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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Angular and Polarization Response of Multimode Sensors with Resistive-Grid Absorbers

High sensitivity receiver systems with near ideal polarization sensitivity are highly desirable for development of millimeter and sub-millimeter radio astronomy. Multimoded bolometers provide a unique solution to achieve such sensitivity, for which hundreds of single-mode sensors would otherwise be required. The primary concern in employing such multimoded sensors for polarimetery is the control of the polarization systematics. In this paper, we examine the angular- and polarization- dependent absorption pattern of a thin resistive grid or membrane, which models an absorber used for a multimoded bolometer. The result shows that a freestanding thin resistive absorber with a surface resistivity of eta/2, where eta is the impedance of free space, attains a beam pattern with equal E- and H-plane responses, leading to zero cross polarization. For a resistive-grid absorber, the condition is met when a pair of grids is positioned orthogonal to each other and both have a resistivity of eta/2. When a reflective backshort termination is employed to improve absorption efficiency, the cross-polar level can be suppressed below −30 dB if acceptance angle of the sensor is limited to < or approx. 60deg. The small cross-polar systematics have even-parity patterns and do not contaminate the measurements of odd-parity polarization patterns, for which many of recent instruments for cosmic microwave background are designed. Underlying symmetry that suppresses these cross-polar systematics is discussed in detail. The estimates and formalism provided in this paper offer key tools in the design consideration of the instruments using the multimoded polarimeters.

High sensitivity receiver systems↗
DOE OSTI2024

Effect of Minor Ce Additions on Corrosion Behavior of Experimental Pipeline Steel

Minor additions of rare earth elements (REEs) have been shown to improve various steel properties. In particular, Cerium (Ce), as a relatively abundant and inexpensive element, has received attention as a potentially beneficial minor alloying addition for a variety of steel applications, including pipelines materials. The objective of this work is to investigate the effect of Ce on corrosion performance of experimental high-strength pipeline steel. Electrochemical corrosion experiments were carried out on steel without and with 0.006, 0.018, and 0.03 wt.% of Ce in 3.5 wt.% NaCl saturated with CO2 at 20 oC. For comparison purposes, X100 carbon steel specimens machined from an experimental pipe with a yield strength of 731 MPa were tested under the same conditions. The electrochemical techniques employed included: potentiodynamic polarization (PDP), linear polarization resistance (LPR), and electrochemical impedance spectroscopy (EIS). In addition, post-corrosion surface characterization was performed using scanning electron microscopy (SEM) equipped with energy dispersive X-ray spectroscopy (EDS), while crystalline phases were determined by X-ray diffraction (XRD). The corrosion of base metal without Ce was lower (0.15 mm/y) compared to carbon steel X100 (0.9 mm/yr). The electrochemical results showed that adding Ce accelerates corrosion rates compared to base metal without Ce. No pitting corrosion of tested steel was detected.

Belarbi, Zineb↗
NASA NTRSDate not supplied

Evaluation of a Variable Facesheet Liner Configuration in Grazing Incidence for Broadband Noise Reduction

Abstract Tests were conducted in the NASA Langley Grazing Flow Impedance Tube (GFIT) to determine the broadband noise reduction capability of a variable facesheet liner. Three uniform liners were designed to achieve sound absorption over distinct frequency regimes at Mach 0.0. Each liner was fabricated and tested in the GFIT at sound pressure levels of 120 and 140 dB, and at tangential flow velocities up to Mach 0.5. A variable facesheet liner was fabricated to combine the geometries of these three liners, such that the facesheet geometry (hole diameter and porosity) was varied across the liner surface. The Prony method was used to educe the impedance of each sample, and these impedances were input to the CHE (Convected Helmholtz Equation) propagation code to predict the acoustic pressure profiles in the GFIT. Comparisons of predicted and measured acoustic pressure profiles were used to confirm the uniformity of all four liners, and to demonstrate the suitability of the CHE code in analysis of the variable facesheet concept. Results showed good comparison at no flow and Mach 0.3, and acceptable comparison at Mach 0.5. The variable facesheet liner provides enhanced broadband noise reduction at the no-flow condition for which it was designed, but further optimization is needed to target flow conditions.

