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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7's finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7's FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from single- to specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7's FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Dosimetric evaluation of PLATO and Oncentra treatment planning systems for High Dose Rate (HDR) brachytherapy gynecological treatments

This study compares the dosimetric differences in HDR brachytherapy treatment plans calculated with Nucletron's PLATO and Oncentra MasterPlan treatment planning systems (TPS). Ten patients (1 T1b, 1 T2a, 6 T2b, 2 T4) having cervical carcinoma, median age of 43.5 years (range, 34-79 years) treated with tandem and ring applicator in our institution were selected retrospectively for this study. For both Plato and Oncentra TPS, the same orthogonal films anterior-posterior (AP) and lateral were used to manually draw the prescription and anatomical points using definitions from the Manchester system and recommendations from the ICRU report 38. Data input for PLATO was done using a digitizer and Epson Expression 10000XL scanner was used for Oncentra where the points were selected on the images in the screen. The prescription doses for these patients were 30 Gy to points right A (RA) and left A (LA) delivered in 5 fractions with Ir-192 HDR source. Two arrangements: one dwell position and two dwell positions on the tandem were used for dose calculation. The doses to the patient points right B (RB) and left B (LB), and to the organs at risk (OAR), bladder and rectum for each patient were calculated. The mean dose and the mean percentage difference in dose calculated by the two treatment planning systems were compared. Paired t-tests were used for statistical analysis. No significant differences in mean RB, LB, bladder and rectum doses were found with p-values > 0.14. The mean percent difference of doses in RB, LB, bladder and rectum are found to be less than 2.2%, 1.8%, 1.3% and 2.2%, respectively. Dose calculations based on the two different treatment planning systems were found to be consistent and the treatment plans can be made with either system in our department without any concern.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2013

Efficacy and Safety of Transarterial Radioembolization Versus Chemoembolization in Patients With Hepatocellular Carcinoma

Purpose. Intermediate-stage hepatocellular carcinoma (HCC) is usually treated with locoregional therapy using transarterial chemoembolization (TACE). Transarterial radioembolization (TARE) using {beta}-emitting yttrium-90 integral to the glass matrix of the microspheres is an alternative to TACE. This retrospective case-control study compared the outcomes and safety of TARE versus TACE in patients with unresectable HCC. Materials and Methods. Patients with unresectable HCC without portal vein thrombosis treated with TARE between 2005 and 2008 (n = 61) were retrospectively frequency-matched by age, sex, and liver dysfunction with TACE-treated patients (n = 55) in the Mayo Clinic Hepatobiliary Neoplasia Registry. Imaging studies were reviewed, and clinical and safety outcomes were abstracted from the medical records. Results. Complete tumor response was more common after TARE (12 %) than after TACE (4 %) (p = 0.17). When complete response was combined with partial response and stable disease, there was no difference between TARE and TACE. Median survival did not differ between the two groups (15.0 months for TARE and 14.4 months for TACE; p = 0.47). Two-year survival rates were 30 % for TARE and 24 % for TACE. TARE patients received fewer treatments (p < 0.001). Fifty-nine (97 %) TARE patients received outpatient treatment. In contrast, 53 (98 %) TACE patients were hospitalized for {>=}1 day (p < 0.001). Compared with TACE, TARE was more likely to induce fatigue (p = 0.003) but less likely to cause fever (p = 0.02). Conclusion. There was no significant difference in efficacy between TARE and TACE. TARE patients reported more fatigue but had less fever than TACE patients. Treatment with TARE required less hospitalization than treatment with TACE. These findings require confirmation in randomized trials.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

Unpacking model inadequacy: The quantification of silver release from TRISO fuel by considering empirical and mechanistic approaches

