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Developing Accelerated Test Protocols and Tuning Microstructures of the Common Materials to Improve Robustness, Reliability, and Endurance of SOFC Cells

This work is built on our prior work where we found that phase transformation in praseodymium nickelates, e.g. Pr 2 NiO 4 (PNO) and (Pr 1-x Nd x ) 2 NiO 4 (PNNO), can be electrochemically driven, and is substantially faster when compared to thermal annealing studies. The first task aims at an attempt to further accelerate the phase transformation in the oxygen electrode by alternating the current input in the cells, which lead to the development of accelerated test protocols (ATPs). ATPs showed up to 60x faster phase transformation and up to 10x faster performance degradation in (Pr 0.50 Nd 0.50 ) 2 NiO 4 electrodes, when compared to long-term operation under constant current density. Furthermore, the phase stable Nd 2 NiO 4 and (La 0.6 Sr 0.4 )(Co 0.8 Fe 0.2 )O 3 (LSCF6482) electrodes were tested in full cells under ATPs, and showed up to 10x faster performance degradation within 1,100 hours in a comparison with long-term thermal annealing studies and electrochemical operation under constant current density. The second task aims at the quantification of the contributions of cell components to the total impedance of a solid oxide fuel cell (SOFC) using electrochemical impedance spectroscopy (EIS) and distribution of relaxation times (DRT). Specifically, the role of gas composition at both anode and cathode was systematically studied, aiming at deconvoluting, identifying and quantifying the contributions of different electrode processes. This was achieved by first tuning the partial pressure of H 2 at the anode and subsequently varying the partial pressure of O 2 at the cathode. The results suggest that, while DRT offers a viable way of deconvoluting different times distributions, additional attention is needed before assigning a peak to a specific electrode process due to the significant overlap of the contributions from the cathode and the anode. Density function theory studies show that both Pr-vacancies and O-defects play a key role on the activity and stability for nickelates towards oxygen reduction reaction. The resident O-interstitials and oxygen ions in the PrO layer form peroxide (O 2 2- ) nearby Pr vacancies. The O 2 2- limits oxygen-ion transport due to the required additional energy to break its O-O bond. We further calculated the formation and segregation energies for different Ln ions (La, Pr, Nd, Pm, Sm, Gd, Tb, Dy, and Ho) in PNO and CeO 2 (111) surfaces. In addition to Nd, Pm and La are suggested as potential dopants in PNO to enhance it stability without decomposition due to their more negative formation energies, lower diffusion energies, and positive separation energies.

01 COAL, LIGNITE, AND PEAT↗

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Science & Technology - Other Topics↗

Progress report on analytic and numerical studies of x-ray-induced impulse

In a variety of high-energy-density (HED) systems, x-rays of a given energy are used to generate shockwaves, bulk motion, and impulse in materials. As radiation energy is deposited within the material, the material is heated. The number of photons of a certain wavelength absorbed is determined by the spectral intensity of the radiation and the material’s opacity evaluated at that wavelength. This heating results in a pressure increase dictated by the material’s equation of state. Depending on the intensity of the absorbed radiation, it may also cause the material to change phase into a liquid, gas, or plasma. The increased pressure drives the heated surface layer to blow off, imparting impulse and sending a compressive wave into the bulk of the material. Additionally, the compression wave interacts with the solid boundary of the material, resulting in a tensile wave that may cause the material to spall. The impulse generated by the deposition of x-ray energy within the sample can be modeled using purely analytical methods, e.g. the Bethe, Bade, Averell, and Yost (BBAY) model. However, the blow-off process is rather complicated, and proper modeling efforts must account for material ejected by spallation, vaporization, jetting, and plasma ablation. For this reason, analytical models have an unclosed term describing the final energy of the blown-off material Ef(z). Prior modeling efforts have arbitrarily fixed this at some value or modeled it using a limiting set of thermodynamic assumptions. The work we are currently performing uses validated simulations using sophisticated photon transport, equation of state, and strength models/data to provide a fit for Ef(z) that is useful for predictive calculation of impulse. We will apply our methodology and show results for different materials and x-ray sources. This work is particularly useful for the design of experiments studying x-ray impulse generation. The present report is outlined as follows. Section 1.2 describes a series of HED experiments investigating x-ray-generated impulse in materials. Section 1.3 describes the computational approach we employ in this study, and presents validation results against the aforementioned experiments. Section 1.4 introduces analytical models for impulse generation, as well as our method for utilizing impulse from simulations to close the models. We discuss the concept of impulse-spectrum sensitivity, it’s application to uncertainty quantification, and derive a very useful analytical expression for it in 1.5. We then summarize recent progress in this project and discuss future work in section 1.6.

36 MATERIALS SCIENCE↗

Development of Novel Ferritic-Martensitic Steels with Superior Creep Properties for Power Plant Applications

