Search NASA⌕ Search

SEARCH · Search NASA

Results for “light scattering”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Ultra-High-Sensitivity Aerosol Spectrometer (UHSAS) Instrument Handbook

The Ultra-High-Sensitivity Aerosol Spectrometer (UHSAS) (Figure 1) is an optical-scattering, laser-based aerosol particle spectrometer system for sizing particles in the 60 to 1000 nanometer (nm) range [1–3]. The instrument counts particles in up to 100 user-specified sizing bins. The instrument’s laser illuminates particles, which scatter light. The system captures the peak light signals that are generated. These signals are used for particle sizing, since the amount of light scattered correlates strongly with particle size.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A Novel Dew Point Meter: Application to the Measurement of the Sulfuric Acid Dew Point for Combustion Flue Gas

Accurate knowledge of acid dew point is essential for industrial and applied combustion applications. Sulfur in the fuel or raw materials is converted to sulfur dioxide (SO2) during combustion, and a portion of the SO2 is oxidized to sulfur trioxide (SO3). The SO3 will react to form H2SO4 vapor when in the presence of water vapor. Even with just trace levels of H2SO4 vapor in the gas phase (1-10 ppm), the dew point can reach 100°C and higher. To avoid acid condensation and the resulting corrosion on heat recovery equipment, plant engineers must ensure that surface temperatures are above the acid dew point, but this decreases the efficiency of thermal energy recovery. Thus, there is a trade-off between minimizing equipment corrosion and maximizing thermal energy recovery, and the acid dew point is a key parameter for this optimization. Commercially available acid dew point meters use electric conductivity sensors. These sensors are known to greatly underestimate the dew point due to their low sensitivity. In addition, no validation testing has been reported for these units and they are often expensive. In this work, we analyze the theory of the sulfuric acid condensation and develop a novel dew point meter based on this analysis. The meter consists of a novel optical instrument that is designed to monitor the slightest appearance of condensation on a hydrophobic window surface as the surface temperature of the window is slowly decreased. In this way, an accurate measurement of the dew point is obtained under a wide range of concentrations. The basis of the instrument is that a collimated beam from a diode laser will generate forward scattered light when the beam encounters surface condensate, and a sophisticated array detector is used to sensitively monitor the onset of light scattering. The measurement procedures are established to rapidly find the acid dew point, while minimizing error. Further, to calibrate the dew point meter we developed a calibration system based on a liquid bubbler that can generate a stable gas flow with a known sulfuric acid dew point. Test results show that the dew point meter can accurately measure acid dew point over a wide range. For H2SO4 vapor concentrations as low as 6 ppm the acid dew point is measured with an error of only ~1°C. To demonstrate the versatility of this instrument, the dew point meter was adapted for use with a high-pressure flow cell to allow for measurements of the dew point of flue gas from pressurized oxy-fuel combustion in a 100 kWth pressurized reactor.

Cheng, Mao↗
DOE OSTI2023

A Novel Dew Point Meter: Application to the Measurement of the Sulfuric Acid Dew Point for Combustion Flue Gas

Accurate knowledge of acid dew point is essential for industrial and applied combustion. Sulfur in the fuel or raw materials is converted to sulfur dioxide (SO2) during combustion, and a portion of the SO2 is oxidized to sulfur trioxide (SO3). The SO3 will react to form H2SO4 vapor when in the presence of water vapor. Even with just trace levels of H2SO4 vapor in the gas phase (1-10 ppm), the dew point can reach 100°C and higher. To avoid acid condensation and the resulting corrosion on heat recovery equipment, plant engineers must ensure that surface temperatures are above the acid dew point, but this decreases the efficiency of the thermal energy recovery. Thus, there is a trade-off between minimizing equipment corrosion and maximizing thermal energy recovery efficiency, and the acid dew point is a key parameter for this optimization. In this work, we analyze and discuss the theory of the sulfuric acid condensation process and develop a novel dew point meter based on this analysis. The meter consists of a novel optical instrument that is designed to monitor the slightest appearance of condensation on a hydrophobic window surface, and the surface temperature of the window is slowly decreased until condensation is first observed, yielding an accurate measurement of the dew point. The basis of the instrument is that a collimated beam from a diode laser generates scattered light when encountering surface condensate, and a sophisticated array detector is used to sensitively monitor the light scattering. The measurement procedures are established to rapidly find the acid dew point, while minimizing error. Further, we propose a calibration system based on a liquid bubbler, which can generate a stable gas flow with known sulfuric acid dew point, to test the dew point meter. Test results show that the dew point meter can accurately measure the acid dew point over a wide range.

