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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Development of SAM Code Capabilities for Safety Analysis of GCR Air-ingress Events

Air-ingress following a depressurized loss-of-forced-cooling (DLOFC) event is a challenging, multiphysics safety scenario for High-Temperature Gas-Cooled Reactors (HTGRs), involving coupled gas composition transport, buoyancy-driven flow redistribution, graphite oxidation, and structural heat-up. Despite its importance — air ingress is a key scenario identified in the PIRT process for the HTGRs — existing system-level safety codes have lacked the integrated capability to simulate the complete event sequence with high confidence. This report documents the development, validation, and demonstration of three new capabilities in the SAM code to address this gap: (1) a multi-component gas mixture flow model with binary diffusion to track the helium-air composition and its effect on system density and flow; (2) a 0-D graphite oxidation model based on the Roes correlation, including oxygen consumption and exothermic heat release; and (3) an isentropic critical flow model for accurate representation of primary system depressurization through a break. These capabilities are validated against two benchmark experiments. The NSTF heavy-gas ingress experiment validates the multi-component flow model: SAM correctly reproduces the rapid buoyancydriven flow stagnation and subsequent natural circulation recovery driven by composition-dependent density changes. The NACOK graphite oxidation experiment validates the oxidation model: SAM predicts a bottom-level graphite weight loss of 25%, in close agreement with the measured 24%, and reproduces the strong axial nonuniformity and block-geometry dependence of oxidation, at a level comparable to the SPECTRA and TINTE codes. The validated capabilities are then exercised together in an integrated, reactor-scale simulation of a DLOFC air-ingress transient in a simplified HTR-PM pebble-bed reactor. In a single calculation spanning approximately 8 days, SAM reproduces the complete accident sequence: rapid depressurization, densityand diffusion-driven air ingress over ˜15 hours, onset of buoyancy-driven natural circulation, exothermic graphite oxidation with a peak fuel temperature at ˜62 hours, and eventual passive cooldown. These results demonstrate that SAM now provides the nuclear community with a preliminarily validated, modern systemlevel tool for HTGR air-ingress safety analysis, filling a recognized capability gap. Future extensions to broaden species tracking, improve oxidation chemistry, and refine the reactor model are discussed.

Yang, Gang↗
DOE OSTI2021

Galvanostatic Intermittent Titration Technique Reinvented: Part I. A Critical Review

The galvanostatic intermittent titration technique (GITT), introduced in 1977 by Weppner and Huggins, provided a readily accessible means to measuring the chemical diffusion coefficient of electrochemical electrode materials. The method continues to be widely used today, but the reported diffusivity values are highly inconsistent, ranging as much as four orders of magnitude for some Li layered oxide compositions. Even qualitative trends of diffusivity are inconsistent, suggesting significant flaws in the implementation of the method. Other variants of the GITT method also suffer from similar inconsistency problems. Here we identify numerous sources of significant error including composition-dependent reaction overpotentials, mathematical flaws in the relaxation analysis methods, finite-size and non-planar geometry effects, inter-particle inhomogeneity issues, early transient effects, and surface area uncertainties. We propose a simple relaxation analysis scheme using the time variable t relax + τ - t relax , where t relax is relaxation time and τ is the galvanostatic pulse duration. We also propose to use dense diffusion-limited samples to isolate the bulk-diffusion process in the time domain. Chemical diffusivity can be extracted much more reliably with this improved implementation of the GITT method.