A creep resistant martensitic steel, CPJ-7, was developed with an operating temperature approaching 650°C. Subsequently, another creep resistant martensitic steel, JMP, was designed with the potential to operate at, or slightly above, 650°C. This report describes the development of these alloys from early iterations of CPJ steels to the final CPJ-7 formulation as well as the more heat resistant JMP steel formulation. The design originated from computational modeling for phase stability and precipitate strengthening using fifteen constituent elements. Approximately forty heats of CPJ and ten of JMP, each weighing ~7 kg, were vacuum induction melted. A computationally optimized heat treatment schedule was developed to homogenize the ingots prior to hot forging and rolling prior to final normalization and tempering. Overall, wrought and cast versions of CPJ-7 present superior creep properties when compared to wrought and cast versions of COST alloys for steam turbine and wrought and cast versions of P91/92 for boiler applications. For instance, the Larson Miller Parameter curve for CPJ-7 at 650°C almost coincides with that of COST E at 620°C. The prolonged creep life was attributed to slowing down the process of the destabilization of the MX and M 23 C 6 precipitates at 650°C. On the other hand, the cast version of CPJ-7 also revealed superior mechanical performance, well above commercially available cast 9% Cr martensitic steel or derivatives, especially for creep life at 650°C. The casting process employed slow cooling to simulate the conditions of a thick wall full-size steam turbine casing but utilized a separate homogenization step prior to final normalization and tempering. To advance the development of CPJ-7 for commercial applications, a process was used to scale up the production of the alloy using vacuum induction melting (VIM) and electroslag remelting (ESR), which underlined the importance of melt processing control of intentionally designed minor and trace elements in these advanced alloys. Following the work on CPJ-7, the JMP steels were designed with higher Co for increased solid solution strengthening, Si for oxidation resistance and increased W (with low Mo content) for matrix strength and stability as well as solid solution strengthening. The JMP steels showed increases in creep life compared to CPJ-7 between 118 to 150% at 650°C for testing at various stresses between 138 MPa and 207 MPa. On a Larson-Miller plot, the performance of the JMP steels surpasses that of state-of-the-art MARBN and other MARBN-type steels. The influence of various elements within the composition of the alloys on the microstructure and mechanical properties are discussed. This report presents approximately 420,000 h of in-house creep testing, the equivalent of almost 50 years of cumulative creep tests.

36 MATERIALS SCIENCE↗

Electro-chemo-mechanically Driven Ni Exsolution from (Pr,Ce,Ni)O 2−δ : Controlled Nucleation Density and Enhanced Electrode Kinetics

In situ exsolution of metal nanoparticles is a promising strategy to prepare electrocatalysts with enhanced activity and resistance to agglomeration for efficient chemical transformations and energy conversion. Achieving a high nucleation density of nanoparticles under mild conditions and understanding how to tailor the process is important for performance of these electrodes in electrochemical cells. In this work, we demonstrate facile exsolution of Ni nanoparticles using fluorite-structured (Pr,Ce)O 2−δ as the support oxide, driven by electrochemical potential and aided by the metastability of Ni in the solid solution (elastic driving force). We prepare single-phase oriented thin films of (Pr,Ce,Ni)O 2−δ (NPCO) on (Zr,Y)O 2−δ (YSZ) substrates by pulsed laser deposition. With the aid of a high-throughput electrochemical cell that provides a lateral gradient in Nernst voltage, we apply in situ near-ambient pressure synchrotron X-ray photoelectron spectroscopy and ex situ atomic force microscopy to investigate the impact of electrochemical potential on Ni nucleation density. We find that metallic Ni can be successfully exsolved at 550 °C upon cathodic biasing in 20 mTorr O 2 , and its nucleation density increases with increasing electrochemical driving force/decreasing oxygen chemical potential. We further evaluate the electrochemical performance under highly reducing (fuel electrode) conditions by electrochemical impedance spectroscopy. With the exsolved Ni nanoparticles, the surface exchange coefficient of the NPCO is found to be ∼4× higher than for PCO without exsolution. This work confirms mixed conducting fluorites as beneficial host lattices for facile transition-metal exsolution and suggests the possibility for constructing an all ceria-based electrochemical cell with PCO serving as both the cathode and the anode.

36 MATERIALS SCIENCE↗

Minimizing Fraud in the Carbon Offset Market Using Blockchain Technologies

Fraud in the Environmental Benefit Credit (EBC) markets is pervasive. To make matters worse, the cost of creating EBCs is often higher than the market price. Consequently, a method to create, validate, and verify EBCs and their relevance is needed to mitigate fraud. The EBC market has focused on geologic (fossil fuel) CO 2 sequestration projects that are often over budget and behind schedule and has failed to capture the "lowest hanging fruit" EBCs - terrestrial sequestration via the agricultural industry. This project reviews a methodology to attain possibly the least costly EBCs by tracking the reduction of inputs required to grow crops. The use of bio- stimulant products, such as humate, allows a farmer to use less nitrogen without adversely affecting crop yield. Using less nitrogen qualifies for EBCs by reducing nitrous oxide emissions and nitrate runoff from a farmer's field. A blockchain that tracks the bio-stimulant material from source to application provides a link between a tangible (bio-stimulant commodity) and the associated intangible (EBCs) assets. Covert insertion of taggants in the bio-stimulant products creates a unique barcode that allows a product to be digitally tracked from beginning to end. This process (blockchain technology) is so robust, logical, and transparent that it will enhance the value of the associated EBCs by mitigating fraud. It provides a real time method for monetizing the benefits of the material. Substantial amounts of energy are required to produce, transport, and distribute agricultural inputs including fertilizer and water. Intelligent optimization of the use of agricultural inputs can drive meaningful cost savings. Tagging and verification of product application provides a valuable understanding of the dynamics in the water/food energy nexus, a major food security and sustainability issue. As technology in agriculture evolves so to must methods to verify the Enterprise Resource Planning (ERP) potential of innovative solutions. The technology reviewed provides the ability to combine blockchain and taggants ("taggant blockchains") as the engine by which to (1) mitigate fraudulent carbon credits; (2) improve food chain security, and (3) monitor and manage sustainability. The verification of product quality and application is a requirement to validate benefits. Recent upgrades to humic and fulvic quality protocols known as ISO CD 19822 TC134 offers an analytical procedure. This work has been assisted by the Humic Products Trade Association and International Humic Substance Society. In addition, providing proof of application of these products and verification of the correct application of prescriptive humic and bio-stimulant products is required. Individual sources of humate have unique and verifiable characteristics. Additionally, methods for prescription of site- specific agricultural inputs in agricultural fields are available. (See US Patents 734867B2, US 90658633B2.) Finally, a method to assure application rate is required through the use of taggants. Sensors using organic solid to liquid phase change nanoparticles of various types and melting temperatures added to the naturally occurring materials provide a barcode. Over 100 types of nanoparticles exist ensuring numerous possible barcodes to reduce industry fraud. Taggant materials can be collected from soil samples of plant material to validate a blockchain of humic, fulvic and other soil amendment products. Other non-organic materials are also available as taggants; however, the organic tags are biodegradable and safe in the environment allowing for use during differing application timeliness.

