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At least 163 records · Page 9

Radiation‐Induced Defects in Uranyl Trinitrate Solids

Abstract Actinides are inherently radioactive; thus, ionizing radiation is emitted by these elements can have profound effects on its surrounding chemical environment through the formation of free radical species. While previous work has noted that the presence of free radicals in the system impacts the redox state of the actinides, there is little atomistic understanding of how these metal cations interact with free radicals. Herein, we explore the effects of radiation (UV and γ) on three U(VI) trinitrate complexes, M[UO 2 (NO 3 ) 3 ] (where M=K + , Rb + , Cs + ), and their respective nitrate salts in the solid state via electron paramagnetic resonance (EPR) and Raman spectroscopy paired with Density Functional Theory (DFT) methods. We find that the alkali salts form nitrate radicals under UV and γ irradiation, but also note the presence of additional degradation products. M[UO 2 (NO 3 ) 3 ] solids also form nitrate radicals and additional DFT calculations indicate the species corresponds to a change from the bidentate bound nitrate anion into a monodentate NO 3 • radical. Computational studies also highlight the need to include the second sphere coordination environment around the [UO 2 (NO 3 ) 3 ] 0,1 species to gain agreement between the experimental and predicted EPR signatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Path Integral Monte Carlo Simulations of Iron Plasmas (Final Technical Report)

This documents is the final technical report for our grant entitled "Path Integral Monte Carlo Simulations of Iron Plasmas" that focused on developing path integral Monte Carlo (PIMC) computer simulations. This techniques will be developed to study plasmas composed of heavier elements including iron and other third row elements. Equations of state (EOS) and transport properties will be derived in the regime of warm dense matter (WDM) and dense plasmas where existing first-principles methods cannot be applied. While standard density functional theory (DFT) has been used to accurately predict the structure of many solids and liquids up to temperatures on the order of 100,000 K, this method is not applicable at much higher temperature because the number of partially occupied electronic orbitals reaches intractably large numbers or the use of finite-temperature free energy functionals in orbital-free DFT introduces an uncontrolled approximation. Here we focus on PIMC methods that become more and more efficient with increasing temperatures and still include all electronic correlation effects. In this approach, electronic excitations increase the efficiency rather than reduce it. While it had commonly been assumed this method could only be applied to elements without core electrons, we showed that PIMC with free-particle nodes works well for first-row elements (PRL 108 (2012) 115502). Most recently, we extended the applicability range of all-electron PIMC to second-row elements by adopting localized nodal surfaces (PRL 115 (2015) 176403). To simulate third-row elements efficiently under WDM conditions, we propose a new method to remove core electrons by introducing pseudo-nodes. We explain our approach step by step and present preliminary results. We focus our method development on getting PIMC simulations of iron to work because of its fundamental importance for WDM and astrophysics. Then we move on to krypton and copper-doped beryllium, a ICF ablator material. We plan to continue working on key second-row material such as Na, Mg, MgO, Al, silica, and silicon-doped plastic ablators. Our collaborators at LLNL, will use our PIMC EOS data both as comparisons to existing semi-empirical, EOS-generating schemes, and as input for continuum radiation hydrodynamics simulations. We will establish an efficient pipeline from PIMC to macroscopic continuum studies of materials response. An emphasis will be placed on benchmarking such methods for plasmas of heavy elements at the very high temperatures (~100 eV) and low densities that are generated when Hohlraum radiation heats the ablator material in indirect drive laser experiments. Results from changes to the EOS will be of immeasurable importance to the designers at the National Ignition Facility (NIF) and at other facilities. Starting with our EOS of Cu-doped Be, our second collaborator at LLE, will perform real-time simulations of laser fusion experiments at the Omega laser and at the NIF to determine how sensitive the compression path depends on the ablator EOS. Since our collaborator also has experience in performing orbital-free DFT calculations, we propose to compare predictions from this method with PIMC results. In joint publications, we plan to analyze the accuracy of different free-energy functionals in order to understand why existing orbital-free DFT calculations do not predict compression peaks along the shock Hugoniot curve that we see with PIMC. The peaks are caused by the ionization of various electron shells. Their accurate characterization is important to compare with experimental results. We will break new ground by developing PIMC techniques that can simulate iron and all other third row elements in the plasma and WDM regimes. We introduce the concept of pseudo-nodes for the efficient treatment of the core-electrons. The EOS and transport properties will be derived and published online in the form of a new WDM database. Our PIMC EOS calculations will benchmark and possibly replace semi-analytical EOS tables like QEOS or SESAME, which will impact the hydrocode simulation community and will affect the design of NIF targets. Our PIMC results will help to improve the accuracy of orbital-free DFT simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fundamental data for modeling electron-induced processes in plasma remediation of perfluoroalkyl substances

