Search NASA⌕ Search

SEARCH · Search NASA

Results for “Variational Analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Exploring stages of resilience maturity as communities confront climate risks

Coastal communities are facing increased risks due to climate change, as evidenced by heightened shocks such as hurricanes and wildfires, and stressors including sea-level rise and drought. To confront these risks, many coastal communities are planning and designing their built environments in new ways, with the overall goal of increasing their resilience. However, resilience practices have been widely guided by an event-based timeframe, which may not be sufficient to confront the multiple and overlapping threats expected over the coming decades. To address this concern, this study investigated a long-term perspective on resilience progression, termed resilience maturity. To better understand resilience maturity in practice, this study drew directly on community perspectives, thereby identifying common challenges. Furthermore, variation in resilience maturity across communities provided an opportunity to identify existing successful strategies. Inductive qualitative analysis was used to examine perspectives from 15 interviews with local practitioners across 12 coastal communities. The analysis revealed that communities in early stages of resilience maturity often struggle with local stakeholder alignment and minimal dedicated resilience resources. In contrast, those further along the maturity path often face technology barriers and challenges in aligning regional stakeholders. Few examples of a fully mature resilience culture were found within the communities studied, underscoring systemic barriers to achieving advanced resilience maturity. Overall, these findings supported development of a practical framework for classifying community resilience efforts, identifying common obstacles, and informing localized resilience advancement.

Resilience maturity↗

Hyperspectral radiance mapping and chromatic correction for temperature measurement in laser-heated diamond anvil cells

In laser-heated diamond anvil cell (DAC) experiments, the effective heated region typically decreases in size with increasing pressure, leading to steeper thermal gradients. Under these conditions, chromatic aberration in the optical path from sample to detector can significantly create bias in spectro-radiometric temperature measurement. We present a radiance-mapping approach using a hyperspectral camera that records 25 spectral channels spanning 605–875 nm at each pixel in a single exposure, providing spatially and spectrally resolved radiance in each frame. This enables chromatic effects to be recorded and corrected in data processing. We developed a procedure for hyperspectral mapping, involving per-camera calibration, crosstalk removal, measured spectral throughput functions, and optional sub-pixel co-registration to minimize chromatic distortion. The calibrated radiance maps are then used to derive temperature maps of the laser-heated hotspots. For smaller heating spots, the radiance mapping approach reveals chromatic shifts that conventional spectro-radiometric methods cannot quantify. Ambient-pressure heating experiments confirm accurate temperature retrieval. At high pressure, application of the hyperspectral system to a platinum-heating experiment at 12 GPa demonstrates stable temperature reconstruction under steep thermal gradients. Beyond mitigating chromatic aberrations, the ability to diagnose optical artifacts separately from emissivity variations during controlled test experiments or in situ suggests a path toward more rigorous spectral emissivity analysis and improved modeling of thermal transport in laser-heated DAC experiments.

47 OTHER INSTRUMENTATION↗

Cosmological neutrino mass: a frequentist overview in light of DESI

We derive constraints on the neutrino mass using a variety of recent cosmological datasets, including DESI BAO, the full-shape analysis of the DESI matter power spectrum and the one-dimensional power spectrum of the Lyman-α forest (P1D) from eBOSS quasars as well as the cosmic microwave background (CMB). The constraints are obtained in the frequentist formalism by constructing profile likelihoods and applying the Feldman-Cousins prescription to compute confidence intervals. This method avoids potential prior and volume effects that may arise in a comparable Bayesian analysis. Parabolic fits to the profiles allow one to distinguish changes in the upper limits from variations in the constraining power σ of the different data combinations. We find that all profiles in the ΛCDM model are cut off by the ∑m ν ≥ 0 bound, meaning that the corresponding parabolas reach their minimum in the unphysical sector. The most stringent 95% C.L. upper limit is obtained by the combination of DESI DR2 BAO, Planck PR4 and CMB lensing at 53 meV, below the minimum of 59 meV set by the normal ordering. The corresponding constraining power σ is 43 meV, which highlights the importance of the cut-off by negative values in the determination of the upper limit. Extending ΛCDM to non-zero curvature and w 0 w a CDM relaxes the constraints past 59 meV again, but only w 0 w a CDM exhibits profiles with a minimum at a positive value. Additionally, we extend the formalism to constrain the lightest neutrino mass. For DESI DR2 BAO, Planck PR4 and CMB lensing, we find confidence limits at 20 and 19 meV for normal and inverted ordering, respectively. Using a combination of DESI DR1 full-shape, BBN and eBOSS Lyman-α P1D, we successfully constrain the neutrino mass independently of the CMB. This combination yields m l ≤ 97 and 98 meV in the normal and inverted orderings, and total neutrino mass ∑m ν ≤ 285 meV (95% C.L.). The addition of DESI full-shape or Lyman-α P1D to CMB and DESI BAO results in small but noticeable improvement of the constraining power of the data. Lyman-α free-streaming measurements especially improve the constraint. Since they are based on eBOSS data, this sets a promising precedent for upcoming DESI data.