acoustic↗
NASA NTRSDate not supplied

Evaluation of a Variable Facesheet Liner Configuration in Grazing Incidence for Broadband Noise Reduction

Tests were conducted in the NASA Langley Grazing Flow Impedance Tube (GFIT) to determine the broadband noise reduction capability of a variable facesheet liner. Three uniform liners were designed to achieve sound absorption over distinct frequency regimes at Mach 0.0. Each liner was fabricated and tested in the GFIT at sound pressure levels of 120 and 140 dB, and at tangential flow velocities up to Mach 0.5. A variable facesheet liner was fabricated to combine the geometries of these three liners, such that the facesheet geometry (hole diameter and porosity) was varied across the liner surface. The Prony method was used to educe the impedance of each sample, and these impedances were input to the CHE (Convected Helmholtz Equation) propagation code to predict the acoustic pressure profiles in the GFIT. Comparisons of predicted and measured acoustic pressure profiles were used to confirm the uniformity of all four liners, and to demonstrate the suitability of the CHE code in the analysis of the variable facesheet concept. Results showed good comparison at no flow and at Mach 0.3, and acceptable comparison at Mach 0.5. The variable facesheet liner provided enhanced broadband noise reduction at the no-flow condition for which it was designed, but further optimization is needed to target flow conditions.

acoustic↗
DOE OSTI2021

Understanding the Selective Deposition of Li Metal on Nonuniform Electrode Surfaces Using Atomic Force Microscopy

The use of lithium metal in secondary batteries has been impeded by its tendency to form dendrites: branching conductive structures of metal that can lead to capacity loss and, ultimately, internal shorts in the battery. Patterned electrodes, in addition to artificially increasing the current density of cells by increasing the surface area available for reaction, also generate a nonuniform electric field in the vicinity of the electrode surface. This nonuniform electric field, though rapidly screened by the electrolyte, can promote inhomogeneous deposition and Solid Electrolyte Interphase formation. As the consequence of these effects is not theoretically apparent since Solid Electrolyte Interphase volume and conductivity changes can, in principle, offset variations in local current density, we have performed experiments to examine the deposition of Li on nonuniform electrode surfaces using Atomic Force Microscopy. In this work, we measure the local variations in topography, SEI thickness, and composition, and discuss their implications for the formation of dendrites in Li metal.

25 ENERGY STORAGE↗
NASA NTRSDate not supplied

An Overview of LO-DuSST (Lunar Occupancy Dust Surface Separation Technologies) Objectives

Of the myriad of issues facing lunar exploration and maintaining an extended lunar presence, lunar dust is possibly the most pervasive. These jagged, chemically reactive, electrostatically charged, sometimes magnetic particles can impact every aspect of a lunar surface mission ranging from abrading extra-vehicular activity (EVA) suits to disrupting lunar vehicle thermal management systems to impeding efficacy of excavation equipment to impacting lunar inhabitant health. NASA’s Lunar Occupancy Dust Surface Separation Technologies (LO-DuSST) task, as a part of the broader Lunar Surface Innovation Initiative (LSII) project, seeks to implement synergistic active and passive lunar dust management and mitigation technologies for an array of applications. One such application is protection of power generation capabilities via solar panel arrays. Plasma dust lofting coupled with a piezoelectric-driven vibration technology will be demonstrated on solar panel surfaces contaminated with lunar dust simulant. Intrinsically low adhesion coatings will be applied to these surfaces to enhance dust removal. Electrostatic repulsion in confined geometries and materials to manage high velocity lunar dust wear will also be investigated. Collectively, these active and passive mitigation technologies will facilitate lunar surface operations including occupancy logistics, landing pad operations, power generation, and transportation. Initial results regarding lunar simulant-contaminated solar panel performance experiments, dust lofting using an electron beam, surface interactions of high velocity lunar dust arising from lunar lander plume-surface interactions, and lunar dust simulant-material interaction experiments will be discussed.