Plasma treatment of per- and polyfluoroalkyl substances (PFAS) contaminated water is a potentially energy efficient remediation method. In this treatment, an atmospheric pressure plasma interacts with surface-resident PFAS molecules. Developing a reaction mechanism and modeling of plasma–PFAS interactions requires fundamental data for electron–molecule reactions. In this paper, we present results of electron scattering calculations, potential energy landscapes and their implications for plasma modelling of a dielectric barrier discharge in PFAS contaminated gases, a first step towards modelling of plasma–water–PFAS intereactions. It is found that the plasma degradation of PFAS is dominated by dissociative electron attachment with the importance of other contributing processes varying depending on the molecule. All molecules posses a large number of shape resonances – transient negative ion states – from near-threshold up to ionization threshold. These states lie in the region of the most probable electron energies in the plasma (4–5 eV) and consequently are expected to further enhance the fragmentation dynamics in both dissociative attachment and dissociative excitation.

54 ENVIRONMENTAL SCIENCES↗

Ion fluxes and memory effects in an Ar–O 2 modulated radiofrequency-driven atmospheric pressure plasma jet

In this work we used molecular beam mass spectrometry to characterize ion fluxes produced by a modulated radiofrequency (RF)-driven atmospheric pressure plasma jet operating in a homogeneous gas environment (Ar + 1% O 2 ). The influence of the RF modulation frequency (100 Hz to 20 kHz) on the ion fluxes was investigated by time-resolved measurements, and the lifetimes of the dominant ions, O 2 + , NO + , O − , O 2 − and O 3 − , were found to be 28 ± 2, 117 ± 8, 7.3 ± 0.4, 17 ± 1 and 23 ± 2 μs, respectively. The absolute ion densities in the near afterglow region were found to be of the order of 1011 cm−3. Significant differences in the dynamics of the positive and negative ions were found; these are explained by the presence of electrons at similar densities in the afterglow produced by electron detachment reactions from negative ions due to the large concentrations of atomic oxygen and singlet delta oxygen. Transitions in ion flux dynamics for different modulation frequencies and at the startup of the plasma were analyzed together with intensified charge coupled device images recording the plasma propagation in order to assess the dynamics of plasma plume propagation and how it is impacted by ‘memory effects’. Quantitative measurements of the ion densities enabling these memory effects are reported. The results in this paper highlight the tremendous impact of memory effects on plasma propagation and the corresponding pre-ionization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Outer midplane neutral density measurements and H-mode fueling studies in NSTX-U

Neutral density profiles are measured on the outboard midplane of the National Spherical Torus Experiment Upgrade (NSTX-U) using a two dimensional camera (ENDD, edge neutral density diagnostic) filtered for deuterium Balmer α (D α ) emission interpreted via simulations using the Monte Carlo neutral transport code DEGAS 2. Deuterium atomic densities n D are calculated by inverting the line-integrated D α brightness and using local measurements of electron density ne and temperature T e to determine atomic rate coefficients. The assumptions used in the derivation of n D from D α emissivity are validated using DEGAS 2 to estimate contributions to emissivity due to electron impact excitation and molecular processes. In this work, experimental measurements and DEGAS 2 simulations are compared over a database of L- and H-mode discharges, showing good agreement in D α emissivity profiles. Residual disagreement between experiment and simulations is suggestive of the possible role of intermittent transport and uncertainties in the molecular data. DEGAS 2 simulations are further used to complement the ENDD diagnostic, extracting neutral (atomic and molecular) densities at locations where the ENDD measurement are not made or where the assumptions used in the ENDD analysis are not valid. Deuterium atomic densities and ionization profiles on the outer midplane are compared for L-mode and H-mode discharges in NSTX-U. One-way coupling of DEGAS 2 to UEDGE multi-fluid simulations constrained by experimental data is used to study edge fueling and neutral penetration in NSTX-U discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nature of native atomic defects in ZrTe 5 and their impact on the low-energy electronic structure

