). Thus, this study is inspiring for developing high-energy Li||NMC lithium metal batteries.

25 ENERGY STORAGE↗

An electrochemically stable homogeneous glassy electrolyte formed at room temperature for all-solid-state sodium batteries

All-solid-state sodium batteries (ASSSBs) are promising candidates for grid-scale energy storage. However, there are no commercialized ASSSBs yet, in part due to the lack of a low-cost, simple-to-fabricate solid electrolyte (SE) with electrochemical stability towards Na metal. In this work, we report a family of oxysulfide glass SEs (Na 3 PS 4-x O x , where 0 < x ≤ 60) that not only exhibit the highest critical current density among all Na-ion conducting sulfide-based SEs, but also enable high-performance ambient-temperature sodium-sulfur batteries. By forming bridging oxygen units, the Na 3 PS 4-x Ox SEs undergo pressure-induced sintering at room temperature, resulting in a fully homogeneous glass structure with robust mechanical properties. Furthermore, the self-passivating solid electrolyte interphase at the Na|SE interface is critical for interface stabilization and reversible Na plating and stripping. The new structural and compositional design strategies presented here provide a new paradigm in the development of safe, low-cost, energy-dense, and long-lifetime ASSSBs.

25 ENERGY STORAGE↗

Measurements of the quantum geometric tensor in solids

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, in this work, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.

36 MATERIALS SCIENCE↗

Space-dependent calculation of the multiplicity moments for shells

In earlier work, we extended the methodology of multiplicity counting in nuclear safeguards, by elaborating the one-speed stochastic transport theory of the calculation of the so-called multiplicity moments, i.e. the factorial moments of the number of neutrons emitted from a fissile item, following a source event from an internal neutron source (spontaneous fission and (α, n) reactions). Calculations were made for spheres and cylinders of various shapes. In all our work so far, the material of the items was homogeneous, and the distribution of the internal source was assumed to be uniformly distributed within the item, with the neutron emission assumed to be isotropic. In the present work the calculations are extended to the case of a point source inside either a solid sphere or in a spherical shell. This necessitates the extension of the theory to non-homogeneous items and non-uniform and non-isotropic sources. This work describes the extension of the theory and provides some quantitative results. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