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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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Synergistic double-atom catalysts of metal-boron anchored on g-C 2 N for electrochemical nitrogen reduction: Mechanistic insight and catalyst screening

The rational design of a novel catalytic center with a sound basis remains both challenging and rewarding for the electrochemical reduction of N 2 (eNRR), which has provided a feasible route for achieving clean and sustainable NH 3 production under ambient conditions. Herein, using density functional theory calculations, we demonstrate that hybrid metal (M)-boron (B) double-atom catalysts (DACs) embedded in g-C 2 N substrate (M-B@C 2 N, M = 3d, 4d and 5d transition metals) can achieve both high catalytic activity and high selectivity in eNRR. The proposed M-B@C 2 N DACs have exhibited impressive feasibility and stability thanks to the resilient and robust C 2 N substrate with abundant pyridinic N atoms distributed among right-sized pore structures. Our results reveal that like the metal center, the embedded B atom can actively involve in Ntriple bondN bond activation via π*-backdonation mechanism concomitant with the substantial charge transfer to adsorbed *N 2 , leading to sizable Nsingle bondN bond elongation. Accordingly, both adsorption energy and Nsingle bondN bond length of *N 2 can be employed as catalytic descriptors for predicting eNRR activity in terms of the limiting potentials (UL). Using high-throughput screening method, we found that six M-B@C 2 N candidates have stood out as the outstanding electrocatalysts for driving eNRR, namely, M = Ti (U L = 0 V), Mo (U L = 0 V), Nb (U L = -0.04 V), W (U L = -0.23 V), Zr (U L = -0.26 V), V (U L = -0.28 V). The underlying origin is attributed to the balanced and constrained N-affinity of M-B dual site working in synergy, which can thus be used as one important guide of catalyst design.

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

Crystal mechanics-based thermo-elastic constitutive modeling of orthorhombic uranium using generalized spherical harmonics and first-order bounding theories

In earlier works, a mathematical procedure for invertible microstructure-property linkages was developed using computationally efficient spectral methods for polycrystalline cubic and hexagonal metals. This paper formulates such invertible microstructure–property linkages for orthorhombic polycrystalline metals relying on the generalized spherical harmonics (GSH) spectral basis. The procedure is used to compute property closures of orthorhombic polycrystals. The closures represent the complete set of theoretically possible combinations of effective properties for a selected material. The procedure relies on the first-order bounding theories and considers orientation distribution functions (ODFs) as the main microstructural descriptor influencing homogenized properties. Numerous examples of these closures involving second-rank thermal expansion and fourth-rank elastic stiffness tensorial properties over a broad range of temperatures are presented for α-uranium (α-U). In doing so, certain key properties of these closures are exploited to facilitate their computation with drastically reduced computational effort. Along with the recently developed GSH-based interpolation procedure for ODFs from coarsely spaced experimental measurement grids to finely spaced finite element mesh resolution grids presented in Barrett et al., the developed computationally efficient ODF-effective property linkages are used to establish a crystal mechanics-based simulation framework coupled with the finite element method (FEM). The ODF dependent thermal expansion and elastic stiffness tensors are efficiently calculated at every integration point and used by the FEM to predict the overall distortion of a hemispherical part made of α-U during heating. In conclusion, it is shown that the developed framework can be used to simulate microstructurally heterogeneous components under thermo-mechanical loadings in a computationally efficient manner.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A machine learning approach to quantify degradation of nuclear fuels and the effects of fission products

