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DOE OSTI2025

Rapid Oxidation of Uranium Steel Alloys: Combustion Synthesis

This project explored the use of combustion synthesis as a rapid, high-temperature method for oxidizing uranium-bearing steel alloys. Traditional laboratory-scale synthesis methods often fail to replicate the thermal and kinetic conditions experienced by real-world particulates, particularly those formed under rapid quenching or high-temperature scenarios. Combustion synthesis offers a promising alternative by enabling fast, localized heating and flexible precursor selection. A series of targeted experiments were conducted using a U 2 NiCrFe 4 alloy as the precursor. The alloy was oxidized using combustion synthesis reactions fueled by uranyl nitrate and glycine, achieving peak temperatures exceeding 1,200 °C. Postreaction analysis using scanning electron microscopy (SEM), elemental mapping, and Raman spectroscopy revealed the formation of iron-based oxides, with limited but detectable evidence of uranium oxide phases such as UO 2 . The results indicate that under the rapid reaction and cooling conditions of combustion synthesis, iron oxides form preferentially, but uranium oxide formation is kinetically limited. These findings validate combustion synthesis as a viable method for simulating the oxidation behavior of uranium steels in extreme environments and lay the groundwork for future studies aimed at enhancing uranium oxide formation through higher temperatures or modified precursor compositions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Magnetic field dependence of the martensitic transition and magnetocaloric effects in Ni 49 BiMn 35 In 15

The structural, magnetic, and magnetocaloric properties of the Bi-doped Heusler alloy Ni 49 BiMn 35 In 15 have been investigated using room temperature X-ray diffraction (XRD) and magnetization measurements in a temperature interval of 5-400 K. The alloy at room temperature was found to be in a mixture of a high temperature austenite phase (AP) and a low temperature martensite phase (MP). A drastic shift in the martensitic transition temperature at the rate of 16 K/T from 197 K to lower temperatures was observed. A kinetic arrest phenomenon of the AP was observed in the magnetization and electrical resistivity measurements during field-cooled (FC) measurements at 5T. A metamagnetic behavior characterized by a jump in magnetization in the isothermal M ( H ) curves near T M was observed. The maximum value of the magnetic entropy change and refrigerant capacity at Curie temperature were found to be 5.5 Jkg -1 K -1 and 312 Jkg -1 for μ o Δ H = 5T, respectively. A large magnetoresistance value of -56% was found near the martensitic transition.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Silicon alloying enhances fast heating rate combustion of aluminum particles

Alloys and composites of aluminum (Al) have shown promise in regulating and enhancing particle combustion for energy generation applications. Recent work on aluminum-silicon (Al-Si) spherical alloy particles has shown improved combustion at low heating rates through enhanced diffusion accompanying a lower melting temperature. This study extends reactivity analysis to higher heating rates, comparing oxidation of Al-Si with Al. Flame speeds of Al-Si powder mixed with molybdenum trioxide (MoO 3 ) powder (Al-Si+MoO 3 ) exhibited a faster transition to steady propagation relative to Al+MoO 3 . Bomb calorimetry experiments revealed up to 5.8% greater early temperature rise for Al-Si powder. Rapid steady propagation for Al-Si mixture and faster temperature rise for Al-Si particles were attributed to accelerated kinetics evidenced in thermal equilibrium analysis of the mixtures using a differential scanning calorimeter (DSC). Larger DSC exotherms in the early stages of oxidation (i.e., 480–720 °C) correlated with early heat release and promoted steady flame propagation for Al-Si+MoO 3 compared with Al+MoO 3 . Furthermore, in multiple heating rate DSC studies, Al-Si+MoO 3 ignited at a lower heating rate (i.e., 15 ⁰C/min) than Al+MoO 3 (i.e., 20 ⁰C/min). Both mixtures ignited at temperatures less than 625 °C which is above the melting temperature of Al-Si (574 °C) and below Al (659 °C). Thus, alloy particle fuels with enhanced diffusion-controlled kinetics promote steady flame propagation and show promise for energy generation applications. This is especially promising for technologies driven by enhanced condensed phase combustion such as some propellant additives or applications dependent on reliable burn rates such as pyrotechnic time delay formulations and primers.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Trailblazing Kr/Xe Separation: The Birth of the First Kr-Selective Material

