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At least 703 records · Page 39

Variability and associated uncertainty in image analysis for soiling characterization in solar energy systems

The accumulation of soiling on photovoltaic modules and on the mirrors of concentrating solar power systems causes non-negligible energy losses with economic consequences. These challenges can be mitigated, or even prevented, through appropriate actions if the magnitude of soiling is known. Particle counting analysis is a common procedure to characterize soiling, as it can be easily performed on micrographs of glass coupons or solar devices that have been exposed to the environment. Particle counting does not, however, yield invariant results across institutions. The particle size distribution analysis is affected by the operator of the image analysis software and the methodology utilized. The results of a round-robin study are presented in this work to explore and elucidate the uncertainty related to particle counting and its effect on the characterization of the soiling of glass surfaces used in solar energy conversion systems. An international group of soiling experts analyzed the same 8 micrographs using the same open-source ImageJ software package. The variation in the particle analyses results were investigated to identify specimen characteristics with the lowest coefficient of variation (CV) and the least uncertainty among the various operators. The mean particle diameter showed the lowest CV among the investigated characteristics, whereas the number of particles exhibited the largest CV. Additional parameters, such as the fractional area coverage by particles and parameters related to the distribution's shape yielded intermediate CV values. These results can provide insights on the magnitude inter-lab variability and uncertainty for optical and microscope-based soiling monitoring and characterization.

14 SOLAR ENERGY↗

Variable voltage electron microscopy: Toward atom-by-atom fabrication in 2D materials

The precisely focused electron beam (e-beam) in scanning transmission electron microscopy has been found to be a versatile tool for patterning matter on the atomic level and enabling atom-by-atom fabrication, however, beam-induced phenomena are known to be extremely sensitive to the e-beam energy and are closely correlated with the proximity of the knock-on threshold. Here we provide a method to control the energy transferred to the sample while facilitating much faster changes in accelerating voltages by maintaining a nearly constant temperature in the electron microscope lenses. We use this method to demonstrate in-situ nano-milling of a graphene film followed rapidly by “gentler” imaging at lower energy. Additionally, the insertion and controlled movement of silicon dopants in graphene is demonstrated by employing a different e-beam energy during each process. We believe the incorporation of variable e-beam energy will broaden the potential for atomic scale e-beam fabrication.

36 MATERIALS SCIENCE↗

Automatic detection of cataclysmic variables from SDSS images

Abstract Investigating rare and new objects have always been an important direction in astronomy. Cataclysmic variables (CVs) are ideal and natural celestial bodies for studying the accretion process of semi-detached binaries with accretion processes. However, the sample size of CVs must increase because a lager gap exists between the observational and the theoretical expanding CVs. Astronomy has entered the big data era and can provide massive images containing CV candidates. CVs as a type of faint celestial objects, are highly challenging to be identified directly from images using automatic manners. Deep learning has rapidly developed in intelligent image processing and has been widely applied in some astronomical fields with excellent detection results. YOLOX, as the latest YOLO framework, is advantageous in detecting small and dark targets. This work proposes an improved YOLOX-based framework according to the characteristics of CVs and Sloan Digital Sky Survey (SDSS) photometric images to train and verify the model to realise CV detection. We use the Convolutional Block Attention Module to increase the number of output features with the feature extraction network and adjust the feature fusion network to obtain fused features. Accordingly, the loss function is modified. Experimental results demonstrate that the improved model produces satisfactory results, with average accuracy (mean average Precision at 0.5) of 92.0%, Precision of 92.9%, Recall of 94.3%, and $F1-score$ of 93.6% on the test set. The proposed method can efficiently achieve the identification of CVs in test samples and search for CV candidates in unlabeled images. The image data vastly outnumber the spectra in the SDSS-released data. With supplementary follow-up observations or spectra, the proposed model can help astronomers in seeking and detecting CVs in a new manner to ensure that a more extensive CV catalog can be built. The proposed model may also be applied to the detection of other kinds of celestial objects.

