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At least 757 records · Page 42

Instrumentation development and testing of a wind turbine blade for sub-scale wake studies

Wind turbine blade aerodynamics and the resulting wake flow are complex, and wind tunnel testing of these flows can provide critical insight. The data from such tests are also valuable for validation of numerical models. For experiments using sub-scale turbines to be useful, the blade aerodynamics and wakes must exhibit the important features observed in utility-scale turbine flows. In this work, ~1 m blades designed to produce physics relevant to larger scale turbines were manufactured and affixed to an existing turbine. One of the blades was instrumented for blade surface pressure measurements. Time-dependent surface pressure measurements coupled with instantaneous measurements of the inflow with Cobra probes and the wake with particle image velocimetry allowed for characterization of the inflow, blade flow, and near wake. The results demonstrate that the instrumentation was effective in characterizing the blade loading and the flow field. For the one test case discussed in this paper, the measurements of inflow, blade loading, and wake properties facilitate understanding of the wake's behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗

X-Band Radar and Surface-Based Observations of Cold-Season Precipitation in Western Colorado’s Complex Terrain

Abstract Hydrologic processes associated with intermountain cold-season precipitation in the Upper Colorado River basin have important impacts on avalanche forecasting and water resource management. However, traditional weather radar networks struggle with observations in this complex terrain. Data collected during the Study of Precipitation, the Lower Atmosphere, and the Surface for Hydrometeorology (SPLASH) and its sister campaign, Surface Atmosphere Integrated Field Laboratory (SAIL) in the East River watershed of western Colorado, are used to examine a multistorm period from 23 December 2021 to 1 January 2022 that contributed 35% of the total winter precipitation in this watershed. Dual-polarization X-band radar and disdrometer measurements show ∼30-mm differences in precipitation amount at two sites in proximity over four distinct storm events within the period. Wind patterns, synoptic forcings, microphysical characteristics of precipitation, and surface meteorology are analyzed to explain the observed spatial variability of cold-season precipitation in complex mountainous terrain. Analysis shows that differences over time within this event are mainly accounted for by synoptic forcings, such as frontal passages; differences between sites are accounted for by the impact of variations in local wind patterns on precipitation microphysics. Patterns of surface precipitation intensity are compared and found to be correlated with X-band radar signatures; a relationship between a strong dendritic growth stage and intense low-density surface precipitation is reinforced by this study. This relationship demonstrates the importance of particle growth mechanisms on surface snowfall patterns in high-altitude complex terrain, underscoring the importance of realistic microphysical parameterizations. Significance Statement The amount and density of snowpack from western Colorado winter storms have significant impacts on water resources in the Upper Colorado River basin. Snowpack characteristics are affected by small-scale differences in how snow forms in the atmosphere. These differences are hard to study in the complex terrain of the Rockies, but data from the SPLASH and SAIL field campaigns allows us to investigate how snow crystal formation and mountain-driven wind patterns affect snow near the surface. Our study finds that snow crystal growth varies over small space and time scales and is likely controlled by the terrain beneath a given location and resultant local wind patterns. These results imply that predicting snowpack in the Rockies requires properly representing local wind patterns and crystal growth processes in models.

Heflin, Stella↗

Development of Explainable, Knowledge-Guided AI Models to Enhance the E3SM Land Model Development and Uncertainty Quantification