54 ENVIRONMENTAL SCIENCES↗

Influence of physical and chemical hydrology on bioremediation of a U-contaminated aquifer informed by reactive transport modeling incorporating 238 U/ 235 U ratios

Microbially-catalyzed reductive immobilization of aqueous uranium (U) as a solid phase has been proposed as a U remediation technique. Both laboratory and field experiments have demonstrated that this reduction reaction alters the 238 U/ 235 U ratio, producing a 238 U-enriched U(IV) solid. In contrast, other major U reactive transport processes fractionate these isotopes much less. This suggests the potential to quantify the extent of bioreduction occurring in groundwater containing U using the 238 U/ 235 U ratio, which would substantially improve upon current practices largely relying on U concentration measurements alone. Current reactive transport models for uranium dynamics include only concentration measurements, which are strongly influenced by highly coupled reactive transformation and aqueous transport processes. The complex physical and chemical behavior of U potentially compromises such quantitative analysis of U storage and release. Here we report the first numerical reactive transport model which explicitly incorporates variations in the 238 U/ 235 U ratio of U and demonstrates improved interpretation of the principal chemical reactions and groundwater transport processes affecting the subsurface mobility and distribution of this widespread contaminant. Recent U bioreduction studies performed in a contaminated aquifer in Rifle, Colorado, USA applied Rayleigh distillation models to interpret U stable isotope fractionation observed as a result of acetate amendment. These simplified models were unable to resolve the spatiotemporal pattern of U isotope fractionation recorded in the aqueous solutes. Here, we employ the multi-component, isotope-enabled CrunchTope reactive transport software to interpret these measured U isotope ratios, and demonstrate accurate reproduction of observed trends in both geochemistry and 238 U/ 235 U ratios for two consecutive years of field experiments. Overall, our results indicate that accurately modeling both the U concentration and isotope ratio distributions greatly constrains the parameter space of the model. We find that the transport properties of U in the Rifle aquifer are governed by the presence of low-permeability regions, which the isotopes are uniquely sensitive to. When U reduction is spatially constrained by these low-permeability regions, the shift in the 238 U/ 235 U ratio becomes more muted. Accurate modeling of observed U isotope ratios thus provides a powerful means to better understand bioremediation, and the current study serves to advance the application of this novel method.

238U/235U↗

High Performance SOFCs with a Superior Stability for Reliable and Durable Power Systems

Next generation of fuel cells, electrolyzers, and batteries requires higher power, faster kinetics, and larger energy density, which necessitate the use of compositionally complex oxides to achieve multifunctionalities and activity. These compositionally complex oxides may change their phases and structures during an electrochemical process – a so-called “electrochemically driven phase transformation”. The origin for such a phase change has remained obscure. More importantly, there is a need to develop high performance solid oxide fuel cells with an enhanced stability. In this work, the La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3 (LSCF) cathode surface is modified by infiltration of Pr 6 O 11 and the power density at 0.8V and 750 °C is improved by 21%. In addition, by replacing the traditional barrier layer Gd 0.2 Ce 0.8 O 1.9 with mixed conducting Pr 0.1 Gd 0.1 Ce 0.8 O 1.9 , the power density increases by 38%. The different mechanism of promotions was investigated by electrochemical impedance spectroscopy. The ohmic resistance is dramatically reduced by applying the PGCO interlayer, and the distribution of relaxation time was used to analyze the mechanism for which the polarization resistance was decreased attributing to the mixed conduction nature in PrO x . An increase of power density at 0.8 V of 0.358 W/cm 2 (71%) is achieved with the implementation of both surface modification and buffer layer engineering. An experimental study and a theoretical analysis were then carried out on phase evolution in praseodymium nickelates. Nickelate-based electrodes show up to 60× greater phase transformation during operation when compared to thermally annealed ones. Theoretical analysis suggests that the presence of a reduced oxygen partial pressure at the interface between the oxygen electrode and the electrolyte is the origin for the phase change in an oxygen electrode. Guided by the theory, an addition of the electronic conduction in the interface layer leads to the significant suppression of phase change, while improving cell performance and performance stability. When an oxygen electrode is under polarization, the oxygen partial pressure at the interface between the oxygen electrode and the electrolyte is lower than that of incoming oxidant. Under a high polarization, the environment at the aforementioned interface may lead to phase transformation of the oxygen electrode. The local oxygen partial pressure is determined by the transport properties at the interfaces. An addition of the electronic conduction in the interface layer, for instance using (Pr,Gd)-doped ceria to replace Gd-doped ceria, results in improved cell performance and performance stability, while the phase transformation is significantly suppressed. This work provides a fundamental understanding of the origin for phase transformation in oxygen electrodes during operation and use this knowledge to develop a high-performance electrode that exhibits improved performance stability.

