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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Near-Infrared Spectroscopy can Predict Anatomical Abundance in Corn Stover

Feedstock heterogeneity is a key challenge impacting the deconstruction and conversion of herbaceous lignocellulosic biomass to biobased fuels, chemicals, and materials. Upstream processing to homogenize biomass feedstock streams into their anatomical components via air classification allows for a more tailored approach to subsequent mechanical and chemical processing. Here, we show that differing corn stover anatomical tissues respond differently to pretreatment and enzymatic hydrolysis and therefore, a one-size-fits-all approach to chemical processing biomass is inappropriate. To inform on-line downstream processing, a robust and high-throughput analytical technique is needed to quantitatively characterize the separated biomass. Predictive correlation of near-infrared spectra to biomass chemical composition is such a technique. Here, we demonstrate the capability of models developed using an “off-the-shelf,” industrially relevant spectrometer with limited spectral range to make strong predictions of both cell wall chemical composition and the relative abundance of anatomical components of the corn stover, the latter for the first time ever. Gaussian process regression (GPR) yields stronger correlations (average R 2 v = 88% for chemical composition and 95% for anatomical relative abundance) than the more commonly used partial least squares (PLS) regression (average R 2 v = 84% for chemical composition and 92% for anatomical relative abundance). In nearly all cases, both GPR and PLS outperform models generated using neural networks. These results highlight the potential for coupling NIRS with predictive models based on GPR due to the potential to yield more robust correlations.

09 BIOMASS FUELS↗
DOE OSTI2021

Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Using Best Basis Inventory Data to Direct Strategies for Real Time Monitoring of Hanford High Level Waste – 26226

The potential to accelerate the processing of low- and high-level tank waste by applying real-time monitoring (RTM) of chemical and physical properties has prompted research into the suitability of multiple analytical methods for that purpose. The broad variety of waste stream properties and the large number of analytes of interest (as evidenced by Waste Acceptance Criteria (WAC) and Process Control Limit (PCL) lists) lead to an overwhelming set of possible analytical scenarios. This report describes the use of Best Basis Inventory (BBI) data to find the most relevant analytical targets for the specific case of monitoring the blending of High Level Waste from multiple tanks prior to introduction into a vitrification facility. Campaigns for blending this waste to minimize the risk of exceeding WACs and PCLs have been proposed. However, the predicted compositions of the blended materials do not incorporate any uncertainties that may be associated with the representativeness of the waste layer samples or the laboratory analyses that generated the BBI data. Also, they do not include any uncertainty associated with the precision of collecting highly specific fractions of the layers during a blending campaign or any inhomogeneities that may exist in those layers. Monte Carlo methods are used to apply uncertainties to the compositions of the individual layers specified in the campaign recipes. The resulting variations in the compositions of the blended materials allow estimation of the risks of exceeding WACs and PCLs for each campaign. A critical subset of WACs/PCLs – NOx, NaK, AlFeZr, and S – are especially at risk of being exceeded in multiple campaigns. These analytes should be the focus of instrument development. We also have extracted the expected solid/supernate distribution for these analytes, which establishes important performance criteria for individual analytical methods. The BBI data also permits an understanding of the different chemical forms in which the analytes appear. Thus, the need to establish instrumental sensitivity to these forms can be gainfully addressed. Although concentrating on one specific application – the blending of tank waste - this approach should be generalizable for the analysis of other possible RTM applications for waste processing.

Lascola, Robert [Savannah River National Laborator↗
DOE OSTI2020

Computationally efficient optimization models for preliminary distillation column design and separation energy targeting

We propose versatile shortcut distillation column and separation energy targeting models that are well-suited for superstructure-based process synthesis. The models are based on a novel reformulation of the Underwood equations to address systems where the components that are present in the feed can vary due to zero flow rates of some components. Also, we propose valid constraints, resulting in a significant enhancement of the computational performance of the models. Furthermore, the proposed distillation column model can automatically identify adequate key components and the energy requirement of a desired separation task, while considering a wide range of types of separations including non-sharp/sloppy splits. Also, the proposed separation energy targeting model can be used to estimate an energy requirement target for the separation of a mixture without finding detail network configurations. Due to their versatility and computational efficiency, the proposed models can be readily used for and expand the scope of superstructure-based process synthesis approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer

