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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Transferring predictions of formation energy across lattices of increasing size*

In this study, we show the transferability of graph convolutional neural network (GCNN) predictions of the formation energy of the nickel-platinum solid solution alloy across atomic structures of increasing sizes. The original dataset was generated with the large-scale atomic/molecular massively parallel simulator using the second nearest-neighbor modified embedded-atom method empirical interatomic potential. Geometry optimization was performed on the initially randomly generated face centered cubic crystal structures and the formation energy has been calculated at each step of the geometry optimization, with configurations spanning the whole compositional range. Using data from various steps of the geometry optimization, we first trained our open-source, scalable implementation of GCNN called HydraGNN on a lattice of 256 atoms, which accounts well for the short-range interactions. Using this data, we predicted the formation energy for lattices of 864 atoms and 2048 atoms, which resulted in lower-than-expected accuracy due to the long-range interactions present in these larger lattices. We accounted for the long-range interactions by including a small amount of training data representative for those two larger sizes, whereupon the predictions of HydraGNN scaled linearly with the size of the lattice. Therefore, our strategy ensured scalability while reducing significantly the computational cost of training on larger lattice sizes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A TOpographic Mapping (ATOM) Method to Design Magnetic Cores

Wireless power transfer offers safe, convenient, and efficient way of charging electric vehicles. Ongoing research is targeting wireless charging pad design optimization; designing the magnetic component is the most important part of the coupler design because the magnetic part determines the coupling factor and efficiency. Optimizing the coil layout and geometry as well as ferrite design requires finite elements analysis based modeling and simulation for minimized core losses, maximized magnetic coupling, and minimized material use for cost-effectiveness. Although parametric finite element analysis or emerging artificial intelligence methods can generate very accurate results, simulation times are extremely long. To address this issue, this study proposes a simple, effective core design called A TOpographic Mapping (ATOM). The proposed design is based on the design of magnetic core by using the magnetic flux distribution. The thickness of the core increases with increasing magnetic flux density, forming a variable thickness core design with less material and minimized core losses compared to conventional designs. A superimposing method is used to create an optimal design for a rotational magnetic field-based system. According to simulation results, the ATOM design reduces the required material volume by 13.19% and yields the lowest core loss and highest mutual inductance compared to other designs. In addition, misalignment, electromagnetic interference, and thermal performance were evaluated for the proposed design.

Aydin, Emrullah [Oak Ridge National Laboratory (OR↗
DOE OSTI2021

Fast and Accurate Machine Learning Strategy for Calculating Partial Atomic Charges in Metal–Organic Frameworks

Computational high-throughput screening using molecular simulations is a powerful tool for identifying top-performing metal–organic frameworks (MOFs) for gas storage and separation applications. Accurate partial atomic charges are often required to model the electrostatic interactions between the MOF and the adsorbate, especially when the adsorption involves molecules with dipole or quadrupole moments such as water and CO 2 . Although ab initio methods can be used to calculate accurate partial atomic charges, these methods are impractical for screening large material databases because of the high computational cost. We developed a random forest machine learning model to predict the partial atomic charges in MOFs using a small yet meaningful set of features that represent both the elemental properties and the local environment of each atom. The model was trained and tested on a collection of about 320 000 density-derived electrostatic and chemical (DDEC) atomic charges calculated on a subset of the Computation-Ready Experimental Metal–Organic Framework (CoRE MOF-2019) database and separately on charge model 5 (CM5) charges. The model predicts accurate atomic charges for MOFs at a fraction of the computational cost of periodic density functional theory (DFT) and is found to be transferable to other porous molecular crystals and zeolites. In conclusion, a strong correlation is observed between the partial atomic charge and the average electronegativity difference between the central atom and its bonded neighbors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a “ring polymer” whose spread is related to the quantum mechanical uncertainty in the particle’s position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Numerical simulation study of impurity B transport during real-time B powder injection in EAST

To understand the beneficial effects of impurity boron (B) on the plasma, the transport of B species in both atomic and ionic states in the edge plasma and the ensuing evolution of the background plasma are simulated during real-time B powder injection by using two-dimensional fluid code SOLPS-ITER. The initial background plasma profiles for the simulation are reconstructed based on an EAST upper-single null discharge (shot No. 70601). With the injection rate of B atoms, 4.0 × 10 21 atoms/s, the simulation shows that effective charge number is less than 1.1 at the inner boundary R - R sep = -5.2 cm (background plasma density, 5.1 × 10 19 m -3 ) at the outer mid-plane indicating that the B impurity does not have much influence on the energy confinement. The present work finds that the impurity B exhibits very specific features in the edge plasma, mostly present in the narrow region just outside the separatrix. The particular distribution pattern can reduce the heat flux greatly, leading to the divertor detachment. The divertor detachment can be achieved easily under an injection rate of B powder in a reasonable range. This study suggests that the impurity B has a promising potential application in future tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Energetics and structural properties of twist grain boundaries in Cu

