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At least 289 records · Page 16

Cosmology meets cohomology

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated relative twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

Recent and future developments in pultrusion technology with consideration for curved geometries: A review

Herein this paper examined the current state and future developments in pultrusion with particular emphasis on its application in curved part manufacturing. The relationship between factors such as resin chemistry, fiber characteristics, and die geometry that influences the properties of pultruded product were highlighted. Moreover, the specific challenges associated with pultruding curved parts such as the complexities in achieving uniformity and structural integrity in such geometries were discussed. The review emphasized mold design, process improvement, adaptive control systems for precise resin impregnation and material selection to address these challenges. Additionally, the paper suggests the integration of real-time monitoring and data analytics as ways to enhance quality control during curved parts pultrusion. These advancements will help to overcome challenges specific to curved pultrusion and make the process more efficient. Other manufacturing techniques such as filament winding, thermoforming, pulforming were mentioned as alternatives to curved parts pultrusion. The review also explores pultruded variable curvature processes, highlighting some notable patents and article related to this subject matter. Production of pultruded variable curvature parts was seen as a key driver that can shape the future of pultrusion. Finally, the paper anticipates future trends, with sustainability, customization, integration of advanced materials, and development of techniques for pultrusion of composites parts.

42 ENGINEERING↗

Enhancing Top-Down Proteomics of Brain Tissue with FAIMS

Proteomic investigations of Alzheimer’s and Parkinson’s disease have provided valuable insights into neurodegenerative disorders. Thus far, these investigations have largely been restricted to bottom-up approaches, hindering the degree to which one can characterize a protein’s “intact” state. Top-down proteomics (TDP) overcomes this limitation, however it is typically limited to observing only the most abundant proteoforms and of a relatively small size. Therefore, offline fractionation techniques are commonly used to reduce sample complexity, limiting throughput. A higher throughput alternative is online fractionation, such as gas phase high-field asymmetric waveform ion mobility spectrometry (FAIMS). Using a high complexity sample derived from Alzheimer’s disease brain tissue, we describe how the addition of FAIMS to TDP can robustly improve the depth of proteome coverage. For example, implementation of FAIMS at -50 compensation voltage (CV) more than doubled the mean number of non-redundant proteoforms observed (1,833 ± 17, n = 3), compared to without (754 ± 35 proteoforms). We also found FAIMS can influence the transmission of proteoforms and their charge envelopes based on their size. Importantly, FAIMS enabled the identification of intact amyloid beta (Aß) proteoforms, including the aggregation-prone Aß1-42 variant which is strongly linked to Alzheimer’s disease.

59 BASIC BIOLOGICAL SCIENCES↗

Bio-based oxalic acid production in Issatchenkia orientalis enables sustainable rare earth recovery

The growing demand for rare earth elements (REEs) in clean energy and high-tech industries underscores the need for sustainable recovery methods and a reliable supply of processing chemicals. Here, we establish a microbial platform using the acid-tolerant yeast Issatchenkia orientalis SD108 to produce bio-oxalic acid for REE recovery. By introducing an oxaloacetate cleavage pathway and applying metabolic engineering, the engineered strain produces 39.53 g·L -1 oxalic acid at pH 4.0 in fed-batch fermentation. The crude fermentation broth, used without purification, efficiently precipitates over 99% neodymium (Nd), 99% dysprosium (Dy), and 98% lanthanum (La) from individual REE chloride solutions. Recovery from a low-grade ore leachate achieves over 99% total recovery. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) confirm that REE oxalates precipitated with bio-oxalic acid closely resemble those obtained using commercial oxalic acid. Techno-economic analysis (TEA) and life cycle assessment (LCA) further demonstrate that bio-oxalic acid can be produced at a competitive price of $1.79·kg -1 while reducing carbon intensity (CI) by 112% to 63.5% with and without electricity displacement, respectively, relative to the fossil-based benchmark. These results highlight bio-oxalic acid as a green, economically viable alternative to synthetic oxalate for sustainable REE recovery.