Over the past decades, investigations of the anomalous low-energy electronic properties of ZrTe 5 have reached a wide array of conclusions. An open question is the growth method's impact on the stoichiometry of ZrTe 5 samples, especially given the very small density of states near its chemical potential. In this work, we report on high-resolution scanning tunneling microscopy and spectroscopy measurements performed on samples grown via different methods. Using density functional theory calculations, we identify the most prevalent types of atomic defects on the surface of ZrTe 5 , namely, Te vacancies and intercalated Zr atoms. Finally, we precisely quantify their density and outline their role as ionized defects in the anomalous resistivity of this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Impact of Nd ions on the chemical kinetic behavior of radiolytic transients in molten LiCl-KCl-NdCl3 salt mixtures

Pyrochemical reprocessing technologies can be used to recover valuable materials from used nuclear fuel (UNF), such as uranium. However, other critical materials, such as fission product neodymium, are challenging to recover from molten chloride eutectic mixtures (LiCl-KCl) due to the presence of multivalent states (Nd2+/Nd3+), disproportionation reactions, and re-dissolution in the molten chloride salt. Understanding, predicting, and controlling these processes is further complicated by the presence of ionizing radiation fields, for which little is known on the interaction of neodymium ions with the radiolytic transients (es– and Cl2.–) in molten LiCl-KCl salt mixtures. Here, chemical kinetics, from integrated electron pulse irradiation and transient absorption spectroscopy, are presented for the reaction of Nd3+ ions with es– and Cl2.– as a function of temperature (400–600 ?).

36 - MATERIALS SCIENCE↗

O 2 based resonantly ionized photoemission thermometry analysis of supersonic flows

Characterization of the thermal gradients within supersonic and hypersonic flows is essential for understanding transition, turbulence, and aerodynamic heating. Developments in novel, impactful non-intrusive techniques are key for enabling flow characterizations of sufficient detail that provide experimental validation datasets for computational simulations. In this work, Resonantly Ionized Photoemission Thermometry (RIPT) signals are directly imaged using an ICCD camera to realize the techniques 1D measurement capability for the first time. The direct imaging scheme presented for oxygen-based RIPT (O 2 RIPT) uses the previously established calibration data to direct excite various resonant rotational peaks within the S-branch of the C 3 Π, ( v = 2) ← X 3 Σ( v ′ = 0) absorption band of O 2 . The efficient ionization of O 2 liberates electrons that induce electron avalanche ionization of local N 2 molecules generating N 2 + , which primarily deexcites via photoemissions of the first negative band of N 2 + ( B 2 Σ <#comment/> u + − <#comment/> X 2 Σ <#comment/> g + ) . When sufficient lasing energy is used, the ionization region and subsequent photoemission signal is achieved along a 1D line thus, if directly imaged can allow for gas temperature assignments along said line; demonstrated here of up to five centimeters in length. The temperature gradients present within the ensuing shock train of a supersonic under expanded free jet serves as a basis of characterization for this new RIPT imaging scheme. The O 2 RIPT results are extensively compared and validated against well-known and established techniques (i.e., CARS and CFD). The direct imaging capability fully realizes the technique’s fundamental potential and is expected to be the standard of implementation going forward. The direct imaging capability can play instrumental roles in future scientific studies that rely upon acute characterization of thermal gradients within a medium that cannot be easily resolved by a point. Furthermore, the removal of the spectrometer greatly reduces the cost, complexity, and optical alignment associated with prior RIPT measurements.

