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At least 703 records · Page 39

Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise bound imposed by its initial and boundary conditions. Here, the MBP plays a crucial role in understanding the physical meaning and the well-posedness of the mathematical model. Investigation on numerical algorithms with preservation of the MBP has attracted increasingly attentions in recent years, especially for the temporal discretizations, since the violation of MBP may lead to nonphysical solutions or even blow-ups of the algorithms. In this paper, we study high-order MBP-preserving time integration schemes by means of the integrating factor Runge-Kutta (IFRK) method. Beginning with the space-discrete system of semilinear parabolic equations, we present the IFRK method in general form and derive the sufficient conditions for the method to preserve the MBP. In particular, we show that the classic four-stage, fourth-order IFRK scheme is MBP preserving for some typical semilinear systems although not strong stability preserving, which can be instantly applied to the Allen-Cahn type of equations. To our best knowledge, this is the first time to present a fourth-order linear numerical method preserving the MBP. In addition, convergence of these numerical schemes is proved theoretically and verified numerically, as well as their efficiency by simulations of 2D and 3D long-time evolutional behaviors. Numerical experiments are also carried out for a model which is not a typical gradient flow as the Allen-Cahn type of equations.

97 MATHEMATICS AND COMPUTING↗

The Two-Energies Turbulence Scheme Coupled to the Assumed PDF Method

An update of the two-energy turbulence scheme is presented, the 2TE + APDF scheme. The original version of the two-energy scheme is able to successfully model shallow convection without the need of an additional parameterization for non-local fluxes. However, the performance of the two-energy scheme is worse in stratocumulus cases, where it tends to overestimate the erosion of the stable layers. We have identified the causes: the non-local stability parameter does not consider local stratification, the scheme lacks an internal parameter that could distinguish between a shallow convection regime and a stratocumulus regime, and it uses an inflexible turbulence length scale formulation. To alleviate this problem, we propose several modifications: an update of the stability parameter, a modified computation of the turbulence length scale, and the introduction of the entropy potential temperature to distinguish between a shallow convection and a stratocumulus regime. In addition, the two-energy scheme is coupled to a simplified assumed probability density function method in order to achieve a more universal representation of the cloudy regimes. The updated turbulence scheme is evaluated for several idealized cases and one selected real case in the ICOsahedral Nonhydrostatic (ICON) modeling framework. The results show that the updated scheme corrects the overmixing problem in the stratocumulus cases. The performance of the updated scheme is comparable to the operational setup, and can be thus used instead of the operational turbulence and shallow convection scheme in ICON. Additionally, the updated scheme improves the coupling with dynamics, which is beneficial for the modeling of coherent flow structures in the atmospheric boundary layer.

54 ENVIRONMENTAL SCIENCES↗

Measuring dynamics of differentially rotating, unmagnetized, free-boundary plasma produced by soft x-ray irradiation

We present results from a new experiment, fielded on the MAGPIE pulsed power generator, producing a rotating, boundary-free plasma with no pre-imposed magnetic field. Angular momentum is introduced to the rotating system by the oblique collision of multiple plasma flows, which are driven by x-ray ablation of solid targets using the soft x-rays emitted from the implosion of wire array z-pinches. This produces a hydrodynamically stable plasma which undergoes ~2-3 rotations over the duration of the experiment, significantly more than previous pulsed-power platforms. Estimating the angular frequency from the electron density profile in the inner part of the rotating plasma shows that it has a quasi-Keplerian rotation profile. The system also allows for the addition of a controllable magnetic field. This, combined with the sufficiently large Reynolds (~10 5 ) and magnetic Reynolds (~10) numbers, will enable investigation of the effect of magnetic field on the structure and stability of the rotating plasma.