Increasing adoption of the proposed tristructural isotropic (TRISO) particle fuel for both advanced and existing reactors makes it critical to assess and address any uncertainties and inadequacies of TRISO fission product release models. Model inadequacy stems from simplifications made to the computational model when compared to the experiments. The modeling and simulation efforts conducted using the BISON fuel performance code, along with the experimental campaigns carried out under the Advanced Gas Reactor Fuel Development and Qualification Program, afford a unique opportunity to conduct a rigorous modeling inadequacy assessment within the Bayesian uncertainty quantification (UQ) framework. Here, this study compares the standard Bayesian framework against the Kennedy-O'Hagan (KOH) framework, which explicitly represents modeling inadequacy, in regard to UQ for TRISO silver release models. For this purpose, both the traditional Arrhenius equation fitted to experimental data and the more advanced lower-length-scale (LLS)-informed model, which considers microstructure information, are independently considered. Applying the inverse UQ process on the AGR-2 and -3/4 datasets revealed modeling inadequacy to be the most dominant source of uncertainty. Experimental noise uncertainty is also significant; however, model parameter uncertainty can be considered negligible. Interestingly, both the Arrhenius equation and the LLS-informed model demonstrated similar levels of modeling inadequacy. For the forward predictive UQ, the KOH framework improved both the accuracy and quality of quantified uncertainties in comparison to the standard Bayesian framework. This is true for both the Arrhenius equation and the LLS-informed model. In comparing these modeling approaches, both demonstrated similar performance at the engineering scale, while the LLS-informed model expectedly outperformed the Arrhenius equation at the mesoscale. These conclusions highlight the importance of explicitly accounting for modeling inadequacy in the UQ process, and reinforce the need for continuous refinement of physics-based models in order to address the modeling inadequacy.

Advanced reactors↗
DOE OSTI2019

Power Conversion Efficiencies of Perovskite and Dye-Sensitized Solar Cells under Various Solar Radiation Intensities

We present the results of a comparative study on behaviour of the photovoltaic parameters in perovskite (PSC), dye-sensitized (DSC) and crystalline silicon (c-Si) solar cells under various intensities of solar radiation (10–1000 W/m{sup 2}). It was found that unlike c-Si, the power conversion efficiencies of PSC and DSC under low radiation intensities are comparable with the corresponding values observed under standard light intensity of 1000 W/m{sup 2} (AM1.5G). We have shown that high performance of the PSC and DSC at low and diffuse lighting conditions can be explained by the properties of the nanostructured TiO{sub 2}-based photoelectrodes depending on the structure, morphology and the thickness of the TiO{sub 2} layers.

14 SOLAR ENERGY↗
DOE OSTI2015

Examining the Critical Roles of Protons in Facilitating Oxidation of Chloride Ions by Permanganates: A Cluster Model Study

The oxidation power of permanganates (MnO4–) is known to be strongly dependent on pH values, and is greatly enhanced in acidic solutions, in which, for example, MnO4– can even oxidize Cl– ions to produce Cl2 molecules. Although such dependence has been ascribed due to the different reduced states of Mn affordable in different pH media, a molecular level understanding and characterization of initial redox pair complexes available in different pH solutions is very limited. Herein, we report a comparative study of [MnO4]– and [MnO4•Sol]– (Sol = H2O, KCl, and HCl) anion clusters by negative ion photoelectron spectroscopy (NIPES) and theoretical computations to probe chemical bonding and electronic structures of [MnO4•Sol]– clusters, aimed to obtain a microscopic understanding of how MnO4– interacts with surrounding molecules. Our study shows that H2O behaves as a solvent molecule, KCl is a spectator bound by pure electrostatic interactions, both of which do not influence the MnO4– identity in their respective clusters. In contrast, in [MnO4•HCl]–, the proton is found to interact with both MnO4– and Cl– with appreciable covalent characters, and the frontier MOs of the cluster are comprised of contributions from both MnO4– and Cl– moieties. Therefore the proton serves as a chemical bridge, bringing two negatively charged redox species together to form an intimate redox pair. By adding more H+ to MnO4–, the oxygen atom can be taken away in the form of a water molecule, leaving MnO4– as an electron deficient MnO3+ species, which can subsequently oxidize Cl– ions.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2020