25 ENERGY STORAGE↗
DOE OSTI2023

Diffusion in undoped and Cr-doped amorphous UO 2

UO 2 fuel pellets are often doped with chromium oxide to obtain favourable properties such as higher density, improved thermal stability, large grain sizes, improved pellet-clad interaction margins, and increased fission gas retention during transients. Chromium has a low solubility limit in UO 2 , with past experimental work reporting solubility limits ranging between 0.004 to 0.06 wt.% Cr. Due to its low solubility, segregation of Cr ions to the grain boundary may occur. Further, the complexity of these boundaries may be high as observed in other ceramics resulting in disordered or amorphous regions along the boundary, affecting a range of material and operational properties of the fuel pellet. To assess these disordered regions, in this work we study amorphous undoped and Cr doped UO 2 systems (containing 10–50 at.% Cr 3+ ) that have been modelled using classical molecular dynamics methods incorporating Cr 3+ into the well-used CRG potential library. Diffusion coefficients, pre-exponential factors, and activation energies for diffusion were computed for oxygen ions, assessing the impact of structure and extrinsic species on migration. Oxygen diffusion was observed to be much faster in the undoped amorphous system compared to its crystalline counterpart. Oxygen diffusion in doped systems decreased with increasing Cr concentration, highlighting the importance of additives to retain fission products and other migratory species.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Analysis of Silver Release from Furnace-Tested TRISO Particles

High temperature testing of intact TRISO particles previously irradiated in the AGR-5/6/7 experiment was performed in the Furnace for Irradiated TRISO Testing (FITT) to directly confirm diffusive release of silver and europium from intact TRISO particles. Testing was conducted from 1,100–1,600°C for exposure times up to 100 h to directly confirm silver through layer release below safety testing temperatures. The FITT analysis showed highest levels of silver release at 1,300–1,400°C which confirms athermal release behaviors previous observed in step-wise and transient safety tests. Additionally, release was non-uniform with some particles releasing a majority of their inventory while others did not appear to release silver under identical testing conditions, which was consistent with historic observations. An assessment of the effective silver diffusion coefficient in the SiC layer was conducted and indicated maximum values in the 1,300–1,400°C range. The magnitude of the calculated diffusion coefficients also exceeded currently accepted diffusion coefficients. The release behavior of europium from intact particles was also analyzed in FITT for at 1,450–1,550°C for 500 h to 750 h. Direct confirmation of europium release below safety testing temperatures was confirmed absent contributions from matrix release. The analysis indicated europium release follows a general Arrhenius behavior and suggests general uniform release and indicates irradiation conditions influence observed release response. Calculated diffusion kinetics agree well with historic experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Model‐Based Interpretation of Solute Exports and Carbon Partitioning During Shale Weathering in a Mountainous Hillslope

The weathering of sedimentary rocks in high-elevation catchments influences freshwater quality and the global carbon cycle. While individual biogeochemical mechanisms involved in this process are relatively well understood, quantifying their contributions to solute export and carbon fluxes under natural, transient conditions remains challenging. Here, we implement a numerical multidimensional and multiphase model to simulate coupled hydrological and biogeochemical processes in a shale-underlain, snow-dominated hillslope in the Rocky Mountains, Colorado. The model captures the dynamic interplay between soil respiration, mineral weathering, and climate-driven hydrological forcing, reproducing observed soil CO 2 dynamics, groundwater chemistry, and subsurface flow. Our results reveal that seasonal snowmelt enhances carbonate weathering by promoting the infiltration of CO 2 -rich water to depth, while pyrite oxidation is primarily sensitive to low water saturation that facilitates O 2 diffusion through the regolith. Topography modulates the spatial distribution of shale weathering, as steeper slopes enhance lateral drainage, favoring the delivery of reactants to greater depths. While shale weathering at our site acts as a transient carbon sink, with silicates and carbonates buffering acidity and promoting atmospheric CO 2 consumption (1% of soil-derived CO 2 ), the exported dissolved inorganic carbon is predominantly geogenic (∼73%). Consequently, when accounting for long-term marine carbonate precipitation. The current weathering regime represents a net source of carbon to the atmosphere. The oxidation of pyrite and petrogenic organic carbon together release approximately 0.9 mol·m −2 ·yr −1 of CO 2 . Our findings highlight the role of topography, hydroclimate, and the coupling between acid-base reactions in shaping the carbon balance and the solute exports in mountainous critical zones.

carbon cycling↗
DOE OSTI2020

Conversion between triplet pair states is controlled by molecular coupling in pentadithiophene thin films