42 ENGINEERING↗

Revealing the Crystalline Architecture of Semicrystalline Ion Exchange Membranes for the Design of Conductive and Durable Alkaline Anion Exchange Membranes

Alkaline anion exchange membrane (AAEM) fuel cells offer a cost-effective alternative to proton exchange membrane (PEM) fuel cells by eliminating the need for expensive precious metal catalysts. In both PEMs and AAEMs, semicrystalline polymers are a common choice, as the crystalline domains can act as mechanical reinforcements that limit swelling and promote mechanical durability in the material. However, spatially resolved characterization of crystalline organization in ion exchange membranes beyond ensemble-averaged X-ray scattering is underrepresented, likely in part due to ionization damage limitations in soft materials. Here, in this study, we resolve the nanometer-size crystallites in semicrystalline ion exchange membranes by applying cryogenic four-dimensional scanning transmission electron microscopy (cryo-4D-STEM) along with data-processing algorithms designed to optimize signals at a low dose to minimize radiation damage. We investigate the effects of synthesis components, including molecular weight and thermal treatment, on a model system of AAEMs in comparison to Nafion, the most commonly used and commercially successful PEM today. We find that excess water uptake in polymer membranes, a property directly associated with weak mechanical durability and with possible negative impacts on ion conductivity, can be reduced by over 30% by varying the polymer's crystalline morphology through changes in synthesis parameters such as molecular weight and thermal history. Our results indicate that this improvement is correlated with smaller crystalline domains with a more homogeneous distribution. More broadly, these results demonstrate how the crystalline architecture of polymer membranes can be tuned through their chemistry and thermal treatment in order to improve their conductivity and durability for commercial fuel cell performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Radiation-Induced Plutonium Redox Chemistry

Plutonium plays a key role in global actinide research and nuclear fuel cycle technologies, and yet, our fundamental understanding of its inherent radiation-induced chemical behavior is limited. These radiation-induced processes cannot simply be switched off, as they are as fundamentally inherent to plutonium as the impact of relativistic effects on its f-electrons. In less chemically complex actinide systems, such as aqueous solutions of neptunium and americium, , radiolysis products play a significant role in the redox cycling of their oxidation states. However, plutonium's multiple, coexisting, and chemically active oxidation states, which comprise of bare ions and dioxo cations, provide additional redox pathways that complicate radiation-induced processes. Oxidation state control is critical for the manipulation of plutonium, especially in used nuclear fuel reprocessing technologies, where oxidation specific states are successfully extracted, and others rejected. Consequently, mechanistically understanding the behavior of plutonium’s multiple oxidation states in the presence of intense ionizing radiation fields is essential for predicting the behavior of this element under multiple conditions that support the development and innovation of nuclear fuel cycle technologies. Here, we present recent advances in our understanding of plutonium radiation chemistry, including the first-ever multiscale model for predicting gamma radiation-induced plutonium redox chemistry, and new chemical kinetics for the reaction of plutonium and its complexes of tributyl phosphate (TBP), N,N-di-(2-ethylhexyl)butyramide (DEHBA), and N,N-di-(2-ethylhexyl)isobutyramide (DEHiBA) with transients radiolysis products, a measured using electron pulse radiolysis.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Erratum to: Soft- and reactive landing of ions onto surfaces: concepts and applications

Soft- and reactive landing of mass-selected ions is gaining attention as a promising approach for the precisely-controlled preparation of materials on surfaces that are not amenable to deposition using conventional methods. A broad range of ionization sources and mass filters are available that make ion soft-landing a versatile tool for surface modification using beams of hyperthermal (<100?eV) ions. The ability to select the mass-to-charge ratio of the ion, its kinetic energy and charge state, along with precise control of the size, shape, and position of the ion beam on the deposition target distinguishes ion soft landing from other surface modification techniques. Soft- and reactive landing have been used to prepare interfaces for practical applications as well as precisely-defined model surfaces for fundamental investigations in chemistry, physics, and materials science. For instance, soft- and reactive landing have been applied to study the surface chemistry of ions isolated in the gas-phase, prepare arrays of proteins for high-throughput biological screening, produce novel carbon-based and polymer materials, enrich the secondary structure of peptides and the chirality of organic molecules, immobilize electrochemically-active proteins and organometallics on electrodes, create thin films of complex molecules, and immobilize catalytically active organometallics as well as ligated metal clusters. In addition, soft landing has enabled investigation of the size-dependent behavior of bare metal clusters in the critical subnanometer size regime where chemical and physical properties do not scale predictably with size. The morphology, aggregation, and immobilization of larger bare metal nanoparticles, which are directly relevant to the design of catalysts as well as improved memory and electronic devices, have also been studied using ion soft landing. This review article begins in section 1 with a brief introduction to the existing applications of ion soft- and reactive landing. Section 2 provides an overview of the ionization sources and mass filters that have been used to date for soft landing of mass-selected ions. A discussion of the competing processes that occur during ion deposition as well as the types of ions and surfaces that have been investigated follows in section 3. Section 4 discusses the physical phenomena that occur during and after ion soft landing, including retention and reduction of ionic charge along with factors that impact the efficiency of ion deposition. The influence of soft landing on the secondary structure and biological activity of complex ions is addressed in section 5. Lastly, an overview of the structure and mobility as well as the catalytic, optical, magnetic, and redox properties of bare ionic clusters and nanoparticles deposited onto surfaces is presented in section 6. © 2015 Wiley Periodicals, Inc. Mass Spec Rev 35:439–479, 2016.

