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

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At least 109 records · Page 6

Characterization data of an (AlFeNiTiVZr) 1-x Cr x multi-principal element alloy continuous composition spread library

The data provided in this article is related to the research article entitled “Phase stabilization and oxidation of a continuous composition spread multi-principal element (AlFeNiTiVZr) 1-x Cr x alloy”. This data article describes the high-throughput synthesis and characterization processes of an (AlFeNiTiVZr) 1-x Cr x alloy system. Continuous composition spread (CCS) thin-film libraries were synthesized by co-depositing an AlFeNiTiVZr metal alloy target and Cr target via magnetron sputtering. Post-processing was performed on the sample libraries with a vacuum anneal at 873 K and an air anneal at 873 K. Compositional data was determined via WDS in order to verify parameters provided by an in-house sputter model. Crystallographic data was captured via synchrotron diffraction and diffractograms were compared as a function of the change in Cr concentration. These measurements were taken in order to observe phase behavior after oxidation throughout the composition library. Furthermore, vibrational spectrographic data is provided of the oxidized library to show surface speciation along the composition gradient of the alloy system. The structural and oxidative behavior of the (AlFeNiTiVZr) 1-x Cr x alloy can be analysed using the data provided in this article. Additionally, this characterization dataset can be utilized in machine learning algorithms for determining important features and parameters for future hypothesis generation of functional multi-principal element alloys (MPEAs).

36 MATERIALS SCIENCE↗

Separation of K + and Bi 3+ displacements in a Pb-free, monoclinic piezoelectric at the morphotropic phase boundary

The best piezoelectric properties of any perovskite oxide known are found in the solid solution of the relaxor Pb (Mg 1/3 Nb 2/3 )O 3 and ferroelectric PbTiO 3 . Despite its impressive properties, this system has limited analogy. We present the compositional exploration of the Pb-free analogue (1-x)(K 1/2 Bi 1/2 )(Mg 1/3 Nb 2/3 )O 3 -x(K 1/2 Bi 1/2 )TiO 3 (KBMN-KBT). We locate the morphotropic phase boundary between x = 0.86 and 0.88 changing from Cm to Pm symmetry and the optimally performing composition at x = 0.88. We report a piezoelectric figure of merit (d 33 *) of 192 pm V —1 from strain measurements. Diffraction methods reveal disordered displacements of K + and Bi 3+ which persist from the KBMN endmember through multiple changes in symmetry. Rearrangement of the Bi 3+ displacements along the uncommon [011] c direction drives the physical response. Ferroelectric, dielectric, and piezoresponse force microscopy are used to study the progression of physical properties through the MPB and attribute the mechanism to a polarization rotation. Taking account for local, short-range, and average structural features yield a balanced perspective on the structure and properties of this system, isolating the driving force within this system to the Bi 3+ bonding configuration. This work yields a strong analogy to the Pb-based analogue, and provides strategies for further optimization.

36 MATERIALS SCIENCE↗

Cooling Mixed A-Site Halide Perovskites: Impact of Temperature on Optical and Structural Properties

The widespread utilization of perovskite-based photovoltaics requires probing both the structural and optical properties under extreme operating conditions to gain a holistic understanding of the material behavior under stressors. Here, in this study, we investigate the temperature-dependent behavior of mixed A-site cation lead triiodide perovskite thin films (85% methylammonium and 15% formamidinium) in the range from 300 to 20 K. Through a combination of optical and structural techniques, we find that the tetragonal-to-orthorhombic phase transition occurs at similar to 110 K for this perovskite composition, as indicated by the change in the diffraction pattern. With decreasing temperature, the quantum yield increases with a concurrent elongation of the carrier lifetimes, indicating suppression of nonradiative recombination pathways. Interestingly, in contrast to single A-site cation perovskites, an additional optical transition appears in the absorption spectrum when the phase transition is approached, which is also reflected in the emission spectrum. We propose that the splitting of the optical absorption and emission is due to local segregation of the mixed cation perovskite during the phase transition.