Nuclear fuel performance is critically dependent on understanding the evolution of fuel properties under operational conditions, a complex challenge driven by chemical changes and substantial radiation damage during fission. Traditionally, property evolution has been determined via empirical data collected following irradiation. However, these empirical correlations are limited in their applicability beyond the specific conditions in which they were obtained. This study explores a novel approach to address this challenge by applying materials informatics to develop a machine learning random forest (ML-RF) model that captures the effects of fission products on fuel compounds. The model predicts formation enthalpy (ΔH f ) by leveraging extensive quantum materials property data and correlating it with material descriptors such as composition, atomic and site features, and crystal lattice properties. This ML-RF model enables rapid interpolation across the compositional and structural spaces covered by the training data, thus supporting high-throughput screening and energetic ranking of candidate phases. The model demonstrates the ability to predict ΔH f with a mean absolute error (MAE) of approximately 0.1 to 0.2 eV/atom across a wide range of compounds, including key nuclear fuel systems (U-O, U-N, U-C, U-Si, and U-Mo). For example, it was used to assess shifts in stoichiometry for UO 2 (O/M) and UN (N/M) fuels, revealing their distinct tendencies in chemical potential variation and enabling preliminary convex hull analyses. Furthermore, the model provides insights into how individual fission products affect fuel properties. Results indicate that larger fission products (e.g., Nd, Pu, Ce) have a more pronounced impact on UO 2 , while lighter ones (e.g., Zr) strongly influence UN. Here, the model developed in this work can be used to support the Accelerated Fuel Qualification approach by facilitating preliminary evaluations prior to extensive materials modeling and experimentation. To this end, the trained model has been made available to the fuel community to support ongoing fuel development efforts.

Accelerated fuel qualification↗
DOE OSTI2023

Degradation and recovery of solid oxide fuel cell performance by control of cathode surface acidity: Case study – Impact of Cr followed by Ca infiltration

Solid oxide fuel cells (SOFC) have attracted attention as clean and efficient energy conversion devices with low emissions. However, several degradation mechanisms limit the electrochemical performance of current SOFCs, with cathode degradation due to Cr-poisoning from metal interconnects particularly problematic. The acidity/basicity of binary additives has been found to be a sensitive descriptor of the oxygen exchange kinetics, indicating that acidic Cr-species/basic Ca-species can be expected to deactivate/activate the cathode surface, respectively. Inspired by recent advances, the feasibility of relative acidity as a tool for reviving degraded SOFCs is demonstrated by neutralizing Cr-poisoned SOFCs by subsequent serial infiltration of Ca-species. Furthermore, a model mixed ionic and electronic conducting oxide, Pr 0.1 Ce 0.9 O 2-δ (PCO), is selected as the cathode material. Area-specific resistances (ASR) of symmetric cells obtained by electrochemical impedance spectroscopy show that Cr-infiltration results in a seven-fold increase in ASR, while subsequent infiltration of Ca-species leads to complete recovery. Performance degradation and recovery are attributed to depressed/enhanced redox properties at the PCO surface, as supported by XPS analysis. Experiments using anode-supported fuel cells show a reduction in peak power density by 26% upon Cr-infiltration, reversed following Ca-infiltration, after which no degradation is observed during subsequent operation for 100 h.

(Pr,Ce)O2-δ↗
DOE OSTI2026

Influence of solvents on electrochemical stability window of ionic liquid solutions

The electrochemical stability window (ESW) defines the voltage range within which an electrolyte remains stable against oxidation and reduction, serving as a key descriptor for ionic liquid (IL)-based systems. The ESWs of 15 ILs with diverse cation-anion combinations were systematically investigated, both in their neat forms and as binary mixtures with three representative solvents, i.e., propylene carbonate (PC), ethylene glycol (EG), and tetrahydrofuran (THF). Cyclic voltammetry on a glassy carbon electrode determined anodic and cathodic stability limits, revealing that ESW protection in IL-solvent mixtures strongly depends on solvent polarity, proticity, and IL compatibility. PC, with a high dielectric constant and aprotic character, broadened anodic limits and moderately stabilized cathodic limits. THF maintained compact interfacial structure, offering additional cathodic protection, whereas EG, being protic, reduced ESWs via proton-coupled electron transfer and hydrogen evolution. The solvent protection trend followed by PC > THF > EG, with bulky, hydrophobic cations ([HMIM] + , [BMPYRR] + ) and weakly coordinating anions ([NTF 2 ] - , [DCA] - , [DEP] - ) showing the highest ESW protection for 50 mol% IL in these solvents. Among the neat ILs, [EMIM][DEP], [HMIM][PF 6 ], and [BMPYRR][DCA] showed wide ESWs of ∼5.5 V. These results provide valuable insight into solvent-modulated electrochemical stability, enabling rational design of IL-based electrolytes for energy storage and electrosynthesis.