Shock tube and laser absorption study of CO time-histories during combustion of branched alkenes

Combustion experiments of the three isomers of methyl butene compound - 2-methyl-1-butene (2M1B), 2-methyl-2-butene (2M2B), and 3-methyl-1-butene (3M1B), have been carried out in a shock tube using laser absorption technique. Carbon monoxide (CO) time-histories are obtained behind reflected shockwaves over the temperature range of 1350–1630 K near 9.3 atm with stoichiometric mixtures of 0.075% fuel in O2/Ar. Comparative study of CO time-histories reveals different rates of CO formation indicating different ignition delay time of the methyl butene isomers.

09 BIOMASS FUELS↗
DOE OSTI2025

Securing Smart Manufacturing: Detection of Cyber-Physical Attacks in CNC-Based Systems

As Industry 4.0 advances, the integration of computer numerical control (CNC) machines and advanced manufacturing technologies is transforming production into smart manufacturing systems that blend physical and digital processes as cyber-physical systems. However, this increased cyber-physical connectivity exposes manufacturing systems to cyber threats that can cause severe operational and financial disruptions. This paper presents a comparative study on cyber attacks and anomaly detection techniques in manufacturing, focusing on network traffic from CNC machines. The data extracted from network packets includes machine commands and control signals exchanged between the machine's interface and control system, crucial for maintaining operational integrity. We explore two types of cyber attacks, design modification and command injection, which pose substantial risks to CNC machine productivity and system integrity. Our investigation involves experiments on a real CNC system, highlighting the urgent need for effective detection mechanisms. To address these threats, we evaluate three anomaly detection methods: dynamic time warping (DTW), rolling average, and a deep learning, long short-term memory (LSTM) time-series-based autoencoder. Each is assessed for its effectiveness in identifying anomalous behaviors caused by the attacks. Our findings demonstrate the unique strengths and limitations of each detection technique, providing a deeper understanding of their applicability in realworld manufacturing environments. The comparative analysis indicates that while certain methods are highly effective against specific attack types, others offer broader applicability across different attacks. This study contributes to the accurate detection of anomalies in CNC machining processes, thereby enhancing the reliability and security of smart manufacturing systems against diverse cyber threats.

Williams, Bethanie [Tennessee Technological Univer↗
DOE OSTI2025

Optical image analysis of WSe 2 − thresholding for layer detection

The fast and reliable layer identification of two-dimensional transition metal dichalcogenide (TMD), such as WSe 2 , is essential to investigating their thickness-dependent electronic and optical properties. This article presents efficient optical image thresholding methodology designed to segment the mono, bi, and tri-layer regions of WSe 2 flakes mechanically exfoliated onto a SiO 2 /Si substrate. The optical images were first preprocessed to exclude the background effect and analyzed using the pixel medians and interquartile ranges for fundamental color channels—red, green, and blue (RGB). The analysis of red channel pixel intensities yielded three distinct ranges, serving as thresholds for layer segmentation: monolayer (111.0–118.0), bilayer (103.0–110.0), and tri-layer (93.0–103.0). Similarly, thresholds were established for each color channel, facilitating a comparative study of the segmentation performances. Further, the intersection-over-union ($IoU$) calculations revealed that the red and green channels demonstrated greater than 99 % and 90 % accuracy in differentiating each layer, respectively. This approach yields remarkable results without substantial data calibration that utilizes time-intensive heuristic techniques. Moreover, the proposed methodology offers the flexibility to compare performances across different color channels, expanding the applicability for other 2D material systems.