Physics - Plasma physics↗

Synthesis and Characterization of a New Ferroelectric with Low Lead Content, a High Curie Temperature, and a High Piezoelectric Response

Abstract A new solid solution (1− x )Bi(Fe 2/8 Ti 3/8 Mg 3/8 )O 3 –( x )PbTiO 3 (BFTM‐PT) is synthesized and the electromechanical properties are measured. This system is defined as a low‐lead material with ferroelectric/piezoelectric behavior and a morphotropic phase boundary (MPB) that leads to enhanced properties. The MPB is located between x = 0.30 and 0.35 and coincides with a structural phase transition and a sharp increase in the piezoelectric response. The system demonstrates ferroelectric hysteresis where x = 0.325 displays the best properties with a maximum polarization of 39 µC cm −2 and a remnant polarization of 26 µC cm −2 . The range of compositions has high Curie temperature ( T c ), ranging from 625–650 °C. Materials with a T c above 400 °C typically have a low d 33 of <50 pC N −1 at room temperature. However, BFTM‐PT has a higher d 33 that most other compositions with a T c in this range, with the highest being 145 pC N −1 for x = 0.375. The d 33 drops off above 100 °C, but doping studies can be done in the future to stabilize the piezoelectric response at higher temperatures. These outstanding properties open the possibility of new transducer applications, in particular ones requiring high temperature and high power.

36 MATERIALS SCIENCE↗

Neural-Network-Enhanced COTSIM: Advancing Predictive Capabilities for Fast DIII-D Simulations

Sustaining fusion reactions in tokamaks requires heating plasma to thermonuclear temperatures while maintaining confinement and stability. Neutral beam injection (NBI) provides heating, current drive, torque, and fueling, while electron cyclotron (EC) waves are widely used for heating and current drive; together, these actuators shape the plasma current, temperature, and density profiles. The control-oriented tokamak simulator (COTSIM), a predictive, control-oriented code, has been enhanced with neural-network surrogates for transport and sources. Turbulent transport is predicted by MMMnet—a neural-network version of the updated multimode model (MMM 9.0.10)—with significantly reduced computation time relative to MMM; neoclassical transport follows the Chang–Hinton model. NUBEAMnet, a surrogate of the Monte Carlo NUBEAM module, predicts beam-driven heating, current, and torque. EC heating and current drive use a control-oriented, empirically scaled source model; plasma resistivity follows the Spitzer formulation; bootstrap current uses the Sauter model. Equilibrium is computed using both prescribed and fixed-boundary solvers (FBSs), and the pedestal structure is modeled with an empirical pedestal model. For a representative DIII-D discharge, COTSIM predicts electron and ion temperature and safety-factor profiles in close agreement with TRANSP predictive and interpretive simulations while extending predictions through the pedestal region to the plasma edge (versus 80% of the minor radius in TRANSP). Furthermore, the equivalent COTSIM simulation runs in under 3 min compared to about 2 h for TRANSP, enabling rapid scenario planning, optimization of tokamak operation, and between-pulse control design.

Control-oriented tokamak simulator (COTSIM)↗

Safety First: Stability and Dissipation of Line-tied Force-free Flux Tubes in Magnetized Coronae

Abstract Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes ( m = 1) and efficient magnetic energy dissipation develop for plasma safety factors q ≲ 1, where q is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes ( m > 1) can distort equilibrium flux tubes for q > 1 but induce significantly less dissipation. In our analysis, the characteristic pitch μ ˜ 0 of flux-tube field lines determines the growth rate ( ∝ μ ˜ 0 3 ) and minimum wavelength of the kink instability ( ∝ μ ˜ 0 − 1 ). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given μ ˜ 0 . By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions.

79 ASTRONOMY AND ASTROPHYSICS↗

A cross-dimensional analysis of data-driven short-term load forecasting methods with large-scale smart meter data

