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At least 793 records · Page 44

Circularity in polymers: addressing performance and sustainability challenges using dynamic covalent chemistries

The circularity of current and future polymeric materials is a major focus of fundamental and applied research, as undesirable end-of-life outcomes and waste accumulation are global problems that impact our society. The recycling or repurposing of thermoplastics and thermosets is an attractive solution to these issues, yet both options are encumbered by poor property retention upon reuse, along with heterogeneities in common waste streams that limit property optimization. Dynamic covalent chemistry, when applied to polymeric materials, enables the targeted design of reversible bonds that can be tailored to specific reprocessing conditions to help address conventional recycling challenges. In this review, we highlight the key features of several dynamic covalent chemistries that can promote closed-loop recyclability and we discuss recent synthetic progress towards incorporating these chemistries into new polymers and existing commodity plastics. Next, we outline how dynamic covalent bonds and polymer network structure influence thermomechanical properties related to application and recyclability, with a focus on predictive physical models that describe network rearrangement. Finally, we examine the potential economic and environmental impacts of dynamic covalent polymeric materials in closed-loop processing using elements derived from techno-economic analysis and life-cycle assessment, including minimum selling prices and greenhouse gas emissions. Throughout each section, we discuss interdisciplinary obstacles that hinder the widespread adoption of dynamic polymers and present opportunities and new directions toward the realization of circularity in polymeric materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A new approach to model geomaterials with heterogeneous properties in thermo-hydro-mechanical coupled problems

The main objective of this article is to present a new approach to model coupled thermo-hydro-mechanical problems considering geomaterials with heterogeneous properties. This approach has been implemented in the software CODE_BRIGHT and it provides the possibility of considering geomaterials with a spatially correlated heterogeneous field of porosity, following a normal distribution. This spatial correlation can be isotropic or anisotropic. An important feature of this approach is that material properties such as intrinsic permeability, thermal conductivity, diffusivity, retention curve, elastic modulus or cohesion are defined as a function of porosity and, thus, they become heterogeneous with spatial correlation and, eventually, anisotropic. A validation exercise and other basic numerical examples have been carried out to illustrate the possibilities of the proposed approach. The results, which have been compared with a homogeneous case, show that considering heterogeneous fields can be relevant in different modelling problems, especially coupled thermo-hydro-mechanical problems.

42 ENGINEERING↗

Benchmarking graph neural networks for materials chemistry

Graph neural networks (GNNs) have received intense interest as a rapidly expanding class of machine learning models remarkably well-suited for materials applications. To date, a number of successful GNNs have been proposed and demonstrated for systems ranging from crystal stability to electronic property prediction and to surface chemistry and heterogeneous catalysis. However, a consistent benchmark of these models remains lacking, hindering the development and consistent evaluation of new models in the materials field. Here, we present a workflow and testing platform, MatDeepLearn, for quickly and reproducibly assessing and comparing GNNs and other machine learning models. We use this platform to optimize and evaluate a selection of top performing GNNs on several representative datasets in computational materials chemistry. From our investigations we note the importance of hyperparameter selection and find roughly similar performances for the top models once optimized. We identify several strengths in GNNs over conventional models in cases with compositionally diverse datasets and in its overall flexibility with respect to inputs, due to learned rather than defined representations. Meanwhile several weaknesses of GNNs are also observed including high data requirements, and suggestions for further improvement for applications in materials chemistry are discussed.