Focal Area(s): (2)Predictive modeling using AI techniques and AI-derived model components; use of AI and other tools to design a prediction system comprising of a hierarchy of models. (3) Insight gleaned from complex data (both observed and simulated) using AI, big data analytics, and other advanced methods, including explainable AI and physics- or knowledge- guided AI. Science Challenge: The Energy Exascale Earth System Model (E3SM) is a fully coupled, state-of-the-science Earth system model that uses code optimized for DOE's advanced computers to address the most critical scientific questions facing our nation and society (Golaz et al., 2019). The E3SM Land model (ELM) is designed to understand how the changes in terrestrial land surfaces will interact with other Earth system components and has been used to understand hydrologic cycles, biogeophysics, and ecosystem dynamics. In spite of great successes, the ELM has several known issues that restrain rapid improvements. For example, the ELM uses equilibrium models to simulate dynamic land-climate interactions and it requires long model spin-up time to identify suitable initial conditions for transient simulations. The ELM lacks built-in uncertainty mechanisms that can improve the robustness of model predictions. The ELM is a holistic, deterministic model system with a rigid design, and in many situations, it is hard to modify the ELM system to incorporate new theory/hypothesis and new data across scales to address emerging science problems (such as predicting the impacts of water cycle extremes). In addition, The ELM is technically optimized for traditional CPU-centric computers and it cannot fully utilize the current and incoming leadership computers for model simulations and uncertainty quantification (UQ). The success of artificial intelligence (AI) has inspired scientists to use AI models to discover intrinsic features from simulation data (Chattopadhyay et al., 2020) and observational data (Reichstein et al., 2019) to gain further process understanding of Earth science problems. However, autonomous AI model training through deep learning usually requires a huge amount of annotated data. To overcome the limitations from the data and computing resources, knowledge-guided AI models are necessary where human-knowledge is ingested in model construction (Banino et al., 2018) and training process (Silver et al., 2016) for efficient learning. Herein, we present a new way that leverages the process understanding from the ELM to guide AI model development for the ELM enhancement and UQ. We hope this study can inspire further Earth and environmental system model developments and transformations.

54 ENVIRONMENTAL SCIENCES↗

DeepGhostBusters: Using Mask R-CNN to Detect and Mask Ghosting and Scattered-Light Artifacts from Optical Survey Images

Wide-field astronomical surveys are often affected by the presence of undesirable reflections (often known as "ghosting artifacts" or "ghosts") and scattered-light artifacts. The identification and mitigation of these artifacts is important for rigorous astronomical analyses of faint and low-surface-brightness systems. However, the identification of ghosts and scattered-light artifacts is challenging due to a) the complex morphology of these features and b) the large data volume of current and near-future surveys. In this work, we use images from the Dark Energy Survey (DES) to train, validate, and test a deep neural network (Mask R-CNN) to detect and localize ghosts and scattered-light artifacts. We find that the ability of the Mask R-CNN model to identify affected regions is superior to that of conventional algorithms and traditional convolutional neural networks methods. We propose that a multi-step pipeline combining Mask R-CNN segmentation with a classical CNN classifier provides a powerful technique for the automated detection of ghosting and scattered-light artifacts in current and near-future surveys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Effect of Laser Beam Profile on Rotating Lattice Single Crystal Growth in Sb2S3 Model Glass

Laser heating of chalcogenide glasses has successfully produced rotating lattice single crystals through a solid-solid transformation. To better understand the nature of complex, orientation-dependent lattice rotation, we designed heat profiles of the continuous wave laser by beam shaping, fabricated larger Sb2S3 crystal dots in Sb2S3 glass, and investigated the lattice rotation where the crystal could grow in all radial directions under a circular thermal gradient. The results show that the rate of lattice rotation is highly anisotropic and depends on crystallographic direction. The nature of this rotation is the same in crystals of different orientation relative to the surface. The growth directions that align with the slip planes show the highest rate of rotation and the rotation rate gradually decreases away from this direction. Additionally, the presence of multiple growth directions results in a complicated rotation system. We suggest that the growth front influences the density of dislocations introduced during growth under confinement and thus affects the lattice rotation rate in these crystals.