Electricity load forecasting is essential to utility operation and power grid stability. A wide spectrum of data-driven methods, ranging from linear regression models to more recent deep learning models have been adopted to forecast electric load over the years. However, there still lacks a holistic evaluation of the applicability of conventional statistical and machine learning based algorithms with respect to different temporal and spatial scopes, computational requirements, and sensitivity of model-tuning. Enabled by a large-scale electricity load profile dataset of over 40,000 residential customers in a utility region, we conducted a cross-dimensional analysis of data-driven load forecasting methods. Three regression-based and seven deep learning algorithms with different model configurations were evaluated in terms of their overall and peak load prediction accuracy, and training burdens, across spatial aggregation levels ranging from the transformer, feeder, substation, to neighborhood. We found, first, the load forecasting accuracy is constrained by a predictability boundary, influenced by the forecasting horizon and spatial aggregation level. Specifically, RandomForest, XGBoost, TFT, TSMixer, and TiDE models achieved less than 10 % prediction error for up to 96-h ahead forecasting for district, substation, and feeder levels, while other models struggle at long-horizon predictions; Second, for winter and summer peak load dates, most models were able to predict the peak demand timing within ± 1 h, but the prediction percentage error varied by models, with TFT and TiDE models being the top performers; Third, models with similar prediction accuracy can differ in training burden by an order of magnitude. Therefore, choosing model configurations that balance prediction performance and computational resource is an important practical consideration for large-scale deployment of the machine learning based load forecasting. The outcome of this study can guide researchers and practitioners to choose the proper load forecasting algorithms based on their problem scope, required accuracy, and available resources. The predictability boundary can serve as a benchmark for electricity load forecasting problems with new algorithms and datasets.

Li, Han↗

Impact of Meteorological Factors on the Mesoscale Morphology of Cloud Streets during a Cold-Air Outbreak over the Western North Atlantic

We report postfrontal clouds (PFC) are ubiquitous in the marine boundary layer, and their morphology is essential to estimating the radiation budget in weather and climate models. Here we examine the roles of sea surface temperature (SST) and meteorological factors in controlling the mesoscale morphology and evolution of shallow clouds associated with a cold-air outbreak that occurred on 1 March 2020 during phase I of the Aerosol Cloud Meteorology Interactions over the Western Atlantic Experiment (ACTIVATE). Our results show that the simulated PFC structure and ambient conditions by the Weather Research and Forecasting (WRF) Model are generally consistent with observations from GOES-16 and dropsonde measurements. We also examine the thermodynamical and dynamical influences in the cloud mesoscale morphology using WRF sensitivity experiments driven by two meteorological forcing datasets with different domain-mean SST and spatial gradients, which lead to dissimilar values of hydrometeor water path and cloud core fraction. The SST from ERA5 leads to weaker stability and higher inversion height than the SST from FNL does. In addition, the use of large-scale meteorological forcings from ERA5 yields a distinctive time evolution of wind direction shear in the inner domain, which favors the formation and persistence of longer cloud rolls. Both factors contribute to a change in the time evolution of domain-mean water path and cloud core fraction of cloud streets. Our study takes advantage of the simulation driven by the differences between two large-scale forcing datasets to illustrate the importance of SST and wind direction shear in the cloud street morphology in a realistic scenario.

54 ENVIRONMENTAL SCIENCES↗

MoS 2 nanosheet integrated electrodes with engineered 1T-2H phases and defects for efficient hydrogen production in practical PEM electrolysis

Low electrical conductivity and poor accessibility of MoS 2 reaction sites raise great challenges in maximizing the triple-phase-boundary (TPB) sites of MoS 2 -based electrodes and minimizing ohmic losses for efficient hydrogen evolution reaction (HER) in practical proton exchange membrane (PEM) water electrolysis. Herein, we report a scalable hydrothermal approach to fabricate ionomer-free integrated electrodes with engineered 1 T-2 H heterophase and defect-rich MoS 2 nanosheets (MoS 2 NSs) in-situ grown onto the carbon fiber paper (CFP). With an ultralow loading of 0.14 mg/cm 2 , a small voltage of 2.25 V was obtained at 2000 mA/cm 2 in a practical cell with Nafion115 membrane, which outperforms all previously reported high-loading non-precious catalyst-based electrodes. Impressively, it shows 44 times higher mass activity than a high-loading and ionomer-mixed MoS 2 assemblies electrode. Furthermore, this work builds a bridge from catalyst optimization to electrode fabrication and provides a promising direction for improving intrinsic catalytic activity, electrode conductivity and stability for practical PEM water electrolysis.