36 MATERIALS SCIENCE↗

Uranium nitride (UN) pellets with controllable microstructure and phase – fabrication by spark plasma sintering and their thermal-mechanical and oxidation properties

Dense uranium mononitride (UN) pellets with controlled microstructures and tailored grain size from large-grained to a few microns are synthesized by spark plasma sintering (SPS) combined with high energy ball milling. The impacts of the sintering conditions on fuel microstructure, grain size, physical density, and phase behavior are systematically investigated, and the thermal-mechanical properties and oxidation behavior of the SPS densified UN pellets are characterized. Higher sintering temperatures and longer ball milling durations and thus finer starting UN powders promote sintering and densification, and dense UN pellets above 95% theoretical density can be achieved by SPS at 1873 K for 10 min. UN phase purity is maintained in the SPS-densified pellets sintered at a lower temperature and short duration. A phase heterogeneity with secondary UO 2 or uranium sesquinitride (U 2 N 3 ) occurs for the UN pellets sintered at higher temperatures using finer UN powders. The hardness and fracture toughness of the SPS-densified UN pellets increase with smaller grain sizes and higher densities to 7.9 GPa and 3.5 MPa m 1/2 , respectively. Furthermore, both small (1–2 μm) and large grain-sized (30–50 µm) UN pellets exhibit good thermal conductivity. Dynamic oxidation testing by a thermogravimetric analyzer in air shows that the onset temperature for oxidation varies with microstructure and phase heterogeneity of the SPS densified UN pellets. Particularly, the smaller-grained (micron-sized) UN pellets containing uranium oxides and U 2 N 3 display lower weight gain and significantly-reduced oxidation kinetics, and full oxidation completes at a temperature above 1173 K when tested with a ramp rate of 10 K/min.

36 MATERIALS SCIENCE↗

Isotopic heterogeneities in the solar system - Special report

The paper discusses the nature of isotopic anomalies in solar system material with emphasis on correlated anomalies in refractory elements. Evidence for the existence of short-lived radioactive nuclides in the early solar system is used to estimate the time scale for the last injection of freshly synthesized nuclear material. It is shown that the early solar nebula was incompletely mixed and contained debris which was injected from a stellar source at most a few million years prior to the formation of the solar system. The average solar system material consists of ambient interstellar material deficient in certain nuclear species to which a small fraction of freshly synthesized material was added. The isotopic variations reflect slightly different proportions of nuclei from different stellar sources which were locally well mixed and homogenized prior to or during the formation of the early solar nebula condensates.

Wasserburg, G. J.↗

Hematite Crystallization from a Two-Line Ferrihydrite Suspension

Rational design and synthesis of materials, determination of environmental conditions at the time of mineral formation, and definition of mechanisms in biomineralizing systems all require an understanding of the effect of multiple factors on modulating crystallization pathways. In this study, we investigate the influence of temperature, oxalate additive, aging time, and addition of seed crystals on hematite (α-Fe 2 O 3 , Hm) crystallization from a two-line ferrihydrite (Fe 2 O 3 ·xH 2 O, Fh) suspension. We also investigate the effect of temperature on the aging of spindle-shaped Hm mesocrystals, which we synthesize through the addition of sodium oxalate. The results show that Hm mesocrystals form in a temperature window of 45 °C-130 °C. Temperatures ≥ 140 °C favor formation of rhombohedral Hm, suggesting classical monomer-by-monomer growth dominates, whereas crystallization by particle attachment (CPA) is dominant between 45 and 90 °C, while the two processes compete in the intermediate temperature range. Aging of mesocrystals in the original solution at 90 °C or 180 °C leads to a slow morphological evolution towards rhombohedral crystals due to Ostwald ripening. Then, by utilizing rhombohedral Hm and rod-shaped goethite as substrates on which to assemble the mesocrystals, we demonstrate formation of complex heterogeneous structures.

36 MATERIALS SCIENCE↗

Image-Based Failure Assessment of Li-Ion Batteries

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. In this work, a digital twin is created to investigate the performance of a heterogeneous Li-ion battery cathode and simulate degradation accumulation. Pixel-based model construction is used to represent the complex material geometries from microstructural images supplied by the National Renewable Energy Laboratory (NREL). Because of the expected large deformation and crack opening, the reproducing kernel particle method (RKPM), a meshfree method with discretization at the image pixels, is used to approximate the field variables: electrostatic potential, concentration, and displacement. An interface modified reproducing kernel (IM-RK) is constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. IM-RK is additionally used to inform how crack evolution in turn affects the coupled electro-chemo-mechanical behavior of the Li-ion battery cathode.