30 DIRECT ENERGY CONVERSION↗

Recovery of Oxpure 612C-50 Coconut Carbon Particles Using Bump Arrays

Cyanide is used to leach gold from crushed ore (solid matrix) into a gold cyanide solution. The gold is extracted from the cyanide solution by adsorption onto activated carbon. The gold extraction process occurs when the activated coconut carbon is placed into tanks that contain the gold cyanide solution either in a batch process or into a continuous flow circuit. The coconut carbon is then removed from the solution for gold recovery. The use of the mesofluidic separation system (a deterministic lateral displacement system) can significantly reduce costs and waste generated from the process of removing the coconut carbon from the solution. In the coconut carbon recovery process used at many gold mines in Nevada, the gold is attached to carbon particles that are still in the cyanide liquor. The mesofluidic system can rapidly remove the gold bearing carbon particles from the cyanide liquor quickly and with no operating costs. The benefits include: • Reduce operational costs related to filtration and hydro-cyclones • Reduced acid usage for the elution gold stripping phase as only 25% of the fluids will follow the carbon particles to the final express lane when two mesofluidic systems are used in series This alternative particle removal techniques would be advantageous. A promising technique for removing larger particles from slurries is mesofluidic separation, similar to deterministic lateral displacement arrays or “bump” arrays [1] but operates at much larger flow rates. As described by Pease, et al. [2], “Bump arrays in deterministic lateral displacement devices separate large particles from small particles using arrays of staggered posts. Large particles, defined as those with radii larger than the distance between the edge of a post and the stagnation streamline from the next downstream post, must bump toward one side of the device, whereas particles smaller than this distance slalom from entrance to exit without net lateral displacement.” Unlike filters or sieves, the posts in the arrays that cause separation do not block or occlude particle flow but work because particles go around the posts. Unlike hydrocyclones separation, separation is not driven by particle density, because gravitational forces are unimportant to mesofluidic separation. Burns, et al., and Pease, et al., have shown that particles may be separated from complex suspensions, under turbulent flow conditions, and at industrially important flow rates [3-5]. They have also recently shown that mesofluidic devices may be arranged in series to increase separation performance [6]. In this paper, we evaluate the mesofluidic system for the separation of commercial OxPure GR 612 Charred Coconut shell particles as a proof of principle test for the rapid separation using the 1500 micron cut mesofluidic separator. We first describe the experimental system and conditions. We then present the experimental results. [1] Huang, L.R., E.C. Cox, R.H. Austin, J.C. Sturm. 2004. Continuous particle separation through deterministic lateral displacement. Science, 304, 987–990. https://doi.org/10.1126/science.1094567. [2] Pease L.F., J.A. Bamberger, C.A. Burns, and M.J. Minette. 2021. Large Particle Separation from Non-Newtonian Slurries using Bump Arrays. In Proceedings of the ASME 2021 Fluids Engineering Division Summer Meeting FEDSM2021-65904, V003T08A023. New York, New York: ASME. doi:10.1115/FEDSM2021-65904 [3] Burns C.A., T.G. Veldman, J. Serkowski, R.C. Daniel, X.-Y. Yu, M.J. Minette, L.F. Pease. 2021. Mesofluidic separation versus dead-end filtration. Separation and Purification Technology, 254, 117256. https://doi.org/10.1016/j.seppur.2020.117256. [4] Pease L.F., J.E. Serkowski, T.G. Veldman, J. Williams, X.-Y. Yu, M.J. Minette, J.A. Bamberger, C.A. Burns. 2021. Can Bump Arrays Separate Particles from Turbulent Flows?. In Proceedings of the ASME 2021 Fluids Engineering Division Summer Meeting FEDSM2021-67696, V003T08A024. New York, New York: ASME. doi:10.11

mesofluidic separation, slurry, bump array↗

Multi-physics Topology OPtimization and Additive Manufacturing for High-temperature Heat Exchangers

This research significantly advances the understanding of high-temperature heat exchanger design through an integrated approach that combines topology optimization (TO), triply periodic minimal surface (TPMS) structures, additive manufacturing (AM) and thermohydraulic testing. Each of these components contributes uniquely to a unified, high-performance design, fabrication and testing workflow. Topology optimization serves as the foundation of the design methodology by providing a systematic way to determine the most effective material layout for separating hot and cold fluids while maximizing thermal performance. The researchers introduced a novel three-material optimization framework using two density fields to represent hot fluid, cold fluid, and solid domains. This approach enables automated discovery of optimal shapes and flow paths that cannot be intuitively designed, especially under constraints imposed by manufacturing technologies. Furthermore, constraints such as minimal wall thickness and overhang angles were embedded into the optimization process, ensuring that resulting designs are not only thermally efficient but also manufacturable using modern additive techniques. In parallel, the study delves into the use of Gyroid-based TPMS geometries for constructing the core of the heat exchanger. TPMS structures are known for their high surface area, excellent fluid mixing capabilities, and minimal pressure drop characteristics. The researchers applied a data-driven modeling framework using Heteroscedastic Sparse Gaussian Process Regression (HSGPR) combined with genetic algorithms. This allowed for the rapid evaluation and optimization of key geometric parameters such as frequency, iso-value, and phase shift. The result was a set of Gyroid structures tailored for high heat transfer and low flow resistance, demonstrating clear improvements over conventional straight-channel designs. After the designing process, additive manufacturing played a critical role by turning these highly complex, optimized geometries into physical components. Utilizing Laser Powder Bed Fusion (LPBF) with Haynes 282, the study demonstrated the feasibility of fabricating these heat exchangers at high precision. Post-processing methods, including dilation-erosion operations, were applied to ensure local features adhered to self-supporting constraints. The fabricated structures were then subjected to thermohydraulic testing under conditions representative of supercritical CO 2 Brayton cycles, validating the predicted performance and confirming the viability of the full design-to-fabrication pipeline. Finally, thermohydraulic testing across the above studies served as a crucial experimental validation of advanced heat exchanger. Under consistent high-temperature and high-pressure conditions using supercritical CO 2 , the testing demonstrated that both TO and Gyroid-based TPMS designs significantly outperformed conventional straight-channel HXs. The TO design achieved a 115% increase in UA and NTU and a 27.6% boost in gravimetric power density, while the data-driven optimized Gyroid design delivered a 166% increase in UA and NTU and improved effectiveness from 68.7% to 86.1%. These results validate the simulation models, confirm the manufacturability of complex geometries under AM constraints, and provide key insights into design-performance trade-offs, thereby advancing the development of high-efficiency, compact heat exchangers for extreme environments.