59 BASIC BIOLOGICAL SCIENCES↗

Investigating the clinico-anatomical dissociation in the behavioral variant of Alzheimer disease

We previously found temporoparietal-predominant atrophy patterns in the behavioral variant of Alzheimer’s disease (bvAD), with relative sparing of frontal regions. Here, we aimed to understand the clinico-anatomical dissociation in bvAD based on alternative neuroimaging markers. We retrospectively included 150 participants, including 29 bvAD, 28 “typical” amnestic-predominant AD (tAD), 28 behavioral variant of frontotemporal dementia (bvFTD), and 65 cognitively normal participants. Patients with bvAD were compared with other diagnostic groups on glucose metabolism and metabolic connectivity measured by [ 18 F]FDG-PET, and on subcortical gray matter and white matter hyperintensity (WMH) volumes measured by MRI. A receiver-operating-characteristic-analysis was performed to determine the neuroimaging measures with highest diagnostic accuracy. bvAD and tAD showed predominant temporoparietal hypometabolism compared to controls, and did not differ in direct contrasts. However, overlaying statistical maps from contrasts between patients and controls revealed broader frontoinsular hypometabolism in bvAD than tAD, partially overlapping with bvFTD. bvAD showed greater anterior default mode network (DMN) involvement than tAD, mimicking bvFTD, and reduced connectivity of the posterior cingulate cortex with prefrontal regions. Analyses of WMH and subcortical volume showed closer resemblance of bvAD to tAD than to bvFTD, and larger amygdalar volumes in bvAD than tAD respectively. The top-3 discriminators for bvAD vs. bvFTD were FDG posterior-DMN-ratios (bvAD bvFTD, area under the curve [AUC] range 0.85–0.91, all p < 0.001). The top-3 for bvAD vs. tAD were amygdalar volume (bvAD>tAD), MRI anterior-DMN-ratios (bvAD<tAD), FDG anterior-DMN-ratios (bvAD<tAD, AUC range 0.71–0.84, all p < 0.05). Subtle frontoinsular hypometabolism and anterior DMN involvement may underlie the prominent behavioral phenotype in bvAD.

59 BASIC BIOLOGICAL SCIENCES↗

Robust Large-Scale Dynamic Windows using Reversible Metal Electrodeposition

This project funded the study and development of dynamic windows based on reversible metal electrodeposition (RME). Dynamic windows allow user control over light and heat flow into and out of buildings, which offer both advantages in building aesthetics (with worker productivity improvement of 2%) and energy efficiency (up to 20% savings) compared to static controls such as low emissivity coatings and blinds/shades. Despite these advantages, dynamic windows, which traditionally rely on electrochromic metal oxides or conductive organic molecules for light modulation have failed to significantly impact the market due to issues related to cost, color, and optical dynamic range. Dynamic windows based on reversible metal electrodeposition (RME) are an exciting alternative approach and have the potential to overcome the issues associated with traditional technologies. A RME dynamic window is an electrochemical cell that modulates light using the reversible electrodeposition of metal on and off a transparent conducting oxide (TCO), which serves as the working electrode. The electrolyte has nearly colorless metal salts dissolved, and application of a cathodic potential on the TCO reduces the metal cations across the TCO surface to their metallic form, making a thin film that is efficient at blocking out light. A reverse in polarity oxidizes the metal, where it dissolves into solution, returning the window back to transparent. The counter electrode typically employed is a metal mesh, which is used to balance the electrochemical reactions happening on the TCO working electrode. These RME dynamic windows have the largest dynamic range (capable of reaching <<0.1% transmission) with color neutral tinting of any existing technology using solution processed techniques, which positions the technology as a promising candidate to penetrate the residential market. We have successfully scaled up the windows from 25 cm2 to 929 cm 2 , and we have demonstrated significant improvements to both the cycle life (10,000 cycles in a 3-electrode half-cell) and shelf life (>1 month) of our windows. We have published our work in high impact journals (6 published and 2 manuscripts in prep), filed 5 patents, and have incorporated TYNT Technologies to commercialize the technology.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Practical CO2—WAG Field Operational Designs Using Hybrid Numerical-Machine-Learning Approaches