Frequentist statistics↗

Open Source Software Prevalence Ingest Tool

The OSSP Ingest Tool accepts user-input organizational information, ingests IT/OT asset lists in Excel format, and ingests the associated CycloneDX SBOM's. It then performs analytics demonstrating the ability to answer the follow research questions: o RQ1. Ability to identify all OSS services running on, and all OSS components present within, an OT device o RQ1a: Ability to differentiate multiple versions of the same OSS component within each OT device. o RQ1b: Ability to differentiate running from not-running OSS components. o RQ1c: Ability to differentiate based on the originator of the component, because a supplier may have modified it after retrieval from the upstream software source. o RQ2. Ability to correlate the identity of a single OSS component across multiple OT devices, mitigating common name variations such as differences in capitalization, '-' vs '_', and so on. o RQ3. Ability to perform subset analysis of OSS components across multiple OT devices o RQ3a: Ability to perform subset analysis across OSS libraries, generating density & distribution graphs to identify commonly-used libraries and outliers. o RQ3b: Ability to perform subset analysis of a single OSS library, generating density & distribution by CI sector, by device type, by device make/model, and/or by firmware version. o RQ3c: Ability to perform subset analysis by grouping OSS libraries according to programming language, then overlay with RQ4b. o RQ3d: Ability to perform subset analysis by OSS upstream source, providing insight into degree of modifications performed by suppliers. o RQ4. Ability to identify dependencies (transitive and direct) of each differentiated OSS library within each OT device, and enable RQ1,2,3 iteratively for dependencies. o RQ1. Ability to identify all OSS services running on, and all OSS components present within, an OT device o RQ1a: Ability to differentiate multiple versions of the same OSS component within each OT device. o RQ1b: Ability Page

Kapadia, Shayna [Lawrence Livermore National Labor↗

Coupling of high-resolution mass spectrometer and photosynthesis system for comprehensive leaf volatile metabolite profiling

Background Leaf-level biogenic volatile organic compounds (BVOCs) emissions represent a major source of organic gases in the atmosphere, influencing both climate and air quality. These emissions are strongly driven by environmental perturbations, which affect individual plant- to ecosystem-level processes. Uncovering all the BVOCs and understanding how their emissions respond to altered environmental conditions provide critical insights into vegetation-driven changes in atmospheric chemistry. We developed a tandem instrumentation setup that integrates a proton transfer reaction time-of-flight mass spectrometer (PTR-ToF-MS) with parts-per-trillion detection limits and a photosynthetic infrared gas exchange system for the untargeted survey of all the BVOCs. This novel system enables simultaneous, real-time monitoring of BVOC emissions and photosynthetic parameters at the leaf level, offering new opportunities to disentangle the physiological and environmental drivers of VOC release. Furthermore, we established the VOC Analysis and Processing Optimization Resource (VAPOR), an open-access software tool designed for rapid data post-processing and the analysis of the variability of hundreds of BVOCs. We assessed the performance of the tandem system under varying background conditions, using standard gas mixtures and a range of environmental factors. Results Blank emissions were substantially lower for major BVOCs (e.g., isoprene) compared to those observed in plant emissions. Despite this, the observation of background-level VOCs highlights the importance of routinely acquiring and accounting for blank measurements in analyses using the coupled instrumentation. Introduction of known VOC concentrations to the system demonstrated a linear response across different compounds with varying molecular compositions, indicating minimal gas loss regardless of chemical moieties within the coupled instrumentation. We applied the optimized system to investigate the physiological mechanisms driving BVOC emissions across different genotypes of poplar and pennycress. The high mass resolution capabilities of the PTR-ToF-MS, coupled with comprehensive VAPOR-driven data analysis, enabled the identification of several important BVOCs, including methanol and methanethiol; these BVOCs displayed substantial variation across pennycress genotypes and showed concentrations ~ 100–350% higher than the blank. Moreover, isoprene emissions varied significantly among poplar genotypes grown in different potting media. Conclusions Tandem instrumentation offers a powerful tool for profiling volatile molecular markers and elucidating their genetic and environmental underpinnings. This approach enhances our ability to predict BVOC emissions in response to genotype by environmental interactions and contributes to a deeper understanding of vegetation responses to environmental changes.