Astronomy & Astrophysics↗

Temporal variabilities of soil carbon dioxide fluxes from cornfield impacted by temperature and precipitation changes through high-frequent measurement and DAYCENT modelling

Soil carbon dioxide (CO 2 ) emissions from the field of corn (Zea mays L.) play an important role in global warming. This study investigated temporal variability of soil CO 2 fluxes (R s ) with soil temperature (T s ) and moisture (θ) and built DAYCENT models for predicting future impacts of climate changes on R s using the measured high-frequency data. R s trend was tested by Mann–Kendall and Sen Estimator. Predicted R s s under different climate scenarios were compared using Parallel-line Analysis. Herein, the findings indicated that daily R s exponentially increased with T s constrained by θ. During the θ of 27–31%, there was a strong exponential relationship between R s and T s , but the relationship was weaker for the θ of 38–41% and 22–26%. Soil environmental index (SEI, T s × θ) significantly impacted R s with linear regression R s 0.5 = 0.4599 + 0.002059 × SEI in 2008, 2009 and 2011. At the diurnal scale, there were different trends in R s s and relationships among R s and T s and θ in different years. Predicted yearly R s s, root R s s and corn yield in 2014–2049 increased with an increase in temperature scenarios, but the R s s significantly increased as temperature rose by 1°C or higher. Predicted yearly R s s, root R s s and yield reduced with precipitation scenario increase, and the root R s s and yield significantly diminished as precipitation increased by 15 and 30%. Predicted yearly R s from cornfields had a significantly increasing trend. Future research is needed to explore methods for mitigating cornfield R s and evaluating sensitivities of different cropland R s s to temperature changes.

54 ENVIRONMENTAL SCIENCES↗

Cyclable Variable Path Length Multilevel Structures for Lossless Ion Manipulations (SLIM) Platform for Enhanced Ion Mobility Separations

Ion mobility-mass spectrometry (IMS-MS) is increasingly used to analyze complex samples and provide structural information of unknown compounds. As the complexity of samples increases, there is a need to improve the resolution of IMS-MS instruments to increase the rate of molecular identification. In this work, we evaluated a cyclable and variable-pathlength multilevel Structures for Lossless Ion Manipulations (SLIM) platform to achieve a higher resolving power than previously possible. This new multilevel SLIM platform has eight separation levels connected by ion escalators and a path length of ~88 meters (~11 meters per level). Our new multilevel SLIM can also be operated in an ‘ion cycling’ mode where a set of return ion escalators transport ions from the eighth back to the first level, allowing even longer path lengths (and higher IMS resolution). The platform has been improved to enhance the ion transmission and IMS separation quality by reducing the spacing between SLIM boards as well as board thickness, reducing the ions’ escalator residence time. Compared to the previous generation, the new multilevel SLIM demonstrated a better transmission for a set of phosphazene ions, especially for the low-mobility ions. The new multilevel SLIM achieved better resolving powers than our previous 4-level SLIM. The collision cross-section-based resolving power of the SLIM platform was tested using a pair of singly-charged reverse sequence peptides (SDGRG 1+ , GRGDS 1+ ). We achieved 1100 resolving power using 88 meters of path length (i.e., 8 levels) and 1400 following an additional pass through the eight levels (i.e., 16 levels or 173.5 m). The multilevel SLIM was further evaluated to demonstrate the enhanced separation for a positively and negatively charged brain total lipid extract sample. Finally, the new multilevel SLIM enables much higher resolving powers for a wide range of ion mobilities, improved transmission for low-mobility ions, and the ability to perform even higher resolving power for ions of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural Design of Bismuth Telluride Nanoplates through Process Variables

Binary pnictogen chalcogen compounds, primarily bismuth tellurides and selenides, are of great interest due to their applications in emerging quantum devices, as well as thermoelectric generators. The performance of bismuth telluride in these roles depends on its structure at the nanoscale, particularly the size, shape, and crystallinity of its nanocrystalline forms. However, current methods for controlling these features are often slow, inconsistent, or difficult to scale. Here, we demonstrate that through a solvothermal synthesis and hot injection process, precise control over the morphology of bismuth telluride nanoplates is possible with independent tuning of process variables, such as temperature and reaction time. We find that the nanoplate shape and internal porosity vary systematically with synthesis temperature and that the same morphological outcomes can be rapidly achieved at a fixed temperature by adjusting reaction duration. These results reveal that both the temperature and time can independently direct bismuth telluride morphological features, allowing for rapid, tunable synthesis strategies. Our approach offers a scalable framework, not only for bismuth telluride but also for related layered chalcogenides used in energy harvesting and quantum technologies.