2D Materials↗
DOE OSTI2025

Active Site Dynamics in Molybdenum-Based Silica-Supported Olefin Metathesis Catalysts: Site Renewal and Decay Beyond the Chauvin Cycle

Heterogeneous olefin metathesis catalysts exhibit low active site densities and unpredictable kinetics due to dynamic active site formation and decay processes. Here, in this study, we establish a quantitative framework that captures active site generation, renewal, and decay in olefin metathesis over silica-supported molybdenum oxide catalysts, enabling a mechanistic explanation of catalytic behavior and strategies to achieve high, stable activity. Steady-state active site titrations reveal that 2,3-dimethyl-butene isomers (4MEs) cofeeding increases active site density by up to 4.3-fold, directly correlating with enhanced metathesis rates. Spectroscopic studies demonstrate that 4MEs facilitate Mo(VI) reduction to Mo(IV) and interact strongly with surface Si–OH groups, generating labile protons that promote active site formation via a 1,2-proton shift mechanism. Kinetic modeling indicates that ethylene acts as a decay promoter, shifting kinetic control away from the Chauvin cycle and suppressing metathesis activity. Comparative studies on catalysts with varying Mo loading reveal that promotion is most effective for dispersed molybdate species, with a decline at higher Mo loadings. These findings provide a unified mechanistic framework for heterogeneous olefin metathesis, offering new strategies to enhance active site accessibility, mitigate deactivation, and optimize catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Helical tomotherapy with dynamic running-start-stop delivery compared to conventional tomotherapy delivery

Purpose: Despite superior target dose uniformity, helical tomotherapy{sup ®} (HT) may involve a trade-off between longitudinal dose conformity and beam-on time (BOT), due to the limitation of only three available jaw sizes with the conventional HT (1.0, 2.5, and 5.0 cm). The recently introduced dynamic running-start-stop (RSS) delivery allows smaller jaw opening at the superior and inferior ends of the target when a sharp penumbra is needed. This study compared the dosimetric performance of RSS delivery with the fixed jaw HT delivery. Methods: Twenty patient cases were selected and deidentified prior to treatment planning, including 16 common clinical cases (brain, head and neck (HN), lung, and prostate) and four special cases of whole brain with hippocampus avoidance (WBHA) that require a high degree of dose modulation. HT plans were generated for common clinical cases using the fixed 2.5 cm jaw width (HT2.5) and WBHA cases using 1.0 cm (HT1.0). The jaw widths for RSS were preset with a larger size (RSS5.0 vs HT2.5 and RSS2.5 vs HT1.0). Both delivery techniques were planned based on identical contours, prescriptions, and planning objectives. Dose indices for targets and critical organs were compared using dose-volume histograms, BOT, and monitor units. Results: The average BOT was reduced from 4.8 min with HT2.5 to 2.5 min with RSS5.0. Target dose homogeneity with RSS5.0 was shown comparable to HT2.5 for common clinical sites. Superior normal tissue sparing was observed in RSS5.0 for optic nerves and optic chiasm in brain and HN cases. RSS5.0 demonstrated improved dose sparing for cord and esophagus in lung cases, as well as penile bulb in prostate cases. The mean body dose was comparable for both techniques. For the WBHA cases, the target homogeneity was significantly degraded in RSS2.5 without distinct dose sparing for hippocampus, compared to HT1.0. Conclusions: Compared to the fixed jaw HT delivery, RSS combined with a larger jaw width provides faster treatment delivery and improved cranial-caudal target dose conformity. The target coverage achieved by RSS with a large jaw width is comparable to the fixed jaw HT delivery for common cancer sites, but may deteriorate for cases where complex geometry is present in the middle part of the target.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Photoluminescence study of the structural evolution of amorphous and crystalline silicon nanoclusters during the thermal annealing of silicon suboxide films with different stoichiometry

The effect of the stoichiometry of thin silicon suboxide films on the processes of the formation and evolution of silicon nanoclusters during thermal annealing is studied by photoluminescence measurements. The samples are produced by the thermal sputtering of a SiO powder in an oxygen atmosphere, with the subsequent deposition of a 500 nm-thick SiO{sub x} layer onto a Si substrate. The morphological properties and size of Si nanoclusters are explored by analyzing the photoluminescence spectra and kinetics. A comparative study of the luminescence properties of thin SiO{sub x} layers with different stoichiometric parameters, x = 1.10, 1.29, 1.56, and 1.68, is accomplished for samples annealed at different temperatures in the range 850 to 1200 Degree-Sign C. The dependences of the photoluminescence decay time on the annealing temperature, the stoichiometric parameter of the initial silicon suboxide film, and the nanocluster size are studied.