Machine-learning technologies have exhibited robust competences in solving many petroleum engineering problems. The accurate predictivity and fast computational speed enable a large volume of time-consuming engineering processes such as history-matching and field development optimization. The Southwest Regional Partnership on Carbon Sequestration (SWP) project desires rigorous history-matching and multi-objective optimization processes, which fits the superiorities of the machine-learning approaches. Although the machine-learning proxy models are trained and validated before imposing to solve practical problems, the error margin would essentially introduce uncertainties to the results. In this paper, a hybrid numerical machine-learning workflow solving various optimization problems is presented. By coupling the expert machine-learning proxies with a global optimizer, the workflow successfully solves the history-matching and CO2 water alternative gas (WAG) design problem with low computational overheads. The history-matching work considers the heterogeneities of multiphase relative characteristics, and the CO2-WAG injection design takes multiple techno-economic objective functions into accounts. This work trained an expert response surface, a support vector machine, and a multi-layer neural network as proxy models to effectively learn the high-dimensional nonlinear data structure. The proposed workflow suggests revisiting the high-fidelity numerical simulator for validation purposes. The experience gained from this work would provide valuable guiding insights to similar CO2 enhanced oil recovery (EOR) projects.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Community Engagement - A Citizen-Centric Approach to Seeking a Social License - 20017

The long regulatory road has finally been completed-after years of effort a Record of Decision has been signed and a Permit to Construct has been granted or a Permit to Operate has been obtained. But what about the other road that should be taken in parallel-community engagement? Working with the public is not a sequential activity, rather it is a consequential one and needs to be integrated with overall project planning. Unless you have effectively, meaningfully, and patiently engaged with the project's communities of impact, you may find your project trying to obtain a social license or a social license to operate (SLO). The SLO has its origins in the mining industry and its roots in the business model of corporate social responsibility and sustainability. These latter practices are well known to the US DOE and its contractor community. Aspects of the SLO are emerging as individuals and communities are becoming more informed and have increased expectations for being able to influence and shape decisions. When local community issues are not sought out, listened to, or addressed early, and questions are left unanswered, they can become agenda items for larger unaffiliated groups, and project loss (through delays and/or cancellation) can occur. Issues can transition from resolvable to intractable, a type of SLO face-off. Social media campaigns, serial negative media coverage, and protest signs at project sites opposing regulatory decisions already made are no longer anomalies. These types of incidents demonstrate the increasingly delicate relationship between approved regulatory/technical decisions and public acceptance of those decisions. A SLO is not a requirement. However, the building-blocks of a SLO - working with members of affected communities to build understanding, potentially to obtain and maintain community acceptance or even gain approval or support - are evidence of leadership by project sponsors. Actions taken, or not taken, by project sponsors truly have the ability to influence an outcome. While projects are not assured of success or failure, engaging the community in an empowered process is an investment of time and resources toward success for the project and thus for the communities of impact. Authors Note: Extensive literature searches were performed in developing this paper. The majority of the published literature on SLO as a 'movement' was found from sources in Canada, the European Union (Germany and France in particular), South Asia, South Korea, and many Latin American countries. The literature addressed resource development (mining), infrastructure, and energy projects. Articles written by US sources often spoke to origins and structural theory, specific project issues such as Not in My Back Yard (NIMBY) and to protests/demonstrations related to those projects, rather than systemic opposition/conflict phenomena. For these reasons many international SLO experiences and sources are cited in the discussion. The authors recognize these non-US experiences with SLO as having a 'forecast' value to US projects, especially those related to nuclear projects of any type, waste treatment and disposal, energy development (especially fossil fuels as well as alternative sources), mining, and infrastructure. The body of future SLO experiences in the US will shape the future responses to it. (authors)