36 MATERIALS SCIENCE↗

Formation of a Secondary Phase in Thermally Evaporated MAPbI 3 and Its Effects on Solar Cell Performance

Thermal evaporation is a promising deposition technique to scale up perovskite solar cells (PSCs) to large areas, but the lack of understanding of the mechanisms that lead to high-quality evaporated methylammonium lead triiodide (MAPbI 3 ) films gives rise to devices with efficiencies lower than those obtained by spin coating. Here this work investigates the crystalline properties of MAPbI 3 deposited by the thermal coevaporation of PbI 2 and MAI, where the MAI evaporation rate is controlled by setting different temperatures for the MAI source and the PbI 2 deposition rate is controlled with a quartz crystal microbalance (QCM). Using grazing incident wide-angle X-ray scattering (GIWAXS) and X-ray diffraction (XRD), we identify the formation of a secondary orthorhombic phase (with a Pnma space group) that appears at MAI source temperatures below 155 °C. With synchrotron-based X-ray fluorescence (XRF) microscopy, we show that the changes in crystalline phases are not necessarily due to changes in stoichiometry. The films show a stochiometric composition when the MAI source is heated between 140 to 155 °C, and the samples become slightly MAI rich at 165 °C. Increasing the MAI temperature beyond 165 °C introduces an excess of MAI in the film, which promotes the formation of films with low crystallinity that contain low-dimensional perovskites. When they are incorporated in solar cells, the films deposited at 165 °C result in the champion power conversion efficiency, although the presence of a small amount of low-dimensional perovskite may lead to a lower open-circuit voltage. We hypothesize that the formation of secondary phases in evaporated films limits the performance of PSCs and that their formation can be suppressed by controlling the MAI source temperature, bringing the film toward a phase-pure tetragonal structure. Control of the phases during perovskite evaporation is therefore crucial to obtain high-performance solar cells.

36 MATERIALS SCIENCE↗

Salt Hydrate Eutectic Thermal Energy Storage for Building Thermal Regulation (Final Technical Report)

Thermal energy storage is anticipated to play an important role in developing the power grid of the future - a power grid that meets increasing demands of users, is resistant to disruptions, but also allows for greater penetration of renewable resources. Specifically, thermal energy storage materials can be integrated into HVAC systems and building envelopes, where they can be used to shift power demands for building climate control from periods of peak demand to periods of low demand. Phase change materials (PCMs) are compelling as low-cost, high energy density thermal energy storage materials for building thermal management. However, there is a lack of high performance low-cost PCMs within the specific temperature ranges which would most effectively allow for power load shifting. Inorganic salt hydrates represent a promising class of PCMs, but their inherent limitations cause them to be currently unavailable for reliable building applications. The overarching goals of this research effort are to: 1) Discover low-cost, high volumetric density salt hydrate eutectic PCMs to store low-quality heat (10 to 40 °C); 2) Introduce a high thermal conductivity matrix to reduce the time constant for energy storage to ~0.1 to 1 hr, incorporate nucleation catalysts to decrease undercooling, and utilize microencapsulation and shape stabilization approaches, minimizing moisture loss/gain, mitigating phase separation, and maintaining stable melting behavior over the lifetime of the compounds; 3) Evaluate the impact these systems have on peak load shifting, and the potential for overall energy savings under different climatic scenarios and building configurations. These goals will be achieved by an integrated research program consisting of six cohesive research subtasks: 1) Materials discovery of eutectic salt hydrate PCMs by using computationally predicted thermodynamic equilibria, coupled with high-throughput experimental validation, 2) Rapid experimental screening of nucleation catalysts identified through robust computational databases, 3) Embedding salt hydrate PCM into a low cost and scalable high conductivity matrix, 4) Microencapsulation of salt hydrate microspheres using hybrid inorganic-polymer microencapsulation approach, 5) Shape stabilization by thermoreversible salt hydrate salogels, and 6) Analysis of end-use using thermal simulations, and characterization of mock-up energy storage finished components.

25 ENERGY STORAGE↗

Complete miscibility of immiscible elements at the nanometre scale

Understanding the mixing behaviour of elements in a multielement material is important to control its structure and property. When the size of a multielement material is decreased to the nanoscale, the miscibility of elements in the nanomaterial often changes from its bulk counterpart. However, there is a lack of comprehensive and quantitative experimental insight into this process. Here, in this study, we explored how the miscibility of Au and Rh evolves in nanoparticles of sizes varying from 4 to 1 nm and composition changing from 15% Au to 85% Au. We found that the two immiscible elements exhibit a phase-separation-to-alloy transition in nanoparticles with decreased size and become completely miscible in sub-2 nm particles across the entire compositional range. Quantitative electron microscopy analysis and theoretical calculations were used to show that the observed immiscibility-to-miscibility transition is dictated by particle size, composition and possible surface adsorbates present under the synthesis conditions.