1T-2H heterophase↗

Advances in prediction of tokamak experiments with theory-based models

The successful validation of theory-based models of transport, MHD stability, heating and current drive, with tokamak measurements over the last 20 years, has laid the foundation for a new era where these models can be routinely used in a "predict first" approach to design and predict the outcomes of experiments on tokamaks today. The capability to predict the plasma confinement and core profiles with a quantified uncertainty, based on a multi-machine, international, database of experience, will provide confidence that a proposed discharge will remain within the operational limits of the tokamak. Developing this predictive capability for the first generation of burning plasma devices, beginning with ITER, and progressing to tokamak demonstration reactors, is a critical mission of fusion energy research. Major advances have been made implementing this predict first methodology on today's tokamaks. In this work, an overview of several of these recent advances will be presented, providing the integrated modeling foundations of the experimental successes. The first steps to include boundary plasmas, and tokamak control systems, have been made. A commitment to predicting experiments as part of the planning process is needed in order to collect predictive accuracy data and evolve the models and software into a robust whole discharge pulse design simulator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of ZrN coating and heat treatment on U-Mo dispersion fuel systems under irradiation

The stability of U-Mo fuel particles embedded in an Al matrix under irradiation can be enhanced through ZrN coatings and/or heat treatment. Here, the present study investigates the irradiation behavior of fuel plates containing U-Mo fuel particles fabricated under various heat-treatment conditions and ZrN coating thicknesses. Different fission densities were also applied to each fuel plate to evaluate the effects of these variables. Results indicate that higher fission densities lead to more grain recrystallization and high burnup structure (HBS) development in the fuel particles. Heat treatment was found to mitigate the accumulation of fission gas bubbles in fuel particles at low fission densities by coarsening their grains. Fuel particles with ZrN coatings of a 1.2 μm thickness or above exhibited reduced formation of U-Mo/Al interaction layers, suggesting the existence of a critical ZrN coating thickness that minimizes the development of these layers. Fission gas bubbles were predominantly observed at grain boundaries of U-Mo fuel particles irradiated at low fission densities. Subgrain boundaries, which appeared to originate from the original grain boundaries containing fission gas bubbles or HBSs, were also observed, indicating the early stage of HBS propagation in the fuel particles.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Hierarchical Defect Engineering for LiCoO 2 through Low-Solubility Trace Element Doping

Real-world industry-relevant battery composite electrodes are hierarchically structured. Their structural and chemical complexity is featured by ubiquitous multi-scale porosity and cracks, solid-solid and solid-liquid interfaces, compositional and redox heterogeneity, as well as lattice disordering and deformation. In particular for the active cathode particles, which are the fundamental building blocks for the energy reservoir, it is a consensus that these structural and chemical defects could have a profound impact on the battery performance. An in-depth understanding of the underlying mechanisms could critically inform the cathode material engineering, which would have a tremendous potential but remains a daunting challenge at present. In this work, we tackle this question by studying LiCoO 2 (LCO) with trace doping of Ti, which exhibits a low solubility in the LCO layered lattice. Additionally, we observed the spontaneous and heterogeneous segregation of the dopant (Ti) across a wide range of length scales. In addition to the modification of the particle surface and the buried grain boundaries within the particle, we reveal that the Ti doping has induced a significant amount of lattice distortions, which, in turn, promotes the robustness of the LCO lattice at high state of charge (above 4.5V). Our result formulates a multi-scale defect engineering strategy that could be applicable to the synthesis of a broad range of energy materials for applications in batteries and beyond.

36 MATERIALS SCIENCE↗

Boundary Layer Height Variation over the Savannah River Site during a Heat Wave

With the number of heat waves expect to increase in both in their severity and frequency in the coming years, an insight into their impact on planetary boundary layer (PBL) heights is essential for one development of future emergency and safety plans. Using High-Resolution Rapid Refresh (HRRR) atmospheric model output, an analysis is done on the effects a heat wave has on PBL heights and temperature inversions across the Savannah River Site (SRS). This study showed that due to its adjacency to anthropogenic land use, SRS experiences a non-negligible gradient in its PBL height, with higher heights to the northwest. The singular location PBL heigh measurement and forecasts for SRS do not account for this gradient, which has potential implications on pollutant and smoke dispersion onsite. During a heat wave this gradient is present but PBL heights are less impacted than surrounding developed areas, possibly attributable to the woody wetlands that surround the Savannah River's banks. Additionally, the heat wave appears to strongly enhance the nocturnal temperature inversions that the site and surrounding areas experience. This is possibly due to increased stability from higher pressure conditions, which are often associated with heat waves. This influence on nocturnal inversions, however, is limited to their intensity, leaving their timing relatively unaltered. The impact a heat wave has on PBL heights and temperature inversions across SRS is seen to be more dependent on adjacent land use and features rather than the unique land use types onsite.