36 MATERIALS SCIENCE↗

High-Temperature 2D Optical Relaxation Visualizes Enhanced Oxygen Exchange Kinetics at Metal-Mixed Conducting Oxide Interfaces

Solid-state heterointerfaces are of interest for emergent local behavior that is distinct from either bulk parent compound. One technologically relevant example is the case of mixed ionic/electronic conductor (MIEC)–metal interfaces, which play an important role in electrochemistry. Metal–MIEC composite electrodes can demonstrate improved catalytic activity vs single-phase MIECs, improving fuel cell efficiency. Similarly, MIEC surface reaction kinetics are often evaluated using techniques that place metal current collectors in contact with the surface under evaluation, potentially altering the response vs the native surface. Here, techniques enabling direct and local in situ observation of the behavior at and around such heterointerfaces are needed. Here, we develop a spatially resolved optical transmission relaxation (2D-OTR) method providing continuous evaluation of local, high-temperature, controlled atmosphere defect kinetics across a ~1 cm2 sample area simultaneously in a contact-free manner. We apply it to observe the spatial variance of oxygen incorporation and evolution rates at ~525–620 °C, in response to step changes in oxygen partial pressure, on MIEC SrTi 0.65 Fe 0.35 O 3–x films as a function of distance from porous Pt and Au layers. Using this model geometry, we find significant enhancements in kinetics adjacent to the metals that decay over a few millimeter distance. To extract kinetic parameters, we fit the short-term optical data (initial portion of relaxations) with an exponential decay function appropriate for surface-exchange-limited kinetics, yielding apparent surface exchange coefficients (k chem ) with spatial resolution, decreasing with distance from the metal. To understand the kinetic processes governing the complete (long-term) optical relaxations, we performed COMSOL simulations, which demonstrated that a combination of laterally varying k chem and in-plane diffusion controls the observed kinetics over the full time range. Further support for spatially varying kchem comes from demonstrations of changing surface and bulk chemistry vs distance from the metal–MIEC interface, by X-ray photoelectron and optical absorption spectroscopies, respectively. Although microporous Pt and Au are not excellent electrodes in isolation, both metals exert a synergistic effect on the oxygen surface exchange rate in the presence of the mixed conducting film.

36 MATERIALS SCIENCE↗

Development of Corrosion- and Erosion-Resistant Coatings for Advanced Ultra-Supercritical Materials

This final report summarized the research efforts and major findings of the Phase I Project “Development of Corrosion- and Erosion-Resistant Coatings for Advanced Ultra-Supercritical Materials”, for the period of October 1, 2019 – Sept. 30, 2021. This project is a collaborative endeavor between Tennessee Tech University, Purdue University, Oak Ridge National Laboratory, Siemens Corporation, and Eastern Plating, LLC, aiming at improving the durability and lifetime of high-pressure (HP) steam turbine blades in advanced ultra-supercritical (A-USC) coal-fired power plants through the development of corrosion/erosion-resistant coatings manufactured via a low-cost electrolytic codeposition process. While Tribaloy alloy T-400C was identified by the U.S. A-USC Materials Consortium as a promising coating composition, further composition optimization is needed to enhance its corrosion and erosion resistance for protecting the A-USC Ni-base turbine components. An integrated computational and experimental approach was employed to optimize coating composition/microstructure and processing parameters. In order to identify candidate coating compositions that could offer balanced properties, thermodynamic calculations were performed to explore the γ+Laves composition space in the Co-Ni-Cr-Mo-Si system with different alloying additions at 600-800 °C. Guided by the calculation results, experimental assessment of selected alloys led to the development of a new generation of Tribaloy compositions with the optimal levels of Cr, Mo and Si, reactive element (e.g., 0.4-0.6 wt.% Y) and other alloying additions. The low-cost and non-line-of-sight electro-codeposition process was employed to deposit a Ni(Co)-CrMoSiY composite coating on commercial Haynes 282 (H282) Ni-base alloy. A diffusion treatment was subsequently applied to convert the composite to the Tribaloy-type coating. Both the codeposition parameters and heat treatment conditions were varied to achieve the desired coating composition, microstructure and phase constituents. In addition, since additive manufacturing (AM) may be an alternative cost-saving option for potential A-USC turbine repair, laser direct deposition was explored to fabricate the H282 alloy with minimal defects. The electro-codeposited Tribaloy coating was also applied to the AM H282 substrate to demonstrate the viability of the coating process in improving the surface finish of AM alloys. Both high-temperature oxidation performance and solid particle erosion (SPE) resistance of model alloys and electro-codeposited coatings were evaluated. About 25 model alloys with various Cr/Mo ratios and reactive element levels, as well as partial substitution of Mo with Nb were evaluated with regard to their oxidation resistance in both air and pure steam at 760-800°C. Compositions based on Ni(Co)-20Cr-18Mo-2.6Si-0.6Y (wt.%) showed significantly improved oxidation resistance over the baseline T400-C. Based on the alloy development results, three generations of new Tribaloy coatings (Gen-1, Gen-2, and Gen-3) with various Mo/Cr contents and Y levels were prepared via electro-codeposition and their microstructure/performance were evaluated. Outstanding air and steam oxidation resistance was achieved for the Gen-2 and Gen-3 coatings. Furthermore, while the SPE resistance of the coatings depended on many factors such as temperature, environment, erodent, velocity and impact angle, the coated samples exhibited similar or better SPE resistance compared to the H282 substrate when magnetite was used as erodent (which is a realistic erodent in A-USC steam turbines). The new Tribaloy coatings also had good long-term compatibility with the H282 alloy substrate. The two large-sized rotating barrels were designed, constructed, and employed to coat dummy HP blades. Uniform coating thickness and microstructure were achieved at various blade locations. Also, a preliminary techno-economic analysis of the proposed coating process was conducted to quantify the cost-effectiveness and to assess the commercial viability of the corrosion- and erosion-resistant coatings. It is estimated that a cost reduction of ~30% could be achieved with the electro-codeposition coating process over the state-of-the-art high velocity oxygen fuel (HVOF) thermal spray. Compared to the leading Tribaloy coating technologies such as HVOF and plasma transfer alloying, electro-codeposition based process has advantages such as low-cost process equipment, uniform deposition even for complex shapes, low levels of contaminants/porosities, reduction of powder waste, and potentially better surface finish and longer turbine service life. The Phase 1 study has demonstrated that it is feasible to develop an electro-codeposited Tribaloy coating with balanced corrosion and erosion properties, even though additional research efforts such as further coating process scale-up and longer-term performance evaluation under realistic A-USC conditions are clearly needed.