36 MATERIALS SCIENCE↗

Basin-Size Mapping: Prediction of Metastable Polymorph Synthesizability Across TaC–TaN Alloys

The sizes of the basins of attraction on the potential energy surface are helpful indicators in determining the experimental synthesizability of metastable phases. In principle, these basins can be controlled with changes in thermodynamic conditions such as composition, pressure, and surface energy. Herein, we use random structure sampling to computationally study how alloying smoothly perturbs basin of attraction sizes. The TaC 1-x N x pseudobinary is an ideal test system given the structural and polymorphic contrast of its parent compounds and their technological relevance as epitaxial substrates for Al 1-x Ga x N. While we find limited thermodynamic stability across all computationally observed phases, random structure sampling shows a significant composition region where the rocksalt basin dominates. As such, we predict the potential for the nonequilibrium synthesis of metastable rocksalt TaC 1-x N x alloys as substrates for Al 1-x Ga x N. At higher nitrogen concentrations, other low-energy metastable polymorphs emerge that continue to retain the hexagonal close packing suitable for III-N growth. Confidence in these trends was established through uncertainty quantification of the basin sizes and energy distributions; such analysis utilized the Beta and Dirichlet distributions. In conclusion, we also find (a) polymorph basin sizes can be rationalized in terms of energetic preferences for different coordination environments; and (b) basin sizes universally shrink with increasing nitrogen content, making the system more prone to amorphous growth.

36 MATERIALS SCIENCE↗

Phase Stability and Electrochemical Performance of La-Site-Doped Li6La3Zr0.5Nb0.5Ta0.5Hf0.5O12 High-Entropy Garnets

We investigate La-site substitution in the high-entropy garnet Li6La3Zr0.5Nb0.5Ta0.5Hf0.5O12 (LLZNTH) using Ba2+, Sr2+, and Sm3+ to elucidate how dopant governs phase stability, Li-site distribution, and electrochemical behavior. X-ray diffraction shows that Sr2+ is incorporated homogeneously into the garnet lattice, whereas the larger Ba2+ and smaller Sm3+ ions partially exceed the structural tolerance, generating secondary phases. Nevertheless, the Sm-doped composition (x = 0.05) exhibits the highest room-temperature ionic conductivity (2.7 × 10–4 S cm–1). Neutron powder diffraction reveals that Sm substitution drives a redistribution of Li+ from the tetrahedral 24 d sites into the higher-mobility 96 h positions, enhancing the connectivity of the three-dimensional Li-ion migration network. A Sm-doping series (x = 0.01–0.05) further shows that only sufficiently high Sm levels induce this redistribution, whereas lower concentrations retain Li arrangements similar to the undoped garnet. Critical current density measurements demonstrate that La-site dopants also influence interfacial stability against Li metal, underscoring a trade-off between bulk transport enhancement and mechanical robustness. Collectively, these findings reveal that in high-entropy garnets improved ionic conductivity can originate not only from phase-pure structures but also from targeted modification of the Li sublattice, even when accompanied by secondary phases, offering a compositional design principle for garnet electrolytes.

Li, Chang [Mechanical Engineering, School of Scien↗

Sulfur isotopes from the Paleoproterozoic Francevillian Basin record multigenerational pyrite formation, not depositional conditions

Bulk-rock sulfur isotope data from pyrite in the ~2.1 billion-year sedimentary rocks of the Francevillian Basin, Gabon, have underpinned ideas about initial oxygenation of Earth’s surface environments and eukaryote evolution. In this paper, we show, using micro-scale analytical methods, that the bulk sulfur isotope record represents progressive diagenetic modification. Our findings indicate no significant change in microbial sulfur cycling processes and seawater sulfate composition throughout that initial phase of atmosphere-ocean oxygenation of Paleoproterozoic time. This offers an alternative view of Earth system evolution during the transition from an anoxic to an oxic state and highlights the need for a judicious reappraisal of conceptual models using sulfur isotope data as primary depositional signals linked to global-scale biogeochemical processes.