Biogenic volatile organic compounds↗

Mauka Energy FEVER Tool Dataset

Mauka Energy’s dataset, developed under the Forestry Electric Vehicle Energy Routing (FEVER) project and funded by the U.S. Department of Energy’s Small Business Innovation Research program, is a high-resolution geospatial resource designed to support energy modeling for electric log trucks in complex forestry environments. The dataset integrates detailed spatial and road network data to enable accurate simulation of vehicle performance across varied terrain. At its core, the dataset incorporates lidar-derived elevation models, road alignments, and surface classifications from Oregon State University’s McDonald-Dunn Research Forest. These data capture fine-scale variations in slope, curvature, and surface conditions across forest road systems, allowing for vehicle-level analysis of energy consumption and recovery. The dataset also includes data collected on the surrounding public and private road networks in Benton County, Oregon, used in real-world haul routes. These connecting segments provide critical context for modeling transitions between forest operations and regional transportation infrastructure, incorporating attributes such as grade profiles, elevation change, and speed constraints. This combined dataset underpins the development of Mauka Energy’s rolldown tool, which quantifies energy use and regenerative braking potential on downhill and variable-grade segments. By leveraging high-resolution terrain and road data, the FEVER project enables more accurate assessment of electric vehicle feasibility and performance in forestry applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., N$\gg$M, where N is the dimension of the input matrices and M is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

97 MATHEMATICS AND COMPUTING↗

Central Compact Finite‐Difference Scheme With High Spectral Resolution for KdV Equation

This work presents a combination of cell‐node and cell‐centered compact finite difference scheme for the approximation of third derivatives involved in Korteweg–de Vries (KdV) equations. This approach employs a half‐shifted derivative construction at cell centers, avoiding the need for compact interpolation, thereby removing transfer errors; hence, it improves spectral resolution and maintains high‐order accuracy. Fourier analysis is performed to show the spectral properties of the proposed formulation, which provides higher spectral resolutions as compared to node‐based compact schemes. A filtering strategy is incorporated to suppress high‐frequency oscillations without compromising the accuracy of the numerical scheme, and the total variation diminishing Runge Kutta (TVDRK3) method is applied for time integration. Numerical experiments on linear, nonlinear, and coupled KdV systems are conducted, and a comparative analysis with cell‐node compact schemes confirms that the proposed scheme consistently reduces errors by up to an order of magnitude and achieves high spectral resolution properties.

97 MATHEMATICS AND COMPUTING↗

Exploring Nonmotorized Travel in New York State Using 2017 National Household Travel Survey Data

This report presents systematic analysis of nonmotorized travel behavior within New York State (NYS) utilizing 2017 National Household Travel Survey data. As walking and biking assume increasingly prominent roles in advancing active transportation objectives, accessible mobility, and sustainable transportation systems, comprehensive understanding of these modal patterns becomes essential for evidence-based policy development and strategic planning initiatives. Recognizing the substantial geographic, demographic, and socioeconomic heterogeneity characterizing NYS—spanning from the concentrated urban fabric of New York City (NYC) to dispersed suburban and rural contexts—this analysis employs the structured "4Ws" analytical framework to examine participant demographics, spatial and temporal distributions, and motivational factors underlying active transportation choices relative to motorized alternatives. This methodological approach captures modal behavior patterns, user characteristics, trip purposes, and temporal variations across the state's diverse contexts. Additionally, the research examines behavioral differences among distinct user classifications, including walk-only and bike-only travelers, while conducting comparative analysis of nonmotorized travel patterns between ALICE (Asset Limited, Income Constrained, Employed) and non-ALICE household categories.

