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Porous structured silicon has been regarded as a promising candidate to overcome pulverization of silicon-based anodes. However, poor mechanical strength of these porous particles has limited their volumetric energy density towards practical applications. Here we design and synthesize hierarchical carbon-nanotube@silicon@carbon microspheres with both high porosity and extraordinary mechanical strength (>200 MPa) and a low apparent particle expansion of ~40% upon full lithiation. The composite electrodes of carbon-nanotube@silicon@carbon-graphite with a practical loading (3 mAh cm−2) deliver ~750 mAh g−1 specific capacity, 92% capacity retention over 500 cycles. This work is a leap in silicon anode development and provides insights into the design of electrode materials for other batteries., The authors here construct hierarchical porous CNT@Si@C microspheres as anodes for Li-ion batteries, enabling both high electrochemical performance and excellent mechanical strength. The work highlights the importance of mechanical properties in developing battery materials for practical applications.

A simulation model of recrystallization and grain growth has been developed to investigate grain structure evolution during deformation and heat treatment in polycrystalline U-10 wt pct Mo (U-10Mo) fuel. Experimentally obtained U-10Mo post-homogenization microstructures were used as input for closed-loop simulations of multiple rolling passes, intermediate heating, and final annealing. Finite element model calculations of deformation and Potts model simulations of recrystallization and grain growth were used to iteratively inform each subsequent stage of simulation. The model was then applied to predict the grain structure evolution during multiple-pass hot rolling and annealing of U-10Mo and benchmarked against experimentally observed U-10Mo recrystallization behavior. The results showed that our model was able to capture the coupling between deformation and recrystallization as a function of microstructure, including particle stimulated nucleation and recrystallization nucleation on grain boundaries. Additionally, we have achieved reasonable quantitative agreement with U-10Mo recrystallization and grain growth behavior.

Prediction of material performance in fusion reactor environments relies on computational modelling, and will continue to do so until the first generation of fusion power plants come on line and allow long-term behaviour to be observed. In the meantime, the modelling is supported by experiments that attempt to replicate some aspects of the eventual operational conditions. In 2019, a group of leading experts met under the umbrella of the IEA to discuss the current position and ongoing challenges in modelling of fusion materials and how advanced experimental characterisation is aiding model improvement. This review draws from the discussions held during that workshop. Topics covering modelling of irradiation-induced defect production and fundamental properties, gas behaviour, clustering and segregation, defect evolution and interactions are discussed, as well as new and novel multiscale simulation approaches, and the latest efforts to link modelling to experiments through advanced observation and characterisation techniques. MRG, SLD, and DRM acknowledge funding by the RCUK Energy Programme [grant number EP/T012250/1]. Part of this work has been carried out within the framework of the EUROFusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. JRT acknowledges funding from the US Department of Energy (DOE) through grant DE-SC0017899. ZB, LY,BDW, and SJZ acknowledge funding through the US DOE Fusion Energy Sciences grant DE-SC0006661ZB, LY and BDW also were partially supported from the US DOE Office of Science, Office of Fusion Energy Sciences and Office of Advanced Scientific Computing Research through the Scientific Discovery through Advanced Computing (SciDAC) project on Plasma-Surface Interactions. JMa acknowledges support from the US-DOEs Office of Fusion Energy Sciences (US-DOE), project DE-SC0019157. Pacific Northwest National Laboratory is operated by Battelle Memorial Institute for the US Department of Energy (DOE) under contract DE-AC05-76RL01830. YO and YZ were supported as part of the Energy Dissipation to Defect Evolution (EDDE), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under contract number DE-AC05-00OR22725. TS and TT are supported by JSPS KAKENHI Grant Number 19K05338.

Conventional rate theory often uses the mean field concept to describe the effect of inhomogeneous microstructures on the evolution of radiation induced defect and solute/fission product segregation. However, the spatial and temporal evolution of defects and solutes determines the formation and spatial distribution of radiation-induced second phase such as precipitates and gas bubbles/voids, especially in materials with complicated microstructures and subject to high dose radiation. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed to investigate the effect of inhomogeneous thermodynamic and kinetics properties of defects on diffusion and accumulations of solute A in AB binary alloys. Four independent concentrations: atom A, interstitial A, interstitial B, and vacancy on [A, B] sublattice are used as field variables to describe temporal and spatial distribution and evolution of defects and solute A. The independent concentrations of interstitial A and interstitial B allow to describe their different generation rates, thermodynamic and kinetic properties, and release the assumptions of interstitial generation and sink strength used in the conventional rate theory. Microstructure and concentration dependent chemical potentials of defects are used to calculate the driving forces of defect diffusions. With the model, the effects of defect chemical potentials and mobilities on the RIS in polycrystalline AB model alloys have been simulated. The results demonstrated the model capability in predicting defect evolution in materials with inhomogeneous thermodynamic and kinetic properties of defects. The model can be extended to materials with complicated microstructures such as a wide range of grain size distribution, coating structure and multiphases as well as radiation-induced precipitation subject to severe radiation damage.