36 MATERIALS SCIENCE↗

Characterizing the Geometry and Quantifying the Impact of Nanoscopic Electrocatalyst/Semiconductor Interfaces under Solar Water Splitting Conditions

The materials that are receiving the most attention in photoelectrochemical water splitting are metallic nanoparticle electrocatalysts (np-EC) attached to the surface of a semiconductor (SC) light absorber. In these multicomponent systems, the interface between the semiconductor and electrocatalysts critically affects performance. However, the np-EC/SC interface remains poorly understood as it is complex on atomic scales, dynamic under reaction conditions, and inaccessible to direct experimental probes. This contribution sheds light on how the electrocatalyst/semiconductor interface evolves under reaction conditions by investigating the behavior of nickel electrocatalysts (as nanoparticles and films) deposited on silicon semiconductors. Rigorous electrochemical experiments, interfacial atomistic characterization, and computational modeling are combined to demonstrate critical links between the atomistic features of the interface and the overall performance. It is shown that electrolyte-induced atomistic changes to the interface lead to (1) modulation of the charge carrier fluxes and a dramatic decrease in the electron/hole recombination rates and (2) a change in the barrier height of the interface. Additionally, the critical roles of nonidealities and electrocatalyst coverage due to interfacial geometry are explored. Each of these factors must be considered to optimize the design of metal/semiconductor interfaces which are broadly applicable to photoelectrocatalysis and photovoltaic research.

36 MATERIALS SCIENCE↗

Pitting Corrosion in 316L Stainless Steel Fabricated by Laser Powder Bed Fusion Additive Manufacturing: A Review and Perspective

Abstract 316L stainless steel (316L SS) is a flagship material for structural applications in corrosive environments, having been extensively studied for decades for its favorable balance between mechanical and corrosion properties. More recently, 316L SS has also proven to have excellent printability when parts are produced with additive manufacturing techniques, notably laser powder bed fusion (LPBF). Because of the harsh thermo-mechanical cycles experienced during rapid solidification and cooling, LPBF processing tends to generate unique microstructures. Strong heterogeneities can be found inside grains, including trapped elements, nano-inclusions, and a high density of dislocations that form the so-called cellular structure. Interestingly, LPBF 316L SS not only exhibits better mechanical properties than its conventionally processed counterpart, but it also usually offers much higher resistance to pitting in chloride solutions. Unfortunately, the complexity of the LPBF microstructures, in addition to process-induced defects, such as porosity and surface roughness, have slowed progress toward linking specific microstructural features to corrosion susceptibility and complicated the development of calibrated simulations of pitting phenomena. The first part of this article is dedicated to an in-depth review of the microstructures found in LPBF 316L SS and their potential effects on the corrosion properties, with an emphasis on pitting resistance. The second part offers a perspective of some relevant modeling techniques available to simulate the corrosion of LPBF 316L SS, including current challenges that should be overcome.

Voisin, T. (ORCID:0000000287462659)↗

Controls and process planning strategies for 5-axis laser directed energy deposition of Ti-6Al-4V using an 8-axis industrial robot and rotary motion

Interest in multi-axis additive manufacturing has grown significantly in recent years due to associated benefits that range from improved quality to support for greater geometric complexity. A method of 5-axis Laser Hot-Wire Directed Energy Deposition is developed and demonstrated in this study using an 8-axis industrial robot, comprised of a 6-axis serial link robot and a 2 degree-of-freedom positioner. Coordinated 5-axis motion is used to print Ti-6Al-4V objects predominantly through build plate rotation. Methods of slicing and toolpath generation are presented, including the use of an alternating toolpath direction philosophy and the manipulation of the CAD model surface normal vectors for determining the required build plate tilt angles for maintaining consistent deposition orientations relative to gravity. Another objective of the study was to determine the limits of conventional slicing and layer height control techniques for printing geometries with significant unsupported overhangs. A comparison is made between the behavior of normal and conformal bead alignment in this regard, and the performance of the layer height controller is reported as it relates to process stability and the limits of printing overhang geometries. Unsupported overhangs were successfully printed at 35° without build plate tilt and 45° with build plate tilt. Toolpath velocity and net-shape printing performance are reported as well, with 3D scans of the printed surfaces used for net-shape characterization. In all, the printing of three geometries is presented, including the overhang geometry, a 5-axis toolpath geometry, and a large-scale, multi-bead demonstrator part, which exceeded 500 mm in height and weighed 44 kg (97 lbs).