Ackley, Jordan [Boise State Univ., ID (United Stat↗

Integrating Contaminant Source Indicators, Water Quality Measures, and Ecotoxicity to Characterize Contaminant Mixtures and Per- and Polyfluoroalkyl Substance (PFAS) Variability in an Urban Watershed

Thousands of chemical contaminants threaten watersheds but are time and cost prohibitive to monitor. Identifying their sources, transport, and ecological risk is limited in heterogeneous urban watersheds. We present an integrative watershed approach using source-specific indicator compounds, common water quality measures, and ecotoxicity assays to examine the distribution of contaminant mixtures in an urbanized watershed. Indicator compound concentrations were temporally and spatially distributed for treated/untreated sewage (sucralose, artificial sweetener), road runoff (diphenyl-guanidine [DPG] and 6PPD-quinone [6PPD-Q], automobile tire additives), and lawncare runoff (aminomethanephosphonic acid (AMPA), major degradant of the herbicide glyphosate). Sucralose was predominately sourced from treated wastewater; measurable concentrations in tributaries indicated raw sewage inputs. DPG and 6PPD-Q concentrations correlated to road density during base flow and were elevated during stormflow. AMPA was measurable spring through fall, especially where lawns were dense. When specific sources dominated flow, water quality measures correlated with wastewater (sulfate, potassium, chloride, and sodium) and road runoff (chromium and lead) indicators. The limited behavioral toxicity observed in exposed zebrafish (Danio rerio) (18%) was not well explained by source-indicators. PFAS concentrations were highly variable spatially but not well explained by our source-specific indicator compounds. Here, more costly compound-specific monitoring may be necessary when multiple sources exist or when unexpected toxicity trends occur.

computer simulations↗

Multiobjective Optimal Controlled Variable Selection for a Gas Turbine–Solid Oxide Fuel Cell System Using a Multiagent Optimization Platform

Hybrid gas turbine–fuel cell systems have immense potential for high efficiency in electrical power generation with cleaner emissions compared with fossil-fueled power generation. We report a systematic controlled variable (CV) selection method is deployed for a hybrid gas turbine–fuel cell system in the HyPer (hybrid performance) facility at the U.S. Department of Energy’s National Energy Technology Laboratory (NETL) for maximizing its economic and control performance. A three-stage approach is used for the CV selection comprising a priori analysis, multiobjective optimization, and a posteriori analysis. The a priori analysis helps to screen off several candidate CVs, thus reducing the size of the combinatorial optimization problem for multiobjective CV selection. For optimal CV selection, a transfer function model of the HyPer facility is identified. By considering several candidate models, the final transfer function model is selected using Akaike’s Final Prediction Error criterion. Experimental data from the HyPer facility are used to estimate the noise in the measurement data. For solving the combinatorial multiobjective optimization problem for CV selection, a multiagent optimization platform comprising simulated annealing, genetic algorithm, and efficient ant colony optimization algorithms is used. Pareto-optimal CV sets exhibit a high trade-off between the economic and control objective. The a posteriori analysis is undertaken for several top Pareto-optimal CV sets. An optimal CV set is selected that shows the best compromise between process economics and controllability under both nominal and off-design conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multitask Machine Learning of Collective Variables for Enhanced Sampling of Rare Events