20 FOSSIL-FUELED POWER PLANTS↗

BWR Spent Nuclear Fuel Acquisition and Testing to Support DOE-NE High Burnup Spent Fuel Data Project

The Office of Spent Fuel and Waste Disposition (SFWD) within the US Department of Energy (DOE) Office of Nuclear Energy (NE) established the Spent Fuel and Waste Science and Technology (SFWST) campaign to conduct research and development (R&D) activities related to the storage, transportation, and disposal of spent nuclear fuel (SNF) and high-level radioactive waste. The SFWST program was created within SFWD to address issues of extended or long-term SNF storage and transportation. Some near-term objectives of SFWST are to use a science-based, engineering-driven approach to: Support the enhancement of the technical bases to support the continued safe and secure dry storage of SNF for extended periods; Support the enhancement of the technical bases for retrieving SNF after extended dry storage; Support the enhancement of the technical bases for transporting high burnup (HBU) fuel and transporting low burnup fuel and HBU fuel after dry storage DOE-NE, in partnership with the Electric Power Research Institute, developed the High Burnup Spent Fuel Data Project to perform a large-scale demonstration and laboratory-scale testing of HBU pressurized water reactor (PWR) fuels (exceeding 45 gigawatt-days per metric ton of uranium [GWd/MTU]). Under this project, 25 sister rods—which are rods that have the same design, power histories, and other characteristics—were removed from assemblies at the North Anna Nuclear Power Station and sent to Oak Ridge National Laboratory (ORNL) in January 2016. ORNL performed detailed nondestructive examination (NDE) on all 25 rods. The NDE consisted of visual examinations, gamma and neutron scanning, profilometry and rod length measurements, and eddy current examinations. After completing the NDE, 10 of the sister rods were delivered to Pacific Northwest National Laboratory (PNNL) in a NAC International, Inc. legal-weight truck cask in September 2018 for destructive examination (DE). To date, SFWD work has focused on the PWR fuel that is part of the Sister Rod Test program. No boiling water reactor (BWR) fuel has been tested in the program, and the data needs that were identified for the PWR fuel have not been collected for BWR fuel. The goal to obtain six to nine BWR rods and test them at ORNL will support closing this important data gap. BWR fuel comprises approximately 56% of the total fuel assemblies currently in storage at nuclear power plants in the United States. BWR nuclear fuel and cladding designs and manufacturing are significantly different from PWRs. Differences include the following: BWR fuel pellets are larger than PWR pellets; Variations of Zircaloy-2 (including liners) are used instead of the Zircaloy-4 cladding materials used in PWRs; Clad manufacturing and stress-relief processes are different between PWRs and BWRs; The fuel rod dimensions are different because larger rod diameters and thicker cladding are used in BWRs; BWR fuel typically has lower internal rod pressures and sees vastly different operating conditions than PWR fuel (i.e., two-phase flow); BWR assemblies are “canned,” meaning each assembly is surrounded by a metal fuel channel; BWR cladding is often composed of an inner pure Zr liner that has widely different mechanical properties than the Zircaloy-2 alloy and exhibits a stronger affinity for hydrogen; The BWR SNF generally has more total hydrogen in the cladding/liner than typical PWR fuel; The construction of the PWR and BWR assemblies is vastly different; BWR rods are solidly attached to the assembly nozzles and experience a much different vibration and shock load than PWR rods, which are “floating” within a grid system attached to guide tubes, and the rods sit loosely on the bottom end plates. These numerous differences will affect the way the BWR SNF responds under dry storage preparation processes (e.g., vacuum drying) and during transportation. The results collected in the PWR experimental program must be compared with a subset of similar data collected on BWR SNF to establish a technical basis for whether the larger PWR database is sufficient to bound the BWR SNF end-of-life conditions as is currently assumed for several fuel/clad properties. Changes that occur in both fuel types at HBU could exacerbate any mechanical property differences. As the fuel burnup increases, several changes occur that might affect the performance of the fuel, cladding, and assembly hardware in storage and transportation. These changes include increased cladding corrosion layer thickness, increased cladding hydrogen content, increased cladding creep strains, increased fission gas release, and the formation of the HBU structure at the surface of the fuel pellets. The Nuclear Regulatory Commission (NRC) limits the current maximum rod-averaged burnup to 62 GWd/MTU due to these changes and the lack of data at higher burnups.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Task Sharing of Proton Incorporation in Vertically Aligned Nanocomposite Triple Conductors: Growth, Structure, and Surface Exchange Kinetics

