Elucidating effects of cell architecture, electrode material, and solution composition on overpotentials in redox flow batteries
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catalysis (heterogeneous)↗
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Measurement of Fission Product Concentration Profiles in AGR-3/4 TRISO Fuel Graphitic Matrix and Nuclear Graphites
The third Advanced Gas Reactor (AGR) irradiation experiment, AGR-3/4, was designed to investigate the migration of fission products in fuel compact graphitic matrix and reactor graphite components. Using destructive methods, radial fission product concentration profiles were measured for gamma-emitting fission products (e.g., Ag-110m, Cs-134, and Eu-154) and beta-emitting Sr-90 in irradiated graphitic and graphite components from six different AGR-3/4 irradiation capsules. These new measured concentration profiles can now be compared to non-destructive measurements and fission product transport simulations and will be used to derive new diffusivities and sorptivities to support refinement of fission product transport models and high-temperature gas-cooled reactor (HTGR) source-term analyses. Each capsule in the AGR-3/4 experiment had four fuel compacts in the middle of two concentric rings of graphitic matrix material, PCEA graphite, or IG-110 graphite. In addition to the approximately 1898 tristructural isotropic (TRISO) coated particles in each compact, there were 20 designed to fail (DTF) particles coated only in pyrocarbon so that they released fission products into the surrounding cylindrical rings of carbonaceous materials. Destructive sampling of the rings involved machining/milling material from around the circumference of the rings, collecting that material, and performing radiochemical analyses on it. Milling operations were performed in multiple steps or segments, and each segment was generally 0.508 mm (0.020 in) thick. Knowing the radial position at which each segment was milled, the volume of the milled material at each segment, and the fission product content in each segment, the radial fission product concentrations were constructed for select isotopes in each ring. Ag-110m profiles had the most variation. Some profiles were peaked at an inner or outer surface. Some were peaked at the middle of the ring wall thickness. Some increased radially outward, and some decreased radially outward. These types of variations and the fact that the measured profiles do not generally compare favorably with the transport model employed for AGR-3/4 may adversely impact the ability to extract reasonable transport parameters for this isotope. In many cases, the Cs-134 profiles decreased somewhat linearly in the outward radial direction, and in cursory comparisons, the shapes of these profiles appeared similar to those from model predictions. The step changes in concentration across the inner-outer ring gap were generally consistent with the model predictions as well. In some cases, there were local maxima in concentration at the outer surface of the rings. This suggests that fission products could have transported in the small gaps between the inner ring and the outer ring and between the outer ring and the sink ring such that some portion of a given fission product can bypass diffusion through the ring itself. The analysis of the small nubs on the outer surfaces of some of the outer rings revealed fission product concentrations in the nubs that were often higher than in the outermost segments of the rings. This further supports the hypothesis that short-circuit, gap transport occurred, causing relatively high surface concentrations on the outer surfaces of the rings. Eu-154 and Sr-90 profiles tend to have very similar shapes, suggesting that they transport via the same mechanisms. The observed profiles were indicative of a transport process where the isotopes are sorbed on the inner surface of the ring, but diffusion into the ring from that surface is quite slow. Some elevated concentrations of Sr-90 (relative to Eu-154) on the outer surface of a ring suggested that rapid, gas-gap transport of gaseous precursor Kr-90 and volatile Rb-90 could have occurred prior to their decaying to Sr-90. Overall, the Eu 154 and Sr-90 profiles were still very similar, which indicates that the transport of short-lived Sr-90 precursors is not a major effect. In some capsules, the qualitative Sr-90 behavior across the ring gaps was consistent with the model (using the available legacy Sr-90 transport parameters), but in other capsules the model was inconsistent with the measurements and seems to underestimate the amount of Sr-90 in the outer rings. The total ring Sr-90 inventories were estimated for all the rings that were subject to physical sampling. These results will be used to adjust the predicted particle and/or compact releases used in the AGR-3/4 fission product transport model. Given the different irradiation temperatures among the capsules and the rings, it was not possible to discern fundamental differences in the transport of isotopes within the different carbon materials, i.e., graphitic matrix, IG-110, or PCEA. It may be possible to do this in the course of determining transport from the concentration profiles in future work.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Propagation and attenuation of sound in one-dimensional quantum liquids