Computing accurate reaction rates is a central challenge in computational chemistry and biology because of the high cost of free energy estimation with unbiased molecular dynamics. In this work, a data-driven machine learning algorithm is devised to learn collective variables with a multitask neural network, where a common upstream part reduces the high dimensionality of atomic configurations to a low dimensional latent space and separate downstream parts map the latent space to predictions of basin class labels and potential energies. Here, the resulting latent space is shown to be an effective low-dimensional representation, capturing the reaction progress and guiding effective umbrella sampling to obtain accurate free energy landscapes. This approach is successfully applied to model systems including a 5D Müller Brown model, a 5D three-well model, the alanine dipeptide in vacuum, and an Au(110) surface reconstruction unit reaction. It enables automated dimensionality reduction for energy controlled reactions in complex systems, offers a unified and data-efficient framework that can be trained with limited data, and outperforms single-task learning approaches, including autoencoders.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for data-driven discovery of CVs parameterizing the important large scale motions of the system. A challenge to CV discovery is learning CVs invariant to symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multi-molecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate Permutation Invariant Vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation, and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand sampling of configurational phase space and obtain converged CVs and free energy landscapes. Here, we demonstrate the Permutationally Invariant Network for Enhanced Sampling (PINES) approach in applications to the self-assembly of a 13-atom Argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C 45 H 92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Characterizing Defect Dynamics in Silicon Carbide Using Symmetry-Adapted Collective Variables and Machine Learning Interatomic Potentials

Silicon carbide (SiC) divacancies are attractive candidates for spin-defect qubits possessing long coherence times and optical addressability. The high activation barriers associated with SiC defect formation and motion pose challenges for their study by first-principles molecular dynamics. In this work, we develop and deploy machine learning interatomic potentials (MLIPs) to accelerate defect dynamics simulations while retaining ab initio accuracy. We employ an active learning strategy comprising symmetry-adapted collective variable discovery and enhanced sampling to compile configurationally diverse training data, calculation of energies and forces using density functional theory (DFT), and training of an E(3)-equivariant MLIP based on the Allegro model. Here, the trained MLIP reproduces DFT-level accuracy in defect transition activation free energy barriers, enables the efficient and stable simulation of multidefect 216-atom supercells, and permits an analysis of the temperature dependence of defect thermodynamic stability and formation/annihilation kinetics to propose an optimal annealing temperature to maximally stabilize VV divacancies.

Computer simulations↗

A Gauss-Radau-Laguerre Discrete Variable Representation for Use in Continuum Electron Dynamics

In this work, we detail an implementation, suitable for calculations on highly correlated ionizing systems, of a modified finite element discrete variable representation (FE-DVR) appended with a Gauss-Radau-Laguerre element. The appended element includes exterior complex scaling (ECS) to impose outgoing wave boundary conditions on treatments of processes involving continuum electrons. In this “infinite range” ECS (irECS), the complications that introduce reflections from the end of the grid when the last ECS finite element has finite range are avoided by the use of the Laguerre-weighted exponentially decaying tails, while outgoing wave boundary conditions are still imposed via the ECS transformation. For highly correlated systems in the absence of strong external fields we find that accurate two-electron integrals are essential in this modified FE-DVR. To accurately compute the two-electron integrals over the entire ECS contour, we present a detailed examination of the implications from the boundary terms that arise in a solution of Poisson’s equation with the Radau-Laguerre basis. A boundary term correction is necessary, and when included, the Radau-Laguerre DVR can accurately describe highly correlated states such as the doubly excited states of helium over the entire ECS contour.

elements↗

Charge Carrier Transport in Iron Pyrite Thin Films: Disorder-Induced Variable-Range Hopping

Here, the origin of p-type conductivity and the mechanism responsible for low carrier mobility were investigated in pyrite (FeS 2 ) thin films. Temperature-dependent resistivity measurements (10-400 K) were performed on polycrystalline and nanostructured thin films prepared by three different methods: (1) spray pyrolysis, (2) hot-injection synthesized and spin-coated nanocubes, and (3) pulsed laser deposition. The films have a high hole density (10 18 -10 19 ) cm -3 and low mobility (0.1-4 cm 2 V -1 s -1 ) regardless of the method used for their preparation. The charge transport mechanism is determined to be thermally activated conduction (TAC) at near room temperature, with Mott-type variable-range hopping (VRH) of holes via localized states occurring at lower temperatures. The density functional theory (DFT) predicts that sulfur vacancy induces localized defect states within the band gap and the charge remains localized around the defect. The data indicates that the electronic properties including hopping transport in pyrite thin films can be correlated to sulfur vacancy-related defects. The results provide insights into the electronic properties of pyrite thin films and their implications for charge transport.