99 GENERAL AND MISCELLANEOUS↗

Importance of Spatially Continuous Urban Surface Properties in Urban‐Resolving Earth System Modeling

Accurate representation of urban properties and processes at higher resolutions in global modeling systems is essential for advancing our ability to capture the complexities of urban systems and informing effective resilience strategies. However, the prescription of coarse global-scale urban properties in most state-of-the-art Earth system models (ESMs) is limiting their potential for capturing urban signals as they advance toward kilometer-scale simulation capabilities. To bridge this gap in inadequate urban property representation and to advance urban-resolving Earth system modeling, this work integrates the newly-developed global 1 km-resolution facet-level urban surface property data set, U-Surf, into the land component of Community Earth System Model (CESM)—Community Terrestrial System Model (CTSM). The land-only CTSM simulations are validated against satellite measurements, ground-based urban weather stations, flux tower observations, and reanalysis data. Results demonstrate that the enhanced urban properties allow improved simulations of urban meteorology and surface energy fluxes compared to the default coarse-resolution categorical urban canopy parameters. Spatial scaling analysis reveals regime-dependent information loss during resolution aggregation, as well as substantial scale-dependent variations in urban surface energy flux representation. Furthermore, these findings have critical implications for coupled Earth system modeling when including the effect of land-atmosphere interaction. This work establishes a foundation for future urban-resolving kilometer-scale ESM development, which will enable systematic intra- and inter-city comparisons that inform urban adaptation strategies across diverse global urban environments.

Cheng, Yifan [University of Illinois Urbana-Champa↗

Pulse-by-pulse transient thermal deformation in crystal optics under high-repetition-rate FEL

Time-domain modeling of the thermal deformation of crystal optics can help define acceptable operational ranges across the pulse-energy repetition-rate phase space. In this paper, we have studied the transient thermal deformation of a water-cooled diamond crystal for a cavity-based X-ray free-electron laser (CBXFEL), either an X-ray free-electron laser oscillator (XFELO) or a regenerative amplifier X-ray free-electron laser (RAFEL), by numerical simulations including finite-element analysis and advanced data processing. Pulse-by-pulse transient thermal deformation of a 50 µm-thick diamond crystal has been performed with X-ray pulse repetition rates between 50 kHz and 1 MHz. Results for temperature and thermal deformation have been compared with the results of transient analysis using a continuous wave (CW) power loading. Temperature and thermal deformation results from pulse-by-pulse transient analysis vary with time about the results for the CW case for the same average power. The variation amplitude increases with pulse energy and decreases with repetition rate. When the repetition rate increases to infinity, both temperature and thermal deformation converge to the results for the CW case. Two critical time scales for the operation of crystal optics in a CBXFEL are (1) first-turn time, i.e. the time for the XFEL pulse to complete the first turn around the cavity so that the crystal sees the recirculated XFEL pulse, and (2) period-end time, i.e. the time that the next electron bunch arrives for the amplification, so that the crystal outcouples the amplified FEL power. For the same average power, simulation results show that the crystal thermal deformation seen by the XFEL beam decreases with repetition rate at the first-turn time of a 300 m-long cavity and increases with repetition rate at the period-end time. For the wavefront preservation requirement of the crystal optics, a pulse-energy versus repetition-rate phase space has been established. The upper bounds of the pulse energy at both first-turn and period-end times decreases with repetition rate, especially at the period-end time. The upper bound of the thermal deformation of the crystal at the period-end time for any repetition frequency can be estimated from the CW case. For a water-cooled diamond crystal of dimension 5 mm × 5 mm × 0.05 mm, the time to reach a quasi steady-state is about 50 ms for temperature and 50 µs for thermal deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cost Projections for Utility-Scale Battery Storage: 2025 Update