36 MATERIALS SCIENCE↗
DOE OSTI2025

From carbon to climate action: harnessing basalt for geological carbon dioxide (CO 2 ) storage onshore and offshore

Abating emissions and reducing atmospheric concentrations of carbon dioxide (CO 2 ) are crucial in avoiding catastrophic climate change. Basalt reservoirs offer suitable CO 2 storage sites and are present onshore and offshore. This study compares the geological, economic and social aspects of CO 2 storage in both domains using two basalt formations from the Republic of Ireland: the Limerick Igneous Suite and the Druid Formation. Offshore reservoirs offer larger storage resources but are more expensive to develop. Nevertheless, both offer gigatonne-scale theoretical CO 2 storage. Reviewing public perception studies on wind energy demonstrates that the commonly held belief that offshore projects face less opposition owing to their distance from communities has been dispelled, while similar studies on carbon capture and removal show no preference for onshore or offshore development. Instead, a general scepticism towards carbon removal is observed, with concerns that it hinders broader decarbonization efforts. The desire of all stakeholders to be involved throughout project development is consistently observed. Lessons from offshore natural gas projects highlight the consequences of failing to engage with local communities. The Republic of Ireland has significant potential to deploy geological CO 2 storage in basalt reservoirs, but policy hurdles such as legal limits on storage volumes must be overcome to reconcile climate ambition and legislative capacity.

54 - ENVIRONMENTAL SCIENCES/GLOBAL CLIMATE CHANGE ↗
DOE OSTI2023

Detailed Simulations of a Three-Stage Supercritical Carbon Dioxide Axial Compressor with a Focus on the Shrouded Stator Cavities Flow

This paper describes the findings of detailed simulations performed to investigate the impact of seal teeth cavity leakage flow on the aerodynamic and thermal performance of a three-stage supercritical CO 2 axial compressor. The study compares a shrouded stator configuration (with cavities) to a cantilevered stator configuration (without cavities) to highlight their differences. High-fidelity computational fluid dynamics simulations were performed using non-linear harmonic (NLH) and mixing plane assumptions, considering various possible rotor/stator interface configurations for mixing plane calculations. The key performance parameters for each case were compared, and the best-performing configuration selected for further analysis. The individual stage performance parameters are also examined and compared between the cantilevered and shrouded configurations. It was observed that in the shrouded case, the leakage flow enters the cavity downstream of the stator trailing edge and gets entrained into the primary flow upstream of the stator, leading to boundary layer changes at the hub and degradation of stator and downstream rotor performance. Vortical flow structures were also observed in the stator wells, which tended to change the flow angles around the region, thereby affecting mixing and velocity distribution, resulting in a slight deterioration of compressor performance. Additionally, the study examines windage heating due to shear work from rotating walls, including the seal teeth surface. The amount of shear work done on the leakage flow and the corresponding rise in fluid temperature were quantified, tabulated, and further compared with a simple analytical model, showing good agreement between them and, hence, validating the numerical approach used.