In singlet fission (SF) the initially formed correlated triplet pair state, 1 (TT), may evolve toward independent triplet excitons or higher spin states of the (TT) species. The latter result is often considered undesirable from a light harvesting perspective but may be attractive for quantum information sciences (QIS) applications, as the final exciton pair can be spin-entangled and magnetically active with relatively long room temperature decoherence times. In this study we use ultrafast transient absorption (TA) and time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy to monitor SF and triplet pair evolution in a series of alkyl silyl-functionalized pentadithiophene (PDT) thin films designed with systematically varying pairwise and long-range molecular interactions between PDT chromophores. The lifetime of the (TT) species varies from 40 ns to 1.5 μs, the latter of which is associated with extremely weak intermolecular coupling, sharp optical spectroscopic features, and complex TR-EPR spectra that are composed of a mixture of triplet and quintet-like features. On the other hand, more tightly coupled films produce broader transient optical spectra but simpler TR-EPR spectra consistent with significant population in 5 (TT) 0 . These distinctions are rationalized through the role of exciton diffusion and predictions of TT state mixing with low exchange coupling J versus pure spin substate population with larger J. The connection between population evolution using electronic and spin spectroscopies enables assignments that provide a more detailed picture of triplet pair evolution than previously presented and provides critical guidance for designing molecular QIS systems based on light-induced spin coherence.

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

Pushing the heterometal doping limit while preserving long-lived charge separation in a Ti-based MOF photocatalyst

Here, this study explores the nature, dynamics, and reactivity of the photo-induced charge separated excited state in a Fe 3+ -doped titanium-based metal organic framework (MOF), xFeMIL125-NH 2 , as a function of iron concentration. The MOF is synthesized with doping levels x = 0.5, 1 and 2 Fe node sites per octameric Ti-oxo cluster and characterized by powder x-ray diffraction, UV-vis diffuse reflectance, atomic absorption, and steady state Fe K-edge X-ray absorption spectroscopy. For each doping level, time-resolved X-ray transient absorption spectroscopy studies confirm the electron trap site role of the Fe sites in the excited state. Time scan data reveal multiexponential decay kinetics for the charge recombination processes which extend into the microsecond range for all three concentrations. A series of dye photodegradation studies, based on the oxidative decomposition of Rhodamine B, demonstrates the reactivity of the charge separated excited state and the photocatalytic capacity of these MOF materials compared to traditional heterometal-doped semiconductor photocatalysts.

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

Creating Hydride Rim Structures in Zircaloy 4 Cladding Tubes to Mimic High Burnup

During their long service in commercial light water reactors, zirconium alloy cladding tubes are subject to oxidation and subsequent hydrogen pickup which can degrade the materials mechanical properties [1]. These degradations can lead to premature cladding ruptures during reactor power transients [2] as well as negatively impact the claddings post quench ductility following high temperature steam oxidation in thermal hydraulic transients [3]. Hydrogen has low solid solubility in zirconium and usually precipitates as brittle zirconium hydride platelets in the cladding metal matrix. Due to temperature driven diffusion (Soret effect) and the grain texture of stress relieved zirconium metal tubes, these hydrides precipitate with a circumferential orientation near the outer surface of the cladding tubes forming a hydride rim which can serve as a site for crack initiation during circumferential ‘hoop’ loading of the cladding [4rim formation][5]. In order to better understand the effect of hydride rims on the fracture behavior of stress relieved zirconium alloy cladding tubes a procedure to produce these rim-like structures is being developed at Idaho National Laboratory (INL).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Infrared thermography NDT for in-situ defect detection in sandwich composite panel manufacturing

Composite manufacturing presents numerous challenges, as defects can arise from various sources throughout the process. In sandwich composite structures, the integration of a foam core introduces additional complexity and increases the likelihood of defect formation like delamination. To mitigate these issues and reduce the risk of future structural failures, in-situ monitoring during manufacturing is essential. This study investigates infrared (IR) thermography as a non-destructive technique for detecting manufacturing defects in foam-core sandwich composite panels under thermally excited conditions representative of in-situ processing. A stationary FLIR A8590 IR camera (640 × 512 pixels, 30Hz, 17mm lens, 9 ft stand-off distance) was used to monitor prefabricated panels subjected to controlled external heating simulating compression molding and resin cure exotherm. Interlaminar delamination defects with characteristic sizes ranging from 0.25 × 0.25in² to 5 × 5in² produced measurable surface temperature depressions of approximately 4–10°C during transient cooling, exceeding the effective noise floor of the camera by more than two standard deviations. Thicker laminates exhibited prolonged defect detectability windows due to increased thermal diffusion time. In contrast, embedded Teflon inclusions generated weak thermal contrasts of ≤ 3°C, approaching the measurement noise floor, due to limited thermal property contrast with the surrounding glass fiber composite. These results establish quantitative detectability limits for stationary thermographic inspection of sandwich composite panels under manufacturing-representative thermal cycles.