Ni segregation at the interfaces of Cu-rich precipitates in Fe–Cu–Ni alloys is investigated using ab initio based models with Monte Carlo simulations and density functional theory calculations. It is demonstrated that Ni segregation decreases with increasing temperature and increases in proportion to global Ni concentration. The predicted Ni segregation profiles are in quantitative agreement with experiments. Analysis show that both the temperature dependent alloy energetics and the configurational entropy are important for predicting Ni segregation. The results also reveal that Ni segregation reduces the interfacial structure stability, especially at low temperatures and with high global Ni concentrations, which could be used to explain the Ni enhanced hardening in Fe–Cu–Ni alloys.

Experiments show that irradiation-induced recrystallization speeds up the swelling kinetics in U-10 wt% Mo fuels. However, recrystallization mechanisms and the effect of initial grain microstructures on recrystallization kinetics are still unclear. In this work a Monte Carlo model coupling the rate theory of defect evolution has been developed to study the irradiation-induced recrystallization. The rate theory is used to describe the spatial evolution of gas bubbles, interstitials and interstitial loops; First-Passage Kinetic Monte Carlo (FPKMC) approach is used to describe the fast and strongly anisotropic migration of interstitials, and a Cellular Automata method is used to model the formation of recrystallized grains. With the assumption that recrystallization may occur when the local interstitial loop density is larger than a given critical value, simulation results reveal that 1) recrystallized grains first nucleate on grain boundaries and the recrystallization zone front moves to the center of original coarse grains in the UMo matrix, and 2) recrystallization starts earlier in coarse polycrystalline structures, while the overall recrystallization kinetics decreases with increasing grain size. These results agree with experimental observations. The comparison of recrystallization kinetics obtained from experiments and modeling suggests that the interstitial loop accumulation leads to the recrystallization and the interstitial loop growth is suppressed inside coarse grains due to the over-pressured intra-granular gas bubbles.

Modeling of crack deflection/penetration or manifested as intergranular/transgranular fracture in polycrystals has long been a challenge in both fracture mechanics and materials science. A phase-field model formulated with two-set order parameters describing the crack field and the microstructure field respectively, is herein established to investigate the competition between crack penetration and deflection at an interface. The advantages of the proposed model are three-fold: (1) the fracture toughness of grain boundaries and/or interfaces, besides single crystal properties (e.g., Young’s modulus, Poisson ratio, and fracture toughness), can be automatically incorporated, (2) cohesive interfaces are treated in one phase-field framework in comparison with the integrated phase-field and cohesive zone model in which cohesive elements have to be manually placed at the interface, and (3) two-set order parameters enable to describe the concurrent crack propagation and microstructure evolution. The proposed model is validated by comparing the simulated critical deflection angles with the results from theoretical analysis of the linear elastic fracture mechanics and the experiments. The model is then applied to a heterogeneous Silicon Nitride polycrystal to determine the effect of interface fracture toughness on the intergranular/transgranular fracture transition and the effective toughness of the materials.

Multiscale, hierarchical, porous materials are promising nuclear wasteform materials with potential for efficiently adsorbing and sequestering radionuclides. However, fundamental understanding of such complex micro- and meso-structures on radionuclide diffusion and uptake kinetics is lacking, which is essential for designing advanced nuclear wasteform materials. In this work we develop a microstructural-dependent diffusion model that accounts for three-dimensional (3D) microstructural features, including heterogeneous thermodynamic and kinetic properties, to predict radionuclide uptake kinetics in complex porous structures. Na+ and Sr2+ ionic exchange in LTA zeolite multiscale materials in batch tests is taken as a model system to demonstrate the model and its application to hierarchical materials with multiscale porosity. It is found that the reduction of ionic mobility associated with chemistry, structure, and/or phase changes has more profound impact on the uptake kinetics in a large 3D porous particle than that in a small one. Uptake kinetics in large particles are limited by two diffusion processes: bulk diffusion and surface layer transport. Decreasing particle size and increasing mesoscale pore volume fraction changes the uptake kinetics from two diffusion processes to a single process and dramatically increases the uptake kinetics. Predicted uptake kinetics and the effect of microstructures on the effective capacity of radionuclides and uptake efficiency are consistent with results observed in Na+/Sr2+ exchange experiments. The results demonstrate that the developed model should be adaptable to transport problems in other hierarchical material systems.