58 GEOSCIENCES↗

Phase evolution and morphology in Cu-In-Ga sputtered precursors

The reaction of metallic precursors has become the primary method of industrial manufacturing for Cu(In,Ga)Se2. Commonly used Cu3Ga sputter targets have thus far dictated that the relative Ga composition of these precursors is Ga/(In+Ga) ≈ 0.25. Cu-In-Ga precursors are prepared with varying DC sputtering conditions and Ga compositions ranging from 0 ≤ Ga/(In+Ga) ≤ 0.75. The phase evolution and morphology of these precursors is characterized using x-ray diffraction (XRD) and scanning electron microscopy, including in situ annealing of precursors during XRD measurements. It is observed that the Ga composition of as-deposited precursors affects phase evolution with annealing. Consistent morphology changes were not observed with changing Ga, however, film morphology was controlled by adjusting In sputter conditions.

Lam, Isaac K. (ORCID:0000000198002765)↗

Disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y alloys

This dataset contains input and output files from density functional theory (DFT) simulations used to study the disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y (0 ≤ x + y ≤ 1) alloys and their binary end members MnTe, MnSb, and MnBi. The alloys adopt the hexagonal NiAs-type (nickeline) structure and span ternary (MnTexSb1-x, MnTexBi1-x, MnBixSb1-x), and quaternary compositions across the full MnTe–MnSb–MnBi composition triangle. For each alloy composition, the dataset provides DFT calculations in three magnetic configurations: A-type antiferromagnetic (AFM), C-type AFM, and ferromagnetic (FM). Every magnetic configuration folder contains the fully relaxed crystal structure (CONTCAR), VASP input parameters (INCAR), and the main VASP output file (OUTCAR), from which total electronic energies, Mn magnetic moments, lattice parameters, and percent volume changes between magnetic states are extracted. These data are used to construct compositional phase diagrams, evaluate thermodynamic stability (formability), and map magnetoelastic responses across the alloy space. For A-type AFM and FM configurations, additional data are provided as follows: (i) FORCE_CONSTANTS and thermal_properties.yaml files at the top level of A-type_AFM/ and FM/ folders — present only for compositions marked with an asterisk (*) in Table I of the main text. These are derived from Phonopy finite-displacement calculations on full disordered 128-atom supercells and provide vibrational free energy, entropy (Svib)contribution from explicit disorder calculations. (Table I of the associated main manuscript) (ii) A VCA/ subfolder within A-type_AFM/ and FM/, containing FORCE_CONSTANTS and thermal_properties.yaml from Virtual Crystal Approximation phonon calculations (without spin-orbit coupling). VCA data are available for all compositions and are used to estimate vibrational contributions to the Gibbs free energy across the full composition space. (iii) A SOC/ subfolder containing CONTCAR, INCAR, and OUTCAR from spin-orbit coupling calculations, providing relativistic corrections to electronic energies and lattice parameters (Tables S2–S3 of the SM, and Table I of the main manuscript). (iv) A SOC/VCA/ subfolder containing FORCE_CONSTANTS and thermal_properties.yaml from VCA phonon calculations performed within the SOC framework, combining relativistic and vibrational thermodynamic corrections. The computed properties are used to map the AFM–FM magnetic crossover near MnTe0.75Sb0.25, demonstrate disorder- and spin-induced phonon broadening, identify a semiconductor-to-metal crossover, and quantify the pronounced magnetoelastic volume response near the magnetic phase boundary.

36 MATERIALS SCIENCE↗

Revealing Coexisting Cu0–Cu+ Sites in Cu3N Nanoensembles for Selective CC Coupling of CO2 Under Low Overpotential

To address a long-existing debate on what copper species are responsible for efficient CC coupling, especially ethanol formation, in electrochemical CO2 reduction reaction, herein, a comprehensive study using Cu3N nanocubes with a uniform size and shape, alongside a single crystalline phase is reported. The Cu3N nanoensemble electrode has a remarkable Faradaic efficiency (FE) of 64% for ethanol production at a relatively low potential of -0.6 V versus reversible hydrogen electrode. Through in-operando X-ray absorption spectroscopy study, a dynamic phase evolution that directly correlates with changes in FE across varying applied potentials is observed. Notably, the nanoensemble with a composition of ≈71% Cu+ and 29% Cu0 is identified as being selective for ethanol formation at the low overpotential. Conversely, a predominantly metallic Cu phase formed at potentials more negative than -0.6 V favors the hydrogen evolution reaction. Density functional theory calculations at the Cu3N-Cu interface substantiate that the coexistence of Cu0-Cu+ not only energetically favors the ethanol reaction pathway but also destabilizes the intermediates for ethylene pathway.