25 ENERGY STORAGE↗
DOE OSTI2021

Operando leaching of pre-incorporated Al and mechanism in transition-metal hybrids on carbon substrates for enhanced charge storage

Insufficient exposure and utilization of active sites often induces an inferior reactivity for transition-metal-based two-dimensional (2D) materials. In response, we for the first time propose a universal "nano-tailoring" strategy to incorporate abundant defects and active sites into low-crystallinity nanosheets by electrochemically leaching of Al species. With MnAl layered double hydroxides (LDHs) as a representative example, potassium-birnessite MnO 2 (AK-MnO 2 ) with oxygen vacancies and abundant edge sites is successfully produced. The oxygen vacancies are shown to help optimize the electron-transfer and ion-adsorption capability. These integrated advantages endow the AK-MnO 2 with a high capacitance value of 239 F g –1 at 100 A g –1 . By further combining with soft X-ray absorption spectroscopy techniques, we unravel that the reducibility of M 2+ in M 2+ Al-LDH serves as the key descriptor for the reconstruction rate. Here, this "nano-tailoring" strategy can provide some important implications and clues to manipulating 2D materials for efficient energy storage and conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Digital polycrystalline microstructure generation using diffusion probabilistic models

Accurate micromechanical simulation of polycrystalline materials requires a realistic digital representation of the grain scale microstructure. Here, this work demonstrates the use of a generative diffusion probabilistic model for synthesizing single phase polycrystalline realizations. The model performs well and is capable of producing realistic microstructures consisting of not just simple equiaxed structures but also structures exhibiting more complex spatial arrangements. Masked microstructure generation reveals that the model is context aware of morphological descriptors which may be encoded in the latent space. Training on more diverse data sets, with scaled up architectures, may enable development of future models capable of synthesizing even more complex microstructural features.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Chemometric modeling of power conversion efficiency of organic dyes in dye sensitized solar cells for the future renewable energy

The present study reports chemometric modeling of power conversion efficiency (PCE) of dye sensitized solar cells (DSSCs) using the biggest available data set till date which comprises around 1200 dyes covering 7 chemical classes. To extract the best structural features required for higher PCE, we have developed multiple partial least squares (PLS) quantitative structure-property relationship (QSPR) models for the Triphenylamine, Phenothiazine, Indoline, Porphyrin, Coumarin, Carbazole and Diphenylamine chemical classes using descriptors derived from the best subset selection method followed by selection of best five models in each dataset based on the Mean Absolute Error (MAE) values. The models were validated both internally and externally followed by the consensus predictions employing “Intelligent Consensus Predictor” tool to examine whether the quality of predictions can be improved with the “intelligent” selection of multiple PLS models. The quality of predictions for the respective external sets showed that the consensus models (CM) are better than the individual models (IM) in most of the cases. From the insights of the developed models, we concluded that attributes like a packed structure toward higher conductivity of electrons, auxiliary donor fragment of aromatic tertiary amines, number of thiophenes inducing the bathochromic shift and augmenting the absorption, presence of additional electron donors, enhancement of electron-donating abilities, number of non-aromatic conjugated C(sp 2 ) which helps as conjugation extension units to broaden the absorption and highly conjugated $π$-systems exert positive contributions to the PCE. On the contrary, features negatively contributing to PCE are the followings: fragments which lower the tendency of localized $π–π*$ transition, fragments related to larger volume and surface area of dyes along with hydrophobicity resulting in poor adhesion, fragment RC = N causing dye hydrolysis, steric hindrance for π electronic mobility, fragments enhancing polarity, etc. Finally, the identified features from the best QSPR model of the coumarin dataset was employed in designing of ten more efficient coumarin dyes (predicted %PCE ranging from 8.93 to 10.62) than the existing ones.