Johnson, Grant E.↗

Pre-main-sequence Brackett Emitters in the APOGEE DR17 Catalog: Line Strengths and Physical Properties of Accretion Columns

Very young (t ≲ 10 Myr) stars possess strong magnetic fields that channel ionized gas from the interiors of their circumstellar disks to the surface of the star. Upon impacting the stellar surface, the shocked gas recombines and emits hydrogen spectral lines. To characterize the density and temperature of the gas within these accretion streams, we measure equivalent widths of Brackett (Br) 11–20 emission lines detected in 1101 APOGEE spectra of 326 likely pre-main-sequence accretors. For sources with multiple observations, we measure median epoch-to-epoch line strength variations of 10% in Br11 and 20% in Br20. We also fit the measured line ratios to predictions of radiative transfer models by Kwan & Fischer. We find characteristic best-fit electron densities of n e = 10 11 –10 12 cm -3 , and excitation temperatures that are inversely correlated with electron density (from T ~ 5000 K for n e ~ 10 12 cm -3 to T ~ 12,500 K at n e ~ 10 11 cm -3 ). These physical parameters are in good agreement with predictions from modeling of accretion streams that account for the hydrodynamics and radiative transfer within the accretion stream. We also present a supplementary catalog of line measurements from 9733 spectra of 4255 Brackett emission-line sources in the APOGEE Data Release 17 data set.

79 ASTRONOMY AND ASTROPHYSICS↗

Generation of gamma radiation by a subterawatt ultrashort laser pulse: optimisation of preplasma and pulse duration

We report an experimental and numerical study of the acceleration of electrons in a plasma interacting with a subterawatt laser pulse (intensity of ∼3 × 10{sup 18} W cm{sup −2} at a pulse duration of 50 fs). A preplasma layer on the surface of a molybdenum target is formed by an additional laser pulse with a duration of 8 ns and an intensity of ∼2 × 10{sup 12} W cm{sup −2}. It is shown that an increase in the laser pulse duration to 1700 fs at a constant energy (and a proportional decrease in intensity) leads to an increase in the yield of bremsstrahlung γ-radiation by more than an order of magnitude when the nanosecond pulse is ahead of the femtosecond one by 15 − 25 ns. Interferometry data and results of diagnostics of optical and γ-radiation of a plasma demonstrate that the collisional ionisation of atoms by electrons oscillating in the field of such a laser pulse plays an essential role in the formation of electron density profile. The sensitivity of the described effect to the level of amplified spontaneous emission is determined, despite the nanosecond pulse impact. Numerical simulations show that at a large pulse duration, the acceleration of electrons is stipulated by the beaking of plasma waves excited during stimulated Raman scattering of laser radiation. (paper)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-resolution Laboratory Measurements of K-shell X-Ray Line Polarization and Excitation Cross Sections in Helium-like S XV Ions