Cheng, Mao↗
DOE OSTI2023

Using light and X-ray scattering to untangle complex neuronal orientations and validate diffusion MRI

Disentangling human brain connectivity requires an accurate description of nerve fiber trajectories, unveiled via detailed mapping of axonal orientations. However, this is challenging because axons can cross one another on a micrometer scale. Diffusion magnetic resonance imaging (dMRI) can be used to infer axonal connectivity because it is sensitive to axonal alignment, but it has limited spatial resolution and specificity. Scattered light imaging (SLI) and small-angle X-ray scattering (SAXS) reveal axonal orientations with microscopic resolution and high specificity, respectively. Here, we apply both scattering techniques on the same samples and cross-validate them, laying the groundwork for ground-truth axonal orientation imaging and validating dMRI. We evaluate brain regions that include unidirectional and crossing fibers in human and vervet monkey brain sections. SLI and SAXS quantitatively agree regarding in-plane fiber orientations including crossings, while dMRI agrees in the majority of voxels with small discrepancies. We further use SAXS and dMRI to confirm theoretical predictions regarding SLI determination of through-plane fiber orientations. Scattered light and X-ray imaging can provide quantitative micrometer 3D fiber orientations with high resolution and specificity, facilitating detailed investigations of complex fiber architecture in the animal and human brain.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Unraveling the Effects of Cobalt on Crystal Growth and Solution Behavior of Nb 6 P 2 W 12 -based Dimeric Clusters

We report the synthesis, characterization, and solution self-assembly of plenary Nb 6 P 2 W 12 -based transition-metal substituted polyoxometalate, which is obtained by simply adding transition metals (Co 2+ ) into aqueous solution containing cluster [(NbO 2 ) 6 P 2 W 12 O 56 ] 12- , which is obtained by an in situ synthetic method. The incorporation of Co 2+ ions significantly affects the crystal structure, resulting in the formation of a 1D chain-like crystal and the first example of a niobotungstate-based cobalt derivative cluster. The behavior and stability of this cluster in solution are confirmed by time-resolved static light scattering, dynamic light scattering, small-angle X-ray scattering, and electrospray mass spectrometry studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Nephelometer Instrument Handbook

The Integrating Nephelometer (Figure 1) is an instrument that measures aerosol light scattering. It measures aerosol optical scattering properties by detecting (with a wide angular integration – from 7 to 170°) the light scattered by the aerosol and subtracting the light scattered by the carrier gas, the instrument walls and the background noise in the detector (zeroing). Zeroing is typically performed for 5 minutes every day at midnight UTC. The scattered light is split into red (700 nm), green (550 nm), and blue (450 nm) wavelengths and captured by three photomultiplier tubes. The instrument can measure total scatter as well as backscatter only (from 90 to 170°) (Heintzenberg and Charlson 1996; Anderson et al. 1996; Anderson and Ogren 1998; TSI 3563 2015) At ARM (Atmospheric Radiation Measurement), two identical Nephelometers are usually run in series with a sample relative humidity (RH) conditioner between them. This is possible because Nephelometer sampling is non-destructive and the sample can be passed on to another instrument. The sample RH conditioner scans through multiple RH values in cycles, treating the sample. This kind of setup allows to study how aerosol particles’ light scattering properties are affected by humidification (Anderson et al. 1996). For historical reasons, the two Nephelometers in this setup are labeled “wet” and “dry”, with the “dry” Nephelometer usually being the one before the conditioner and sampling ambient air (the names are switched for the MAOS measurement site due to the high RH of the ambient air).