Structural and energetics properties of atoms near a grain boundary are of great importance from theoretical and experimental standpoints. From various experimental work it is concluded that diffusion at low temperatures at polycrystalline materials take place near grain boundary. Experimental and theoretical results also indicate changes of up to 70 percent in physical properties near a grain boundary. The Embedded Atom Method (EAM) calculations on structural properties of Au twist grain boundaries are in quite good agreement with their experimental counterparts. The EAM is believed to predict reliable values for the single vacancy formation energy as well as migration energy. However, it is not clear whether the EAM functions which are fitted to the bulk properties of a perfect crystalline solid can produce reliable results on grain boundaries. One of the objectives of this work is to construct the EAM functions for Cu and use them in conjunction with the molecular static simulation to study structures and energetics of atoms near twist grain boundaries in Cu. This provides tests of the EAM functions near a grain boundary. In particular, we determine structure, single vacancy formation energy, migration energy, single vacancy activation energy, and interlayer spacing as a function of distance from grain boundary. Our results are compared with the available experimental and theoretical results from grain boundaries and bulk.

Karimi, Majid↗
DOE OSTI2024

Identifying point defects and ordering in the high-entropy layered oxide Li 1.5 MO 3-δ (M=Mn, Al, Fe, Co, Ni) for energy storage applications

High-entropy layered oxides (HELOs) represent a very promising class of next-generation battery cathodes, combining the well-studied properties of layered cathode materials such as LiCoO 2 with the chemical tunability and stability of high-entropy materials. HELO materials often form particles with complex defects and domain structures, complicating accurate characterization of structure and cation mixing. Understanding disorder and order in HELO materials is necessary for understanding their performance and utility as cathodes. Here we demonstrate the characterization of the HELO Li 1.5 MO 3-δ (M = Mn, Al, Fe, Co, Ni), wherein X-ray powder diffraction, transmission electron microscopy imaging, and electron diffraction patterns are analyzed to reveal the presence of ordering in the HELO, with imaging and diffraction simulation employed to compare experimental results to atomic modeling. Finally, without rigorous characterization at the atomic scale, important features such as defect ordering can be easily overlooked and therefore remain unconsidered when interpreting experimental results.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A semiempirical transparency model for dual energy cargo radiography applications

Cargo containers passing through ports are scanned by non-intrusive inspection systems to search for concealed illicit materials. By using two photon beams with different energy spectra, dual energy inspection systems are sensitive to both the area density and the atomic number of cargo contents. Most literature on the subject assumes a simple exponential attenuation model for photon intensity in which only free streaming photons are detected. However, this approximation neglects second order effects such as scattering, leading to a biased model and thus incorrect material predictions. This work studies the accuracy of the free streaming model by comparing it to simulation outputs, finding that the model shows poor atomic number reconstruction accuracy at high- Z and suffers significantly if the source energy spectra and detector response function are not known exactly. To address these challenges, this work introduces a semiempirical transparency model which modifies the free streaming model by rescaling different components of the mass attenuation coefficient, allowing the model to capture secondary effects ignored by the free streaming model. The semiempirical model displays improvement agreement with simulated results at high- Z and shows excellent extrapolation to materials and thicknesses which were not included during the calibration step. Furthermore, this work demonstrates that the semiempirical model yields accurate atomic number predictions even when the source spectra and detector response are not known exactly. In conclusion, using the semiempirical model, manufacturers can perform a simple calibration to enable more precise Z reconstruction capabilities, which has the potential to significantly improve the performance of existing dual energy radiographic systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1984

A low Earth orbit molecular beam space simulation facility

A brief synopsis of the low Earth orbit (LEO) satellite environment is presented including neutral and ionic species. Two ground based atomic and molecular beam instruments are described which are capable of simulating the interaction of spacecraft surfaces with the LEO environment and detecting the results of these interactions. The first detects mass spectrometrically low level fluxes of reactively and nonreactively surface scattered species as a function of scattering angle and velocity while the second ultrahigh velocity (UHV) molecular beam, laser induced fluorescence apparatus is capable of measuring chemiluminescence produced by either gas phase or gas-surface interactions. A number of proposed experiments are described.