At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies, the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid 4 He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies, the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid, the entropy and density oscillations are strongly coupled and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to a single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat-diffusion mode. Lastly, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Graphene: a Barrier to Hydrogen Permeation
Small area freestanding monolayer graphene has been shown to be impermeable to standard gases including hydrogen and helium.1 Several recent reports have suggested that graphene can be used as a hydrogen permeation barrier on metals.2 Those studies have relied on electrochemical hydrogen permeation measurements, which do a good job reproducing bulk permeability compared to gaseous diffusion but do not always reflect the real surface effects due to the difference in driving forces. This problem is magnified when measuring the permeability of thin coatings, which are dominated by surface effects. For this reason, we performed gas driven hydrogen permeation measurements of graphene coated metal samples. The diffusion of hydrogen through a metal can be described using Fick's and Sievert's Laws. Graphene-coated copper foils were prepared using chemical vapor deposition (CVD) with a methane precursor. Photo-reduced graphene samples were prepared by first sputtering a layer (∼15 nm) of copper on top of stainless steel foils. Graphene oxide in ethanol solutions were then drop cast on the surface and photo reduced using a neon lamp. A custom-designed apparatus has been assembled for measuring the hydrogen permeability of various materials. The operating principle of the system is as follows: A sample is sealed between the fore-sample and post-sample chambers using standard vacuum gaskets. Hydrogen is introduced into the fore sample region at varying pressures while the post sample region is maintained under high vacuum. Due to the concentration gradient, hydrogen then diffuses through the material and is detected using a quadrupole mass spectrometer. This process is repeated at several temperatures. The mass spectrometer was calibrated using an orifice with known conductance in place of the sample. Data collection and reduction were automated using scripts written in LabVIEW and Octave, respectively. We saw a decrease in the hydrogen permeability of copper after adding graphene to the surface for small temperature steps. This result is also observed when considering temperature steps of 20 K. Future Work: Apply this methodology to graphene-coated 316L stainless steel. The hydrogen permeability of 316L steel should also decrease with the addition of graphene to the surface. Determine methods for graphene defect reduction.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Solid-state reaction mediated microstructural evolution in a spark plasma sintered in situ Ti–B 4 C composite
For this study, a novel porosity-free in situ Ti–B 4 C composite was fabricated via spark plasma sintering (SPS). Detailed analysis of the phase evolution, coupling results from XRM, XRD and SEM-EBSD-EDS, indicate that primarily TiB 2 precipitates formed due to the in-situ reactions between the boron-carbide and titanium powders. The precipitation of TiB 2 resulted in the formation of a graphitic C-rich thin layer circumscribing the partially reacted B 4 C particles. Further progression of the in-situ reaction leads to the out-diffusion of the excess carbon from the B 4 C particles, across the graphite and TiB 2 phases, forming TiC upon reacting with the titanium matrix. Therefore, the final microstructure primarily consisted of TiB 2 , TiC, and partially reacted B 4 C phases, with small amounts of TiB, α-Ti, and graphite. Furthermore, the microstructure in these SPS processed in situ composites appeared to be the product of a solid-state Ti–B 4 C diffusion couple, substantially different from their fusion-based additively manufactured counterparts. Nano-indentation tests revealed a remarkably high average hardness of ~25 GPa for this SPS-processed Ti–B 4 C composite and comparable (with literature) phase-specific hardness and modulus values for the constituent TiB 2 , TiC, and B 4 C phases.
36 MATERIALS SCIENCE↗
Ensemble variational Fokker-Planck methods for data assimilation
Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.