99 GENERAL AND MISCELLANEOUS↗

Intersubband Transitions in Lead Halide Perovskite-Based Quantum Wells for Mid-Infrared Detectors

Due to their excellent optical and electrical properties as well as versatile growth and fabrication processes, lead halide perovskites have been widely considered as promising candidates for green energy and applications related to optoelectronics. Here, we investigate their potential applications at infrared wavelengths by modeling the intersubband transitions in perovskite-based quantum well systems. Both single-well and double-well structures are studied, and their energy levels as well as the corresponding wave functions and intersubband transition energies are calculated by solving the one-dimensional Schrödinger equations. Via adjustment of the quantum well and barrier thicknesses, the intersubband transition energies can be tuned to cover a broad infrared wavelength range. We also find that the lead halide perovskite-based quantum wells possess high absorption coefficients. In conclusion, the widely tunable transition energies and high absorption coefficients of the perovskite-based quantum well systems, combined with their unique material and electrical properties, may enable an alternative material system for infrared photodetector applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Estimating the impacts of natural gas power generation growth on solar electricity development: PJM's evolving resource mix and ramping capability

Abstract Expansion of distributed solar photovoltaic (PV) and natural gas‐fired generation capacity in the United States has put a renewed spotlight on methods and tools for power system planning and grid modernization. This article investigates the impact of increasing natural gas‐fired electricity generation assets on installed distributed solar PV systems in the Pennsylvania–New Jersey–Maryland (PJM) Interconnection in the United States over the period 2008–2018. We developed an empirical dynamic panel data model using the system‐generalized method of moments (system‐GMM) estimation approach. The model accounts for the impact of past and current technical, market and policy changes over time, forecasting errors, and business cycles by controlling for PJM jurisdictions‐level effects and year fixed effects. Using an instrumental variable to control for endogeneity, we concluded that natural gas does not crowd out renewables like solar PV in the PJM capacity market; however, we also found considerable heterogeneity. Such heterogeneity was displayed in the relationship between solar PV systems and electricity prices. More interestingly, we found no evidence suggesting any relationship between distributed solar PV development and nuclear, coal, hydro, or electricity consumption. In addition, considering policy effects of state renewable portfolio standards, net energy metering, differences in the PJM market structure, and other demand and cost‐related factors proved important in assessing their impacts on solar PV generation capacity, including energy storage as a non‐wire alternative policy technique. This article is categorized under: Photovoltaics > Economics and Policy Fossil Fuels > Climate and Environment Energy Systems Economics > Economics and Policy

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Experimental Examination of Additively Manufactured Patterns on Structural Nuclear Materials for Digital Image Correlation Strain Measurements

Abstract Background There are a limited number of commercially available sensors for monitoring the deformation of materials in-situ during harsh environment applications, such as those found in the nuclear and aerospace industries. Such sensing devices, including weldable strain gauges, extensometers, and linear variable differential transformers, can be destructive to material surfaces being investigated and typically require relatively large surface areas to attach (> 10 mm in length). Digital image correlation (DIC) is a viable, non-contact alternative to in-situ strain deformation. However, it often requires implementing artificial patterns using splattering techniques, which are difficult to reproduce. Objective Additive manufacturing capabilities offer consistent patterns using programmable fabrication methods. Methods In this work, a variety of small-scale periodic patterns with different geometries were printed directly on structural nuclear materials (i.e., stainless steel and aluminum tensile specimens) using an aerosol jet printer (AJP). Unlike other additive manufacturing techniques, AJP offers the advantage of materials selection. DIC was used to track and correlate strain to alternative measurement methods during cyclic loading, and tensile tests (up to 1100 µɛ) at room temperature. Results The results confirmed AJP has better control of pattern parameters for small fields of view and facilitate the ability of DIC algorithms to adequately process patterns with periodicity. More specifically, the printed 100 μm spaced dot and 150 μm spaced line patterns provided accurate measurements with a maximum error of less than 2% and 4% on aluminum samples when compared to an extensometer and commercially available strain gauges. Conclusion Our results highlight a new pattern fabrication technique that is form factor friendly for digital image correlation in nuclear applications.