Barakat, Abdallah [ORNL] (ORCID:0000000296141398)↗
DOE OSTI2025

Reduction of Exciton Diffusion Length with Genetically Tuned Non-Photochemical Quenching in Plant Thylakoid Membranes

Non-photochemical quenching (NPQ) protects plants from excess light by dissipating excitation energy as heat. Limited exciton migration is a key feature of NPQ, reducing the energy flux to reaction centers; however, quantitative evidence for this mechanism in native thylakoid membranes has been lacking. Here, we investigate the correlation between NPQ activity and exciton diffusion length (LD) using Nicotiana benthamiana mutants with distinct NPQ capacities. NPQ under both light- and dark-acclimated conditions was quantified for each genotype via fluorescence lifetime snapshots, and exciton mobility was probed using transient absorption spectroscopy with exciton-exciton annihilation analysis. By comparing the relationship between chlorophyll fluorescence lifetime and LD across mutants, we observed that NPQ activation quantitatively limits the spatial range of exciton migration, thereby reducing the access to reaction centers. Our findings provide direct experimental evidence that NPQ modulates the dynamics of energy transport, advancing our understanding of photoprotective regulation in photosynthetic systems.

Diffusion↗
DOE OSTI2025

Investigating Electron Conductivity Regimes in the Bacterial Cytochrome Wire OmcS

The anaerobic bacterium Geobacter sulfurreducens produces extracellular, electronically conductive cytochrome polymer wires that are conductive over micron length scales. Structure models from cryo-electron microscopy data show OmcS wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. However, the mechanism by which this heme arrangement supports long-range electronic conduction remains unknown. Structure models from cryo-electron microscopy data show these wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. Existing computational models using static heme redox potentials and coupling energies fail to explain experimental observations, predicting conductances 10,000 to 100,000 times lower than measured values. Here, we investigate how dynamic disorder affects site energies, interheme coupling, and long-range electronic conductivity within these cytochrome wires. We introduce an approach to extract charge carrier site information directly from Kohn–Sham density functional theory, without employing projector schemes, and show that site and coupling energies are highly sensitive to changes in interheme geometry and the surrounding electrostatic environment. Unlike models that incorporate dynamic disorder as a thermally averaged quantity, our quantum charge carrier model incorporates proxies for dynamic disorder through decoherence corrections, yielding predicted diffusion coefficient closer to what is expected from experiment and comparable with other organic-based electronic materials. Based on these simulations, we propose that the instantaneous fluctuations of the local electrostatic environment can transiently lift energy degeneracies and delocalize charge carriers. Furthermore, these studies reveal how incorporating dynamic fluctuations associated with the environment resolves the discrepancy between theory and experiment in microbial cytochrome wires and highlight design principles for bioinspired, heme-based conductive materials.

Bioinorganic chemistry↗
DOE OSTI2022

Influence of carrier trapping on radiation detection properties in $\mathrm{CVD}$ grown 4H-SiC epitaxial layers with varying thickness up to 250 µm

We report low doped n-type 4H-SiC epitaxial layers of thickness 50, 150, and 250 µm grown by hot wall chemical vapor deposition were used to fabricate Ni/4H-SiC Schottky radiation detectors. The epitaxial layers were grown on the (0001) face of highly conductive bulk 4H-SiC substrates 8° offcut towards the $\langle 11\bar{2}1\rangle$ direction. The 50, 150, and 250 µm thick epilayer detectors, under optimized settings, showed energy resolutions of 2.0%, 0.78%, and 0.63%, respectively for 5.48 MeV alpha particles. Deep level transient spectroscopy studies showed that the observed variation in the detector resolution is linked to the defect parameters in the devices. Least-squares fitting of the bias dependence of the charge collection efficiency according to a drift-diffusion model, revealed minority carrier diffusion lengths of 16, 10, and 9.2 µm, respectively, implying that the detectors are not limited by minority carrier trapping. The detector performance was observed to be primarily dependent on the concentration and capture cross-sections of the lifetime killing electron traps Z 1/2 and EH 6/7 .