97 MATHEMATICS AND COMPUTING↗
Mechanism of Metal Intercalation under Graphene through Small Vacancy Defects
Metal intercalation under graphene has attracted extensive experimental and theoretical research because of its capability to manipulate the electronic structure and properties of graphene. However, the pathways and mechanisms of intercalation are still not well understood. Here, we systematically investigate the intercalation process of metal atoms through graphene vacancies using first-principles calculations. We show that the energy barrier for metal atom penetration through the vacancies in graphene is small as long as the size of the vacancy is larger than a mono-vacancy. However, metal atoms are strongly bonded to the vacancy so that the detachment energy of a metal atom from the vacancy is extremely high. This inhibits the diffusion of the metal atom into the gallery beneath the surface to complete the intercalation process. On the other hand, our calculation results show that the detachment energy of a metal atom from a metal dimer at small vacancy defects is significantly reduced, making intercalation much easier. Therefore, the key step limiting the intercalation process is the detachment of the metal atoms from vacancy defects. This finding from our study provides useful insight into the defect-assisted intercalation mechanism.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
K-space algorithmic reconstruction (KAREN): a robust statistical methodology to separate Bragg and diffuse scattering
Diffuse scattering occurring in the Bragg diffraction pattern of a long-range-ordered structure represents local deviation from the governing regular lattice. However, interpreting the real-space structure from the diffraction pattern presents a significant challenge because of the dramatic difference in intensity between the Bragg and diffuse components of the total scattering function. In contrast to the sharp Bragg diffraction, the diffuse signal has generally been considered to be a weak expansive or continuous background signal. In this paper, using 1D and 2D models, it is demonstrated that diffuse scattering in fact consists of a complex array of high-frequency features that must not be averaged into a low-frequency background signal. To evaluate the actual diffuse scattering effectively, an algorithm has been developed that uses robust statistics and traditional signal processing techniques to identify Bragg peaks as signal outliers which can be removed from the overall scattering data and then replaced by statistically valid fill values. This method, described as a 'K-space algorithmic reconstruction' (KAREN), can identify Bragg reflections independent of prior knowledge of a system's unit cell. KAREN does not alter any data other than that in the immediate vicinity of the Bragg reflections, and reconstructs the diffuse component surrounding the Bragg peaks without introducing discontinuities which induce Fourier ripples or artifacts from underfilling `punched' voids. The KAREN algorithm for reconstructing diffuse scattering provides demonstrably better resolution than can be obtained from previously described punch-and-fill methods. The superior structural resolution obtained using the KAREN method is demonstrated by evaluating the complex ordered diffuse scattering observed from the neutron diffraction of a single plastic crystal of CBr 4 using pair distribution function analysis.
36 MATERIALS SCIENCE↗
Investigation of Coupled Processes in Fractures and the Bordering Matrix via a Micro‐Continuum Reactive Transport Model
Abstract In multi‐mineral fractured rocks, the altered porous layer on the fracture surface resulting from preferential dissolution of the fast‐reacting minerals can have profound impacts on subsequent chemical‐physical alteration of the fractures. This study adopts the micro‐continuum approach to provide further understanding of reactive transport processes in the altered layer (AL), and mass exchanges with the bordering matrix and fracture. The modeling framework couples the Darcy‐Brinkman‐Stokes (DBS) solver in COMSOL Multiphysics and the geochemical modeling capability of CrunchFlow. Three‐dimensional steady state simulations with systematically varied chemical‐physical parameters of the AL were performed to examine the impacts of individual factors and processes. Our simulation results confirm previous observations that dissolution of the fast‐reacting mineral (i.e., calcite) is largely controlled by diffusion across the AL. We also show that dissolution of the slow‐reacting mineral (i.e., dolomite), which controls AL development and fracture enlargement, increases with surface area and has a complex dependence on different local rate‐limiting processes. In particular, advection can result in evident spatial variations in the local dissolution rates of dolomite, although it does not affect the bulk chemistry significantly. The difference in the spatial patterns between simulations with and without advection in the AL is more noticeable in the locations with smaller apertures, with up to 20% difference in local reaction rates. Therefore, it is important to include a full depiction of advection, diffusion, and reactions for accurately capturing local dynamics that control long‐term fracture evolution.
58 GEOSCIENCES↗
Thermophysical Properties of Cold- and Vacuum Plasma-Sprayed Cu-Cr-X Alloys, NiAl and NiCrAlY Coatings I: Electrical and Thermal Conductivity, Thermal Diffusivity, and Total Hemispherical Emissivity
This two-part paper reports the thermophysical properties of several cold- and vacuum plasma-sprayed monolithic Cu- and Ni-based alloy coatings. Part I presents the electrical and thermal conductivity, thermal diffusivity, and total hemispherical emissivity data, while Part II reports the specific heat capacity data for these coatings. Metallic copper alloys and stoichiometric NiAl and NiCrAlY coatings were fabricated by either the cold spray or the vacuum plasma spray deposition processes for thermal property measurements between 77 and 1223 K. The temperature dependencies of the thermal conductivities, thermal diffusivities, electrical conductivities, and total hemispherical emissivities of these cold- and vacuum-sprayed monolithic coatings are reported in this paper. The electrical and thermal conductivity data correlate reasonably well for Cu-8%Cr-1%Al, Cu-23%Cr-5%Al, and NiAl in accordance with the Wiedemann–Franz (WF) law although a better fit is obtained using the Smith–Palmer relationship. The Lorentz numbers determined from the WF law are close to the theoretical value.