Cross, J. B.↗
DOE OSTI2022

Investigation of the Structure of Atomically Dispersed NiN x Sites in Ni and N-Doped Carbon Electrocatalysts by 61 Ni Mössbauer Spectroscopy and Simulations

Ni and nitrogen-doped carbons are selective catalysts for CO 2 reduction to CO (CO 2 R), but the hypothesized NiNx active sites are challenging to probe with traditional characterization methods. Here, we synthesize 61 Ni-enriched model catalysts, termed 61 NiPACN, in order to apply 61 Ni Mössbauer spectroscopy using synchrotron radiation ( 61 Ni-SR-MS) to characterize the structure of these atomically dispersed NiNx sites. First, we demonstrate that the CO 2 R results and standard characterization techniques (SEM, PXRD, XPS, XANES, EXAFS) point to the existence of dispersed Ni active sites. Then, 61 Ni-SR-MS reveal significant internal magnetic fields of ~5.4 T, which is characteristic of paramagnetic, high-spin Ni 2+ , in the 61NiPACN samples. Finally, theoretical calculations for a variety of Ni-N x moieties confirm that high-spin Ni 2+ is stable in non-planar, tetrahedrally distorted geometries, which results in calculated isotropic hyperfine coupling that is consistent with 61 Ni-SR-MS measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Studies of the Chemistry of the Nightside Ionosphere of Venus

During the tenure of this grant, we have been looking into the chemistry of the nightside ionosphere of Venus with a view toward elucidating the relative roles of electron precipitation and plasma transport as sources of the nightside ionosphere. Secondary goals have included determining the densities of minor species on the nightside, and verifying the relative normalization of the Pioneer Venus orbiter ion mass spectrometer (OIMS) and orbiter neutral mass spectrometer (ONMS) in the photochemical equilibrium region. Our studies have involved a combination of numerical modeling and analysis of the Pioneer Venus UADS data base, specifically data from the OIMS, ONMS and electron temperature probe (OETP). We have set up a one-dimensional model of the Venus nightside ionosphere, in which downward fluxes of atomic ions are introduced at the upper boundary to simulate transport of ions from the dayside. Our model shows that the densities of mass-28 ions (CO+ + N+) resulting from an influx of atomic ions from the dayside are quite small, due to the high ionization potentials of CO and N2 that make chemical production difficult.

Fox, J.L.↗
NASA NTRS2016

Parallel Grand Canonical Monte Carlo (ParaGrandMC) Simulation Code

This report provides an overview of the Parallel Grand Canonical Monte Carlo (ParaGrandMC) simulation code. This is a highly scalable parallel FORTRAN code for simulating the thermodynamic evolution of metal alloy systems at the atomic level, and predicting the thermodynamic state, phase diagram, chemical composition and mechanical properties. The code is designed to simulate multi-component alloy systems, predict solid-state phase transformations such as austenite-martensite transformations, precipitate formation, recrystallization, capillary effects at interfaces, surface absorption, etc., which can aid the design of novel metallic alloys. While the software is mainly tailored for modeling metal alloys, it can also be used for other types of solid-state systems, and to some degree for liquid or gaseous systems, including multiphase systems forming solid-liquid-gas interfaces.