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Simultaneous measurement of the exchange parameter and saturation magnetization using propagating spin waves

The exchange interaction in ferromagnetic ultra thin films is a critical parameter in magnetization-based storage and logic devices, yet the accurate measurement of it remains a challenge. While a variety of approaches are currently used to determine the exchange parameter, each has its limitations, and good agreement among them has not been achieved. To date, neutron scattering, magnetometry, Brillouin light scattering, spin-torque ferromagnetic resonance spectroscopy, and Kerr microscopy have all been used to determine the exchange parameter. Here, we present a method that exploits the wavevector selectivity of Brillouin light scattering to measure the spin wave dispersion in both the backward volume and Damon–Eshbach orientations. The exchange, saturation magnetization, and magnetic thickness are then determined by a simultaneous fit of both dispersion branches with general spin wave theory without any prior knowledge of the thickness of a magnetic “dead layer.” In this study, we demonstrate the strength of this technique for ultrathin metallic films, typical of those commonly used in industrial applications for magnetic random-access memory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Nanomaterial-Engineered Surfaces for Decontamination of Water Resources

Aggregation-dependent shifts in plasmon frequency (colorimetric sensor); • Local refractive index-dependent shifts in plasmon frequency; • Inelastic (surface-enhanced Raman) light scattering; • Elastic (Rayleigh) light scattering CONCLUSIONS Generate unique classes of nanoscale materials for environmental stewardship applications o Characterization of nanomaterials provides understanding of structural properties for sorption of contaminants o Surface charge influences interaction between nanomaterial and contaminant o Surface charge can be modified to allow for more contaminant sorption • Demonstrate innovative nanomaterial science and technology solutions that meet our environmental stewardship needs: • Detect contaminants • Sequester contaminants

Murph, Simona E. [Savannah River National Laborato↗
DOE OSTI2020

Synthesis and Characterization of Pd-based Nanomaterials

Bimetallic nanoparticles (BNPs) consist of two different types of metals or alloys that are bonded together. Unique properties such as optical, electronic, thermal, and catalytic effects differ for each type of BNP. Important BNPs range from Au-Pd, Ag- Pt, Au-Pt, and Ag-Ni. Pd bimetallic nanoparticles are of interest due to their many applications such as catalysis and sensing. Bimetallic catalysts have increase reaction rates and have improved catalyst stability through the geometry and ligand distribution. Pd nanoparticles are considered to be a strong catalyst due to their high activity at low temperatures and high tolerance to moisture. The catalytic properties of bimetallic nanoparticles depend on the structural properties such as size and shape. Core-shell, hollow structure, and multi-shell alloy are three possible structures nanoparticles can form as bimetallic catalysts. BNPs can be synthesized through different methods to control the size, shape, and structure. To obtain different morphologies, a variety of methods can be performed. Different methods can range from the usage of the glancing angle deposition (GLAD) to the galvanic replacement reaction, but the methods all depend on the properties of the metals. The galvanic displacement reaction was the method used to obtain Pd-based nanoparticles. This reaction is best know for obtaining hollow shaped NPs. To determine what redox process was preformed, the activity series of metals was used. From the activity series of metals, silver (Ag) was selected to preform Pd-based nanoparticles. Objectives: Synthesize Ag nanoparticles and Ag-Pd nanoparticles to understand the morphology. Characterize the synthesized nanoparticles using scanning electron microscopy (SEM), phase analysis light scattering (PALS), dynamic light scattering (DLS), energy dispersive X-ray spectroscopy (EDS), and UV-Vis spectroscopy. Results: In the UV-Vis spectrum, the Ag-Pd bimetallic NP's plasmon band decreased as the volume of palladium increased. The surface charge increases as the concentration of palladium increases. The Pd{sup 2+} ions interact with the sodium citrate surface, and decrease the negative charge. Conclusion: Ag-Pd nanoparticles were successfully created and stabilized with sodium citrate. The addition of Pd decreased the prominent plasmon band of the Ag nanoparticles. The SEM analysis showed that Ag nanoparticles had a well-defined structure, while the Ag-Pd nanoparticles showed hollow and rough structure. The EDX analysis confirmed the presence of silver and palladium. This material can be used in many industrial and research fields such as organic synthesis, fuel cells, and environmental sensing and remediation.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Debris Disk Results from the Gemini Planet Imager Exoplanet Survey's Polarimetric Imaging Campaign