Efficient separation of Kr from Kr/Xe mixtures is pivotal in nuclear waste management and dark matter research. Thus far, scientists have encountered a formidable challenge: the absence of a material with the ability to selectively adsorb Kr over Xe at room temperature. This study presents a groundbreaking transformation of the renowned metal–organic framework (MOF) CuBTC, previously acknowledged for its Xe adsorption affinity, into an unparalleled Kr-selective adsorbent. This achievement stems from an innovative densification approach involving systematic compression of the MOF, where the crystal size, interparticle interaction, defects, and evacuation conditions are synergistically modulated. The resultant densified CuBTC phase exhibits exceptional mechanical resilience, radiation tolerance, and notably an unprecedented selectivity for Kr over Xe at room temperature. Simulation and experimental kinetic diffusion studies confirm reduced gas diffusion in the densified MOF, attributed to its small pore window and minimal interparticle voids. The lighter Kr element demonstrates facile surface passage and higher diffusivity within the material, while the heavier Xe encounters increased difficulty entering the material and lower diffusivity. This Kr-selective MOF not only represents a significant breakthrough in Kr separation but also demonstrates remarkable processability and scalability to kilogram levels. Furthermore, the findings presented herein underscore the transformative potential of engineered MOFs in addressing complex challenges, heralding a new era of Kr separation technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A superconducting nanowire binary shift register

We present a design for a superconducting nanowire binary shift register, which stores digital states in the form of circulating supercurrents in high-kinetic-inductance loops. Adjacent superconducting loops are connected with nanocryotrons, three-terminal electrothermal switches, and fed with an alternating two-phase clock to synchronously transfer the digital state between the loops. A two-loop serial-input shift register was fabricated with thin-film NbN and a bit error rate of less than 10 –4 was achieved, when operated at a maximum clock frequency of 83 MHz and in an out-of-plane magnetic field of up to 6 mT. A shift register based on this technology offers an integrated solution for low-power readout of superconducting nanowire single photon detector arrays and is capable of interfacing directly with room-temperature electronics and operating unshielded in high magnetic field environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Chemical Modeling of the Capture of Radioiodine Species

Iodine is a common fission product resulting from the transmutation of uranium fuel in nuclear power reactors. The short-lived radioactive isotope, 131 I, with a half-life of around eight days, would be a particular health concern if released into the environment. Capture materials, such as activated carbon, are used routinely in nuclear power plants and medical isotope production facilities to remove this hazard during normal operations to reduce emissions to acceptable levels. Iodine, unlike other common fission products such as noble gases, is challenging because of the wide range of molecular forms and oxidation states (from +VII in IF 7 to -I in iodide) that it displays, which can interconvert both in the gas phase and in the solution phase for example. The work in this project is focused on three computational tasks. In the first, we consider the binding of iodine-containing molecules of varying oxidation states to the major component of activated carbon – pristine graphene-like sheets. The second task focused on molecular binding and possible chemical transformations resulting from the reaction of molecular iodine with chemical functional groups on the edge of the graphene sheets or surface defects in the sheet itself. The final task was associated with radiolytic breakdown of 131 I to 131 Xe in iodine containing molecules and investigated the resulting molecular fragmentation process both in the gas phase and on the graphene-like surface. For each of the tasks, the intent was to learn about the thermodynamics and kinetics of the chemical transformations and use the calculations to provide parameters for input into kinetic models describing these processes for interpretation of experimental data in future work.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2025

Direct Study of Changes in Catalyst Structure-Kinetic Properties During Redox Transitions

The Temporal Analysis of Products (TAP) pulse response methodology is a transient technique that provides the time resolution needed to deconvolve reaction steps from the complex networks typical in industrial catalytic processes. Traditionally, TAP measurements observe gas phase dynamics at the reactor exit but lack direct measurements of changes in the catalyst itself. Recently, a new operando technique was developed that couples gas phase transients to dynamic changes in metal centers with the precise TAP methodology for nanomole titration. Using an industrial CrOx/Al2O3 catalyst used for propane dehydrogenation, we demonstrate the capabilities of this unique device to reveal key catalytic processes: 1) total propane oxidation not associated with chromia centers, 2) reduction of Cr6+ to Cr3+ correlated with selective product formation, and 3) subsequent carbon accumulation. By utilizing incremental pulsing in a diffusion-only transport regime, the spectrokinetic device allows us to resolve detailed changes in catalyst structure, composition, and kinetic function that are otherwise indistinguishable in conventional operando devices. The unification of the TAP methodology with time-resolved spectroscopic measurements offers new and unique insights into the complex kinetic phenomena regulated by solid catalyst surfaces.