*CH-CHO as an intermediate for ethanol production↗

Stable salt hydrate-based thermal energy storage materials

Heating and cooling systems in building infrastructure utilize conventional materials that account for a considerable amount of energy usage and waste. Phase change material (PCM) is considered a promising candidate for thermal energy storage that can improve energy efficiency in building systems. In this work, a novel salt hydrate-based PCM composite with high energy storage capacity, relatively higher thermal conductivity, and excellent thermal cycling stability was designed and developed. The thermal cycling stability of the PCM composite was enhanced by using dextran sulfate sodium (DSS) salt as a polyelectrolyte additive, which significantly reduced the phase segregation of salt hydrate. The energy storage capacity and the thermal conductivity of the composite were enhanced by the addition of various graphitic materials along with Borax nucleator. A significant increase in thermal cycling stability was observed for the DSS-modified composite, with over 100 thermal cycles without degradation. The final PCM composite exhibited as much as 290% increase in energy storage capacity relative to the pure salt hydrate, and approximately 20% increase in thermal conductivity. In addition, the PCM composite developed can be produced at larger scale, and can potentially change the future of heating/cooling system in building infrastructure.

42 ENGINEERING↗

Interactions between molecular-scale processes and hyporheic exchange for understanding Fe-S-C cycling in riparian wetlands (Final Report)

Wetlands represent some of the most productive ecosystems on the planet and critically influence global environmental health. Specifically, wetlands promote water quality by transforming nutrients and organic compounds and sequestering metals and contaminants. Riparian wetland hyporheic zones, where toxic surface water and anoxic groundwater mix, exhibit dynamic conditions that drive steep redox gradients and promote hotspots of diverse and fluctuating microbial activity. Changes in climate, water quality, and water quantity can disturb hydrologic flow and biogeochemical processing in these environments. Understanding how sulfate loading, impacted by hydrologic flux and anthropogenic inputs, influences iron and carbon cycling in wetlands will be crucial for predicting water quality issues driven by iron mineral precipitation and sorption, such as the release of heavy metals and other toxic elements. We used a fully integrated multi-scale and multi-method approach to develop a mechanistic understanding of how hydrologic flow influences coupled iron and sulfur cycles in riparian wetlands. This entailed hydrological, geochemical, and microbial observations at two locations: an anthropogenic sulfate-impacted riparian wetland in northern Minnesota, and a low-sulfate Fe-rich riparian wetland in Tims Branch at the Savannah River Site (SRS). These sites were characterized by hydrologically dynamic conditions where the stream and wetland systems oscillated between gaining (upward flow) and losing (downward flow) conditions that recharged the system occasionally with oxidants that fueled a variety of biogeochemical reactions. Aqueous geochemical measurements of surface water, groundwater, and porewater samples were made alongside solid-phase geochemical analyses of sediment gravity cores. Bulk X-ray absorption spectroscopy at the Advanced Photon Source (APS; Argonne) interrogated the speciation and distribution of Fe and S mineral phases of the sediments. Interestingly, it was discovered that, despite strongly reducing conditions, Fe(III) compounds and a variety of intermediate valence S compounds were stable in the subsurface. Indeed, compounds like thiosulfate, S(0), and intermediate valence organosulfur compounds were more prevalent than FeS and pyrite. The composition of the sediments did change with changes in hydrologic flow, showing their reactivity in changing redox conditions. The abundance of these intermediate S compounds was likely formed as a result of anaerobic oxidation by aqueous and solid-phase Fe(III) compounds, fueling a cryptic S cycle that is driving the breakdown of organic matter in the hyporheic zone. Microbiome surveys showed a core community that seemed stable across the landscape, but changed with increasing depth into the sediment. The community composition did not seem to change dramatically with changes in season or hydrologic flow, except for some organisms that have the potential to contribute to S cycling. More work is needed to confirm their functional activity. These fine process-scale analyses were placed within a dynamic field context using physical flow parameters from surface water and groundwater level measurements. These data helped shed light on sulfur-driven biogeochemical processes in hydrologically dynamic riparian wetlands, addressing a gap in our understanding about the impacts of pollution and other anthropogenic changes on ecologically sensitive environments.