As protonic ceramic electrolysis cells emerge for efficient H 2 production, there is a need to develop air electrode materials enabling fast, durable steam splitting and proton incorporation. Single-phase triple conductors may fail to satisfy the myriad performance/stability requirements, and their critical charge-carriers (holes, oxygen vacancies, and protons) are in competition, limiting their concentrations. Instead, we propose task-sharing, vertically aligned nanocomposites (VANs), comprising a proton conductor (BaZr 0.9 Y 0.1 O 3-δ ) and a redox-active mixed ionic electronic conductor (Ce 0.9 Pr 0.1 O 2-δ ), that may enable rapid proton surface exchange at the solid–gas interface and transport along the solid–solid heterointerfaces. We grew VANs by pulsed laser deposition and investigated the interplay between their processing conditions, structure, and proton and oxygen surface exchange kinetics. We varied the substrate temperature, laser repetition rate, laser fluence, and processing oxygen pressure. The crystallinity and phases were characterized by grazing-incidence X-ray diffraction, and the strain and structural order as a function of depth were evaluated by angle-dependent synchrotron X-ray pair distribution function analysis. To evaluate the potential for interdiffusion, the formation energies of substitutional defects were simulated with density functional theory. Corresponding structural analysis and elemental mapping were performed by scanning/transmission electron microscopy, energy-dispersive X-ray spectroscopy, and electron energy-loss spectroscopy, indicating distinct nanoscale compositional regions with a hierarchical structure embedded in individual VANs columns and minimal interdiffusion across a bilayer film. Proton and oxygen surface exchange coefficients (k H , k O ) and polarization resistances were evaluated by electrical and optical relaxations and impedance spectroscopy of VAN-incorporated protonic ceramic electrochemical cells, respectively, at 400–500 °C, demonstrating values comparable to some of the best-known triple and mixed conductors.

36 MATERIALS SCIENCE↗

Cryogenic Carbon Capture™ (CCC) Status Report

The Cryogenic Carbon Capture™ (CCC) process separates CO2 from light gases in essentially any continuous process. CCC cools the gases to the frost or desublimation point of CO2 (-100 to -135 °C), separates and pressurizes the solids, and warms all streams to produce a CO2-depleted stream at ambient pressure and a pure (99+%) pressurized liquid CO2 stream typically to about 150 bar, both at ambient temperature. The process also recovers all gas moisture and most gas impurities less volatile than CO2 (NOx, SOx, Hg, PM, UHC, CCC, etc.) in separable streams. CCC nearly eliminates refrigeration energy for sensible temperature changes through heat integration. CCC does require energy to change the CO2 phase from a mixed vapor to a pressurized fluid, which represents the minimum energy required of any process for this separation. CCC uses additional energy for turbomachinery inefficiencies, heat losses, moisture removal and overall process pressure drop. Aside from these real-world energy demands, CCC operates near the minimum energy required to perform this gas separation by minimizing stream recycling. CCC compresses CO2 as a liquid, which is one of several reasons it costs about about half as much and consumes about half as much energy as an amine process when using flue gases with about 15% CO2. The process also has several major additional advantages, including (a) it is a bolt-on retrofit technology that does not need steam or any modification of existing equipment, (b) it recovers water and nearly all pollutants in addition to CO2 from the flue gas, (c) it enables highly efficient and cost effective energy storage at grid scale and on time scales of minutes, (d) it enables NG storage if the energy storage option is used, and (d) it has a small footprint and is minimally disruptive to existing plants, requiring only electrical power and a gas source to operate. Sustainable Energy Solutions (SES) has scaled this technology through several levels, the largest of which captures nominally 1 tonne of CO2/day and is called the skid system. Skid system field tests include utility-scale power plants, cement plants, heating plants, and other utility or industrial sites that burn natural gas, biomass, coal, shredded tires, municipal waste, and combinations of these fuels. These field tests produced 95-99% CO2 capture with CO2 purities of 99+% and initial CO2 contents that range from 4 to 28%. SES currently seeks to scale the system to merchant scale (10-80 tonnes of CO2 per day). In the process of doing so, SES has demonstrated the potential for CCC to contribute to energy storage and direct air capture in innovative and cost-effective ways. This presentation discusses the overall process and highlights results from field and in-house tests. These include (a) measured CO2 capture rates and operating conditions from in-house and field tests, and (b) predicted utility-scale costs and energy demands. This discussion also includes the application of the CCC technology to energy storage and direct air capture.