In this work we describe the development of cost and performance projections for utility-scale lithium-ion battery systems, with a focus on 4-hour duration systems. The projections are developed from an analysis of recent publications that include utility-scale storage costs. The suite of publications demonstrates wide variation in projected cost reductions for battery storage over time. We present the suite of projected cost reductions collected from the literature as well as the low, mid, and high cost projections developed in this work. Storage cost projections are $\$$152/kWh, $\$$247/kWh, and $\$$349/kWh in 2035 and $\$$111/kWh, $\$$184/kWh, and $\$$333/kWh in 2050 for the low, mid, and high cases respectively. Battery variable operations and maintenance costs, lifetimes, and efficiencies are also discussed, with recommended values selected based on the publications surveyed.

25 ENERGY STORAGE↗

Evaluating Thermostats' Deadbands Using HVAC Hardware-In-the-Loop Experiment for Advanced Control Strategies

Smart thermostats have gained significant popularity due to their potential for optimizing energy consumption and enhanced user control while ensuring occupants' comfort. The deadband, also referred to as temperature differential, is defined as the temperature difference between the desired setpoint and upper threshold or lower threshold for the HVAC equipment to turn on. It is a key factor influencing energy efficiency and user satisfaction. This paper presents a comparative analysis of the deadbands of five different smart thermostats, tested with a heat pump, aiming to identify variations in their deadband settings and implications for energy management. The experimental study was conducted using a HVAC hardware-in-theloop (HIL) system that integrates smart thermostats with physical HVAC equipment in a simulated house environment. The study explores the trade-offs between energy efficiency and occupant comfort and highlights how different thermostats participating in demand response event cycle differently based on their deadband settings. The findings offer valuable insights into how selecting the right thermostat or configuring smart thermostat with appropriate deadband settings can be leveraged to enhance demand response capabilities, shift loads effectively and improve operational flexibility in HVAC systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluating Thermostats' Deadbands Using HVAC Hardware-In-the-Loop Experiment for Advanced Control Strategies: Preprint

Smart thermostats have gained significant popularity due to their potential for optimizing energy consumption and enhanced user control while ensuring occupants' comfort. The deadband, also referred to as temperature differential, is defined as the temperature difference between the desired setpoint and upper threshold or lower threshold for the HVAC equipment to turn on. It is a key factor influencing energy efficiency and user satisfaction. This paper presents a comparative analysis of the deadbands of five different smart thermostats, tested with a heat pump, aiming to identify variations in their deadband settings and implications for energy management. The experimental study was conducted using a HVAC hardware-in-theloop (HIL) system that integrates smart thermostats with physical HVAC equipment in a simulated house environment. The study explores the trade-offs between energy efficiency and occupant comfort and highlights how different thermostats participating in demand response event cycle differently based on their deadband settings. The findings offer valuable insights into how selecting the right thermostat or configuring smart thermostat with appropriate deadband settings can be leveraged to enhance demand response capabilities, shift loads effectively and improve operational flexibility in HVAC systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluating Thermostats’ Deadbands Using HVAC Hardware-In-the-Loop Experiment for Advanced Control Strategies

Thermostats play a crucial role in energy consumption, user control, and occupant comfort by serving as the interface between the heating, ventilation, and air conditioning (HVAC) system and the building's occupants. The deadband, also referred to as temperature differential, is defined as the temperature difference between the desired setpoint and upper threshold or lower threshold for the HVAC equipment to turn on or off. It is a key factor influencing energy efficiency and user satisfaction. This paper presents a comparative analysis of the deadbands of five different thermostats, tested with a residential heat pump, aiming to identify variations in their deadband settings and implications for energy usage and management. The experimental study was conducted using a HVAC hardware-in-the-loop (HIL) system that allows thermostats to be connected with physical HVAC equipment, driven by conditions in a simulated residential building. The study explores the trade-offs between energy efficiency and occupant comfort and highlights how different thermostats cycle differently based on their deadband settings. The findings offer valuable insights into how thermostat deadband affects comfort and energy use, as well as the cycling frequency of a heat pump.