It is challenging to develop numerical methods that simultaneously maintain accuracy of resolving boundary conditions and mesh flexibility to handle the interface in interface-coupled multi-physics problems involving large property discontinuity. On the one hand, boundary-fitted methods possess high accuracy in capturing the interfacial phenomenon but involve complicated volumetric mesh generation, mesh-motion, and even re-meshing procedures. On the other hand, immersed boundary methods (IBM) provide mesh flexibility but sometimes suffer from inferior interface representations, leading to poor enforcement of boundary conditions. This paper presents an enriched immersed boundary method (EIBM) to overcome this challenge and demonstrates its efficacy in conjugate heat transfer, a representative example in interface-coupled multi-physics systems that have implications for many industrial processes. Further, the core technique of the method is to enhance IBM’s accuracy of the fluid–solid interface by enriching the degrees of freedom of the cut elements to enforce temperature and flux compatibilities and resolve all the physical unknowns on the background mesh to simplify the volumetric mesh generation. We implement the EIBM under the framework of a variational multiscale formulation for coupled Navier–Stokes and thermodynamics equations. The enriched DoFs enable better enforcement of temperature and flux compatibilities with large conductivity ratios across the fluid–solid interface. At the same time, the immersed nature of the proposed method still attains mesh flexibility. The EIBM’s accuracy is thoroughly evaluated through a set of examples, ranging from benchmark problems with analytical solutions to real-world cooling processes of a moving metallic structure with complex geometry.

42 ENGINEERING↗
DOE OSTI2026

Machine Tool Data Analytics for Digital Twin and Machine Predictive Maintenance

The primary objective of this project is to improve machining process performance using in-process machining data from the machine tool controller and external sensors. Advances in the Industrial Internet of Things (IIoT) enable monitoring of machines using controller data. Examples of the data provided by a controller include execution status of the controller, part count, block of code being executed, door status, tool position, the spindle and axis load, etc. MTConnect and OPC-UA are the two common protocols for capturing machine information. In this collaboration, methods for retrieving the machine controller data from selected machine tool controls and making these data accessible in different subsystems (such as digital twins and machine maintenance portals, etc.) will be developed and tested. In addition, analytics to improve machining process performance (by increasing productivity and reducing downtime) will be developed.

42 ENGINEERING↗
DOE OSTI2021

System Configuration Evaluation for Process Settling of Hanford Waste Solid Particles

Direct Feed High-Level Waste (DFHLW) is a potential flowsheet operations approach to initiating high-level waste (HLW) vitrification prior to completion of the Hanford Waste Treatment and Immobilization Plant (WTP) Pretreatment Facility. A settle/decant process has been proposed to concentrate solids prior to delivery to the WTP HLW Facility during DFHLW operations, wherein the solids in a settled layer would be remixed with the supernatant liquid remaining after decanting operations to provide the feed at required solids concentrations. Settling would be used in lieu of purpose-built filtration or other solids separation equipment. Pacific Northwest National Laboratory (PNNL) is providing baseline technical support to the Washington River Protection Solutions (WRPS) Flowsheet Integration group. To support planning for DFHLW, WRPS previously requested that PNNL evaluate the current data set available to predict the time needed for HLW solids to settle and the solids concentration and strength of that settled layer, to identify gaps in the understanding and predictive capability of HLW solids waste settling times, and to provide scoping estimates of the potential settling times. Eight technical gaps were identified for predicting settling times and characteristics of the formed sediment layers. In addition to the data gaps, an overarching observation was made that there is significant variation in behavior of settling rate and settled layer data. The settling time required to concentrate solids via a settle/decant process was determined from the limited data to have a difference of potentially more than a factor of 5,000 in the estimated settling times, varying from 0.2 to 1,060 days for example depending on process vessel depth and final sediment solids concentration. In contrast, successful processes of liquid-forward output streams resulting from in-tank settling and decanting forward liquid have been reported for operations conducted at the Hanford Site. The purpose of this current report is to further support DFHLW planning by evaluating double-shell tank (DST) and alternate vessel equipment and operational configurations to enable optimization of the settle/decant process to concentrate solids. Hanford waste processing behavior specific to liquid feed availability following a slurry transfer in a DST is summarized, including process stream characteristics and process equipment configurations. The performance of DST process equipment configurations is evaluated for possible improvements using computational fluid dynamics (CFD) and simple analytical models. Potential new vessel design(s) specific to enabling effective settle/decant processes, and cursory summary of other separate and inline solids separations processes, are also provided. The CFD results indicated that improvement in outflow solids concentration was promoted by a reduction in the slurry flow rate, angling the distributor nozzles downward, and lifting the transfer pump. The solid-liquid analysis evaluating particle trajectory confirmed that the potential for particle ingestion (in the transfer pump) was decreased with increased radial separation between the inlet and outlet (transfer pump inlet), decreased inlet flow, and decreased liquid density and viscosity for a neutrally buoyant inlet flow. An assessment was also made of the potential for inflow configuration changes to result in the discrete mounding or piling of solids within the tank. Based on the characterization of the settled waste to date, HLW sediments will be unlikely to sustain a substantial angle of repose to facilitate significant variations in the elevation of the settled solids.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Achieving industrial ammonia synthesis rates at near-ambient conditions through modified scaling relations on a confined dual site