Vesselin I Yamakov↗
DOE OSTI2022

ORNL_AISD_NiNb

This dataset describes the nickel-niobium solid solution binary alloy, where the two constituent elements nickel (Ni) and niobium (Nb) are randomly placed on an underlying crystal lattice. This dataset for nickel-niobium (Ni-Nb) alloys available includes the formation energy and bulk modulus for each crystal structure. Each atomic sample has a disordered phase which is obtained starting from an initial regular crystal structure of type body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal compact packed (HCP). The geometry optimization ensures that all the alloy samples reached the equilibrium with negative formation energy. We perform geometry optimizations using the LAMMPS simulation package [1], a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. We utilized the embedded atom model (EAM) potential for Ni and Nb developed in a previous study [2]. The potential could describe behaviors of the liquid and solid phases of Ni-Nb alloy. The structural factors and angular distributions of three atoms are well-matched with X-ray and ab initio-based molecular dynamics data. We prepared the three different crystals with different initial lattice parameters (3.52 Ã… for FCC, 3.32 Ã… for BCC, and 3.5 Ã… for HCP). We performed energy minimization in two steps. Firstly, we minimized the structures with an isotropic unit cell to minimize the side effects from our arbitrary lattice parameters for all other compositions. Then, we applied geometry optimization with a triclinic (non-orthogonal) unit cell to fully minimize the stress components to calculate the elastic constants. In this procedure, we chose 10,000 as the maximum number of allowable steps aimed at obtaining fully relaxed atomic geometries. The dataset consists of three sets of crystal structures. The first set contains 46,086 irregular crystal structures, each of them with 54 atoms, obtained through optimization starting from a regular BCC crystal structure. The second set contains 24,543 irregular crystal structures, each of them with 32 atoms, obtained through optimization starting from a regular FCC crystal structure. The third set contains 39,303 irregular crystal structures, each of them with 48 atoms, obtained through optimization starting from a regular HCP crystal structure. The atomic configurations within each set span the possible compositional range. The three sets have been unified in a global dataset, which is extremely heterogeneous in terms of crystal structures, lattice volumes, and atomic configurations. Organization of files inside the dataset: the dataset contains three subdirectories called • BCC_opt • FCC_opt • HCP_opt based on the type of initial regular structure used to start the geometry optimization. Inside each of these folders, every atomic structure is identified by a string “A_B_Câ€, where A denotes the number of Nb in the system, B denotes index of structure with a given Nb number, and C denotes the total number of structures generated with a given Nb number. For each optimized crystal structure identified by the unique string of characters “A_B_Câ€, three files are provided: • A_B_C_opt.xyz: The optimized geometries in xyz format • A_B_C_opt.cfg: The optimized geometries in cfg format. It includes cell information and atomic energy, and forces calculated from LAMMPS. • A_B_C.elastic: Raw data of 21 elastic constants from LAMMPS output. • A_B_C.bulk: Calculated upper and lower bounds of bulk modulus and averaged one based on Voigt-Reuss-Hill approach from *.elastic. References: [1] A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comp. Phys. Comm., 271:108171, 2022. [2] Y Zhang, R Ashcraft, MI Mendelev, CZ Wang, and KF Kelton. Experimental and molecular dynamics simulation study of structure of liquid and amorphous ni62nb38 alloy. The Journal of chemical physics, 145(20):204505, 2016.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Density Functional Tight-Binding Simulations Reveal the Presence of Surface Defects on the Quartz (101)–Water Interface

Understanding the structure and reactivity of quartz–water interfaces is critical for numerous applications in the geological, environmental, and biological sciences. However, disagreements on the atomic-level structure of the interfaces between experiments and simulations are hampering our ability to predict the surface reactivity. Here, we used density functional tight-binding (DFTB)-based molecular dynamics to simulate a series of quartz (101) surfaces having different types and densities of surface defects in water and compared them with the structures determined by X-ray reflectivity measurements. The DFTB simulations are able to reproduce previous classical and quantum mechanical predictions of the pristine quartz (101)–water interface that disagree with experimental observations. To remedy this situation, a set of defective quartz surfaces having various surface silicon (Si) vacancies were built as indicated by recent experimental studies. We found that the rotation of surface [SiO 4 ] tetrahedra near Si vacancies can lead to outward displacements of Si atoms similar to those observed in the experiments. The presence of additional surface Si vacancies caused inward relaxations of terminal oxygens through the formation of hydrogen bonds. Finally, the overall results indicate that the quartz (101)–water interface may include a mixture of geminal (≡Si–(OH) 2 )- and vicinal (≡Si–OH)-type silanol groups together with the presence of surface Si vacancies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Temperature-Dependent Properties of Molten Li 2 BeF 4 Salt Using Ab Initio Molecular Dynamics

Molten lithium tetrafluoroberyllate (Li 2 BeF 4 ) salt, also known as FLiBe, with a 2:1 mixture of LiF and BeF 2 is being proposed as a coolant and solvent in advanced nuclear reactor designs, such as the molten salt reactor or the fluoride salt cooled high-temperature reactor. We present the results on the structure and properties of FLiBe over a wide range of temperatures, 0–2000 K, from high-throughput ab initio molecular dynamics simulation using a supercell model of 504 atoms. The variations in the local structures of solid and liquid FLiBe with temperature are discussed in terms of a pair distribution function, coordination number, and bond angle distribution. The temperature-dependent electronic structure and optical and mechanical properties of FLiBe are calculated. The optical and mechanical property results are reported for the first time. The results above and below the melting temperature (~732 K) are compared with the experimental data and with data for crystalline FLiBe. The electronic structure and interatomic bonding results are discussed in correlation with the mechanical strength. A novel concept of total bond order density (TBOD), an important quantum mechanical parameter, is used to characterize the internal cohesion and strength in the simulated models. The results show a variation in the rate of change in properties in solid and liquid phases with anomalous behavior across the melting region. The observed trend is the decrease in mechanical strength, band gap, and TBOD in a nonlinear fashion as a function of temperature. The refractive index shows a surprising minimum at 850 K, among the tested temperatures, which lies above the melting point. These findings provide a new platform to understand the interplay between the temperature-dependent structures and properties of FLiBe salt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