Ramaraj, Sugirdhalakshmi [National Renewable Energ↗

Probing the Mechanism of Selective Phosphate Adsorption from Wastewater Using Aqueous and Synchrotron X-ray Characterization

Ion exchange shows promise for recovering phosphate from wastewater as value-added products, but requires high phosphate selectivity to compete with conventional treatment. Hybrid anion exchange (HAIX) resins, which contain non-selective basic functional groups and selective iron oxide nanoparticles (FeOnp), can effectively remove phosphate from wastewater. However, knowledge gaps remain regarding the mechanisms of phosphate selectivity and influence of competing ions, hindering needed efforts to model adsorption dynamics and design scalable adsorption processes for varying wastewaters. To address these gaps, we integrated aqueous-phase adsorption analysis with solid-phase, synchrotron-based X-ray characterization; this integration facilitated elucidation of the distribution and speciation of iron, phosphate, and competing anions on HAIX resins. We compared a quaternary ammonium-functionalized HAIX resin (SBA) to a tertiary amine version (WBA) to determine the role of functional groups. X-ray radiography revealed differences in FeOnp speciation (goethite vs. ferrihydrite) and distribution (peripheral vs. homogeneous) between the resins, resulting in varied phosphate affinity and intraparticle diffusion resistance. Using micro-X-ray fluorescence (μ-XRF) and micro-X-ray absorption near-edge structure (μ-XANES) spectroscopy, we identified differences in where and how phosphate binds across resin types and wastewaters. Across wastewater compositions, FeOnp sites in WBA contribute more to phosphate adsorption than in SBA, possibly due to variations in Fe distribution and speciation. Phosphate adsorption densities calculated from quantitative μ-XRF maps matched those from aqueous analysis, demonstrating the effectiveness of this integrated approach. Altogether, results demonstrate the use of synchrotron-based X-ray characterization for investigating adsorption mechanisms and advance HAIX as a phosphate recovery technology from complex wastewaters.

Nutrient recovery↗

In‐situ Analysis of Paste Properties in Resonant Acoustic Mixers for Quality Monitoring

Formulation control is key to achieving consistent target properties of energetic materials, as feedstock variations and slight deviations in the ratios of different ingredients can have major effects on final product properties, particularly in dense pastes with high particle loading >65 vol.%. In large‐scale operations, it is imperative to either correct or remove batches of material that perform outside baseline property specifications as early as possible to avoid unnecessary processing of suboptimal material. Quality monitoring is the practice of measuring material properties during processing using process analytical technologies as opposed to only testing the properties of the final product; it is a key principle in the quality‐by‐design frameworks used for designing formulations and manufacturing processes. Herein, a process analytical technology method for correlating material properties of dense pastes directly after mixing in a Resonant Acoustic Mixer to motor data is developed and used to detect differences in the particle content of dense paste formulations. This method was also capable of detecting variations in powder feedstock properties, such as particle packing efficiency, and is sensitive enough to detect changes of 2 wt.% in the total solids content of the formulation. The techniques presented herein show excellent promise for use as a process analytical technology capable of quantifying formulation effects on material movement modes during resonant acoustic mixing.

Materials science↗

Density Functional Theory Study of Iron–Oxygen Divacancies in Magnetite (Fe 3 O 4 ) and Hematite (Fe 2 O 3 )

Density functional theory (DFT) calculations are employed to investigate the formation energies, charge redistribution, and binding energies of iron–oxygen divacancies in magnetite (Fe 3 O 4 ) and hematite (Fe 2 O 3 ). For magnetite, we focus on the low-temperature phase to explore variations with local environments. Building on previous DFT calculations of the variations in formation energies for oxygen vacancies with local charge and spin order in magnetite, we extend this analysis to include octahedral iron vacancies before analyzing the iron–oxygen divacancies. We also assessed the relative stability of iron–oxygen divacancies by comparing their formation energies with those of individual vacancies. Our findings reveal a significant energetic driving force for the formation of divacancy clusters, particularly in magnetite, where divacancies in the +1 charge state exhibit formation energies comparable to those of neutral iron vacancies under oxidizing conditions. In hematite, the results indicate a strong tendency for oxygen vacancies to bind to iron vacancies. These results highlight the significance of iron–oxygen vacancy complexes in the transport properties of iron oxides, with particular relevance to diffusion mechanisms under irradiation conditions.

36 MATERIALS SCIENCE↗