54 ENVIRONMENTAL SCIENCES↗

Precipitation of dopants on acceptor-doped LaMnO3±δ revealed by defect chemistry from first principles

Perovskite oxides degrade at elevated temperatures while precipitating dopant-rich particles on the surface. A knowledge-based improvement of surface stability requires a fundamental and quantitative understanding of the dopant precipitation mechanism on these materials. We propose that dopant precipitation is a consequence of the variation of dopant solubility between calcination and operating conditions in solid oxide fuel cells (SOFCs) and electrolyzer cells (SOECs). To study dopant precipitation, we use 20% (D = Ca, Sr, Ba)-doped LaMnO3+δ (LDM20) as a model system. We employ a defect model taking input from density functional theory calculations. The defect model considers the equilibration of LDM20 with a reservoir consisting of dopant oxide (DO), peroxide (DO2), and O2 in the gas phase. The equilibrated non-stoichiometry of the A-site and B-site as a function of temperature, T, and oxygen partial pressure, p(O2), reveals three regimes for LDM20: A-site deficient (oxidizing conditions), A-site rich (atmospheric conditions), and near-stoichiometric (reducing conditions). Assuming an initial A/B non-stoichiometry, we compute the dopant precipitation boundaries in a p–T phase diagram. Our model predicts precipitation both under reducing (DO) and under highly oxidizing conditions (DO2). We found precipitation under anodic, SOEC conditions to be promoted by large dopant size, while under cathodic, SOFC conditions precipitation is promoted by initial A-site excess. The main driving forces for precipitation are oxygen uptake by the condensed phase under oxidizing conditions and oxygen release assisted by B-site vacancies under reducing conditions. Possible strategies for mitigating dopant precipitation under in electrolytic and fuel cell conditions are discussed.

Hess, Franziska (ORCID:000000024460643X)↗

Self-consistent modeling of tokamak edge plasma transport with lithium sources

Magnetic confinement fusion devices require effective heat and particle exhaust solutions on the divertor plates to operate sustainably, especially under reactor-relevant conditions. Liquid lithium divertors have been proposed to address two major challenges: control of excessive heat flux to plasma-facing components through vapor shielding and minimization of core plasma contamination from impurities. The National Spherical Torus Experiment-Upgrade (NSTX-U) will explore lithium as a divertor material due to its potential to meet both objectives. We present a self-consistent coupling framework between the plasma boundary transport code UEDGE and the lithium wall transport code Wall–Li to evaluate the feasibility and operational limits of lithium-based divertors. The model aims to optimize lithium sourcing levels to prevent core plasma contamination via fuel dilution while ensuring divertor protection through vapor shielding. This integrated framework, applicable to any tokamak with lithium sources, dynamically adjusts lithium sourcing based on local plasma conditions and surface temperature. The coupled model is tested using NSTX-like geometry and plasma conditions to assess its performance and reliability. Wall–Li calculates lithium fluxes from plasma-facing components, incorporating physical sputtering, thermally enhanced sputtering, and evaporation driven by surface temperature and ion flux. These fluxes are reintroduced into UEDGE as neutral lithium atoms, enabling simulation of their transport and distribution within the plasma. UEDGE computes plasma and neutral transport, surface heat flux, and iteratively feeds this information back to Wall–Li. A small time step is employed to ensure numerical stability and convergence, enabling accurate simulations over typical tokamak discharge durations. This integrated modeling approach provides a robust tool for identifying operational regimes that balance effective lithium sourcing with minimal core plasma contamination, offering critical insights for optimizing lithium-based divertor systems in current and future fusion devices.