20 FOSSIL-FUELED POWER PLANTS↗

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗

Scalable Nano-Scaffold SOFC Anode Architecture Enabling Direct Hydrocarbon Utilization

This project is based on WVU’s pending patents, technology and aims to design and modify the internal surfaces of the Ni/YSZ anode from currently commercially viable Solid Oxide Fuel Cells (SOFCs) using the additive manufacturing process of Atomic Layer Deposition (ALD). The surface architecture/scaffold added onto the internal surface of the anode possesses an engineered nanostructure but it features only commonly-used oxide conductors and electro-catalyst materials. The surface layer possesses a minimum thickness of ~2-40 nm and is solely designed to control the surface reforming reactions and to increase catalytic activity. Three-dimensional (3D) nano scaffold architectures with the noble metal nano-catalyst, low-cost bimetallic catalytic alloys, and nano-scale ionic conducting oxide fully compatible with the state-of-the-art Ni/YSZ anode, were applied to the internal surface of the entire porous SOFC anode using ALD. In the present work, the surface scaffold architecture is essentially multi-functional at the nano-scale, facilitated by the multiple heterostructured interfaces. It will significantly enhance the power density and cell durability for direct hydrocarbon utilization by (1) increasing the number of electrochemical reaction sites to enhance the hydrogen/hydrocarbon oxidation reactions; (2) reducing carbon formation; (3) mitigating the coarsening of backbone Ni phase and the oxidation attack of Ni from oxidants (e.g., H2O, CO2); and (4) promoting the internal reforming capabilities, especially for natural gas applications. ALD is employed to generate stable anode surface architectures that are uniform, precisely controllable at the atomic scale, and accurately repeatable for processing. The engineered anode surface nano-scaffold architecture was cataloged and analyzed using High-resolution Transmission Electron Microscopy (TEM), and cell power/durability performance assessed via comprehensive electrochemical performance testing with commercial specimens and relevant environments using hydrocarbon fuels. To the best of our knowledge, this project is the First Report on ALD of Ni/YSZ. The actual achievement of this Project includes (1). Successful demonstration of 7 types of ALD layers on Ni/YSZ anode, including Co, Ni, Mn, Pt, Ru, ZrOx and multi-functional nano-composite. (1). Conformal coating and subsequently spontaneously pinning the discrete nano-catalyst, including the precious metal nano-catalyst and the Ni and Co catalysts, on the YSZ surface upon the electrochemical operation in the reduced atmosphere. Those nano-catalysts on the ionic-conducting YSZ provided excellent sites for promoting internal reforming; (2). Demonstrated ALD coating increased both catalytic activity and conductivity of Ni/YSZ. Conformal coating provided dopants and introduced additional electrical conducting pathways on the YSZ ionic conductor. The doped surface layer of YSZ with mixed conductivity thus further introduces the active triple phase boundaries adjacent to the ALD-coated nano-catalysts such as Pt, Co, and Ni that are pinned on the YSZ surface. The nano-composite ALD coating on Ni/YSZ anode has significantly increased cell durability; and (3). ALD coating of Ni/YSZ anode increased the power density of the entire cell by 300%. For a long time, the SOFC performance, such as the power density, was deemed hindered by the cathode. The sluggish oxygen reduction reaction (ORR) in the cathode was deemed as hindering the power density of the SOFCs. For the anode-supported commercial SOFCs, the cell performance is considered to be limited by the cathode's performance. For the first time in the field of SOFC, this project has demonstrated that (1). the performance of commercial SOFCs can be further increased by the ALD coating on Ni/YSZ anode backbone. (2). ALD coating on Ni/YSZ fuel electrodes results in the enhancement of power density, and increased reliability, robustness, and endurance of SOFCs, for their application using both hydrogen and hydrocarbon fuels over the entire operating temperature range of 650-800ºC for the inherently functional commercial cells. (3). ALD coating provides alternative approaches of exsolutions for introducing the stable catalyst onto the internal surface of the Ni/YSZ electrode. ALD coating could be much more versatile than exsolution in employing the catalysts with various chemistries onto the various backbones. (4). Due to the negligible amount of ALD materials coated onto the internal surface of the porous cathode of the as-fabricated cells, a peak power density increase up to 300 % induced by ALD coating was simultaneously achieved in terms of both power density and specific power. (5). The ALD coating developed through this project was applied to both the SOFC and Solid Oxide Electrolysis Cells (SOEC). SOEC’s face a similar but more demanding need to improve the fuel electrode's performance. It opens further research directions for electrocatalytic surface nanoionics with a wide range of chemistry. It will revolutionize our ability to render the formation of a nanostructured electrode that has been constantly pursued yet barely achieved for practical SOFC/SOEC applications. The research is also immediately transformative since both the preliminary data and the proposed work are on the direct implantation of nanoionics into the state-of-the-art inherently functional SOCs. It represents an immediate impact on the commercial sectors in SOC technology since the applied ALD processing is computer-controlled ALD coating using the commercial ALD systems, and it is scalable to both the single cells and SOC stacks.

36 MATERIALS SCIENCE↗

Thermodynamically consistent incorporation of the Langmuir adsorption model into compressible fluctuating hydrodynamics

For a gas–solid interfacial system where chemical species undergo reversible adsorption, we develop a mesoscopic stochastic modeling method that simulates both gas-phase hydrodynamics and surface coverage dynamics by coupling the Langmuir adsorption model with compressible fluctuating hydrodynamics. To this end, we derive a thermodynamically consistent mass–energy update scheme that accounts for how the mass and energy variables in the gas and surface subsystems should be updated according to the changes in the number of molecules of each species in each subsystem due to adsorption and desorption events. By performing a stochastic analysis for the ideal Langmuir model and the full hydrodynamic system, we analytically confirm that our mass–energy update scheme captures thermodynamic equilibrium predicted by equilibrium statistical mechanics. We find that an internal energy correction term is needed, which is attributed to the difference in the mean kinetic energy of gas molecules colliding with the surface from that computed from the Maxwell–Boltzmann distribution. By performing an equilibrium simulation study for an ideal gas mixture of CO and Ar, with CO undergoing reversible adsorption, we validate our overall simulation method and implementation.

Adsorption↗