The production of ammonia through the Haber–Bosch process is regarded as one of the most important inventions of the 20th century. Despite significant efforts in optimizing the process, it still consumes 1 to 2% of the worldwide annual energy for the high working temperatures and pressures. The design of a catalyst with a high activity at milder conditions represents another challenge for this reaction. Herein, we combine density functional theory and microkinetic modeling to illustrate a strategy to facilitate low-temperature and -pressure ammonia synthesis through modified energy-scaling relationships using a confined dual site. Our results suggest that an ammonia synthesis rate two to three orders of magnitude higher than the commercial Ru catalyst can be achieved under the same reaction conditions with the introduction of confinement. Such strategies will open pathways for the development of catalysts for the Haber–Bosch process that can operate at milder conditions and present more economically viable alternatives to current industrial solutions.

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

The Design and Implementation of a Secure Datastore Based on Ethereum Smart Contract

In this paper, we present a secure datastore based on an Ethereum smart contract. Our research is guided by three research questions. First, we will explore to what extend a smart-contract-based datastore should resemble a traditional database system. Second, we will investigate how to store the data in a smart-contract-based datastore for maximum flexibility while minimizing the gas consumption. Third, we seek answers regarding whether or not a smart-contract-based datastore should incorporate complex processing such as data encryption and data analytic algorithms. The proposed smart-contract-based datastore aims to strike a good balance between several constraints: (1) smart contracts are publicly visible, which may create a confidentiality concern for the data stored in the datastore; (2) unlike traditional database systems, the Ethereum smart contract programming language (i.e., Solidity) offers very limited data structures for data management; (3) all operations that mutate the blockchain state would incur financial costs and the developers for smart contracts must make sure sufficient gas is provisioned for every smart contract call, and ideally, the gas consumption should be minimized. Our investigation shows that although it is essential for a smart-contract-based datastore to offer some basic data query functionality, it is impractical to offer query flexibility that resembles that of a traditional database system. Furthermore, we propose that data should be structured as tag-value pairs, where the tag serves as a non-unique key that describes the nature of the value. We also conclude that complex processing should not be allowed in the smart contract due to the financial burden and security concerns. The tag-based secure datastore designed this way also defines its applicative perimeter, i.e., only applications that align with our strategy would find the proposed datastore a good fit. Those that would rather incur higher financial cost for more data query flexibility and/or less user burden on data pre- and post-processing would find the proposed database too restrictive.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Comparison of modular analytical wake models to the Lillgrund wind plant

Efficient and accurate wake models are required for wind plant performance modeling and the suite of engineering processes that support wind plant layout, control, and monitoring. Although many analytical and engineering wake models with low computational costs have been proposed, their ability to represent the power production of large wind plants in a wide range of atmospheric conditions is not completely understood. The following validation study reviews the underlying theory for analytical wake models, outlines quality control procedures for observational data, and compares model results with observational data from the Lillgrund Wind Plant. Lillgrund makes a valuable case study for wake modeling because of its regular arrangement and the relatively close spacing of constituent wind turbines, which lead to regular and significant wake interactions within the wind plant and the development of deep array flow conditions. Formulations for the velocity deficit, wake-added turbulence, and wake superposition methods are considered in a modular sense, yielding many possible configurations to represent wind turbine wakes, of which seven are examined in detail. Velocity deficit models that account for flow conditions in the near wake are better able to reproduce power production for wind turbines in the transitional region of the wind plant, where wind turbines experience as many as five wakes from upstream turbines. Finally, in the deep array, where power production reaches asymptotic values and wake statistics become quasi-periodic, wake superposition schemes become the largest driver in error reduction; using the linear or maximum wake superposition methods can reduce the relative root mean square error by as much as 40% in the deep array.