Magnetic confinement fusion↗

Validation of an integrated modeling framework for investigating 3D plasma responses in tokamak plasmas

As contemporary experimental tokamaks are pushed toward reactor-relevant operation, they provide essential testbeds for demonstrating and exploring ELM control strategies for deployment in future fusion pilot plants. Accurate predictions of full plasma responses are essential to guide and optimize these demonstrations. This paper introduces and validates an integrated modeling framework over a historical range of DIII-D operational space. The integrated modeling framework uses only scalar plasma parameters and optional reference boundary to self-consistently and flexibly scan through tokamak operational space and estimate the corresponding ELM-suppression relevant plasma response over 3D coil phase space. The framework generates tightly converged equilibria that satisfy a target set of plasma parameters (I p , β N , l i ), with kinetic profiles constrained by an EPED(NN)-computed pedestal and empirical core model. The plasma response of these modeled equilibria is calculated with GPEC. Validated against 55 distinct DIII-D equilibria, the framework consistently reproduces experimentally constrained equilibrium pressure, q, and other representative profiles using the time-varying information from only evolving scalar plasma parameters; plasma response validation is performed for the n=3 perturbation. In particular, the plasma response of a DIII-D discharge scanning q 95 in search of ELM suppression windows is quantitatively reproduced. By accurately reproducing experimental equilibria and plasma responses across wide parameter variation, the framework supports potential for synthetic parameter scans in key operational, stability, and plasma response dimensions to investigate RMP ELM-suppression experiments and inform predictive RMP scenario optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Strain localization criteria for viscoplastic geomaterials

This report presents a viscoplastic localization criterion to detect quasi-instantaneous (i.e., load-induced) and delayed (creep-induced) strain localization in rate-dependent solids. The study is based on the theory of controllability and a viscoplastic description of the mechanical response. Analytical precursors of unstable states are defined through systems of ordinary differential equations (OEDs). The use of the proposed criteria is illustrated at the material point level through a set of strain localization analyses simulating active strain localization of a porous rock. In addition, full-field finite element simulations of compression tests conducted under various pressures are reported to demonstrate the role of local unstable viscoplasticity in the spontaneous propagation of deformation bands under stationary boundary conditions. The study shows that the viscoplastic localization criterion maintains a negative sign as long as the behavior is unstable, that is, the rate of deformation is accelerating. The sign switch coincides with the transition to decelerating deformation. The analyses revealed that pulses of overstress always emerge in correspondence with the growth of unstable behavior, and the peak matches the transition to stable behavior. The local responses recovered from full-field analyses were consistent with those observed in analyses at material point level and the predictions of the presented theory.

36 MATERIALS SCIENCE↗

Investigation of breakaway corrosion observed during oxide growth in pure and low alloying element content Zr exposed in water at 360°C

The addition of small concentrations of alloying elements to pure zirconium can prevent nuclear fuel cladding material from undergoing unstable oxide growth in aqueous environments at light water reactor operating temperatures. The role of alloying elements in stabilizing the oxide growth is examined in this paper, to better understand the oxide growth stabilization mechanism. To this end, a set of initial, short-duration corrosion experiments were performed, followed by oxide layer characterization. Specifically, ten model Zr alloys were selected to test the effect of small alloying additions on the alloy corrosion rate and corrosion breakaway. Additionally, these alloys were corrosion tested in pure water in an autoclave at 360°C for up to 70 days. The alloys included crystal bar Zr, sponge Zr, and model alloys with small concentrations of Sn, Fe, and Cr. After testing, the alloys were characterized using scanning electron microscopy (SEM) and synchrotron µ-X-ray fluorescence (µXRF) to study how the structure of the oxide and alloying element distribution related to unstable oxide growth. Initial results in the 360°C water environment showed breakaway oxidation may be caused by unstable oxide growth due to heterogeneous distribution of the alloying elements. Heterogeneous distribution of alloying elements was correlated to the occurrence of unstable oxide growth (either nodule-like, grain boundary penetration, or differential grain-to-grain growth). It is possible that this heterogeneity, made possible by low alloying element content, can cause breakaway corrosion, but further study is warranted.

36 MATERIALS SCIENCE↗