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At least 1,189 records · Page 66

Pit Stability Predictions of Additively Manufactured SS316 Surfaces Using Finite Element Analysis

Stainless steels are susceptible to localized forms of corrosion attack, such as pitting. The size and lifetime of a nucleated pit can vary, depending on a critical potential or current density criterion, which determines if the pit repassivates or continues growing. This work uses finite element method (FEM) modeling to compare the critical pit radii predicted by thermodynamic and kinetic repassivation criteria. Experimental electrochemical boundary conditions are used to capture the active pit kinetics. Geometric and environmental parameters, such as the pit shape and size (analogous to additively manufactured lack-of-fusion pores), solution concentration, and water layer thickness were considered to assess their impact on the pit repassivation criterion. The critical pit radius (the transition point from stable growth to repassivation) predicted for a hemispherical pit was larger when using the repassivation potential (E rp ) criteria, as opposed to the current density criteria (pit stability product). Including both the pit stability product and E rp into its calculations, the analytical maximum pit model predicted a critical radius two times more conservative than the FEA approach, under the conditions studied herein. The complex pits representing lack-of-fusion pores were shown to have minimal impact on the critical radius in atmospheric conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phases of 2D massless QCD with qubit regularization

We investigate the possibility of reproducing the continuum physics of 2D S U ( N ) gauge theory coupled to a single flavor of massless Dirac fermion using qubit regularization. The continuum theory is described by N free fermions in the ultraviolet (UV) and a coset Wess-Zumino-Witten (WZW) model in the infrared (IR). In this work, we first explore how well these features can be reproduced using the Kogut-Susskind (KS) Hamiltonian with a finite-dimensional link Hilbert space and a generalized Hubbard coupling. We do this by analyzing the renormalization group (RG) flow diagram of the continuum theory and identifying important phases of the theory. Using strong coupling expansions, we show that our lattice model exhibits a gapped dimer phase and a spin-chain phase. Furthermore, for N = 2 , using tensor network methods, we show that there is a second-order phase transition between these two phases, which we identify as the critical surface of the continuum theory that connects the IR and UV fixed points. In the IR, we identify the critical theory at the transition as the expected S U ( 2 ) 1 WZW model. Lastly, we argue that modifications of our model may allow the study of the UV physics of free fermions. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Ni-MH storage test and cycle life test

Gates Aerospace Batteries is conducting two long term test programs to fully characterize the NiMH cell technology for aerospace applications. The first program analyzes the effects of long term storage upon cell performance. The second program analyzes cycle life testing and preliminary production lot testing. This paper summarizes these approaches to testing the NiMH couple and culminates with initial storage and testing recommendations. Long term storage presents challenges to deter the adverse condition of capacity fade in NiMH cells. Elevated but stabilized pressures and elevated but stabilized end-of-charge voltages also appear to be a characteristic phenomenon of long term storage modes. However, the performance degradation is dependent upon specific characteristics of the metal-hydride alloy. To date, there is no objective evidence with which to recommend the proper method for storage and handling of NiMH cells upon shipment. This is particularly critical due to limited data points that indicate open circuit storage at room temperature for 60 to 90 days will result in irrecoverable capacity loss. Accordingly a test plan was developed to determine what method of mid-term to long-term storage will prevent irrecoverable capacity loss. The explicit assumption is that trickle charging at some rate above the self-discharge rate will prevent the irreversible chemical changes to the negative electrode that result in the irrecoverable capacity loss. Another premise is that lower storage temperatures, typically 0 C for aerospace customers, will impede any negative chemical reactions. Three different trickle charge rates are expected to yield a fairly flat response with respect to recoverable capacity versus baseline cells in two different modes of open circuit. Specific attributes monitored include: end-of-charge voltage, end-of-charge pressure, mid-point discharge voltage, capacity, and end-of-discharge pressure. Cycle life testing and preliminary production lot testing continue to dominate the overall technology development effort at GAB. The cell life test program reflects continuing improvements in baseline cell designs. Performance improvements include lower and more stable charge voltages and pressures. The continuing review of production lot testing assures conformance to the design criteria and expectations. This is especially critical during this period of transferring technology from research and development status to production.