17 WIND ENERGY↗
DOE OSTI2020

Effects of Extended Aqueous Processing on Structure, Chemistry, and Performance of Polycrystalline LiNi x Mn y Co z O 2 Cathode Powders

The prospect of aqueous processing of LiNi x Mn y Co z O 2 (NMC) cathodes has significant appeal to battery manufacturers for the reduction in materials cost, toxicological risk, and environmental impact compared to conventional N -methyl-2-pyrrolidone (NMP)-based processing. However, the effects of aqueous processing of NMC powders at industrial timescales are not well studied, with prior studies mostly focusing on relatively brief water washing processes. Here, we investigate the bulk and surface impacts of extended aqueous processing of polycrystalline NMC powders with different compositions. We demonstrate that at timescales of several hours, polycrystalline NMC is susceptible to intergranular fracture, with the severity of fracture scaling with the NMC nickel content. While bulk crystallinity and composition are unchanged, surface sensitive techniques such as X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM) indicate that the exposure of water leads to a level of delithiation, nickel reduction, and reconstruction from the layered to rock-salt structure at the surface of individual grains. Dynamic single NMC microparticle compression testing suggests that the resulting mechanical stresses weaken the integrity of the polycrystalline particle and increases susceptibility of intergranular fracture. The initially degraded surfaces along with the increased surface area lead to faster capacity fade and impedance growth during electrochemical cycling. From this work, it is demonstrated that NMC powders require surface or grain boundary modifications to make industrial-scale aqueous cathode processing viable, especially for next-generation nickel-rich NMC chemistries.

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

Development of a Framework for Data Integration, Assimilation, and Learning for Geological Carbon Sequestration (DIAL-GCS) (Final Report)

This project aimed to develop and demonstrate a Data Integration, Assimilation, and Learning framework for geologic carbon sequestration projects (DIAL-GCS). DIAL-GCS is an intelligence monitoring system (IMS) for automating GCS closed-loop management by leveraging recent developments in machine learning technologies, complex event processing (CEP), and reduced-order modeling. The safe and efficient operation of GCS repositories requires integrated monitoring to track the injected CO¬2 as it moves within a storage reservoir. GCS projects are data intensive, as a result of proliferation of digital instrumentation and smart-sensing technologies. GCS projects are also resource intensive, often requiring multidisciplinary teams performing different monitoring, verification, accounting (MVA) tasks throughout the lifecycle of a project to ensure secure containment of injected CO2. The success of GCS thus depends in a large part on our ability to access, assimilate, and analyze heterogeneous data and information sources in a timely manner. This project included a number of meaningful and necessary tasks to transform the human domain knowledge into machine-interpretable rules for automating knowledge extraction and discovery in GCS. The specific technical objectives of the proposed DIAL-GCS project were to develop an ontology-driven GCS data management module for storing, querying, and exchanging GCS data (both historic and live sensor data) from multiple sources and in heterogeneous formats. Incorporate a CEP engine for detecting abnormal situations by seamlessly combining expert knowledge, rule-based reasoning, and machine learning. Enable uncertainty quantification and predictive analytics using a combination of coupled-process modeling, AI/ML methods, and reduced-order modeling, and integrate and demonstrate the system’s capabilities with both real and simulated data. As far as we know, this is one of the first projects aimed to develop intelligent monitoring systems (IMS) targeting the GCS. Under this project, the team had developed a large number of web applications and scientific algorithms that contribute the main theme of intelligent monitoring. The team has published more than a dozen peer reviewed papers and disseminated the research results at multiple technical meetings.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Integrating Data Sources for Improved Safeguards and Accountancy of Electrochemical Fuel Reprocessing Systems. Final Report

Electrochemical reprocessing (also commonly known as “pyroprocessing”) of used nuclear fuel is an alternative to aqueous reprocessing that confers a number of advantages, including the ability to process more recently-discharged fuel, smaller resultant waste volumes, and the lack of isolation of plutonium in the product stream. While electrochemical reprocessing systems have seen a significant research and development effort, nuclear safeguards and security of these systems remains under-developed, particularly given the significant differences in operating environment and process flowsheet compared with established aqueous methods. Objective 4 of DOE’s nuclear energy research and development activities in Nuclear Energy Research and Development Roadmap is: “Understand and minimize the risks of nuclear proliferation and terrorism.” Material Control & Accountancy (MC&A) programs at nuclear processing plants deter and detect theft and diversion of nuclear material by both outside and inside adversaries. Empirical modeling and data analytics of online measurements and state indicators can improve the timeliness of detection and reduce the uncertainty in accountancy measures. To support the development and demonstration of such methods, data are needed that capture expected measurement values collected throughout electrochemical reprocessing facilities. A review of the available literature of current research in measurements for electrochemical reprocessing systems identified twenty-two candidate measurement methodologies, which characterize fuel/salt composition, concentrations of various isotopes and elements, and operational parameters throughout the reprocessing facility. Four primary measurement methodologies have been simulated based on either physical simulations or empirical correlations: gamma emissions, neutron emissions, hybrid k-edge densitometry (HKED), and cyclic voltammetry. Initial investigation into the use of these measures for process monitoring and detection suggests the approach is viable and worthy of further investigation. This report summarizes efforts to generate signatures of key measurements during operation of electrochemical reprocessing facilities and initial investigation of data analytics to support process monitoring, diversion detection, and accountancy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Laboratory measurements of the physics of auroral electron acceleration by Alfvén waves