36 MATERIALS SCIENCE↗
The role of Frenkel defect diffusion in dynamic annealing in ion-irradiated Si
The formation of stable radiation damage in crystalline solids often proceeds via complex dynamic annealing processes, involving migration and interaction of ballistically-generated point defects. The dominant dynamic annealing processes, however, remain unknown even for crystalline Si. Here, we use a pulsed ion beam method to study defect dynamics in Si bombarded in the temperature range from -20 to 140 °C with 500 keV Ar ions. Results reveal a defect relaxation time constant of ~10–0.2 ms, which decreases monotonically with increasing temperature. The dynamic annealing rate shows an Arrhenius dependence with two well-defined activation energies of 73 ± 5 meV and 420 ± 10 meV, below and above 60 °C, respectively. Rate theory modeling, bench-marked against this data, suggests a crucial role of both vacancy and interstitial diffusion, with the dynamic annealing rate limited by the migration and interaction of vacancies.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Combining Observational and Computational Uncertainty in Calibration Experiments
Traditional computer experiments using emulators have treat the emulator output as containing no error; however, this is not always feasible, as there exist computational codes which produce stochastic output, and future computations may require a balance between the time or resources to run the code and the accuracy of the output. This paper proposes a framework for incorporating both computational uncertainty and observational uncertainty into an analysis using a Gaussian process regression and calibration, and provides an example using simulated output from the one-dimensional diffusion equation. The particular values of observational and computation uncertainty which minimize a cost function are obtained.
97 MATHEMATICS AND COMPUTING↗
Hot Carrier and Surface Recombination Dynamics in Layered InSe Crystals
Layered indium selenide (InSe) is a van der Waals solid that has emerged as a promising material for high-performance ultrathin solar cells. The optoelectronic parameters that are critical to photoconversion efficiencies, such as hot carrier lifetime and surface recombination velocity, are however largely unexplored in InSe. Here, these key photophysical properties of layered InSe are measured with femtosecond transient reflection spectroscopy. The hot carrier cooling process is found to occur through phonon scattering. The surface recombination velocity and ambipolar diffusion coefficient are extracted from fits to the pump energy-dependent transient reflection kinetics using a free carrier diffusion model. The extracted surface recombination velocity is approximately an order of magnitude larger than that for methylammonium lead-iodide perovskites, suggesting that surface recombination is a principal source of photocarrier loss in InSe. The extracted ambipolar diffusion coefficient is consistent with previously reported values of InSe carrier mobility.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Constraining the Evolution of the Proton Distribution Function in the Heliotail
We use Interstellar Boundary Explorer (IBEX) measurements of energetic neutral atoms (ENAs) to constrain the proton (mostly pickup ion, PUI) distribution in the heliotail. In our previous study, we solved the Parker transport equation and found that the velocity diffusion coefficient $D(v)$ for PUIs is approximately $D(v)$ ~ 1.1 × 10 -8 km 2 s -3 ($v/v_0$) 1.3 , assuming the initial proton distribution processed by the termination shock (TS), $f_{p,0}$, is a kappa distribution with kappa index $ₖ_{p,0}$ = 1.63. In this study, we test different forms for $f_{p,0}$. We find that if $f_{p,0}$ is kappa-distributed and $D(v)$ = $D_0(v/v_0)^{1.3}$, any kappa index in the range 1.5 < $κ_{p,0}$ < 10 is consistent with IBEX data if $D_0 ~$ 0.8–1.3 × 10 -8 km 2 s -3 . While the case where $D(v)$ ∝ $v^{1.3}$ yields ENA fluxes that appear to best reproduce IBEX data for any $κ_{p,0}$, it is possible for $D(v)$ to scale close to $~v^{2/3}$ or $~v^2$ within our uncertainties by changing $D_0$. We also show that an upstream PUI filled-shell distribution that is heated by a quasi-stationary TS, generating a downstream filled-shell with large cutoff speed, yields an excess of ENAs > 2 keV compared to IBEX. However, using a fully kinetic particle-in-cell simulation to process a PUI filled-shell across the TS yields ENA spectra consistent with IBEX , reinforcing the significance of self-consistent, preferential PUI heating and diffusion at the TS. Interestingly, an upstream PUI distribution inferred from the particle-in-cell simulation to reproduce Voyager 2 observations of the nose-ward TS is inconsistent with IBEX observations from the heliotail, suggesting differences in the upstream PUI distribution or TS properties.