36 MATERIALS SCIENCE↗
DOE OSTI2025

Co‐Doping Approach for Enhanced Electron Extraction to TiO 2 for Stable Inorganic Perovskite Solar Cells

Inorganic perovskite CsPbI 3 solar cells hold great potential for improving the operational stability of perovskite photovoltaics. However, electron extraction is limited by the low conductivity of TiO 2 , representing a bottleneck for achieving stable performance. In this study, a co‐doping strategy for TiO 2 using Nb(V) and Sn(IV), which reduces the material's work function by 80 meV compared to Nb(V) mono‐doped TiO 2 , is introduced. To gain fundamental understanding of the processes at the interfaces between the perovskite and charge‐selective layer, transient surface photovoltage measurements are applied, revealing the beneficial effect of the energetic and structural modification on electron extraction across the CsPbI 3 /TiO 2 interface. Using 2D drift‐diffusion simulations, it is found that co‐doping reduces the interface hole recombination velocity by two orders of magnitude, increasing the concentration of extracted electrons by 20%. When integrated into n–i–p solar cells, co‐doped TiO 2 enhances the projected T S80 lifetimes under continuous AM1.5G illumination by a factor of 25 compared to mono‐doped TiO 2 . This study provides fundamental insights into interfacial charge extraction and its correlation with operational stability of perovskite solar cells, offering potential applications for other charge‐selective contacts.

14 SOLAR ENERGY↗
DOE OSTI2022

Spontaneous carrier generation and low recombination in high-efficiency non-fullerene solar cells

The current research reveals the unique photo physical properties and carrier generation mechanisms of high efficiency non-fullerene acceptor-based organic photovoltaic blends. The analysis of device performance, morphology, and photo physics reveals that the interface carrier generation cannot support the device's current output. It is seen that primary photon excitons can dissociate into charge carriers in Y6, which displays a time scale of ∼0.3 ps with polaron yields above 28% in neat and blended thin films. This characteristic in combination with a large exciton diffusion length enables high morphology tolerance in Y6-overloaded blends. The carrier generation process is also combined with recombination studies. The recombination rate quantified by flux-dependent transient absorption measurements yields less than 5% total recombination and nearly 0% geminate recombination. Furthermore, these results define the advantages of the Y6 non-fullerene acceptor (NFA) and reveal the fundamental importance of developing new NFA materials with superior photo physical properties.

14 SOLAR ENERGY↗
DOE OSTI2023

Disentangling the evolution of electrons and holes in photoexcited ZnO nanoparticles

The evolution of charge carriers in photoexcited room temperature ZnO nanoparticles in solution is investigated using ultrafast ultraviolet photoluminescence spectroscopy, ultrafast Zn K-edge absorption spectroscopy, and ab initio molecular dynamics (MD) simulations. The photoluminescence is excited at 4.66 eV, well above the band edge, and shows that electron cooling in the conduction band and exciton formation occur in <500 fs, in excellent agreement with theoretical predictions. The x-ray absorption measurements, obtained upon excitation close to the band edge at 3.49 eV, are sensitive to the migration and trapping of holes. They reveal that the 2 ps transient largely reproduces the previously reported transient obtained at 100 ps time delay in synchrotron studies. In addition, the x-ray absorption signal is found to rise in ∼1.4 ps, which we attribute to the diffusion of holes through the lattice prior to their trapping at singly charged oxygen vacancies. Indeed, the MD simulations show that impulsive trapping of holes induces an ultrafast expansion of the cage of Zn atoms in <200 fs, followed by an oscillatory response at a frequency of ∼100 cm−1, which corresponds to a phonon mode of the system involving the Zn sub-lattice.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Constraints on Populations of Neutrino Sources from Searches in the Directions of IceCube Neutrino Alerts