Lunar dust↗
DOE OSTI2024

Carbon Dioxide Pressure and Catalyst Quantity Dependencies in Artificial Photosynthesis of Hydrocarbon Chains on Nanostructured Co/CoO Surfaces

In this study, we investigated the influence of pressure and the quantity of Co/CoO catalyst on an artificial photosynthesis process that converts CO 2 and H 2 O into hydrocarbons (C n H 2n+2 , where n ≤ 18). The adsorption of CO 2 and H 2 O on Co/CoO surfaces proved to be pivotal in this photo-catalytic reaction. Photoexcited carbon dioxide and water molecules ((CO 2 )* and (H 2 O)*) generated by illuminating the catalyst surface led to the formation of alkene hydrocarbon molecules with carbon numbers following an approximate Poisson distribution. The optimal pressure was found to be 0.40 MPa. Pressure less than 0.40 MPa resulted in low CO 2 adsorption, impeding excitation for photosynthesis. At greater pressure, oil/wax accumulation on Co/CoO surfaces hindered CO 2 adsorption, limiting further photosynthesis reactions. The average number of carbon atoms in the hydrocarbons and hydrocarbon yield were correlated. The amount of Co/CoO was also found to affect the hydrocarbon yield. Our study contributes to the understanding of Co/CoO-catalyzed photosynthesis and suggests that an open-flow system could potentially enhance the productivity of long-chain hydrocarbons.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1990

The impedance of a tubular electrode - A model for a porous electrode

A cylindrical tube is used as the basis for a two-dimensional mathematical model to calculate the impedance of a flooded porous electrode. The model incorporates charge-transfer, mass-transfer, and ohmic resistances to obtain the axial and radial dependencies of the concentration and potential profiles. A linearized Butler-Volmer kinetic expression for a simple redox reaction O + e yielding R is used, in conjuction with analytical expressions for the surface concentration and overpotential, to compute the open-circuit impedance. The results of the two-dimensional model, which omits double-layer charging, are compared with the results of a more standardly applied one-dimensional model in which radial variations are neglected, with and without double-layer charging. The simpler-to-apply one-dimensional model is found to be satisfactory when mass-transfer and ohmic resistances are small with respect to charge-transfer resistance. The omission of double-layer charging does not introduce error into the two-dimensional model in the frequency range in which capacitive-like effects are caused by mass-transfer limitations.

Viner, Andrew S.↗
NASA NTRS1987

The corrosion mechanisms for primer coated 2219-T87 aluminum

To investigate metal surface corrosion and the breakdown of metal protective coatings, the ac Impedance Method was applied to zinc chromate primer coated 2219-T87 aluminum. The EG&GPARC Model 368 ac Impedance Measurement System, along with dc measurements with the same system using the Polarization Resistance Method, was used to monitor changing properties of coated aluminum disks immersed in 3.5 percent NaCl solutions buffered at pH 5.5 and pH 8.2 over periods of 40 days each. The corrosion system can be represented by an electronic analog called an equivalent circuit consisting of resistors and capacitors in specific arrangements. This equivalent circuit parallels the impedance behavior of the corrosion system during a frequency scan. Values for resistances and capacitances, that can be assigned in the equivalent circuit following a least squares analysis of the data, describe changes occurring on the corroding metal surface and in the protective coatings. A suitable equivalent circuit has been determined which predicts the correct Bode phase and magnitude for the experimental sample. The dc corrosion current density data are related to equivalent circuit element parameters.

Danford, Merlin D.↗
DOE OSTI2022

Platinum Graphene Catalytic Condenser for Millisecond Programmable Metal Surfaces