Dell, R. Dan↗

Calibration improvements to electronically scanned pressure systems and preliminary statistical assessment

Orifice-to-orifice inconsistencies in data acquired with an electronically-scanned pressure system at the beginning of a wind tunnel experiment forced modifications to the standard, instrument calibration procedures. These modifications included a large increase in the number of calibration points which would allow a critical examination of the calibration curve-fit process, and a subsequent post-test reduction of the pressure data. Evaluation of these data has resulted in an improved functional representation of the pressure-voltage signature for electronically-scanned pressures sensors, which can reduce the errors due to calibration curve fit to under 0.10 percent of reading compared to the manufacturer specified 0.10 percent of full scale. Application of the improved calibration function allows a more rational selection of the calibration set-point pressures. These pressures should be adjusted to achieve a voltage output which matches the physical shape of the pressure-voltage signature of the sensor. This process is conducted in lieu of the more traditional approach where a calibration pressure is specified and the resulting sensor voltage is recorded. The fifteen calibrations acquired over the two-week duration of the wind tunnel test were further used to perform a preliminary, statistical assessment of the variation in the calibration process. The results allowed the estimation of the bias uncertainty for a single instrument calibration; and, they form the precursor for more extensive and more controlled studies in the laboratory.

Everhart, Joel L.↗

Quickbird Satellite in-orbit Modulation Transfer Function (MTF) Measurement Using Edge, Pulse and Impulse Methods for Summer 2003

The spatial characteristics of an imaging system cannot be expressed by a single number or simple statement. However, the Modulation Transfer Function (MTF) is one approach to measure the spatial quality of an imaging system. Basically, MTF is the normalized spatial frequency response of an imaging system. The frequency response of the system can be evaluated by applying an impulse input. The resulting impulse response is termed the Point Spread function (PSF). This function is a measure of the amount of blurring present in the imaging system and is itself a useful measure of spatial quality. An underlying assumption is that the imaging system is linear and shift-independent. The Fourier transform of the PSF is called the Optical Transfer Function (OTF) and the normalized magnitude of the OTF is the MTF. In addition to using an impulse input, a knife-edge in technique has also been used in this project. The sharp edge exercises an imaging system at all spatial frequencies. The profile of an edge response from an imaging system is called an Edge Spread Function (ESF). Differentiation of the ESF results in a one-dimensional version of the Point Spread Function (PSF). Finally, MTF can be calculated through use of Fourier transform of the PSF as stated previously. Every image includes noise in some degree which makes MTF of PSF estimation more difficult. To avoid the noise effects, many MTF estimation approaches use smooth numerical models. Historically, Gaussian models and Fermi functions were applied to reduce the random noise in the output profiles. The pulse-input method was used to measure the MTF of the Landsat Thematic Mapper (TM) using 8th order even functions over the San Mateo Bridge in San Francisco, California. Because the bridge width was smaller than the 30-meter ground sample distance (GSD) of the TM, the Nyquist frequency was located before the first zero-crossing point of the sinc function from the Fourier transformation of the bridge pulse. To avoid the zero-crossing points in the frequency domain from a pulse, the pulse width should be less than the width of two pixels (or 2 GSD's), but the short extent of the pulse results in a poor signal-to-noise ratio. Similarly, for a high-resolution satellite imaging system such as Quickbird, the input pulse width was critical because of the zero crossing points and noise present in the background area. It is important, therefore, that the width of the input pulse be appropriately sized. Finally, the MTF was calculated by taking ratio between Fourier transform of output and Fourier transform of input. Regardless of whether the edge, pulse and impulse target method is used, the orientation of the targets is critical in order to obtain uniformly spaced sub-pixel data points. When the orientation is incorrect, sample data points tend to be located in clusters that result in poor reconstruction of the edge or pulse profiles. Thus, a compromise orientation must be selected so that all spectral bands can be accommodated. This report continues by outlining the objectives in Section 2, procedures followed in Section 3, descriptions of the field campaigns in Section 4, results in Section 5, and a brief summary in Section 6.