03 - NATURAL GAS↗

DOE OSTI2024

Bhatnagar-Gross-Krook subgrid model for neutrino quantum kinetics

Here, we present a new subgrid model for neutrino quantum kinetics, which is primarily designed to incorporate effects of collective neutrino oscillations into neutrino-radiation-hydrodynamic simulations for core-collapse supernovae and mergers of compact objects. We approximate the neutrino oscillation term in a quantum kinetic equation using the Bhatnagar-Gross-Krook (BGK) relaxation-time prescription, and the transport equation is directly applicable for classical neutrino transport schemes. The BGK model is motivated by recent theoretical indications that nonlinear phases of collective neutrino oscillations settle into quasisteady structures. We explicitly provide basic equations of the BGK subgrid model for both multiangle and moment-based neutrino transport to facilitate the implementation of the subgrid model in the existing neutrino transport schemes. We also show the capability of our BGK subgrid model by comparing it to fully quantum kinetic simulations for fast neutrino-flavor conversion. We find that the overall properties can be well reproduced in the subgrid model; the error of angular-averaged survival probability of neutrinos is within ~20%. By identifying the source of error, we also discuss perspectives to improve the accuracy of the subgrid model.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

A mesoscale crystal plasticity model to predict room-temperature deformation and martensitic transformation of high-strength Quenching and Partitioning (Q&P) Steels and validation with synchrotron X-ray diffraction

Renowned for the superior mechanical properties and adeptness at cold-forming, Quenching and Partitioning (QP) steels have gained prominence as a promising candidate material in fabricating safety-critical components in various industries. The pertinent research on QP steels focus on the martensitic transformation of the Retained Austenite (RA) phase during cold-forming, a crucial mechanism that substantially influences the overall strength and ductility of QP steels. The austenite stability and transformation rate heavily rely on the local strain path and the initial microstructure, which is challenging for analytical prediction. In this paper, a mesoscale model is developed to capture the deformation and transformation kinetics of QP steels inside the microstructure. The model integrates the detailed explicit microstructure, acquired from characterization experiments, into a high-resolution finite element (FE) mesh. It distinctly model the deformation and interaction between the various phases and the effect on the transformation of RA. The model is validated with high energy X-ray diffraction (HEXRD) data, and shows excellent capability in predicting the asymmetric stress-strain behavior under uniaxial tension and compression, as well as the martensitic transformation rate. The model is used to investigate the strain and load partitioning effect of surrounding matrix to the transformation of RA, offering insights into the complex behavior of QP980 and facilitates further material development.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Mechanistic Similarities and Differences for Hydrogenation of Aromatic Heterocycles and Aliphatic Carbonyls on Sulfided Ru Nanoparticles

This study establishes the contrasting reactivity trends for the hydrogenation of aromatic hydrocarbons (AHCs = C n H m X, X = N, S, O, and C) and aliphatic carbonyls [R a C(O)R b ; R a = alkyl group, R b = CH 3 or H] on sulfided Ru clusters arising from the difference in the elementary proton and hydride attack catalytic sequence. Both reactions require sequential additions of a proton from either Ru n+ –(SH 2 ) or S 2 –(H δ+ ) species and a hydride from Ru n+ –(H δ– ) species to the unsaturated C=X bonds. For the five-membered-ring aromatic heterocycles (AHCs = pyrrole, thiophene, and furan), an initial proton addition limits the catalytic turnovers; thus, their hydrogenation reactivity increases with increasing gas-phase proton affinities of the AHCs. Pyridine as the more basic six-membered N-AHC is more susceptible to protonation; therefore, it is more reactive, and its initial proton addition is quasi-equilibrated, followed by the kinetically relevant hydride addition. Conversely, aliphatic carbonyls prefer to undergo hydrogen additions in a reverse sequence, where a Ru n+ –(H δ– ) hydride initially attacks the electron-deficient carbonyl C atom as the kinetically relevant step before a subsequent rapid S 2 –(H δ+ ) proton addition on the electron-rich O atom, as confirmed by isotopic exchange studies with butanal-D 2 and 1-butanol-D 2 mixtures and density functional theory calculations on S-deficient RuS 2 (100) surfaces. For these reasons, their hydrogenation reactivity increases with increasing gas-phase hydride affinities of the carbonyls. On metallic Ru surfaces without sulfur, hydrogen adatoms (H*) are the only reactive hydrogen species; the reactivity of their attack on aromatic heterocycles increases with increasing reactant proton affinities much more sensitively than that on sulfided Ru surfaces. This work illustrates the distinct catalytic roles of the diverse hydrogen species in hydrogenation—the interplay between proton and hydride additions has marked catalytic consequences in shaping the free energy landscape of the reactions, which in turn leads to the observed kinetic dependences, kinetic parameters, reactivity trends, and scaling relations between the measured barriers and the appropriate kinetic descriptors, that is, proton affinity of AHCs and hydride affinity of carbonyls in hydrogenation catalysis. Here, these mechanistic similarities and differences provide explanations of the observed reactivity trends and thus have profound implications for industrial hydrogenation and hydrotreating catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Unveiling phase evolution of complex oxides toward precise solid-state synthesis