We report the results of a ∼4 yr direct imaging survey of 104 stars to resolve and characterize circumstellar debris disks in scattered light as part of the Gemini Planet Imager (GPI) Exoplanet Survey. We targeted nearby (≲150 pc), young (≲500 Myr) stars with high infrared (IR) excesses (L {sub IR}/L {sub ⋆} > 10{sup −5}), including 38 with previously resolved disks. Observations were made using the GPI high-contrast integral field spectrograph in H-band (1.6 μm) coronagraphic polarimetry mode to measure both polarized and total intensities. We resolved 26 debris disks and 3 protoplanetary/transitional disks. Seven debris disks were resolved in scattered light for the first time, including newly presented HD 117214 and HD 156623, and we quantified basic morphologies of five of them using radiative transfer models. All of our detected debris disks except HD 156623 have dust-poor inner holes, and their scattered-light radii are generally larger than corresponding radii measured from resolved thermal emission and those inferred from spectral energy distributions. To assess sensitivity, we report contrasts and consider causes of nondetections. Detections were strongly correlated with high IR excess and high inclination, although polarimetry outperformed total intensity angular differential imaging for detecting low-inclination disks (≲70°). Based on postsurvey statistics, we improved upon our presurvey target prioritization metric predicting polarimetric disk detectability. We also examined scattered-light disks in the contexts of gas, far-IR, and millimeter detections. Comparing H-band and ALMA fluxes for two disks revealed tentative evidence for differing grain properties. Finally, we found no preference for debris disks to be detected in scattered light if wide-separation substellar companions were present.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

DENSECL: Haze Mitigation Using Dense Blocks and Contrastive Loss Regularization

Haze, which occurs as a result of the scattering of light in the atmosphere by small particles, diminishes the visibility of scene objects, inflicting important image applications such as object detection. To address the problem, this paper introduces a new physics-based end-to-end deep learning approach to haze mitigation in outdoor scenes, including those in airborne images. The proposed model named DenseCL is designed with dense blocks and adopts a contrastive loss function as an additional regularization. The model also maintains the cycle consistency by remapping the dehazed outputs into a hazy image using the physics-based light scattering function. DenseCL has been trained with publicly available outdoor images and demonstrates outstanding performance on outdoor, indoor, and remotely sensed nonhomogeneous haze satellite images.

Mitra, Somosmita↗
DOE OSTI2025

Investigating the quaternary structure of a homomultimeric catechol 1,2-dioxygenase: An integrative structural biology study

The structural analysis of catechol 1,2 dioxygenase from Stutzerimonas frequens GOM2, SfC12DO, was conducted using various structural techniques. SEC-SAXS experiments revealed that SfC12DO, after lyophilization and reconstitution processes, can form multiple enzymatically active oligomers, including dimers, tetramers, and octamers. These findings differ from previous studies, which reported active dimers in homologous counterparts with available crystallographic structures, or trimers observed exclusively in solution for SfC12DO and its homologous isoA C12DO from Acinetobacter radioresistens under low ionic strength conditions. In some cases, tetramers were also reported, such as for the Rodococcus erythropolis C12DO. The combined results of Small-Angle X-ray Scattering, Dynamic Light Scattering, and Transmission Electron Microscopy experiments provided additional insights into these active oligomers’ shape and molecular organization in an aqueous solution. These results highlight the oligomeric structural plasticity of SfC12DO, proving that it can exist in different oligomeric forms depending on the physicochemical characteristics of the solutions in which the experiments were performed. Remarkably, regardless of its oligomeric state, SfC12DO maintains its enzymatic activity even after prior lyophilization. All these characteristics make SfC12DO a putative candidate for bioremediation applications in polluted soils or waters.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Large- N c constraints for elastic dark-matter–light-nucleus scattering in pionless effective field theory