Helder, Dennis↗

COMETBOARDS Can Optimize the Performance of a Wave-Rotor-Topped Gas Turbine Engine

A wave rotor, which acts as a high-technology topping spool in gas turbine engines, can increase the effective pressure ratio as well as the turbine inlet temperature in such engines. The wave rotor topping, in other words, may significantly enhance engine performance by increasing shaft horse power while reducing specific fuel consumption. This performance enhancement requires optimum selection of the wave rotor's adjustable parameters for speed, surge margin, and temperature constraints specified on different engine components. To examine the benefit of the wave rotor concept in engine design, researchers soft coupled NASA Lewis Research Center's multidisciplinary optimization tool COMETBOARDS and the NASA Engine Performance Program (NEPP) analyzer. The COMETBOARDS-NEPP combined design tool has been successfully used to optimize wave-rotor-topped engines. For illustration, the design of a subsonic gas turbine wave-rotor-enhanced engine with four ports for 47 mission points (which are specified by Mach number, altitude, and power-setting combinations) is considered. The engine performance analysis, constraints, and objective formulations were carried out through NEPP, and COMETBOARDS was used for the design optimization. So that the benefits that accrue from wave rotor enhancement could be examined, most baseline variables and constraints were declared to be passive, whereas important parameters directly associated with the wave rotor were considered to be active for the design optimization. The engine thrust was considered as the merit function. The wave rotor engine design, which became a sequence of 47 optimization subproblems, was solved successfully by using a cascade strategy available in COMETBOARDS. The graph depicts the optimum COMETBOARDS solutions for the 47 mission points, which were normalized with respect to standard results. As shown, the combined tool produced higher thrust for all mission points than did the other solution, with maximum benefits around mission points 11, 25, and 31. Such improvements can become critical, especially when engines are sized for these specific mission points.

Patnaik, Surya N.↗

Space Communications and Navigation (SCaN) Tool Capabilities Updates for Antenna Pattern and Jitter

The ability to accurately simulate the dynamic misalignment of pointing across a communications link is critical to determining the link performance between/across spacecraft and/or ground stations. The communication system antenna pattern and dynamic misalignment are key components to understanding the pointing loss induced on the communications link. Currently, projects performing these analyses use a variety of simulation tools and packages. NASA's Space Communications and Navigation (SCaN) office aims to provide a unified tool set for these functions. However, the analysis tool to calculate antenna patterns is currently static, two-dimensional, and approximated based on limited input. Steps were taken to change the inputs used by the tool to create a more accurate approximation of the antenna's far field pattern as well as create a three-dimensional pattern. An additional tool was also developed to calculate time-dynamic pointing loss from the antenna pattern generated or observed antenna pattern data given dynamic pointing errors.

SCaN↗

A Data Processing Pipeline To Extract A Knowledge Graph From Heterogeneous Data For Socio-technical Analysis Of Critical Infrastructure Influence