36 MATERIALS SCIENCE↗

Isolating Chemical Reaction Mechanism as a Variable with Reactive Coarse-Grained Molecular Dynamics: Step-Growth versus Chain-Growth Polymerization

Here we present a general approach to isolate chemical reaction mechanism as an independently controllable variable across chemically distinct systems. Modern approaches to reduce the computational expense of molecular dynamics simulations often group multiple atoms into a single “coarse-grained” interaction site, which leads to a loss of chemical resolution. In this work we convert this shortcoming into a feature and use identical coarse-grained models to represent molecules that share nonreactive characteristics but react by different mechanisms. As a proof of concept, we use this approach to simulate and investigate distinct, yet similar, trifunctional isocyanurate resin formulations that polymerize by either chain- or step-growth. Because the underlying molecular mechanics of these models are identical, all emergent differences are a function of the reaction mechanism only. We find that the microscopic morphologies resemble related all-atom simulations and that simulated mechanical testing reasonably agrees with experiment.

36 MATERIALS SCIENCE↗

Revealing Variable Dependences in Hexagonal Boron Nitride Synthesis via Machine Learning

Wafer-scale monolayer two-dimensional (2D) materials have been realized by epitaxial chemical vapor deposition (CVD) in recent years. To scale up the synthesis of 2D materials, a systematic analysis of how the growth dynamics depend on the growth parameters is essential to unravel its mechanisms. However, the studies of CVD-grown 2D materials mostly adopted the control variate method and considered each parameter as an independent variable, which is not comprehensive for 2D materials growth optimization. Herein, we synthesized a representative 2D material, monolayer hexagonal boron nitride (hBN), on single-crystalline Cu (111) by epitaxial chemical vapor deposition and varied the growth parameters to regulate the hBN domain sizes. Furthermore, we explored the correlation between two growth parameters and provided the growth windows for large flake sizes by the Gaussian process. Here, this new analysis approach based on machine learning provides a more comprehensive understanding of the growth mechanism for 2D materials.

36 MATERIALS SCIENCE↗

Variable-Temperature Scattering and Spectroscopy Characterizations for Temperature-Dependent Solution Assembly of PffBT4T-Based Conjugated Polymers

The solution structure of conjugated polymers (CPs) from which the films are cast is critical for tailoring the thin-film morphology thus device performance. Here, we used multimodal variable-temperature scattering and spectroscopy tools to fully quantify the solution assembly of poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,3'''-dialkyl-2,2';5',2'';5'',2'''-quaterthiophen-5,5'''-diyl)] (PffBT4T) polymers with varying side-chain lengths at different assembly temperatures. The conformational and aggregation behaviors for PffBT4T-based CPs were found to be very sensitive to both temperature and side chain length using ultraviolet–visible (UV–vis) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, dynamic light scattering (DLS), and small-angle neutron scattering (SANS). We found that with slightly increasing side chain length from 2-octyldodecyl (C8C12) to 2-nonyltridecyl (C9C13), PffBT4T-based CPs show a significant decrease in aggregation-to-dissolved chain transition temperature (10 °C), degree of aggregation, enthalpy change of aggregation, and size of the aggregates in solution. At room temperature, PffBT4T polymer strongly aggregated to form fabric structure with the film thickness of a few nanometers in thickness and hundreds of nanometers in length, as probed by atomic force microscopy (AFM), transmission electronic microscopy (TEM), and dynamic light scattering (DLS). At the elevated temperature above the aggregation-to-dissolved chain transition temperature, PffBT4T is fully dissolved and adopts a semiflexible coil conformation with the persistence length of 3.1 nm for PffBT4T-C8C12 and a slightly increased persistence length of 3.4 nm for PffBT4T-C9C13, according to temperature-dependent SANS measurements. Longer side chains of PffBT4T-C9C13 also lead to less aggregation enthalpy gain compared with PffBT4T-C8C12. This work provides a solution structure manipulating strategy of CPs and thus will inspire the molecular design and processing protocols of CPs toward higher performance electronic devices.