Studies of the chemistry of the nightside ionosphere of Venus

A combination of numerical modeling and analysis of the Pioneer Venus UADS data base is studied, specifically data from the orbiter ion mass spectrometer (OIMS), orbiter neutral mass spectrometer (ONMS), and orbiter electron temperature probe (OETP). A one dimensional model of the Venus nightside ionosphere was set up in which downward fluxes of atomic ions are introduced at the upper boundary to simulate transport of ions from the dayside. The model shows that the densities of mass-28 ions, CO(+) + N(2+), resulting from an influx of atomic ions from the dayside are quite small, due to the high ionization potentials of CO and N2 that make chemical production difficult. A look at the data reveals that the actual densities of mass-28 ions are quite variable, from values near 10 to more than 10(exp 4) cm(exp -3). The excess mass-28 ions are assumed to be produced by electron precipitation and that the presence of high densities of mass-28 ions is a signature of auroral precipitation. A discussion of the atomic oxygen green line in the nightglow of Venus, which is produced mainly by dissociative recombination of O(2+), is presented. Original calculations of production rates of excited states for models based on Pioneer Venus data are also presented.

Fox, J. L.↗
DOE OSTI2023

Sensitivity of Dislocation-GB interactions to simulation setups in atomistic models

Dislocation-grain boundary (GB) interactions play an integral role in strengthening of crystalline materials, and are dependent on external loading conditions and atomic arrangements at the grain boundary. While molecular dynamics (MD) simulations can provide critical insights into relationships between these parameters and the exact interaction, the outcomes are sensitive to the computational setup. Here, in this work, we explore the effect of computational setup (system size, GB orientation and boundary conditions) on stress-controlled dislocation-grain boundary (DGB) reactions using MD simulations for a well-studied copper symmetric $\langle$1 1 2$\rangle$ tilt boundary. The study demonstrates that the DGB reactions (pinning, absorption, transmission, etc.) are sensitive to the system size and the orientation of the GB to the applied stress. Additionally, the current work shows that there is a critical system size for the dislocation-grain boundary reaction stresses to converge, one which was found to be much larger than the setups in comparable MD studies. This was attributed to the specific stress states and the influence of surfaces, fixed or free, as these computational setups are modified. Finally, a stress-controlled setup with minimal model artifacts is examined, and the effect of coupled Schmid and non-Schmid stress components on the dislocation-GB reactions are discussed.

36 MATERIALS SCIENCE↗
NASA NTRS2011

Numerical Prediction of Radiation Measurements Taken in the X2 Facility for Mars and Titan Gas Mixtures

Thermochemical relaxation behind a normal shock in Mars and Titan gas mixtures is simulated using a CFD solver, DPLR, for a hemisphere of 1 m radius; the thermochemical relaxation along the stagnation streamline is considered equivalent to the flow behind a normal shock. Flow simulations are performed for a Titan gas mixture (98% N2, 2% CH4 by volume) for shock speeds of 5.7 and 7.6 km/s and pressures ranging from 20 to 1000 Pa, and a Mars gas mixture (96% CO2, and 4% N2 by volume) for a shock speed of 8.6 km/s and freestream pressure of 13 Pa. For each case, the temperatures and number densities of chemical species obtained from the CFD flow predictions are used as an input to a line-by-line radiation code, NEQAIR. The NEQAIR code is then used to compute the spatial distribution of volumetric radiance starting from the shock front to the point where thermochemical equilibrium is nominally established. Computations of volumetric spectral radiance assume Boltzmann distributions over radiatively linked electronic states of atoms and molecules. The results of these simulations are compared against experimental data acquired in the X2 facility at the University of Queensland, Australia. The experimental measurements were taken over a spectral range of 310-450 nm where the dominant contributor to radiation is the CN violet band system. In almost all cases, the present approach of computing the spatial variation of post-shock volumetric radiance by applying NEQAIR along a stagnation line computed using a high-fidelity flow solver with good spatial resolution of the relaxation zone is shown to replicate trends in measured relaxation of radiance for both Mars and Titan gas mixtures.

Palmer, Grant↗