The code is written in Python and consists of the following pipeline that is implemented in Apache Airflow. This pipeline intends to understand the companies that are directly or indirectly involved with a type of critical infrastructure system at some point in that system's lifecycle. The pipeline takes a configuration file that specifies a list of initial companies to consider, a geographic region of interest, and a set of SEC form types as well as other data sources (e.g. CrunchBase) from which to extract entities and relations. There are four main components to this pipeline as currently implemented: Entity Extraction, Network Construction, Analysis, and Visualization. First, Entity Extraction, is implemented as the `topear-extract_organizations` Apache Airflow workflow. Given an initial query that specifies a geographic region of interest and a time interval, the software will extract CI facilities of interest and organizations that have a direct influence relationship to those facilities (e.g. ownership). During the course of the LDRD, we focused on Electric Vehicle charging stations and this information is available via the Department of Energy (DOE) database on fueling stations maintained by NREL. Within the context of the DOE CESER project, we have focused on Battery Energy Storage Systems (BESS). Second, the Network Extraction component will iteratively construct a social network graph given the set of organizations and people extracted in the previous step. Organizations (and eventually People if desired) are then fed as a query to the `topgear-construct_social_network` Apache Airflow workflow which given a set of initial companies and data sets (e.g. SEC EDGAR form types, OpenCorporates, Crunchbase). This Airflow workflow will iteratively query such data sources to discover relationships with new organizations and people. For example, this module can iteratively query SEC EDGAR for metadata that documents the number of each type of form for the given set of companies and their location. This forms metadata represents a catalog of data sources from SEC EDGAR for the extracted social network knowledge graph. The pipeline then downloads these forms from the website and saves them in a build directory for further processing. These documents are then parsed for entities and relations. Again, we note that in additional to SEC data sources, this step can also pull in information on organizations via API services such as CrunchBase and OpenCorporates or bulk data sources. At the end of this step, the resultant social network, the Critical Infrastructure network, and the edges that encode relationships between organizations and CI facilities, form the Adversarial Socio-Technical Network (ASTN) that informs the analysis. Third, the Analysis component processes these generated ASTN. Previously, that has included the ability to compare prevalence of different vendors for a given infrastructure component type across different regions as well as identify common public and private investors across those vendors. This was demonstrated for EV Charging Stations across several different metropolitan areas within an IEEE PES GridEdge publication. More recently, we have looked at ways to identify infrastructure owners and operators of BESS with the most nameplate capacity across different states as well as other indictors of risk resulting from changes in ownership over time. Finally, the Visualization component consists of an HTML/CSS/JS framework by which users can interact geospatial, operational, and organizational relationships across a given portfolio of Critical Infrastructure facilities. The objective is to provide a library of UI/UX modules that can be repurposed for stakeholder-specific dashboards. All of the modules are related via a common event model that enables UI actions in one view to percolate across the other views.

Weaver, Gabriel [Idaho National Laboratory (INL), ↗

Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking

In this article, we consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between classical long-range order of local order parameters and quantum order of long-range entanglement in the ground states, we study the topological point defects and textures of order parameters in such systems. We show that the universal properties of point defects and textures are determined by the remnant symmetry enriched topological order in the symmetry-breaking ground states with a nonfluctuating order parameter, and provide a classification for their properties based on the inflation-restriction exact sequence. We highlight a few phenomena revealed by our theory framework. First, in the absence of intrinsic topological orders, we show a connection between the symmetry properties of point defects and textures to deconfined quantum criticality. Second, when the symmetry-breaking ground state has intrinsic topological orders, we show that the point defects can permute different anyons when braided around. They can also obey projective fusion rules in the sense that multiple vortices can fuse into an Abelian anyon, a phenomenon for which we coin “defect fractionalization.” Finally, we provide a formula to compute the fractional statistics and fractional quantum numbers carried by textures (skyrmions) in Abelian topological orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The melt memory effects in polymer crystallization

This paper presents a systematic review of the literature on the melt memory effects observed in polymers, an area that has engendered considerable debate for over 50 years. Recent advances in experimental techniques have provided fresh insights into how a polymer's thermal history influences its recrystallization behavior. It has been observed that given other conditions unchanged, the crystallization temperature during recrystallization decreases with an increase in the melt temperature T s above the melting point T m until a critical melt temperature is attained. This phenomenon also extends to the half-time of crystallization and the secondary structures, such as lamellar thickness, of semi-crystalline polymers. Despite these findings, a comprehensive constitutive model that encapsulates polymer melt memory effects remains elusive. Cutting-edge instrumentation, including in situ small and wide-angle X-ray scattering, temperature-controlled Fourier transform infrared spectroscopy, and flash differential scanning calorimetry, have posed significant challenges to the traditional nucleation and growth models established in the 1970s. These models are foundational to our understanding of polymer crystallization, which is an integral part of polymer processing and production. In this review, the historical contours of this discourse are traced, with an examination of both the recent experimental breakthroughs and theoretical advancements pertinent to polymer melt memory effects. In conclusion, this paper delves into the prevailing theories of polymer nucleation and crystallization and engages with theoretical discussions and numerical simulations that attempt to elucidate and rationalize these melt memory phenomena.