While the aurora has attracted attention for millennia, important questions remain unanswered. Foremost is how auroral electrons are accelerated before colliding with the ionosphere and producing auroral light. Powerful Alfvén waves are often found traveling Earthward above auroras with sufficient energy to generate auroras, but there has been no direct measurement of the processes by which Alfvén waves transfer their energy to auroral electrons. Here, we show laboratory measurements of the resonant transfer of energy from Alfvén waves to electrons under conditions relevant to the auroral zone. Experiments are performed by launching Alfvén waves and simultaneously recording the electron velocity distribution. Numerical simulations and analytical theory support that the measured energy transfer process produces accelerated electrons capable of reaching auroral energies. The experiments, theory, and simulations demonstrate a clear causal relationship between Alfvén waves and accelerated electrons that directly cause auroras.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Modelling general-relativistic plasmas with collisionless moments and dissipative two-fluid magnetohydrodynamics

ABSTRACT Relativistic plasmas are central to the study of black hole accretion, jet physics, neutron star mergers, and compact object magnetospheres. Despite the need to accurately capture the dynamics of these plasmas and the implications for relativistic transients, their fluid modelling is typically done using a number of (overly) simplifying assumptions, which do not hold in general. This is especially true when the mean free path in the plasma is large compared to the system size, and kinetic effects start to become important. Going beyond common approaches used in the literature, we describe a fully relativistic covariant 14-moment based two-fluid system appropriate for the study of electron–ion or electron–positron plasmas. This generalized Israel-Stewart-like system of equations of motion is obtained directly from the relativistic Boltzmann–Vlasov equation. This new formulation can account for non-ideal effects, such as anisotropic pressures and heat fluxes, not present in previous formulations of two-fluid magnetohydrodynamics. We show that a relativistic two-fluid plasma can be recast as a single fluid coupled to electromagnetic fields with (potentially large) out-of-equilibrium corrections. We keep all electron degrees of freedom, which provide self-consistent evolution equations for electron temperature and momentum. The out-of-equilibrium corrections take the form of a collisional 14-moment closure previously described in the context of viscous single fluids. The equations outlined in this paper are able to capture the full two-fluid character of collisionless plasmas found in black hole accretion and flaring processes around compact objects, as well Braginskii-like two-fluid magnetohydrodynamics applicable to weakly collisional plasmas inside accretion discs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Near-field infrared microscopy: A novel analytic mapping technique to nanocharacterize calcium silicate-based cement materials

Infrared imaging via scattering-type scanning near-field optical microscopy (s-SNOM) allows chemical mapping of organic and inorganic materials with nanoscale spatial resolution. However, its potential adaptation to the complex multiphase structure of Portland cement is yet to be explored. Here we demonstrate the successful implementation of s-SNOM to spatially resolve coexisting chemical phases in tricalcium silicate, Portland cement's main compound, with 20-nm resolution. We found that s-SNOM is sensitive to different anhydrous polymorphic phases, revealing nanoscale domains that are ‘invisible’ to other microscopic techniques. Furthermore, s-SNOM's ability to distinguish the unhydrated and hydrated phases signifies its great promise as an analytical tool to study the complex hydration process of cement. The key to s-SNOM's application was nano-modifying the surface roughness of the cement samples, allowing nanoscale infrared imaging without topographical artifacts. Our study opens a window for infrared spectral microscopy in cement and other porous inorganic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Fundamentals of Au(111) Surface Dynamics: Coarsening of Two-Dimensional Au Islands

Au(111) surfaces play a central role in many applications, yet studies of fundamental aspects of their dynamics are limited. Thus, using scanning tunneling microscopy (STM) at 300 K, we analyze the coarsening of first-layer 2D Au islands directly on the Au(111) substrate and also of second-layer 2D Au islands. Specifically, we monitor the decay of Au first-layer islands with areas of about 100–500 nm 2 in the vicinity of larger islands or extended step edges over a period of approximately 40 h, the relevant time scale for this process. Experimentally observed behavior is captured by analytical theory for terrace-diffusion-limited decay incorporating DFT results for the Au terrace diffusion barrier and the adatom formation energy.Lastly, experimental observations of second-layer island decay are also compared with appropriate analytical theory and stochastic simulations, thereby determining the effective Ehrlich–Schwoebel barrier for Au on Au(111).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