image-based modeling↗

Learning heterogeneous reaction kinetics from X-ray movies pixel-by-pixel

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries 1 and electrocatalysts 2. Experimental characterizations of such materials by operando microscopy produce rich image datasets 3–6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation 7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

Chueh, William↗

Atomic-scale structure of ZrO 2 : Formation of metastable polymorphs

Metastable phases can exist within local minima in the potential energy landscape when they are kinetically “trapped” by various processing routes, such as thermal treatment, grain size reduction, chemical doping, interfacial stress, or irradiation. Despite the importance of metastable materials for many technological applications, little is known about the underlying structural mechanisms of the stabilization process and atomic-scale nature of the resulting defective metastable phase. Investigating ion-irradiated and nanocrystalline zirconia with neutron total scattering experiments, we show that metastable tetragonal ZrO 2 consists of an underlying structure of ferroelastic, orthorhombic nanoscale domains stabilized by a network of domain walls. The apparent long-range tetragonal structure that can be recovered to ambient conditions is only the configurational ensemble average of the underlying orthorhombic domains. This structural heterogeneity with a distinct short-range order is more broadly applicable to other nonequilibrium materials and provides insight into the synthesis and recovery of functional metastable phases with unique physical and chemical properties.

74 ATOMIC AND MOLECULAR PHYSICS↗

Nanoscopic strain evolution in single-crystal battery positive electrodes

Single-crystal Ni-rich layered oxides (SC-NMC) with a grain-boundary-free configuration have effectively addressed the long-standing cracking issue of conventional polycrystalline Ni-rich materials (PC-NMC) in lithium-ion batteries, prompting a shift in optimization strategies. However, continued reliance on anisotropic lattice volume change—a well-established failure indicator in PC-NMC—as a metric for understanding strain and guiding compositional design for SC-NMC becomes controversial. Here, in this study, by leveraging multiscale diagnostic techniques, we unravelled the distinct nanoscopic strain evolution in SC-NMC during battery operation, challenging the conventional composition-driven strategies and mechanical degradation indicators used for PC-NMC. Through particle-level chemomechanical analysis, we reveal a decoupling between mechanical stability and lattice volume change in SC-NMC, identifying that structural instability in SC materials is primarily driven by multidimensional lattice distortions induced by kinetics-driven reaction heterogeneity and progressively deactivating chemical phases. Using this mechanical failure mode, we redefine the roles of cobalt and manganese in maintaining mechanical stability. Unlike cobalt’s detrimental role in PC-NMC, we find cobalt to be critical in enhancing the longevity of SC-NMC by mitigating localized strain along the extended diffusion pathway, whereas manganese exacerbates mechanical degradation.

36 MATERIALS SCIENCE↗

The rigorous upscaling of advection-dominated transport in heterogeneous porous media via the Method of Finite Averages

Systems involving advection-dominated transport through heterogeneous porous and fractured media are ubiquitous in subsurface engineering applications. However, upscaling such systems continues to challenge rigorous modeling efforts, particularly when advection is stronger than diffusion at fine spatial scales (i.e., when the Péclet number is greater than one at length scales that characterize a system’s unit-cells, representative elementary volumes, or averaging regions). Here, in this work, we propose and validate a strategy for extending the Method of Finite Averages (MoFA), a rigorous upscaling methodology for heterogeneous porous media, to upscale transport systems experiencing stronger advection than diffusion at fine scales (i.e., fine-scale Péclet numbers greater than one). We detail the strategy, the physical conditions under which it can be applied while retaining a priori modeling error guarantees, and implement the strategy to obtain a MoFA model for advective-diffusive transport that accommodates advective physics at fine spatial scales. We then perform two numerical experiments considering systems with system-scale Péclet numbers of 300 and 1000 — which correspond to fine-scale Péclet numbers of 30 and 100, respectively — to verify that the error guarantees are met under the strategy. After, we conduct a numerical study to demonstrate the strategy’s advantages over the original MoFA methodology. The results suggest that rigorously-upscaled transport models for heterogeneous porous media experiencing advective physics at finer spatial scales can be derived through MoFA and resolved orders of magnitude faster than their pore-scale counterparts. The results also suggest that the presented strategy is limited to modeling shallow concentration gradients when there are large differences between the time scales related to advection and a system’s temporally-varying boundary conditions. This limitation hinders the strategy’s practicality in modeling more advective systems, and as such, opportunity exists for developing additional strategies that accommodate rapidly-varying boundary conditions — and consequentially, steeper concentration gradients — while modeling advective systems with MoFA.