Accelerating catalytic chemistry and tuning surface reactions require precise control of the electron density of metal atoms. In this work, nanoclusters of platinum were supported on a graphene sheet within a catalytic condenser device that facilitated electron or hole accumulation in the platinum active sites with negative or positive applied potential, respectively. The catalytic condenser was fabricated by depositing on top of a p-type Si wafer an amorphous HfO 2 dielectric (70 nm), on which was placed the active layer of 2–4 nm platinum nanoclusters on graphene. A potential of ±6 V applied to the Pt/graphene layer relative to the silicon electrode moved electrons into or out of the active sites of Pt, attaining charge densities more than 1% of an electron or hole per surface Pt atom. At a level of charge condensation of ±10% of an electron per surface atom, the binding energy of carbon monoxide to a Pt(111) surface was computed via density functional theory to change 24 kJ mol –1 (0.25 eV), which was consistent with the range of carbon monoxide binding energies determined from temperature-programmed desorption (ΔBE CO of 20 ± 1 kJ mol –1 or 0.19 eV) and equilibrium surface coverage measurements (ΔBE CO of 14 ± 1 kJ mol –1 or 0.14 eV). Impedance spectroscopy indicated that Pt/graphene condensers with potentials oscillating at 3000 Hz exhibited negligible loss in capacitance and charge accumulation, enabling programmable surface conditions at amplitudes and frequencies necessary to achieve catalytic resonance.

Inorganic carbon compounds↗
NASA NTRS2020

INVESTIGATING THE FEASIBILITY AND STABILITY FOR MODELING ACOUSTIC WAVE SCATTERING USING A TIME-DOMAIN BOUNDARY INTEGRAL EQUATION WITH IMPEDANCE BOUNDARY CONDITION

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. This work considers using either an impedance or an admittance (inverse of impedance) boundary condition to allow for acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces. Three acoustic liner models are discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and the Broadband Impedance Model. In both the Helmholtz and Three-Parameter models, liner impedance is specified at a given frequency, whereas the Broadband model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for acoustic liners are derived for each model and coupled with a time-domain boundary integral equation. The scattering solution is obtained iteratively using a boundary element method with constant spatial and third-order temporal basis functions. Time-domain boundary integral equations are unfortunately prone to numerical instabilities due to resonant frequencies resulting from non-trivial solutions in the interior domain. When reformulated with the Burton-Miller method, the instabilities are eliminated. Using a Burton-Miller reformulation, the stability of the boundary element method assuming a liner boundary condition is assessed using eigenvalue analysis. The stability of each liner model is discussed, and it is shown that the Three-Parameter and Broadband models are sufficient for modeling an acoustic liner on the surface of scattering bodies. The Helmholtz model demonstrates strict limitations for stability, whereas the Three-Parameter and Broadband models are stable for most cases. Also included in this work is an assessment of the spatial accuracy of the time-domain boundary element method with respect to the surface element basis functions, as well as a performance study of the numerical algorithm.

computational mathematics↗
DOE OSTI2023

Investigation of Technologies to Improve Condenser Heat Transfer and Performance in a Relevant Coal-Fired Power Plant

Improvements in thermal power-generating plant performance is correlated directly to societal benefits including lower cost of reduced fuel consumption, resulting in lower cost of electricity for the consumer and reduced carbon emissions to the atmosphere. Warm steam exhausted from low-pressure steam turbines is condensed to liquid water on the exterior of thin-walled metal condenser tubes with cooling water passing through the tube interior. The condensation of steam creates a vacuum that supports turbine rotation and the concurrent generation of electricity. This vacuum is optimized when heat transfer across the wall of condenser tube is maximized. Common hindrances to heat transfer include foulants in cooling water that may form and adhere to the interior of condenser tubes, including mineral scale, microbiological films, and particulate deposition. Flowing cooling water may also include a laminar layer at the interior metal surfaces that travels more slowly than bulk water flow, serving to impede heat transfer. On the tube exterior, condensing steam forms an insulating layer of water that flows down the tube and reduces the effectiveness of cooling. Both the interior and exterior barriers to optimal heat transfer may be alleviated to some extent by surface treatments. On the tube interior, hydrophobic coatings may be applied that can reduced the adherence of foulants and of the laminar flow layer to the tube surface. On the tube exterior, hydrophobic coatings or mechanical treatments can be applied that may result in the termination of droplet growth and the departure of droplets from the surface rather than coalescence into a continuous layer of flowing water. Fourteen surface treatments were applied to condenser tubes in this study, including eight interior coatings and six exterior treatments, five of which were coatings and one a microstructural texture. Heat transfer measurement equipment simulating conditions in the condenser of an operating power plant was used to determine heat transfer coefficients by measuring sufficient flow, temperature, water chemistry and other data. Several of the tubes with interior surface treatments showed improvement in heat transfer coefficients compared with a plain (uncoated) tube, and several of the tubes with exterior surface treatments also showed enhanced heat transfer coefficients.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2024