14 SOLAR ENERGY↗
DOE OSTI2022

High-throughput screening to predict highly active dual-atom catalysts for electrocatalytic reduction of nitrate to ammonia

Ammonia is an essential chemical owing to its importance in fertilizer production and other industrial applications. Electrocatalytic nitrate reduction to ammonia (NO 3 RR) holds great promise for low-temperature ammonia production while simultaneously addressing nitrate-based environmental concerns. To provide the mechanistic understanding needed to design an effective electrocatalyst, we systematically investigated the catalytic performance of metal-based dual-atom catalysts (DACs) anchored on two-dimensional (2D) expanded phthalocyanine (Pc) for NO 3 RR. We found that NO 3 RR can efficiently produce ammonia on Cr 2 -Pc, V 2 -Pc, Ti 2 -Pc, and Mn 2 -Pc surfaces with low limiting potentials of – 0.02, – 0.25, – 0.34, and – 0.41 V RHE , respectively. Moreover, using the free energy difference of *NO 3 - and *H as a descriptor, we found that the hydrogen evolution reaction is significantly suppressed on the DAC surface due to an ensemble effect in which the two metal atoms cooperate to selectively form ammonia. We performed high-throughput screening to develop an efficient metal-based DAC for NO 3 - reduction, followed by a mechanistic study to elucidate the NO3RR pathway on the DAC. Finally, this work provides design information for advancing sustainable ammonia synthesis under ambient conditions.

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

Graphene-supported single atom catalysts for high performance lithium-oxygen batteries

The optimal choice of d-block metals in single atom catalysts (SACs) is crucial for designing efficient electrocatalysts for activating the Oxygen reduction reaction (ORR)/ Oxygen evolution reaction (OER) in lithiumoxygen batteries (LOBs). Herein, we used the Quantum Mechanics methods to understand the origin of reactivity for a series of 16 d-block metals supported on nitrogen-doped graphene as SACs for ORR and OER in LOBs. Based on the Gibbs free energy calculations, we found that among the 16 SACs investigated, Zn-SAC exhibits the highest electrochemical activity with the lowest overpotential of 0.17 V. Here we then used machine learning (ML) to develop an intrinsic descriptor, phi, that correlates the catalytic activity with electronic and chemical properties of the catalytic centers at the M-N 4 active site on graphene surface. We established a linear relationship between phi and the catalytic activity that provides guidance for designing efficient SACs for electrocatalysis in LOBs. To validate these predictions, we report electrochemical measurements showing that Zn-SAC exhibits an ultra-stable cyclability with reduced overpotentials over Mo-SAC and nitrogen-doped graphene (NG), confirming our theoretical prediction. This fundamental work provides a deep understanding on the rational design of efficient SACs for OER/ ORR in LOBs.

25 ENERGY STORAGE↗
DOE OSTI2026

Segmentation method comparison for residual fiber length measurement across tiled microscopy images