Recent proposals for the use of light nuclei as dark-matter direct detection targets necessitate a strong theoretical understanding of the nuclear physics involved. We perform relevant calculations for dark-matter–light-nucleus scattering in a combined pionless effective field theory and large-N c expansion, where N c is the number of quark colors. Here, we include a general set of one-nucleon currents that have been used in other effective theories, as well as novel two-nucleon contact currents. First, we obtain constraints for the relative sizes of the dark-matter couplings to the one- and two-nucleon currents through the large-N c expansion. Then, we use these constraints to make predictions for the relative sizes of spin-dependent and spin-independent cross sections for dark-matter scattering off of a nucleon, a deuteron, a triton, and helium-3.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Understanding the stability of a plastic‐degrading Rieske iron oxidoreductase system

Abstract Rieske oxygenases (ROs) are a diverse metalloenzyme class with growing potential in bioconversion and synthetic applications. We postulated that ROs are nonetheless underutilized because they are unstable. Terephthalate dioxygenase (TPA DO PDB ID 7Q05 ) is a structurally characterized heterohexameric α 3 β 3 RO that, with its cognate reductase (TPA RED ), catalyzes the first intracellular step of bacterial polyethylene terephthalate plastic bioconversion. Here, we showed that the heterologously expressed TPA DO /TPA RED system exhibits only ~300 total turnovers at its optimal pH and temperature. We investigated the thermal stability of the system and the unfolding pathway of TPA DO through a combination of biochemical and biophysical approaches. The system's activity is thermally limited by a melting temperature ( T m ) of 39.9°C for the monomeric TPA RED , while the independent T m of TPA DO is 50.8°C. Differential scanning calorimetry revealed a two‐step thermal decomposition pathway for TPA DO with T m values of 47.6 and 58.0°C (Δ H = 210 and 509 kcal mol −1 , respectively) for each step. Temperature‐dependent small‐angle x‐ray scattering and dynamic light scattering both detected heat‐induced dissociation of TPA DO subunits at 53.8°C, followed by higher‐temperature loss of tertiary structure that coincided with protein aggregation. The computed enthalpies of dissociation for the monomer interfaces were most congruent with a decomposition pathway initiated by β‐β interface dissociation, a pattern predicted to be widespread in ROs. As a strategy for enhancing TPA DO stability, we propose prioritizing the re‐engineering of the β subunit interfaces, with subsequent targeted improvements of the subunits.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Aqueous Self‐Assembly of Cylindrical and Tapered Bottlebrush Block Copolymers

The self‐assembly of amphiphilic bottlebrush block copolymers (BCPs), featuring backbones densely grafted with two types of side chains, is less well understood compared to linear BCPs. In particular, the solution self‐assembly of tapered bottlebrush BCPs—cone‐shaped BCPs with hydrophilic or hydrophobic tips—remains unexplored. This study investigates eight tapered and four cylindrical bottlebrush BCPs with varied ratios of hydrophobic polystyrene (PS) and hydrophilic poly(acrylic acid) (PAA) side chains, synthesized via sequential addition of macromonomers using ring‐opening metathesis polymerization (SAM‐ROMP). Self‐assembled nanostructures formed in water were analyzed using cryogenic transmission electron microscopy, small‐angle neutron scattering, and dynamic light scattering. Most BCPs generated multiple nanostructures with surface protrusions, including spherical micelles, cylindrical micelles, and vesicles, alongside transitional forms like ellipsoids and semi‐vesicles. Coarse‐grained molecular dynamics simulations supported the experimental findings, which revealed two distinct self‐assembly pathways. The first involved micelle fusion, producing elliptical and cylindrical aggregates, sometimes forming Y‐junctions. The second pathway featured micelle maturation into semivesicles, which developed into vesicles or large compound vesicles. This work provides the first experimental evidence of vesicle formation via semivesicles in bottlebrush BCPs and demonstrates the significant influence of cone directionality on self‐assembly behavior in these cone‐shaped polymeric amphiphiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Chlorophyllase from Arabidopsis thaliana Reveals an Emerging Model for Controlling Chlorophyll Hydrolysis