Effect of the Chemical States of Copper on Methanol Decomposition and Oxidation

Here, the decomposition and oxidation reactions of CH 3 OH over metallic Cu(100) and Cu 2 O-covered Cu(100) surfaces are studied using a combination of in-situ ambient-pressure X-ray photoelectron spectroscopy, Auger electron spectroscopy, and density functional theory calculations. We identify the sequential chemical transformation pathways from bond cleavage to the formation of intermediates and final products under operational conditions. Accumulative surface adsorption of CH 3 O species on metallic Cu(100) impedes the decomposition of CH 3 OH. Co-dosing on metallic Cu(100) with low pressures of 1·10 -4 Torr CH 3 OH + 1·10 -4 Torr O 2 results in partial oxidation of CH 3 OH, where the chemisorbed O ads reduces surface sites available for CH 3 O adsorption, decreasing the surface activity for CH 3 OH decomposition. In contrast, the Cu 2 O overlayer formed under the elevated pressures of 0.33 Torr CH 3 OH + 0.66 Torr O 2 promotes the total oxidation of CH 3 OH into the final products of CO 2 and H 2 O, arising from the active reaction 2 between lattice O within Cu 2 O and intermediates of CH 3 O, CH 2 O, HCOO, and CO. Despite the more favorable O-H bond scission, C-O bond scission also occurs to result in surface accumulation of CH x on metallic Cu(100), blocking active sites for decomposition reactions of CH 3 OH and CH 3 O. By comparison, the CH x species on the Cu 2 O-covered Cu(100) undergo oxidation into CO 2 and H 2 O with lattice O in the Cu 2 O overlayer, thereby freeing active sites for the total oxidation of CH 3 OH. These results highlight the distinct roles of metallic Cu and Cu 2 O in the pathways of CH 3 OH decomposition and oxidation reactions, offering practical insights for the design of Cu-based catalysts with tailored reactivity and selectivity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Ion Conducting Polymer Interfaces for Lithium Metal Anodes: Impact on the Electrodeposition Kinetics

Electrochemical cells that utilize metals (e.g., lithium, sodium, zinc) as anodes are under intense investigation as they are projected to replace the current lithium-ion batteries to serve as a more energy-dense option for commercial applications. In addition, metal electrodes provide opportunities for fundamental research of different phenomena, such as ion transport and electrochemical kinetics, in the complex environment of reactive metal-electrodeposition. In this work, computationally and experimentally the competing effects related to transport and kinetics during the metal electrodeposition process are examined. Using Brownian dynamics simulations, it is shown that slower deposition kinetics results in a more compact and uniform Li morphology. This finding is experimentally implemented by designing ion-containing polymeric coatings on the electrodes that simultaneously provide pathways for lithium-ion transport, while impeding the charge transfer (Li + + e - → Li) at heterogeneous surfaces. It is further shown that these ionic polymer interfaces can significantly extend the cell-lifetime of a lithium metal battery in both ether-based and carbonate-based electrolytes. Through theoretical and experimental investigations, it is found that a low kinetic to transport rate ratio is a major factor in influencing the Li plating morphology. The plating morphology can be further fine-tuned by increasing ionic conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Enabling fast discharge of Li-ion batteries via electrolyte formulations for urban air mobility applications

High-power discharge requirements are critical for lithium-ion batteries (LIBs) used in electric Vertical Takeoff and Landing (eVTOL) vehicles that are increasingly considered in urban mobility. This investigation places a particular emphasis on understanding the impact of electrolytes on discharge processes and rate capability. We aim to compare the discharge behavior of LiBs using a conventional electrolyte (Gen 2: 1.2 M LiPF 6 in EC:EMC) and the dual salt LiTFSI-LiBOB-based electrolyte. Here we carefully examine the profiles of charging and discharging, the behavior during extended cycles, impedance spectroscopy results, and the characteristics of the electrode surface. Our research findings demonstrate the complex relationship between the composition of electrolytes and the specific high-power discharge requirements of electric vertical takeoff and landing (eVTOL) systems. This research highlights the importance of customizing electrolyte compositions to optimize energy storage density while simultaneously enabling higher power extraction to enhance performance in short-range electric aviation.