The precise synthesis of high-purity materials is crucial in accelerating materials discovery. However, the lack of theoretical understanding and practical guidance poses challenges, particularly for materials with compositional and structural complexity. Here, we propose a feasible principle toward synthesizing complex inorganic solids. This principle involves the introduction of an inducer that induces crucial intermediates, which in turn guide the synthesis pathway toward the target materials through structural templating, named inducer-facilitated assembly through structural templating (i-FAST). We validate this principle with three distinct oxides: garnet Li6.5La3Zr1.5Ta0.5O12, perovskite BaCo0.8Sn0.2O3, and pyrochlore Gd1.5La0.5Zr2O7. This structural templating approach enables synthesis along predesigned pathways, forming intermediates that are thermodynamically favored for prior formation and kinetically preferred for the final product, resulting in precisely synthesizing high-purity target materials. This study not only represents a substantial advancement in comprehending the interplay between thermodynamics/kinetics and phase evolution in complex solid synthesis but also provides an effective strategy for guiding exploratory solid-state synthesis.

Yang, Lin↗

DOE OSTI2025

Investigation of Corrosion Behavior of Carbide Phase Strengthened Nickel‐Based Alloy in Molten Fluoride Salt

The corrosion behavior of a high creep strength carbide-phase strengthened Ni-based alloy in molten FLiNaK (LiF-NaF-KF: 46.5-11.5-42 mol%) salt in the temperature range of 700°C–750°C has been investigated as a part of the development of structural alloys for fluoride salt-based molten salt reactors (MSRs). The alloy composition was designed based on Hastelloy-N, but with the goal of improving creep strength. Cr depletion depth, a measure of corrosion, was observed to be single micrometers after several hundred hours of corrosion testing. Sequential corrosion testing involving testing of pre-tested samples in fresh salt coupled with SEM-EDS, scanning transmission electron microscopy (STEM) examinations and thermodynamic and kinetic modeling, suggest that the corrosion rate at the alloy-salt interface is governed by diffusion of elements from the alloy bulk to the surface. The carbide phases in the corrosion-tested sample microstructure were identified to be largely M 6 C-type Mo-rich carbides and MC-type mixed carbides. Atom probe tomography (APT) showed some partitioning of Cr and Ti to the carbide phase and showed the carbide phases to be stable at the salt-facing surface.

Gordon, Ryan [Univ. of Wisconsin, Madison, WI (Uni↗

DOE OSTI2022

In situ characterization of phase transformations in petroleum pitch by high temperature X-ray diffraction

The phase transformation from isotropic to mesophase of a petroleum-derived pitch was monitored by in situ X-ray diffraction at 410 °C. The kinetics of the transformation were characterized by monitoring the growth of a broad peak at 2θ~24° and could be described by Avrami’s equation. The volatilization of low molecular weight components originally present in the pitch, or produced during the condensation reaction, was assessed by thermal gravimetry analysis, following the same thermal history. Ex situ characterizations of the pitch precursor before and after thermal treatment provided insight into the evolution of the molecular structure associated with mesophase generation (optical polarized microscopy, molecular weight distribution by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry, X-ray photoelectron spectroscopy, Auger spectroscopy, and thermal stability). Here, this investigation demonstrates the value of using complementary in situ and ex situ experimental techniques to characterize complex mechanisms during the processing of organic materials.