79 ASTRONOMY AND ASTROPHYSICS↗
A new method for operating a continuous-flow diffusion chamber to investigate immersion freezing: assessment and performance study
Abstract. Glaciation in mixed-phase clouds predominantly occurs through the immersion-freezing mode where ice-nucleating particles (INPs) immersed within supercooled droplets induce the nucleation of ice. Model representations of this process currently are a large source of uncertainty in simulating cloud radiative properties, so to constrain these estimates, continuous-flow diffusion chamber (CFDC)-style INP devices are commonly used to assess the immersion-freezing efficiencies of INPs. This study explored a new approach to operating such an ice chamber that provides maximum activation of particles without droplet breakthrough and correction factor ambiguity to obtain high-quality INP measurements in a manner that previously had not been demonstrated to be possible. The conditioning section of the chamber was maintained at −20 ∘C and water relative humidity (RHw) conditions of 113 % to maximize the droplet activation, and the droplets were supercooled with an independently temperature-controlled nucleation section at a steady cooling rate (0.5 ∘C min−1) to induce the freezing of droplets and evaporation of unfrozen droplets. The performance of the modified compact ice chamber (MCIC) was evaluated using four INP species: K-feldspar, illite-NX, Argentinian soil dust, and airborne soil dusts from an arable region that had shown ice nucleation over a wide span of supercooled temperatures. Dry-dispersed and size-selected K-feldspar particles were generated in the laboratory. Illite-NX and soil dust particles were sampled during the second phase of the Fifth International Ice Nucleation Workshop (FIN-02) campaign, and airborne soil dust particles were sampled from an ambient aerosol inlet. The measured ice nucleation efficiencies of model aerosols that had a surface active site density (ns) metric were higher but mostly agreed within 1 order of magnitude compared to results reported in the literature.
54 ENVIRONMENTAL SCIENCES↗
The nature of photoinduced phase transition and metastable states in vanadium dioxide
Photoinduced threshold switching processes that lead to bistability and the formation of metastable phases in photoinduced phase transition of VO 2 are elucidated through ultrafast electron diffraction and diffusive scattering techniques with varying excitation wavelengths. We uncover two distinct regimes of the dynamical phase change: a nearly instantaneous crossover into an intermediate state and its decay led by lattice instabilities over 10 ps timescales. The structure of this intermediate state is identified to be monoclinic, but more akin to M 2 rather than M1 based on structure refinements. The extinction of all major monoclinic features within just a few picoseconds at the above-threshold-level (~20%) photoexcitations and the distinct dynamics in diffusive scattering that represents medium-range atomic fluctuations at two photon wavelengths strongly suggest a density-driven and nonthermal pathway for the initial process of the photoinduced phase transition. These results highlight the critical roles of electron correlations and lattice instabilities in driving and controlling phase transformations far from equilibrium.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
On the Radio-emitting Particles of the Crab Nebula: Stochastic Acceleration Model
The broadband emission of pulsar wind nebulae (PWNe) is well described by non-thermal emissions from accelerated electrons and positrons. However, the standard shock acceleration model of PWNe does not account for the hard spectrum in radio wavelengths. The origin of the radio-emitting particles is also important to determine the pair production efficiency in the pulsar magnetosphere. Here, we propose a possible resolution for the particle energy distribution in PWNe; the radio-emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside PWNe. We upgrade our past one-zone spectral evolution model to include the energy diffusion, i.e., the stochastic acceleration, and apply the model to the Crab Nebula. A fairly simple form of the energy diffusion coefficient is assumed for this demonstrative study. For a particle injection to the stochastic acceleration process, we consider the continuous injection from the supernova ejecta or the impulsive injection associated with supernova explosion. The observed broadband spectrum and the decay of the radio flux are reproduced by tuning the amount of the particle injected to the stochastic acceleration process. The acceleration timescale and the duration of the acceleration are required to be a few decades and a few hundred years, respectively. Our results imply that some unveiled mechanisms, such as back reaction to the turbulence, are required to make the energies of stochastically and shock-accelerated particles comparable.
79 ASTRONOMY AND ASTROPHYSICS↗
In-Situ Powder-Directed Energy Process Control for Additively Manufactured Multi-Layer, Functionally Graded Components
Coatings and cladding can experience damage in harsh environments: Erosion Oxidation Delamination External mechanical damage Radiation induced damage Functionally Graded Materials (FGMs) were primarily designed to reduce thermal stress in thermal barrier coatings (TBCs), but can produce coatings which resist a variety of material damage (corrosion, surface damage, diffusion) Powder-fed DED with multiple independent feeders allows for AM FGMs, and provides robust control over process parameters to optimize microstructure and performance. FGMs have a great opportunity for applications in energy applications as a strategy to increase plant efficiency and lifetime.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