25 ENERGY STORAGE↗
DOE OSTI2022

Electrolyte Reactivity at the Charged Ni-Rich Cathode Interface and Degradation in Li-Ion Batteries

The chemical and electrochemical reactions at the positive electrode–electrolyte interface in Li-ion batteries are hugely influential on cycle life and safety. Ni-rich layered transition metal oxides exhibit higher interfacial reactivity than their lower Ni-content analogues, reacting via mechanisms that are poorly understood. Here, we study the pivotal role of the electrolyte solvent, specifically cyclic ethylene carbonate (EC) and linear ethyl methyl carbonate (EMC), in determining the interfacial reactivity at charged LiNi 0.33 Mn 0.33 Co 0.33 O 2 (NMC111) and LiNi 0.8 Mn 0.1 Co 0.1 O 2 (NMC811) cathodes by using both single-solvent model electrolytes and the mixed solvents used in commercial cells. While NMC111 exhibits similar parasitic currents with EC-containing and EC-free electrolytes during high voltage holds in NMC/Li 4 Ti 5 O 12 (LTO) cells, this is not the case for NMC811. Online gas analysis reveals that the solvent-dependent reactivity for Ni-rich cathodes is related to the extent of lattice oxygen release and accompanying electrolyte decomposition, which is higher for EC-containing than EC-free electrolytes. Combined findings from electrochemical impedance spectroscopy (EIS), TEM, solution NMR, ICP, and XPS reveal that the electrolyte solvent has a profound impact on the degradation of the Ni-rich cathode and the electrolyte. Higher lattice oxygen release with EC-containing electrolytes is coupled with higher cathode interfacial impedance, a thicker oxygen-deficient rock-salt surface reconstruction layer, more electrolyte solvent and salt breakdown, and higher amounts of transition metal dissolution. These processes are suppressed in the EC-free electrolyte, highlighting the incompatibility between Ni-rich cathodes and conventional electrolyte solvents. Finally, new mechanistic insights into the chemical oxidation pathways of electrolyte solvents and, critically, the knock-on chemical and electrochemical reactions that further degrade the electrolyte and electrodes curtailing battery lifetime are provided.

25 ENERGY STORAGE↗
DOE OSTI2025

Maximizing Calendering Effects Through the Mechanical Pulverization of Co-Free Nickel-Rich Cathodes in Lithium-Ion Cells

Calendering is a technique used to maximize the volumetric energy density of battery electrodes. However, higher amounts of calendering result in increased tortuosity and particle cracking. We propose a novel packing structure of electrode particles to maximize calendering benefits while minimizing particle fracture. Cobalt-free layered oxide cathode LiNi0.92Mn0.04Al0.04O2 (NMA) particles are pulverized through ball-milling and coated with lithium phosphate. Pulverized and pristine NMA are fabricated into “bimodal” electrodes, whereas “unimodal” electrodes consist of only pristine NMA. Each electrode type was made into 30% porosity, 40% porosity, and uncalendered coin cell samples. X-ray diffraction suggests that the unimodal samples suffer from more particle fracture than the bimodal samples when calendered to the same porosity of 30%. Electrochemical impedance spectroscopy suggests that the bimodal electrodes exhibit lower surface film resistance. This is supported by enhanced capacity retention for the bimodal samples after 100 cycles.

25 ENERGY STORAGE↗
NASA NTRS1992

Transition operators in electromagnetic-wave diffraction theory - General theory

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.

Hahne, G. E.↗