36 MATERIALS SCIENCE↗

The five-point bootstrap

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators 〈σσϵσσ〉 in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff ∆ ⩽ ∆ cutoff . We then compute several OPE coefficients involving ϵ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the thermal oxidation of nuclear graphite relevant to high-temperature gas cooled reactors

Thermal oxidation of nuclear graphite components is highly undesirable because it can cause structural and property degradation that negatively affect a reactor's intended operation. In this work, the body of knowledge of nuclear graphite oxidation is highlighted, including when O 2 , H 2 O, and/or CO 2 are the oxidant. Oxidation conditions relevant to high-temperature gas-cooled reactors (i.e., when oxidation could occur either as an acute or chronic phenomenon) are emphasized. Here, the objective is to summarize graphite oxidation data in a practical and accessible way to inform future research and regulatory requirements. Although each grade of nuclear graphite is different, the oxidation mechanism has underlying commonalities. Although oxidation behavior is grade dependent, the general temperature dependence is well described by a sequence of elementary steps which become rate limiting. Because the regime transition temperature depends on sample microstructure, size, and oxidant supply rate, extrapolating results beyond the experimental range should be done cautiously. Gravimetric oxidation rate measurements generally replicate well. However, caution must be exercised when rates are estimated by other methods or for samples that deviate significantly in size. Air oxidation data for IG-110, NBG-18, and PCEA graphite is critically reviewed to emphasize this point. Despite the amount of experimental data, gaps remain. Sample size and shape effects are not fully explained. Data on the oxidant penetration depth are insufficient. Analytical assessments demonstrate that lower temperature oxidation does not necessarily imply that oxidation is uniform throughout the bulk. Oxidation occurs faster at higher temperature but is more localized to the exposed surface. Paradoxically, at equal mass loss percentage, low temperature oxidation leads to greater property degradation than at high temperature. The isolated effect of oxidation is important; however, a gap remains in the systematic understanding of any potential effect of neutron irradiation on graphite structure and reactivity.

36 MATERIALS SCIENCE↗

A Review on Direct Air Capture of Carbon Dioxide: Sorbent Materials, Process Engineering, Industrial Scale-Up, and Future Perspectives

The relentless accumulation of anthropogenic greenhouse gases has driven atmospheric carbon dioxide concentrations to approximately 426 ppm, necessitating the aggressive deployment of negative-emission technologies to achieve net zero by 2050. Direct air capture (DAC) offers a scalable, location-independent approach to atmospheric carbon removal; however, it is fundamentally constrained by the significant thermodynamic barriers associated with capturing CO 2 from ultradilute ambient conditions, requiring minimum thermodynamic energy inputs substantially higher than those for postcombustion point sources. This comprehensive review critically examines the technological landscape of DAC, focusing on the interdependent triad of sorbent material design, contactor engineering, and regeneration thermodynamics. We evaluate the fundamental boundaries of adsorption, emphasizing that an optimal adsorption enthalpy and isosteric heat of adsorption must balance the high CO 2 uptake capacity with the energetic penalties of sorbent regeneration. A systematic, comparative analysis of state-of-the-art sorbents is presented, encompassing mesoporous silicas, zeolites, carbon-based materials (CBMs), metal−organic frameworks (MOFs), porous organic polymers (POPs), and polymeric membranes. Special attention is devoted to surface functionalization strategies, particularly amine grafting and impregnation, which transition capture mechanisms from physisorption to chemisorption to enhance selectivity under ambient moisture and low partial pressures. Furthermore, we assess the operational merits of various reactor configurations, including gas−solid, gas−liquid, and membrane contactors, alongside regeneration cycles such as temperature, vacuum, pressure, and moisture swing adsorption. Finally, the review bridges fundamental materials science with industrial application by chronicling the scale-up milestones of pioneering entities and providing a strategic roadmap for advancing DAC technology readiness levels toward global deployment.