Novich, K. A. (ORCID:0000000204466022)↗

Geometric prior of multi-resolution yielding manifolds and the local closest point projection for nearly non-smooth plasticity

Elastoplasticity models often introduce a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. Here this paper introduces a new alternative where the yield envelope is represented by a manifold of which the topology and the geometry are learned from a set of data points in a parametric space (e.g. principal stress space, π-plane). Here, deep geometric learning enables us to reconstruct a highly complex yield envelope by breaking it down into multiple coordinate charts. The global atlas that consists of these coordinate charts in return allows us to represent the yield surface via multiple overlapping patches, each with a specific local parametrization. This setup provides several advantages over the classical implicit function representation approach. For instance, the availability of coordinate charts enables us to introduce an alternative stress integration algorithm where the trial stress may project directly on a local patch and hence circumvent the issues related to non-smoothness and the lack of convexity of yield surfaces. Meanwhile, the local parametric approach also enables us to predict hardening/softening locally in the parametric space, even without complete knowledge of the yield surface. Comparisons between the classical yield function approach on the non-smooth plasticity and anisotropic cam-clay plasticity model are provided to demonstrate the capacity of the models for highly precise yield surface and the feasibility of the implementation of the learned model in the local stress integration algorithm.

42 ENGINEERING↗

The Influence of Nonlocal Metal–Dielectric Environments on Physical and Chemical Processes

Plasmonic nanolayers and laminar metallic/dielectric multilayers were originally developed for optical cloaking applications and lensing applications that could potentially image objects whose size was below the diffraction limit. These assemblies were initially formed from gold or silver nanorods grown within an alumina mesh. However, more recently, assemblies with similar properties have also been prepared by sequential thin-layer deposition of alternating layers of gold and magnesium fluoride (MgF 2 ). These metal/dielectric composite materials enable control of the dielectric constant in the directions perpendicular to the layers and balance the real and imaginary dielectric constants of the assembly such that the speed and the amplitude of the waves traveling through the assembly are not attenuated. In this Account, we will also focus on a few of the applications ranging from surface wetting to fluorescence quenching to enhancement of photochemical reactions. First, we will share an introduction to processes used to create these materials, which are combinations of low refractive index metals and transparent higher index materials arranged in a scalable repeating fashion. Two fabrication methods were employed: an electrochemical deposition of Ag nanorods into an anodized alumina matrix which produced materials with an anisotropic negative refractive index material within the plane of the film and lamellar metal/dielectric layers in which the negative index perpendicular to the growth direction. These alternating layers of plasmonic metals and dielectric materials were ultimately chosen to prepare films for further testing, because of their relative ease of fabrication. We will continue with a discussion of a few of the applications of both of these nonlocal dielectric composite materials including more specialized plasmonic, composite, and hyperbolic metamaterials including fluorescence quenching, photochemical reactions, and surface wetting. In each of these applications, the unique response caused by the enhancement of the electric field and the interface between hyperbolic materials and plasmonic materials as they interact photophysically with their near neighbors is presented. In each of the applications, the enhanced electric field extends from the composite substrate layer to interact with its near neighbors and beyond. Furthermore, the presence of this extended interaction can be observed in the form of decreased emission lifetime, enhancement of photochemical reaction rates, and changes in the surface energies measured by contact angle goniometry. In this Account, all of these situations will be addressed. Finally, we will conclude with a summary and vision for the future as well as a discussion of the unique challenges and opportunities available as research active faculty at an HBCU.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spatial defects nanoengineering for bipolar conductivity in MoS 2