36 MATERIALS SCIENCE↗

Epitope topography of agonist antibodies to the checkpoint inhibitory receptor BTLA

B and T lymphocyte attenuator (BTLA) is an attractive target for a new class of therapeutics that attempt to rebalance the immune system by agonizing checkpoint inhibitory receptors (CIRs). Herpesvirus entry mediator (HVEM) binds BTLA in both trans- and cis-orientations. We report here the development and structural characterization of three humanized BTLA agonist antibodies, 22B3, 25F7, and 23C8. We determined the crystal structures of the antibody-BTLA complexes, showing that these antibodies bind distinct and non-overlapping epitopes of BTLA. While all three antibodies activate BTLA, 22B3 mimics HVEM binding to BTLA and shows the strongest agonistic activity in functional cell assays and in an imiquimod-induced mouse model of psoriasis. 22B3 is also capable of modulating HVEM signaling through the BTLA-HVEM cis-interaction. The data obtained from crystal structures, biochemical assays, and functional studies provide a mechanistic model of HVEM and BTLA organization on the cell surface and informed the discovery of a highly active BTLA agonist.

59 BASIC BIOLOGICAL SCIENCES↗

Quantifying Errors in Effective Cluster Interactions of Lattice Gas Cluster Expansions

The promise of lattice gas (LG) cluster expansions (CEs) is that they can describe a given system property to any level of accuracy since the orthogonal “cluster basis functions” span the complete space of available configurations. Such an approach can be constructed to an arbitrarily large surface of a finite number of distinct adsorption sites. Unfortunately, this is only true for the case of an ideal, fixed lattice decorated with components at precise lattice points (the lattice “sites”) with no distortions or relaxations subsequently allowed. Since most systems, and surfaces specifically, do not conform to such an ideal set of constraints, errors in LG CEs must be expected or CE convergence severely hampered. Beyond this, numerical errors in the provided data can complicate the proper construction of a truly predictive and/or physically significant CE. In this work, we show here how reliance on typical statistical tools like confidence intervals cannot be expected to provide an accurate representation of the uncertainty of effective cluster interactions (ECIs) in the CE due to the nature of the target ab initio data and the nature of CEs themselves. We develop a method for estimating these errors that does not rely on statistical assumptions about the model or data. We then use these ECI errors to quantify fundamental consequences on the uncertainty of ECIs in CEs built from O/Fe(100) data whose surface and adsorbates have been allowed to relax in a typical manner and from O/Fe(100) data whose surface and adsorbates are fixed in ideal lattice positions. We also quantify the effect of using a different density functional theory exchange–correlation functional, using these ECI errors to assess the significance in any deviations. In both cases, our method is shown to have remarkable utility in the quantification of errors in the ECIs of CEs. While we stick to the lattice gas convention in this work, the method is equally applicable to the Ising convention or, in principle, any linear model of sufficient complexity.

08 HYDROGEN↗

Nonclassical Behavior in Competitive Ion Adsorption at a Charged Solid–Water Interface

Ion adsorption at solid-water interfaces is commonly described by interactions between specific surface sites and adsorbed ions in classical models. However, energetic contributions from non-site-specific ion-ion interactions have not been explored systematically. Here, we report non-classical behaviors observed during competitive adsorption between Sr 2+ and Na + /Rb + at the negatively-charged muscovite mica (001)-water interface, revealing apparent controls of adsorbed ion speciation over the interfacial reactivity. In the absence of competing cations, Sr 2+ adsorbs in approximately equivalent proportions of inner-sphere and outer-sphere complexes, whereas it adsorbs predominantly as an outer-sphere complex in the presence of Na + /Rb + . This transformation of adsorbed Sr 2+ speciation significantly decreases its adsorption strength, as indicated by ~15-fold shift in the Sr 2+ adsorption edge concentration, compared to that calculated from a classical Langmuir isotherm model developed based on site-specific interactions. Finally, these observations highlight the importance of non-site-specific interactions in controlling the energetics of chemical reactions at the charged interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Machine learning predictions of diffusion in bulk and confined ionic liquids using simple descriptors