36 MATERIALS SCIENCE↗

Constraining composition and temperature variations in the mantle transition zone

The mantle transition zone connects two major layers of Earth’s interior that may be compositionally distinct: the upper mantle and the lower mantle. Wadsleyite is a major mineral in the upper mantle transition zone. Here, we measure the single-crystal elastic properties of hydrous Fe-bearing wadsleyite at high pressure-temperature conditions by Brillouin spectroscopy. Our results are then used to model the global distribution of wadsleyite proportion, temperature, and water content in the upper mantle transition zone by integrating mineral physics data with global seismic observations. Our models show that the upper mantle transition zone near subducted slabs is relatively cold, enriched in wadsleyite, and slightly more hydrated compared to regions where plumes are expected. This study provides direct evidence for the thermochemical heterogeneities in the upper mantle transition zone which is important for understanding the material exchange processes between the upper and lower mantle.

58 GEOSCIENCES↗

Near-Earth Asteroid Returned Sample (NEARS)

The concept of the Near-Earth Asteroid Returned Sample (NEARS) mission is to return to Earth 10-100 g from each of four to six sites on a near-Earth asteroid and to perform global characterization of the asteroid and measure mass, volume, and density to ten percent. The target asteroid for the mission is 4660 Nereus, probably a primitive C-type asteroid, with the alternate target being 1989ML, an extremely accessible asteroid of unknown type. Launch dates will be 1998, 2000, 2002, and 2004 on the Delta II-7925 launch vehicle. The mission objectives are three-fold. (1) Provide first direct and detailed petrological, chemical, age, and isotopic characterization of a near-Earth asteroid and relate it to terrestrial, lunar, and meteoritic materials. (2) Sample the asteroid regolith and characterize any exotic fragments. (3) Identify heterogeneity in the asteroid's isotopic properties, age, and elemental chemistry.

Shoemaker, Eugene M.↗

Constraints on the Nature and Distribution of Iridium Host Phases at the Cretaceous-Tertiary Boundary: Implications for Projectile Identity and dispersal on impact