We report measurements of electron-impact excitation cross sections for the strong K-shell n = 2 → 1 transitions in S xv, using the LLNL EBIT-I electron beam ion trap, two crystal spectrometers, and the EBIT Calorimeter Spectrometer. The cross sections are determined by direct normalization to the well-known cross sections of radiative electron capture, measured simultaneously. Using contemporaneous polarization measurements with the two crystal spectrometers, whose dispersion planes are oriented parallel and perpendicular to the electron beam direction, the polarization of the direct excitation line emission is determined, and in turn the isotropic total cross sections are extracted. We further experimentally investigate various line-formation mechanisms, finding that radiative cascades and collisional inner-shell ionization dominate the degree of linear polarization and total line-emission cross sections of the forbidden line, z.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Direct Quantification of Heat Generation Due to Inelastic Scattering of Electrons Using a Nanocalorimeter

Transmission electron microscopy (TEM) is arguably the most important tool for atomic-scale material characterization. A significant portion of the energy of transmitted electrons is transferred to the material under study through inelastic scattering, causing inadvertent damage via ionization, radiolysis, and heating. In particular, heat generation complicates TEM observations as the local temperature can affect material properties. Here, the heat generation due to electron irradiation is quantified using both top-down and bottom-up approaches: direct temperature measurements using nanowatt calorimeters as well as the quantification of energy loss due to inelastic scattering events using electron energy loss spectroscopy. Combining both techniques, a microscopic model is developed for beam-induced heating and to identify the primary electron-to-heat conversion mechanism to be associated with valence electrons. Building on these results, the model provides guidelines to estimate temperature rise for general materials with reasonable accuracy. This study extends the ability to quantify thermal impact on materials down to the atomic scale.

42 ENGINEERING↗

The Role of Pulse Radiolysis in Advanced Nuclear Fuel Cycles

The effects of ionizing radiation are ubiquitous throughout all aspects of a nuclear fuel cycle. The complexity and intensity of these effects are greatest during reactor operations and in the management of used nuclear fuel and waste. Radiation-induced processes typically promote the chemical transformation of molecules and materials with the formation of potentially detrimental degradation products and corresponding changes in physical and chemical properties, which ultimately impact the effectiveness and longevity of nuclear technologies. Consequently, a molecular-level understanding of radiation effects over multiple time, distance, and material domains is essential for the innovation and deployment of next generation nuclear technologies. Attaining this knowledge necessitates a firm grasp of radiation-induced reaction kinetics, for which pulsed electron radiolysis is the methodology of choice. Presented here are several recent studies from our group that demonstrate the critical role of pulsed electron radiolysis techniques in the advancement of our understanding of radiation-induced chemistry under advanced nuclear fuel cycle conditions. Research topics include late actinide redox chemistry, radiation robustness of used nuclear fuel reprocessing complexants, and the behavior of metal cations in high temperature molten salt media.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Characterization of uncertainties in electron-argon collision cross sections

Abstract The predictive capability of a plasma discharge model depends on accurate representations of electron-impact collision cross sections, which determine the corresponding reaction rates and electron transport properties. The values of cross sections can be known only approximately either through experiments or simulations and are thus subject to uncertainties. Quantifying the uncertainties in plasma simulations allows us to assess the reliability of simulations and to provide a basis for interpreting discrepancies between simulations and experiments. For such uncertainty quantification of plasma simulations, it is essential to quantify the uncertainties of the underlying cross sections. Although much effort has been committed to calibrate the cross section values, their uncertainties are not well investigated. We characterize uncertainties in electron-argon atom collision cross sections using a Bayesian framework. Six collision processes—elastic momentum transfer, ionization, and four excitations—are characterized with semi-empirical models, which effectively capture the features important to the macroscopic properties of the plasma. A probability model for the uncertain parameters of these semi-empirical models is developed. Specifically, a Gaussian-process likelihood model is proposed to capture discrepancies among data sets, as well as the model-form inadequacies of the semi-empirical models. Two other likelihood models are compared with the proposed Gaussian-process model, to illustrate the importance of the choice of the likelihood model. The cross section models are calibrated using the electron-beam experiments and ab-inito quantum simulations. The resulting calibrated uncertainties capture well the scattering among the data sets. The calibrated cross section models are further validated against swarm-parameter experiments and zero-dimensional Boltzmann equation simulations of widely used cross section datasets.

Chung, Seung Whan (ORCID:0000000302501549)↗