Fiber length distribution (FLD), in part, governs mechanical properties in discontinuous fiber composites, yet manual measurement methods limit the high-throughput characterization needed for materials design optimization. This study compares deep learning segmentation approaches for automated FLD measurement in large-field microscopy, evaluating how method choice affects the microstructural descriptors used in structure-property-processing relationships. A critical challenge is that high-resolution microscopy images (10,000×10,000 pixels) must be tiled for deep learning analysis, fragmenting fibers at boundaries. We demonstrate that segmentation method proves crucial for measurement accuracy. For example, instance segmentation with Slicing Aided Hyper Inference (SAHI) preserves individual fiber integrity across tiles while semantic segmentation prioritizes speed. Comparing against manual measurement of extracted carbon fibers, YOLOv11-SAHI matched manual ground truth (238 μm weighted mean) with 40x speedup (4.5 vs 167 minutes per image). U-Net provides rapid quantification although it is at the cost of reduced accuracy due only reliably measuring stand-alone fibers. Our comparative analysis reveals that instance segmentation with SAHI better preserves length measurements while semantic segmentation prioritizes speed, providing empirical guidance for method selection. The characterization provides essential inputs for mechanical property prediction models and inverse design workflows, accelerating composite materials development cycles.

Additive manufacturing↗
DOE OSTI2025

Unveiling X-ray absorption signatures of boron nitride via first-principles simulation and machine learning

Boron nitride (BN) allotropes hold great promise in many advanced applications ranging from optical and photonic devices to energy storage and battery systems to tribological components. The diverse functionalities of this material stem from BN’s highly tunable structural and electronic properties, which are governed by the versatile boron–nitrogen bonding configurations. Exploring the structural landscape of BN can unveil novel structures possessing unique properties suited for specific applications, therefore accelerating the design of next-generation advanced functional materials. In this work, we leverage boron K-edge X-ray absorption spectroscopy (XAS) as an effective probe for local structural features and chemical environments. A total of 210 BN crystal structures are generated via analogies to the extensive array of carbon allotropes, and XAS is simulated for each unique local motif within the resulting collection of structures. A mapping between structural features and spectral signatures was established by synergizing first-principle simulations with data-driven based post-analysis approaches. Specifically, we developed a neural network model that can satisfactorily predict spectra line shapes from local structural descriptors. Toward automatic spectroscopic interpretation of any new BN structures, supervised machine learning models, trained on this structure–spectrum dataset, can accurately infer local coordination environments from simulated XAS, highlighting the strength of this unique approach of combining high-fidelity first-principles simulation and machine-learning to accelerate target design of novel BN materials via rational understanding of local structure-spectrum correlations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Systematic Generation of Moment Invariant Bases for 2D and 3D Tensor Fields

Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. Here, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Universal machine learning framework for defect predictions in zinc blende semiconductors

Our article introduces a universal predictive framework for point defect formation energies and charge transition levels in a wide chemical space of zinc blende semiconductors and possible impurity atoms selected from across the periodic table. This framework was developed by leveraging high-throughput quantum mechanical simulations benchmarked using some experimental data from the literature, as well as machine learning (ML)-based regressions techniques that map unique materials descriptors to computed defect properties and yield optimized and generalizable models. Furthermore, the power and utility of these models is revealed through quick predictions for thousands of new defects and screening of low-energy impurities, which may tune the equilibrium conductivity in the semiconductor. This work presents, to our knowledge, the largest density functional theory (DFT) dataset of defect properties in semiconductors and the largest DFT+ML-based screening of point defects in semiconductors to date.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Automated theoretical chemical kinetics: Predicting the kinetics for the initial stages of pyrolysis

Large scale implementation of high level computational theoretical chemical kinetics offers the prospect for dramatically improving the fidelity of combustion chemical modeling. To facilitate such efforts, we have developed a suite of codes, collectively referred to as AutoMech, that allow for the automatic prediction of the kinetics for large sets of reactions via ab initio transition-state-theory based master-equation calculations. The primary input is simply the mechanism, a dictionary relating chemically identifiable species descriptors (e.g., SMILES or InChIs) to species labels in the mechanism, and a specification of the electronic structure and transition state theory models to be implemented. Here we illustrate the current utility of AutoMech through a study of the initial stages of pyrolysis for 3 sets of fuels: sequences of alkanes, alcohols, and aldehydes. For simplicity, the analysis focuses on abstractions from the fuel by H, CH 3 , and OH, and the decomposition of the resulting radicals. Altogether, there are a total of 166 input channels in these sets (more than 363 forward reactions when expanded to the full set of elementary reactions). The code successfully produces high quality rate estimates (with apparent uncertainties less than a factor of two in limited comparisons with experiment) for > 95% of these. For the radical decomposition reactions, the analysis includes predictions for the pressure dependence of the kinetics. This wide-ranging exploration illustrates (i) the effect of different levels of prediction on the expected accuracy, (ii) the branching between abstractions at different sites for different abstractors, (iii) the dependence of the rates on the chemical structure, and (iv) the variation in radical stabilities across chemical families. These results, as well as the demonstrated feasibility of the methodology, should find further utility in the development of accurate rate expressions for arbitrary fuels. (c) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Elliott, Sarah N.↗
DOE OSTI2022