Beginning in 2016, the IceCube Neutrino Observatory has sent out alerts in real time containing the information of high-energy ($E$ ≳ 100 TeV) neutrino candidate events with moderate to high (≳30%) probability of astrophysical origin. In this work, we use a recent catalog of such alert events, which, in addition to events announced in real time, includes events that were identified retroactively and covers the time period of 2011–2020. We also search for additional, lower-energy neutrinos from the arrival directions of these IceCube alerts. We show how performing such an analysis can constrain the contribution of rare populations of cosmic neutrino sources to the diffuse astrophysical neutrino flux. After searching for neutrino emission coincident with these alert events on various timescales, we find no significant evidence of either minute-scale or day-scale transient neutrino emission or of steady neutrino emission in the direction of these alert events. This study also shows how numerous a population of neutrino sources has to be to account for the complete astrophysical neutrino flux. Assuming that sources have the same luminosity, an $E$ -2.5 neutrino spectrum, and number densities that follow star formation rates, the population of sources has to be more numerous than 7 × 10 -9 Mpc -3 . This number changes to 3 × 10 -7 Mpc -3 if number densities instead have no cosmic evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The role of geographical spreaders in infectious pattern formation and front propagation speeds

The pattern formation and spatial spread of infectious populations are investigated using a kernel-based Susceptible–Infectious–Recovered (SIR) model applicable across a wide range of basic reproduction numbers R O . The goal is to examine the role of geographical spreaders on transient spatial pattern formation of infectious populations and the associated maximum invasive front speeds c max . In the simulations conducted here, geographical spreaders are defined as a portion of the infected population Φ experiencing high mobility between identical communities. The spatial organization of the infected population and c max are determined when the infections are randomly initiated in space within multiple communities. For small but finite , scaling analysis and numerical simulations in 1-dimension suggest that when the spreading kernel is Gaussian-shaped, where is the inverse of the infectious duration. This finding for agrees with a diffusion-based representation of mobility in 1-D. Numerical simulations in 2-D across wide-ranging suggest that , the variance of the spatial kernel describing mobility of long-distance geographical spreaders across communities, determines the spatial organization of infections across communities. When (long-distance mobility, where is the minimum spatial extent defining adjacent communities), the infectious population will experience a transient but spatially coherent pattern with a wavelength that can be derived from the spreading kernel properties. Moreover, the 2-D simulations for the bounded kernel suggest that attainment of is also dictated by but the magnitude is not sensitive to unlike diffusion-based models.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Multicycle flash sintering of cubic Y 2 O 3 -stabilized ZrO 2 : An in situ energy dispersive synchrotron x-ray diffraction study with high temporal resolution

The current induced unit cell volume changes, (111) Bragg peak full width at half maximum (FWHM) and its integrated intensity in 8 % Y 2 O 3 stabilized ZrO 2 (8 %YSZ) solid state electrolyte was monitored during a triple-flash sintering experiment by in situ energy dispersive x-ray diffraction using a polychromatic synchrotron probe (max, photon energy 200 keV) with 2 second temporal resolution. The first spontaneous singularity in the unit cell volume (+0.54 %) was observed at 899 °C under 15 V/mm applied field intensity, which was associated with 13 mA/mm 2 current draw and an increase in density to 97 %. Following anelastic relaxation of the unit cell volume under open circuit conditions, the same applied field was applied twice in a row which resulted in additional induced singularities at 925 °C (+0.48 %) and 944 °C (+0.42 %). A floating baseline, which was above the thermal expansion baseline, was observed from 833 to 969 °C and was attributed to Joule heating. In conclusion, the singularity at 899 °C is associated with a sharp change in (111) FWHM and a 34 % decrease in integrated peak area that was attributed to changes in the distribution of oxygen vacancies and the changes in their concentration as induced by the applied field in the spontaneous transient stage of flash sintering.

36 MATERIALS SCIENCE↗