36 MATERIALS SCIENCE↗

Delineating Variabilities of Groundwater Level Prediction Across the Agriculturally Intensive Transboundary Aquifers of South Asia

We report the groundwater depletion in South Asia’s Himalayan, transboundary Indus-Ganges-Brahmaputra-Meghna (IGBM) rivers basin is among the highest globally. Given the high irrigation demand and population, groundwater sustainability requires an improved understanding of groundwater systems for the accurate prediction of groundwater levels (GWLs). However, the prediction of groundwater system behaviors is a significant challenge since it is dominated by spatiotemporal and subsurface depth-dependent drivers. Earlier studies that address the challenges are mainly based on the short spatial and temporal extent and/or do not separate the renewable (i.e., shallow) vs nonrenewable (i.e., deeper) groundwater signals. Here, we first identified the variable importance of spatial and depth-dependent drivers on GWL in the IGBM basin. Our results indicate a greater influence of anthropogenic factors (i.e., widespread pumping and increased population) in most parts of the IGBM basin, except in the precipitation-dominated basin of the Brahmaputra. Our next purpose was to delineate a multifactorial approach for GWL prediction using the two most used machine learning models (i.e., support vector machine and feed-forward neural network) in the literature. In general, the machine learning model outputs show a good match in comparison to the GWL from the observation wells (n = 2303 distributed across India and Bangladesh) with some limitations in areas with increased groundwater irrigation. We separately compared the results from shallow (<35 m) and deep (>35 m) observation wells, emphasizing the significance of deep groundwater pumping. Our approach highlights the importance of spatiotemporal to multidepth factors in GWL prediction and can be adopted in other parts of the globe to predict GWLs.

54 ENVIRONMENTAL SCIENCES↗

Pursuing Heteroleptic Ligand Design Principles for Photoactive Fe Complexes with Ultrafast X-ray Emission and Variable-Temperature Optical Spectroscopies

Understanding the key parameters that govern the photophysical and photochemical properties of transition metal complexes is essential for the development of efficient photosensitizers for photocatalytic applications. Achieving this objective necessitates clear and detailed investigations of their electronic excited states, for which time-resolved metal Kβ X-ray emission spectroscopy (XES) has proven highly effective. Here, we present a time-resolved Fe Kβ XES study of a heteroleptic Fe(II) polypyridyl carbene complex, [Fe(phen) 2 (C 4 H 10 N 4 )] 2+ (1; phen = 1,10-phenanthroline), utilizing both the valence-to-core and Kβ mainline spectral regions, complemented by variable-temperature transient optical absorption (VT-TA) spectroscopy. Detailed analysis of the time-resolved Kβ XES data, supported by density functional theory (DFT) calculations and an Eyring analysis of the VT-TA data, reveals parallel excited state relaxation dynamics that support an assignment of the long-lived excited state to a triplet metal-centered state. Placing these results in the context of prior studies of heteroleptic Fe(II) polypyridyl cyanide complexes motivated a series of DFT calculations to investigate the effects of ligand structural flexibility and arrangement. These calculations reinforce the experimentally derived conclusion that constraining structural flexibility with multidentate ligands significantly impacts the excited state relaxation dynamics. Furthermore, our study emphasizes that the arrangement of strong field ligands in heteroleptic complexes substantially affects the energy of Jahn–Teller active triplet metal-centered states in low-spin d 6 metal complexes. Together, these findings provide synthetic design principles for extending metal-to-ligand charge transfer excited state lifetimes of heteroleptic Fe complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