54 ENVIRONMENTAL SCIENCES↗

Phase I DOE DE-SC0021823 Entitled “Changing the Design Rules of Rubber to Create Lighter Weight, More Fuel Efficient Tires” Final Technical Report 04/08/2022

Molecular Rebar Design, LLC has successfully developed new rubber composites with individualized carbon nanotubes called MOLECULAR REBAR® (MR), improving tire tread compound performance for use with electric vehicles (EVs). Through the iterative nature of the Phase I experimentation, MRD developed a novel carbon nanotube material that disperses well with other typical tire compound fillers and can be chemically functionalized for unique material property benefits. The new MR material is a chemically functionalized, discrete multi-wall carbon nanotube that binds into the rubber compound using silane technology. This Molecular Rebar based tire tread material drastically improves DIN abrasion resistance 25%+ (correlating to improved tire life), reduces tread weight by 6-7%, and reduces rolling resistance 20%+ (correlating to improved energy efficiency), as compared to an in-use, state-of-the-art, silica-silane tread compound. The formulations can be adjusted to maximize energy efficiency, to maximize wear or to have a blend of improvement depending on the tire performance needs of end use customers.

36 MATERIALS SCIENCE↗

Hidden first-order phase transitions and large magnetocaloric effects in GdNi 1-x Co x

We report a large magnetocaloric effect tunable between 70 and 115 K in a series of rare earth intermetallic compounds GdNi 1-x Co x with x varying from 0 to 0.15 that manifest rather unconventional second-order phase transitions with concurrent changes in both magnetic and crystallographic sublattices. While the Curie temperature, TC, linearly increases with x(Co), the maximum isothermal entropy change induced by magnetic field varying between 0 and 50 kOe slightly decreases from 14 J/kg K at 71 K when x(Co) = 0 to10 J/kg K at 115 K when x(Co) = 0.15. Additionally, the temperature-averaged entropy change figures of merit calculated at temperature spans of 10 K for all examined compositions are comparable to those of the best known magnetocaloric materials that exhibit second-order phase transitions, including elemental Gd and La(Fe,Co,Si) 13 alloys. Through a detailed analysis of the magnetic field-induced entropy changes along with assessment of critical exponents we explore the role magneto-elastic coupling plays in controlling magnetocaloric properties of GdNi 1-x Co x compounds. We also formulate a model based on the mean field theory approximation to describe both magnetic and magnetocaloric properties of the title materials in qualitative agreement with experimental results.

36 MATERIALS SCIENCE↗

Investigating the Impacts of Aqueous-Phase Processing on Organic Aerosol Chemical Climatology Using ARM and ASR Observations

This project improved understanding of how atmospheric aerosol particles form and evolve, with a focus on the role of water-driven (aqueous-phase) chemical reactions in the atmosphere. These processes occur in clouds, fog, and humid air and can significantly change the composition and properties of airborne particles, known as aerosols, which influence air quality and climate. By combining field measurements, laboratory experiments, and advanced analytical techniques, the project identified key chemical signatures that allow scientists to distinguish particles formed through aqueous processes from those formed in the gas phase. Observations from multiple environments, including wildfire smoke, urban regions, and cloud-influenced areas, show that aqueous chemistry is an important pathway for particle formation and aging. The project also developed new measurement approaches using uncrewed aerial systems (UAS) to capture how aerosol composition varies with altitude, providing critical insights into how particles interact with clouds. In addition, new data analysis frameworks were created to better interpret long-term aerosol measurements and improve characterization of particle sources and transformations. These results have been integrated into a global database of aerosol measurements and used to support atmospheric modeling efforts. Overall, the project provides important tools and knowledge to improve predictions of how aerosols affect climate and air quality, particularly through their interactions with radiation and clouds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