Ionic liquids have many intriguing properties and widespread applications such as separations and energy storage. However, ionic liquids are complex fluids and predicting their behavior is difficult, particularly in confined environments. We introduce fast and computationally efficient machine learning (ML) models that can predict diffusion coefficients and ionic conductivity of bulk and nanoconfined ionic liquids over a wide temperature range (350–500 K). The ML models are trained on molecular dynamics simulation data for 29 unique ionic liquids as bulk fluids and confined in graphite slit pores. This model is based on simple physical descriptors of the cations and anions such as molecular weight and surface area. Here, we also demonstrate that accurate results can be obtained using only descriptors derived from SMILES (simplified molecular-input line-entry system) codes for the ions with minimal computational effort. This offers a fast and efficient method for estimating diffusion and conductivity of nanoconfined ionic liquids at various temperatures without the need for expensive molecular dynamics simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗

Deciphering the morphology of transition metal carbonate cathode precursors

The performance and life of Li-ion battery cathode materials are determined by both the composition (crystal structure and transition metal ratio) and the morphology (particle size, size distribution, and surface area). Careful control of these two aspects is the key to long lasting, high-energy batteries that can undergo fast charge. Developing such cathodes requires manipulation of the synthesis conditions, namely the coprecipitation process to develop the precursor and a calcination step to lithiate and convert it to a transition metal oxide. In this paper, we utilize a combination of controlled synthesis, microscopic and spectroscopic characterization, and multi-scale mathematical modeling to shed light on the synthesis of cathode precursors. The complex interplay between the various chemical reactions in the co-precipitation process is studied to provide experimentalists with guidance on achieving composition control during synthesis. Further, the formation of a variety of morphologies of the primary particles and the driving force for agglomeration is mathematically described, for the first time, based on an energy minimization approach. Results suggest that the presence of Ni and/or Co significantly lowers the reaction rate constant compared to Mn, resulting in agglomerated growth in the former and single crystal growth in the latter. Modeling studies are used to provide a phase map describing the synthesis conditions needed to control the secondary particle size and corresponding size distribution. Finally, this paper represents an important step in developing a computationally guided approach to the synthesis of battery cathode materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large Ensemble Diagnostic Evaluation of Hydrologic Parameter Uncertainty in the Community Land Model Version 5 (CLM5)

Abstract Land surface models such as the Community Land Model version 5 (CLM5) seek to enhance understanding of terrestrial hydrology and aid in the evaluation of anthropogenic and climate change impacts. However, the effects of parametric uncertainty on CLM5 hydrologic predictions across regions, timescales, and flow regimes have yet to be explored in detail. The common use of the default hydrologic model parameters in CLM5 risks generating streamflow predictions that may lead to incorrect inferences for important dynamics and/or extremes. In this study, we benchmark CLM5 streamflow predictions relative to the commonly employed default hydrologic parameters for 464 headwater basins over the conterminous United States (CONUS). We evaluate baseline CLM5 default parameter performance relative to a large (1,307) Latin Hypercube Sampling‐based diagnostic comparison of streamflow prediction skill using over 20 error measures. We provide a global sensitivity analysis that clarifies the significant spatial variations in parametric controls for CLM5 streamflow predictions across regions, temporal scales, and error metrics of interest. The baseline CLM5 shows relatively moderate to poor streamflow prediction skill in several CONUS regions, especially the arid Southwest and Central U.S. Hydrologic parameter uncertainty strongly affects CLM5 streamflow predictions, but its impacts vary in complex ways across U.S. regions, timescales, and flow regimes. Overall, CLM5's surface runoff and soil water parameters have the largest effects on simulated high flows, while canopy water and evaporation parameters have the most significant effects on the water balance.