Among Cretaceous-Tertiary boundary sites worldwide, variations in the concentrations and ratios of elements commonly enriched in meteorites complicate traditional geochemical attempts at impactor identification. Yet they may provide constraints on the physical and chemical processes associated with large-body disruption and dispersal, as well as with diagenesis of projectile components. To this end, we continue our efforts to identify the mineral host-phases of projectile-derived elements, particularly for Ir, and to document their partitioning between crater deposits and ejecta resulting from the Chicxulub basin-forming impact. Building on earlier work, we used INAA to measure Ir concentrations in successively smaller splits of finely powdered impact melt breccia from the Chicxulub Crater in Mexico (sample Y6Nl9-R(b)), and K/T boundary fish clay from Stevns Klint, Denmark (sample FC-1, split from 40 kg of homogenized material intended as an analytical standard). Results for the Chicxulub sample show a heterogeneous Ir distribution and document that at least five discrete Ir-bearing host phases were isolated in subsequent splits, having Ir masses equivalent to pure Ir spheres from about 0.8 to about 3.5 mm in diameter. Three of these are within a sufficiently reduced mass of powder to warrant searching for them using backscattered electron microscopy. In contrast, successively smaller splits of the Stevns Klint fish clay show no statistically significant deviation from the reported value of 32 +/- 2 ng/g Ir, suggesting a uniform Ir host-phase distribution. For the smallest split obtained thus far (100 +/- 40 ng/g Ir), a pure Ir sphere of equivalent Ir mass would be <0.05 min in diameter. (n.b. Although homogenizing and sieving of FC-1 to <75 min obviously obscured variations in stratigraphic distribution, it is unlikely to have affected the size-frequency distribution of Ir host phases.) We previously identified micrometer-scale Ir host phases by electron microscopy in melt-rock samples from two widely separated drill holes at the Chicxulub Basin, including a replicate split of Y6-NI9-R. One is an aggregate of subhedral Ir metal grains enclosed in silicate, in which no other Pt group elements (PGE) were detected. A second particle with twice the mass as the first, concentrated predominantly in a single grain, is associated with minor concentrations of Os, Ru, and Pt, and with adhering particles of corundum and perovskite. A third Ir-rich particle, with a greater apparent Os concentration, was identified before being lost as a result of charging under the electron beam. In addition to demonstrating the preservation of projectile components within the Chicxulub Crater, analogous phase associations in Ca- and Al-rich inclusions (CAI) from C2 and C3 chondrites suggest to us that these melt-rock Ir host phases are relics from a carbonaceous chondrite K/T boundary impactor Although the obviously low Ru/Ir ratios of the Chicxulub Ir host phases are qualitatively consistent with suggested PGE fractionation with distance during condensation in an ejecta cloud, it seems difficult to explain the accumulation of the about 3 x 10(exp 11) Ir atoms required to form a about 10(exp -10) g nugget of pure Ir metal within a jet of vaporized projectile expanding at 1-4 km/s, or to effectively exclude or remove commonly alloyed PGE and siderophile elements by fractionation processes resulting from condensation, oxidation, sulfidization, exsolution, or autometamorphism during cooling of the melt. We do not dismiss the importance of these processes entirely; on the contrary, other geochemical and mineralogical aspects of the melt rocks require them, and condensation from the expanding ejecta cloud appears to best explain the primary Ir host-phase distribution in the fish clay, as well as the high Ir concentrations associated with spinel-bearing spheroids at the K/T boundary in the Pacific Ocean . If the "relict" hypothesis is correct, micronuggets of other PGEs and alloys, not detected by our INAA screening, should also occur in the melt rocks. Possibly, the discrete host phases with lesser Ir masses are such alloys with subordinate Ir, rather than simply smaller, predominantly Ir-bearing particles. A CAI source for the relics would be consistent with either a comet or an asteroid K/T impact at Chicxulub. (Additional information contained in the original.)