Evaluation of a rapid, generic human gestational dose model

Chemical risk assessment considers potentially susceptible populations including pregnant women and developing fetuses. Humans encounter thousands of chemicals in their environments, few of which have been fully characterized. Toxicokinetic (TK) information is needed to relate chemical exposure to potentially bioactive tissue concentrations. Observational data describing human gestational exposures are unavailable for most chemicals, but physiologically based TK (PBTK) models estimate such exposures. Development of chemical-specific PBTK models requires considerable time and resources. As an alternative, generic PBTK approaches describe a standardized physiology and characterize chemicals with a set of standard physical and TK descriptors – primarily plasma protein binding and hepatic clearance. Here we report and evaluate a generic PBTK model of a human mother and developing fetus. We used a published set of formulas describing the major anatomical and physiological changes that occur during pregnancy to augment the High-Throughput Toxicokinetics (httk) software package. We simulated the ratio of concentrations in maternal and fetal plasma and compared to literature in vivo measurements. We evaluated the model with literature in vivo time-course measurements of maternal plasma concentrations in pregnant and non-pregnant women. Finally, we prioritized chemicals measured in maternal serum based on predicted fetal brain concentrations. This new model can be used for TK simulations of 859 chemicals with existing human-specific in vitro TK data as well as any new chemicals for which such data become available. Furthermore, this gestational model may allow for in vitro to in vivo extrapolation of point of departure doses relevant to reproductive and developmental toxicity.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty

Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual link failure after some amount of elapsed time. The descriptor loss of assured safety (LOAS) is used because failure of the WL system places the entire system in an inoperable configuration while failure of the SL system before failure of the WL system, although undesirable, does not necessarily result in an unintended operation of the entire system. Thus, safety is “assured” by failure of the WL system before failure of the SL system. Here, the following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation, approximation and illustration of PLOAS with (a) constant delay times, (b) aleatory uncertainty in delay times, and (c) delay times defined by functions of link properties at occurrence times for link failure precursors, and (iii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.

58 GEOSCIENCES↗
DOE OSTI2025

Photon counting with intensified charge coupled device (ICCD) – I. In-depth detector characterization

While the adsorption properties of transition metal catalysts have been widely studied, leading to the discovery of various scaling relations, descriptors of catalytic activity, and well-established computational models, a similar understanding of semiconductor catalysts has not yet been achieved. In this work, we present a high-throughput density functional theory investigation into the adsorption properties of 5 oxides of interest to the photocatalytic CO 2 reduction reaction: TiO 2 (rutile and anatase), SrTiO 3 , NaTaO 3 , and CeO 2 . Using a systematic approach, we exhaustively identify unique surfaces and construct adsorption structures to undergo geometry optimizations. We then perform a data-driven analysis, which reveals the presence of weak adsorption energy scaling relations, the propensity of adsorbates of interest to interact with oxygen surface sites, and the importance of slab deformation upon adsorption. Our findings are presented in the context of experimental observations and in comparison to previously studied classes of catalysts, such as pure metals and tellurium-containing semiconductors, and reinforce the need for a comprehensive approach to the study of site-specific surface phenomena on semiconductors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