54 ENVIRONMENTAL SCIENCES↗

Paleotribological models using preserved fossil tissue properties reveal functional significance of Eurasian mammoth dental evolution

Eurasian mammoths (Mammuthus) underwent substantial modifications in molar morphology as later-diverging species evolved progressively thinner enamel and increased enamel crest complexity. These features have been hypothesized to reduce whole-tooth wear and extend dental longevity as increasingly graze-dominated diets evolved within the lineage. This hypothesis has yet to be directly tested. Here, in this study, we developed an in-silico wear model using experimentally derived wear rates from fossil and extant proboscidean dental tissues. The models revealed that shifts in tissue topology do not affect whole-tooth wear rate, as inverse trends in lamellar frequency and enamel thickness preserve a consistent surface enamel area fraction; the determining factor of wear. Rather, topological shifts produce a wear-emergent secondary occlusal surface with greater numbers of triturating crests that create a regular, low-relief, file-like shearing pavement. These changes in occlusal architecture likely directly impacted the mastication capacity of Mammuthus dentitions, facilitating their dietary expansion to incorporate fibrous, lower-nutrient graze.

Dental wear↗

MS25: Materials Science-Focused Benchmark Data Set for Machine Learning Interatomic Potentials

Here, we present MS25, a benchmark data set for evaluating machine learning interatomic potentials (MLIPs) across diverse materials-relevant systems including MgO surfaces, liquid water, zeolites, a catalytic Pt surface reaction, high-entropy alloys (HEAs), and disordered Zr-oxides. Five MLIP architectures (MACE, NequIP, Allegro, MTP, and Torch-ANI) are trained and tested, focusing not only on traditional metrics (energies, forces, and stresses) but also explicitly validating derived physical observables such as lattice constants, volumes, and reaction barriers. We find that most models reach comparable accuracy on standard error metrics across the simple systems, although equivariant MLIPs offer 1.5–2× improvements over nonequivariant MLIPs in energy and force error for structurally complex or compositionally disordered environments such as HEAs and Zr–O systems. Our analysis highlights that low errors in energy and force predictions do not guarantee reliable observables, emphasizing the necessity of explicit validation. We demonstrate limitations in cross-framework transferability, as models trained on one zeolite framework (CHA) fail to reliably generalize to predictions of structurally distinct frameworks (e.g., MFI). Size-extensive tests show some dependence on system size for MgO, resulting from forced periodicity. The HEA and Zr–O data sets are identified as challenging tests for future benchmarks and MLIP model architecture developments as they show significant differentiation in error between MLIP architectures and are still relatively difficult at 1000 training images. Moving forward, we recommend that benchmarking efforts shift their focus from marginal accuracy improvements in energy and force errors toward identifying and understanding model failure modes, rigorously assessing transferability, and evaluating how their errors affect observable predictions. For researchers looking to choose an MLIP architecture, we suggest selecting equivariant MLIP architectures if the complexity of the system is a challenge. For simple materials problems, auxiliary features such as integration with molecular dynamics engines, trade-offs between computational data set generation cost vs MLIP inference speed, and framework integration may play a more important decision factor than small differences in error metrics that are unlikely to matter for production-level research.

chemical structure↗

Machine learning potential assisted exploration of complex defect potential energy surfaces

Abstract Atomic-scale defects generated in materials under both equilibrium and irradiation conditions can significantly impact their physical and mechanical properties. Unraveling the energetically most favorable ground-state configurations of these defects is an important step towards the fundamental understanding of their influence on the performance of materials ranging from photovoltaics to advanced nuclear fuels. Here, using fluorite-structured thorium dioxide (ThO 2 ) as an exemplar, we demonstrate how density functional theory and machine learning interatomic potential can be synergistically combined into a powerful tool that enables exhaustive exploration of the large configuration spaces of small point defect clusters. Our study leads to several unexpected discoveries, including defect polymorphism and ground-state structures that defy our physical intuitions. Possible physical origins of these unexpected findings are elucidated using a local cluster expansion model developed in this work.

36 MATERIALS SCIENCE↗