Adsorption↗

Fluoropolymer Composites from Partially Perfluoroalkylated Waste Polyethylene

Chemically modified plastics have emerged as practical solutions to plastic waste increases. Here, the inherent novelty of decorating polymer chains with chemical functionality results in distinct properties that expand the available application space. Nevertheless, developing designer materials for specific applications beyond compatibilization or mild property enhancement is difficult due to the synergistic effects of both the polar functionality imparted and the parent materials' intrinsic properties. By incorporating perfluoro-alkyl side-chains onto the backbone of dehydrogenated waste HDPE, unique surface properties intermediate between polytetrafluoroethylene (PTFE, the model fluoropolymer) and HDPE become apparent, while the overall material mechanical and thermal properties result in more LLDPE-like materials. This is demonstrated through moderate decreases in the surface free energy of the perfluoroalkylated polyolefin surface (increase in H 2 O contact angle of ~ 6°) and increased ordering under shear when blended with PTFE nanoparticles where the crossover point occurred at higher strains. Critically, perfluoroalkylated HDPE possesses improved rheological modification properties at elevated temperatures with PTFE nanoparticles, resulting in more thermally robust and stable composite materials.

fluoropolymer↗

CoURAGE KAZR b1 Processing: Corrections, Calibrations, and Processing Report

The U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) User Facility supports atmospheric and earth system research through a comprehensive network of fixed and mobile observatories. These facilities provide long-term and intensive campaign-based observations of clouds, aerosols, precipitation, radiation, and meteorological state variables. ARM observations are designed to improve the physical understanding and numerical representation of atmospheric processes in earth system models, with particular emphasis on cloud-radiation interactions and precipitation processes. The Coast-Urban-Rural Atmospheric Gradient Experiment (CoURAGE) deploys one of the ARM Mobile Facilities (AMF) to the Mid-Atlantic region surrounding Baltimore, Maryland, for the period 1 December 2024 through 30 November 2025. This deployment focuses on characterizing atmospheric structure, cloud properties, and precipitation processes across strong land-use and surface heterogeneity gradients associated with urban, rural, and coastal (Chesapeake Bay) environments. The CoURAGE deployment complements the Baltimore Social-Environmental Collaborative (BSEC), a DOE Urban Integrated Field Laboratory (UIFL), by providing high-quality atmospheric observations needed to connect urban surface processes, emissions, and meteorology to cloud and precipitation responses. In addition to the central urban site, ancillary observing sites were deployed to rural Maryland northwest of Baltimore and to an island site in Chesapeake Bay. These measurements further complement a long-term atmospheric observatory operated in Beltsville, Maryland, by Howard University in collaboration with the Maryland Department of the Environment. Together, these assets form a four-node regional atmospheric observatory network representing Baltimore and its three primary surrounding environments—urban, rural, and coastal/bay. This coordinated observational strategy enables investigation of spatial gradients in boundary-layer structure, cloud occurrence, precipitation evolution, and aerosol-cloud interactions across complex surface regimes. Within this network, vertically pointing cloud radars play a critical role by providing continuous, high-resolution measurements of cloud and precipitation vertical structure.

54 ENVIRONMENTAL SCIENCES↗

Experimental study of external fuel vaporization

The fuel properties used in the design of a flash vaporization system for aircraft gas turbine engines were evaluated in experiments using a flowing system to determine critical temperature and pressure, boiling points, dew points, heat transfer coefficients, deposit formation rates, and deposit removal. Three fuels were included in the experiments: Jet-A, an experimental referree broad specification fuel, and a premium No. 2 diesel fuel. Engine conditions representing a NASA Energy Efficient Engine at sea-level take-off, cruise, and idle were simulated in the vaporization system and it was found that single phase flow was maintained in the heat exchanger and downstream of the throttle. Deposits encountered in the heat exchanger represented a thermal resistance as high as 1300 sq M K/watt and a deposit formation rate over 1000 gC/sq cm hr.

Szetela, E. J.↗

Rate processes in gas phase

Reaction-rate theory and experiment are given a critical review from the engineers' point of view. Rates of heavy-particle, collision-induced reaction in gas phase are formulated in terms of the cross sections and activation energies for reaction. The effect of cross section function shape and of excited state contributions to reaction both cause the slope of Arrhenius plots to differ from the true activation energy, except at low temperature. The master equations for chemically reacting gases are introduced, and dissociation and ionization reactions are shown to proceed primarily from excited states about kT from the dissociation or ionization limit. Collision-induced vibration, vibration-rotation, and pure rotation transitions are treated, including three-dimensional effects and conservation of energy, which have usually been ignored. The quantum theory of transitions at potential surface crossing is derived, and results are found to be in fair agreement with experiment in spite of some questionable approximations involved.

Hansen, C. F.↗