Understanding the atomistic origin of defects in two-dimensional transition metal dichalcogenides, their impact on the electronic properties, and how to control them is critical for future electronics and optoelectronics. Here, we demonstrate the integration of thermochemical scanning probe lithography (tc-SPL) with a flow-through reactive gas cell to achieve nanoscale control of defects in monolayer MoS 2 . The tc-SPL produced defects can present either p- or n-type doping on demand, depending on the used gasses, allowing the realization of field effect transistors, and p-n junctions with precise sub-μm spatial control, and a rectification ratio of over 10 4 . Doping and defects formation are elucidated by means of X-Ray photoelectron spectroscopy, scanning transmission electron microscopy, and density functional theory. We find that p-type doping in HCl/H 2 O atmosphere is related to the rearrangement of sulfur atoms, and the formation of protruding covalent S-S bonds on the surface. Alternatively, local heating MoS 2 in N 2 produces n-character.

36 MATERIALS SCIENCE↗

Cooperative Research and Development Agreement between National Energy Technology Laboratory and University of Kentucky (Abstract)

The National Energy Technology Laboratory (NETL) and University of Kentucky (Participant) will collaborate in the development of “Deep Learning Potential-based Molecular Dynamics Simulation Investigation of Chemical Conversion-Absorption Coupling of CO 2 at Air-Reactive Deep Eutectic Solvent Interface.” This project is supported by DOE-Office of Science Graduate Student Research (SCGSR) program and managed by Oak Ridge Institute for Science and Education (ORISE). Deep eutectic solvents (DESs) are promising alternative sorbents for direct air capture (DAC) CO 2 due to their low vapor pressure, low corrosion, non-toxicity, relatively low cost, and biodegradable nature. Understanding the CO 2 reaction-transport mechanisms at the interface can help develop cost-effective DAC by DESs with high capacity and stability. The collaboration will investigate the absorption and chemical conversion of CO 2 at the air-DES interface to facilitate the development of novel DAC technology using reactive DESs. The anticipated results will make DAC more efficient, allow more sustainable use of our Nation’s fossil energy resources, and advance NETL’s ongoing CO 2 capture efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cooperation or Rivalry? Impact of alternative development pathways on India's long-term electricity generation and associated water demands

The world has witnessed a significant shift in the last decade in the way countries interact with each other. A cooperation based international paradigm is being challenged by countries engaging in rivalry with each other in the name of their national interests. What developmental pathway the world charts in the future is going to be path defining for global energy and emissions use. India, expected to play a critical role in the emissions mitigation debate, would contribute to and would be impacted by these pathways. In India specific literature, however, little attention has been paid to development pathways related uncertainties and their impact on energy futures. We seek to address this gap by modelling India's electricity futures and associated water demands under different development pathways. Our analysis shows that alternative development pathways would have significantly different implications for the energy access, electricity generation mix, associated water withdrawals, and carbon dioxide emissions in India. We conclude by arguing that energy, emissions and water policies should be conceived with an explicit understanding of uncertainties related to potential development pathways that the world and India can chart.

India, Electricity-Water Nexus, Development Pathwa↗

Crystal truncation rods from miscut surfaces with alternating terminations

Miscut surfaces of layered crystals can exhibit a stair-like sequence of terraces having periodic variation in their atomic structure. For hexagonal close-packed and related crystal structures with an αβαβ stacking sequence, there have been long-standing questions regarding how the differences in adatom attachment kinetics at the steps separating the terraces affect the fractional coverage of α vs. β termination during crystal growth. To demonstrate how surface X-ray scattering can help address these questions, we develop a general theory for the intensity distributions along crystal truncation rods (CTRs) for miscut surfaces with a combination of two terminations. We consider half-unit-cell-height steps, and variation of the coverages of the terraces above each step. Example calculations are presented for the GaN (0001) surface with various reconstructions. These show which CTR positions are most sensitive to the fractional coverage of the two terminations. We compare the CTR profiles for exactly oriented surfaces to those for vicinal surfaces having a small miscut angle, and investigate the circumstances under which the CTR profile for an exactly oriented surface is equal to the sum of the intensities of the corresponding family of CTRs for a miscut surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