42 ENGINEERING↗
DOE OSTI2016

Slow Dynamics Model of Compressed Air Energy Storage and Battery Storage Technologies for Automatic Generation Control

Increasing variable generation penetration and the consequent increase in short-term variability makes energy storage technologies look attractive, especially in the ancillary market for providing frequency regulation services. This paper presents slow dynamics model for compressed air energy storage and battery storage technologies that can be used in automatic generation control studies to assess the system frequency response and quantify the benefits from storage technologies in providing regulation service. The paper also represents the slow dynamics model of the power system integrated with storage technologies in a complete state space form. The storage technologies have been integrated to the IEEE 24 bus system with single area, and a comparative study of various solution strategies including transmission enhancement and combustion turbine have been performed in terms of generation cycling and frequency response performance metrics.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2014

Charge-transfer state excitation as the main mechanism of the photodarkening process in ytterbium-doped aluminosilicate fibres

We have studied photodarkening in ytterbium-doped fibre preforms with an aluminosilicate glass core. Analysis of their absorption and luminescence spectra indicates the formation of stable Yb{sup 2+} ions in the glass network under IR laser pumping at a wavelength λ = 915 nm and under UV irradiation with an excimer laser (λ = 193 nm). We have performed comparative studies of the luminescence spectra of the preforms and crystals under excitation at a wavelength of 193 nm. The mechanism behind the formation of Yb{sup 2+} ions and aluminium – oxygen hole centres (Al-OHCs), common to ytterbium-doped YAG crystals and aluminosilicate glass, has been identified: photoinduced Yb{sup 3+} charge-transfer state excitation. (optical fibres)

36 MATERIALS SCIENCE↗
DOE OSTI2018

Dose Rate Evaluation for the ES-3100 Package with HEU Content Using MCNP, ADVANTG, Monaco, and MAVRIC

This paper presents a comparative study of dose rate calculations for the ES-3100 package with highly enriched uranium (HEU) content for different source configurations using computer codes: (1) MCNP; (2) Automated Variance Reduction Generator (ADVANTG)/MCNP; (3) Monaco; and (4) Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC). The Model ES-3100 package was developed at the Y-12 National Security Complex for domestic and international transportation of Type B fissile radioactive material. In this study, six different source configurations (i.e., solid cylinder, cylindrical hemi-shell, cylindrical shell, rectangular plate, cylindrical rod, or cylindrical segment form) having 36 kg of HEU metal inside the package containment vessel (based on configurations in the ES-3100/HEU safety analysis report for packaging) are evaluated. Dose rates at the package surfaces and 1 m from the package surfaces are calculated for these different source configurations. MCNP and Monaco cases are run without any biasing options to accelerate the convergence. Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) methods developed at the Oak Ridge National Laboratory are implemented in ADVANTG/MCNP and MAVRIC codes to accelerate the convergence. ADVANTG generates variance reduction parameters using Denovo code, and MCNP is used with the variance reduction parameters to accelerate the convergence. MAVRIC uses Denovo code to construct an importance map and a biased source distribution that are supplied to Monaco to accelerate the Monte Carlo simulation. The FW-CADIS option in ADVANTG and MAVRIC is used to accelerate the convergence in this study. The accelerated convergence cases (ADVANTG/MCNP and MAVRIC) are about 100 times faster with 100 times less particle simulation than those cases run without biasing options (analog MCNP and analog Monaco). The MCNP, ADVANTG/MCNP, Monaco, and MAVRIC calculated dose rates at the package surfaces and at 1 m from the package surfaces for the different source configurations are compared and are found to be in general agreement.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Comparing Theoretical Salt Concentration Profiles in a Polymer Electrolyte with Experimental Measurements using Operando Raman Spectroscopy

Concentrated solution theory has furthered our understanding of ion transport in electrolytes. This theory can be used to predict salt concentration profiles under an applied current if the transport properties of the electrolyte (conductivity ( κ ), restricted diffusion coefficient ( D ), and the cation transference number with respect to the solvent velocity ( t + 0 )), and the thermodynamic factor ( T f ) are known. In this work, we provide the first study comparing the predicted salt concentration profiles with measurements based on operando Raman spectroscopy. Concentration polarization is asymmetrical; the increase in salt concentration near the positive electrode is a factor of two greater than the decrease in salt concentration near the negative electrode. We find qualitative agreement between theory and experiment. Further work is needed to resolve the quantitative differences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