02 PETROLEUM↗

DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Metal–bicarbonate ion pairing in alkaline aqueous solutions from multilevel embedded correlated wavefunction theory and molecular dynamics

In this work, we examine ion-pairing mechanisms of bicarbonates in alkaline aqueous solutions with the divalent metal ions most abundantly present in seawater, namely, Ca 2+ and Mg 2+ . We employ a rare-event enhanced sampling approach within first-principles molecular dynamics to explore regions of phase space spanning solvent-shared to contact ion pairs. Second-order Møller–Plesset perturbation theory (MP2) corrections are subsequently applied in an embedding framework (EMB) to refine the electronic structure of stationary states and associated reaction barriers along the free-energy profiles while retaining the extended solvent effects at the density functional theory (DFT) level. Ca 2+ –HCO 3 − was previously hypothesized to exist in a solvent-shared ion pair (SSHIP) by DFT studies with an endergonic contact ion pair (CIP) formation; however, our EMB-MP2 refinement of the DFT ion-pairing pathways reveals that Ca 2+ and HCO 3 − form a virtually barrier-free CIP in alkaline solutions, with even more energetic ease than the widely studied Ca–CO 3 ion pair. We find qualitative agreement between DFT and EMB-MP2 for Mg 2+ —unlike Ca 2+ , Mg 2+ refuses to shed its strong hydration shell, thereby preferring a SSHIP state with a significant activation barrier to crossover to the CIP forms—a trait reminiscent of ion pairing in Mg–CO 3 and closely related to the kinetic limitations underlying the famous subject of the dolomite problem. Our study highlights the importance of improved electronic structure descriptions of liquids, modeled as a condensed phase of matter lacking in long-range crystalline order. It also strongly suggests that Ca 2+ –HCO 3 − CIPs are likely precursors involved in prenucleation of CaCO 3 mineral formation in seawater.

Sharma, Vidushi [Princeton Plasma Physics Laborato↗

DOE OSTI2023

On the Interplay between Size and Disorder in Suppressing Intercalation-Induced Phase Transitions in Pseudocapacitive Nanostructured MoS 2

Pseudocapacitors are an emerging class of energy storage materials that offer an attractive compromise between the energy density of batteries and power density of electric double-layer capacitors. Decreasing particle size and increasing surface area of battery materials is a common approach for introducing pseudocapacitive behavior and increasing power density. However, in many cases, as the crystal size is reduced, lattice disorder of unknown extent is also introduced, making it difficult to characterize the relative contribution of size and disorder to fast-charging performance. Here, in this work, a series of nanostructured MoS 2 materials are synthesized with different crystallite sizes and degrees of crystallinity to decouple the effects of size and disorder on charge/discharge kinetics. The extent and type of disorder in each material is quantified by total X-ray scattering experiments and pair distribution function analyses. Electrochemical characterization, including galvanostatic rate capability, cyclic voltammetry, and various kinetic analyses, are used to demonstrate that both decreasing particle size and introducing lattice disorder are effective strategies for increasing charge storage kinetics, and that the effects are additive. Finally, operando X-ray diffraction measurements show that both size and disorder can be used suppress first-order Li + intercalation-induced phase transitions, a key feature for enabling pseudocapacitive charge storage.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Statistically averaged molecular dynamics simulations of hydrogen diffusion in magnesium and magnesium hydrides

Magnesium has a different crystal structure from its dihydride with hydrogenation leading to a phase transition from the hexagonal closely packed Mg into a tetragonal α-MgH 2 rutile type structure. Such materials exhibit complex hydrogen uptake and release kinetics because hydrogen diffusivities significantly change when the crystal structure changes. To provide a foundational understanding of (de)hydrogenation kinetics that is applicable to all stages of the reaction, we performed statistically averaged molecular dynamics simulations to derive hydrogen diffusivities as a function of temperature and hydrogen content for both magnesium and magnesium hydride. Furthermore, our studies confirm that hydrogen diffusivities in magnesium hydride are much lower than in magnesium, in agreement with experimental data. Additionally, we observe that in either magnesium or magnesium hydride, higher hydrogen compositions result in reduced diffusivities. The latter was not revealed by prior experiments, which were conducted at fixed hydrogen composition. Finally, we discover a non-Arrhenius behavior in magnesium hydride. The physical origin of this behavior is also discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A dissolution model of alite coupling surface topography and ions transport under different hydrodynamics conditions at microscale

Portland cement is the most produced material in the world. The hydration process of cement consists of a group of complex chemical reactions. In order to investigate the mechanism of cement hydration, it is vital to study the hydration of each phase separately. An integrated model is proposed in this paper to simulate the dissolution of alite under different hydrodynamic conditions at microscale, coupling Kinetic Monte Carlo model (KMC), Lattice Boltzmann method (LBM) and diffusion boundary layer (DBL). The dissolution of alite is initialised with KMC. Two Multiple-relaxation-time (MRT) LB models are used to simulate the fluid flow and transport of ions, respectively. For solid-liquid interface, DBL is adapted to calculate the concentration gradient and dissolution flux. The model is validated with experiment from literature. The simulation results show good agreements with the results published in the literature.

36 MATERIALS SCIENCE↗