Chlorophyll (Chl) is one of Nature’s most complex pigments to biosynthesize and derivatize. This pigment is vital for survival and also paradoxically toxic if overproduced or released from a protective protein scaffold. Therefore, along with the mass production of Chl, organisms also invest in mechanisms to control its degradation and recycling. One important enzyme that is involved in these latter processes is chlorophyllase. This enzyme is employed by numerous photosynthetic organisms to hydrolyze the phytol tail of Chl. Although traditionally thought to catalyze the first step of Chl degradation, recent work suggests that chlorophyllase is instead employed during times of abiotic stress or conditions that produce reactive oxygen species. However, the molecular details regarding how chlorophyllases are regulated to function under such conditions remain enigmatic. Here, we investigate the Arabidopsis thaliana chlorophyllase isoform AtCLH2 using site-directed mutagenesis, mass spectrometry, dynamic light scattering, size-exclusion multiangle light scattering, and both steady-state enzyme kinetic and thermal stability measurements. Through these experiments, we show that AtCLH2 exists as a monomer in solution and contains two disulfide bonds. One disulfide bond putatively maps to the active site, whereas the other links two N-terminal Cys residues together. These disulfide bonds are cleaved by chemical or chemical and protein-based reductants, respectively, and are integral to maintaining the activity, stability, and substrate scope of the enzyme. This work suggests that Cys residue oxidation in chlorophyllases is an emerging regulatory strategy for controlling the hydrolysis of Chl pigments.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Single-crystal elasticity of (Al,Fe)-bearing bridgmanite up to 82 GPa

Abstract Thermoelastic properties of mantle candidate minerals are essential to our understanding of geophysical phenomena, geochemistry, and geodynamic evolutions of the silicate Earth. However, the lower-mantle mineralogy remains much debated due to the lack of single-crystal elastic moduli (Cij) and aggregate sound velocities of (Al,Fe)-bearing bridgmanite, the most abundant mineral of the planet, at the lower mantle pressure-temperature (P-T) conditions. Here we report single-crystal Cij of (Al,Fe)-bearing bridgmanite, Mg0.88Fe0.1Al0.14Si0.90O3 (Fe10-Al14-Bgm) with Fe3+/ΣFe = ~0.65, up to ~82 GPa using X-ray diffraction (XRD), Brillouin light scattering (BLS), and impulsive stimulated light scattering (ISLS) measurements in diamond-anvil cells (DACs). Two crystal platelets with orientations of (–0.50, 0.05, –0.86) and (0.65, –0.59, 0.48), that are sensitive to deriving all nine Cij, are used for compressional and shear wave velocity (νP and νS) measurements as a function of azimuthal angles over 200° at each experimental pressure. Our results show that all Cij of singe-crystal Fe10-Al14-Bgm increase monotonically with pressure with small uncertainties of 1–2% (±1σ), except C55 and C23, which have uncertainties of 3–4%. Using the third-order Eulerian finite-strain equations to model the elasticity data yields the aggregate adiabatic bulk and shear moduli and respective pressure derivatives at the reference pressure of 25 GPa: KS = 326 ± 4 GPa, µ = 211 ± 2 GPa, KS′ = 3.32 ± 0.04, and µ′ = 1.66 ± 0.02 GPa. The high-pressure aggregate νS and νP of Fe10-Al14-Bgm are 2.6–3.5% and 3.1–4.7% lower than those of MgSiO3 bridgmanite end-member, respectively. These data are used with literature reports on bridgmanite with different Fe and Al contents to quantitatively evaluate pressure and compositional effects on their elastic properties. Comparing with one-dimensional seismic profiles, our modeled velocity profiles of major lower-mantle mineral assemblages at relevant P-T suggest that the lower mantle could likely consist of about 89 vol% (Al,Fe)-bearing bridgmanite. After considering uncertainties, our best-fit model is still indistinguishable from pyrolitic or chondritic models.

Geochemistry & Geophysics↗