Schuraytz, B. C.↗

Volatiles in High-K Lunar Basalts

Chlorine is an unusual isotopic system, being essentially unfractionated ((delta)Cl-37 approximately 0 per mille ) between bulk terrestrial samples and chondritic meteorites and yet showing large variations in lunar (approximately -4 to +81 per mille), martian, and vestan (HED) samples. Among lunar samples, the volatile-bearing mineral apatite (Ca5(PO4)3[F,Cl,OH]) has been studied for volatiles in K-, REE-, and P (KREEP), very high potassium (VHK), low-Ti and high-Ti basalts, as well as samples from the lunar highlands. These studies revealed a positive correlation between in-situ (delta)Cl-37 measurements and bulk incompatible trace elements (ITEs) and ratios. Such trends were interpreted to originate from Cl isotopic fractionation during the degassing of metal chlorides during or shortly after the differentiation of the Moon via a magma ocean. In this study, we investigate the volatile inventories of a group of samples for which new-era volatile data have yet to be reported - the high-K (greater than 2000 ppm bulk K2O), high-Ti, trace element-rich mare basalts. We used isotope imaging on the Cameca NanoSIMS 50L at JSC to obtain the Cl isotopic composition [((Cl-37/(35)Clsample/C-37l/(35)Clstandard)-1)×1000, to get a value in per thousand (per mille)] which ranges from approximately -2.7 +/- 2 per mille to +16.1 +/- 2 per mille (2sigma), as well as volatile abundances (F & Cl) of apatite in samples 10017, 10024 & 10049. Simply following prior models, as lunar rocks with high bulk-rock abundances of ITEs we might expect the high-K, high-Ti basalts to contain apatite characterized by heavily fractionated (delta)Cl-37 values, i.e., Cl obtained from mixing between unfractionated mantle Cl (approximately 0 per mille) and the urKREEP reservoir (possibly fractionated to greater than +25 per mille.). However, the data obtained for the studied samples do not conform to either the early degassing or mixing models. Existing petrogentic models for the origin of the high-K, high-Ti basalts do not include urKREEP assimilation into their LMO cumulate sources. Therefore, Cl in these basalts either originated from source region heterogeneity or through assimilation or metasomatism by volatile and incompatible trace element rich materials. The new data presented here could provide evidence for the existence of region(s) in the lunar interior that are ITE-enriched and contain Cl that does not share isotopic affinities with lunar urKREEP, possibly representing the composition of the purported 'neuKREEP'.

Barnes, Jessica J.↗

Twenty Years of Collaborative Materials Exercises by the Nuclear Forensics International Technical Working Group

The Collaborative Materials Exercise (CMX) series are a critical mechanism used to advance the ITWG's mission of identifying, developing and promoting the best practices of nuclear forensics. These exercises are not designed to test laboratory performance, but as learning experiences that provide opportunities for participants to test and demonstrate state-of-the-practice to the global scientific and law enforcement communities. They are run as mock nuclear forensic investigations under realistic scenarios, with timelines and conditions designed to mimic actual operations. These situations provide the relatively unique opportunity for the appropriate governmental agencies to exercise their collective response to a nuclear security incident. Utilizing well-characterized materials of a known history and origin that are taken from specific process locations within the nuclear fuel cycle, these 'real world' materials are used to fully consider the potential significance of process-derived heterogeneities and characteristics that might be used by investigators to derive useful information such as intended use, point of loss of control, process history or origin. While individual laboratory results are kept confidential, a summary of the major outcomes of each exercise is published in the open literature. The ITWG has carried out six CMXs since 1999. The sixth (CMX-6) and largest (21 participants) was completed in June 2019. Each CMX has contributed demonstrably to advancements in the state of practice and the emergence of novel techniques in nuclear forensic science.

Schwantes, Jon M.↗

Monolayer Support Control and Precise Colloidal Nanocrystals Demonstrate Metal-Support Interactions in Heterogeneous Catalysts

We report that electronic and geometric interactions between active and support phases are critical in determining the activity of heterogeneous catalysts, but metal-support interactions are challenging to study. Here, it is demonstrated how the combination of the monolayer-controlled formation using atomic layer deposition (ALD) and colloidal nanocrystal synthesis methods leads to catalysts with sub-nanometer precision of active and support phases, thus allowing for the study of the metal-support inter-actions in detail. The use of this approach in developing a fundamental understanding of support effects in Pd-catalyzed methane combustion is demonstrated. Uniform Pd nanocrystals are deposited onto Al2O 3 /SiO 2 spherical supports prepared with control over morphology and Al 2 O 3 layer thicknesses ranging from sub-monolayer to a ≈4 nm thick uniform coating. Dramatic changes in catalytic activity depending on the coverage and structure of Al 2 O 3 situated at the Pd/Al 2 O 3 interface are observed, with even a single monolayer of alumina contributing an order of magnitude increase in reaction rate. By building the Pd/Al 2 O 3 interface up layer-by-layer and using uniform Pd nanocrystals, this work demonstrates the importance of controlled and tunable materials in determining metal-support interactions and catalyst activity.

36 MATERIALS SCIENCE↗

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

Beggs, John H.↗