δ-hydride structures in Zr nuclear fuel-rod cladding significantly affect mechanical properties. A micromechanical phase-field model is developed to investigate the effect of interfacial energy anisotropy and elastic interaction on the nucleation, stacking structure formation, and stacking structure transition of δ-hydrides. It is found that the nucleation probability and growth of δ-hydride near pre-existing hydrides are strongly spatially dependent. Results show that (1) the δ-hydride has a platelet-like shape. The large shear deformation associated with lattice mismatches and a small interfacial energy of its broad interface cause the orientation of the δ-hydride off the basal plane approximately 14.7°. (2) Stress-induced nucleation of δ-hydrides near a pre-existing hydride results in the unique stacking structure formation. (3) The morphology and alignment of stacking structures, called as macroscopic hydrides which consist of microscopic hydrides with certain stacking sequences, change under stresses. The alignment of macroscopic hydrides changes from along the circumferential direction to along the radial direction under tensile hoop stress while the orientation of microscopic hydrides remains parallel to the basal plane. These results are in agreement with experimental observations. The simulations reveal that stress-induced heterogeneous nucleation and growth is the mechanism for the formation and transition of unique macro-hydride stacking structures.

Samples of U-10 wt%Mo (U Mo) alloy were thermomechanically processed and annealed at 600 °C and 700 °C for periods lasting up to 8 h. Annealed microstructures were examined using electron backscattered diffraction in order to estimate the completeness of recrystallization. Hardness measurements of the U Mo samples were taken to further qualify the progress of recovery and recrystallization. This allowed us to evaluate the recrystallization activation energy and the recrystallization kinetics with a Johnson-Mehl-Avrami-Kolmogorov equation. The results show that the activation energy of recrystallization is approximately 100.6 ± 23.1 kJ/mol. The mechanisms active in the recrystallization of cold-rolled U-10 wt% Mo are discussed in the context of these results.

Experiments show that zeolites, such as Linde Type A (LTA), are promising materials for radioactive decontamination processes. In this work, the thermodynamic properties associated with alkaline earth ion (Ca2+, Sr2+ and Ba2+) exchange in pure silica LTA was studied using periodic first-principles calculations. The adsorption energies of alkaline earth ions compared with that of Na+ were investigated. The driving forces for alkaline earth exchange and related isotherms were calculated, and analyzed as a function of the electron chemical potential. The results demonstrate that Na+ in a pure silica LTA can completely be removed by Ba2+ and almost completely be removed by Sr2+ from a stream, but cannot be effectively exchanged by Ca2+. We also showed that electron-donating dopants should suppress Sr2+ and Ba2+ ion exchange, and that there is a substantial preference for incorporating Ba2+ over Sr2+. Lastly, the substantial difference between the adsorption energies of the ions in an assumed vacuum and those computed in water suggests that a solvation model is needed for accurate representation of ion adsorption in an LTA zeolite.

Metal-organic frameworks (MOFs) have been used to sequester radionuclides and seal them inside of porous scaffolds using postsynthetic modification procedures. Experiments show that certain Zr-MOF with different capping linkers significantly affects the radionuclide release kinetics. In this work, we developed a leaching model of radionuclides in Zr-MOF particles. The model assumes that uranyl species occupy two energetically favored sites: the metal node and the MOF pores. For a given overall concentration of uranyl species, the partitions of uranyl species at the metal nodes and within the pores are determined by their chemical potentials. The model also considers the effect of particle surface and concentration on chemical potentials and diffusivity. The effects of spatial and structural dependent chemical potentials and diffusivity as well as particle sizes on leaching kinetics are investigated with the model. Predicted and measured uranyl leaching kinetics in Zr-MOF particles under batch experiments are compared. The results demonstrate the model’s capability for exploring the mechanisms of leaching and provide guidance for material design.

Monolithic UMo fuels have a higher uranium density than previously developed fuels. They have become the most promising fuels to be used in high-flux research and test reactors after the US Office of Material Management and Minimization Reactor Conversion Program (formerly Reduced Enrichment Research and Test Reactor (RERTR) program). In this study, a computational method is established to couple the macro-scale irradiation-induced thermo-mechanical behavior simulation with the hydrostatic-pressure-dependent fission gas swelling calculation in the UMo grain. The stress update algorithms and consistent stiffness moduli are respectively presented for UMo fuel, in which both the hydrostatic-pressure-dependent irradiation swelling and deviatoric-stress-directed irradiation creep are taken into account. Accordingly, the user subroutines to define the thermo-mechanical non-homogeneous constitutive relations for the UMo fuel meat and Al cladding are developed and validated. The in-pile behavior in a monolithic UMo fuel plate under a location-dependent irradiation condition is calculated and discussed.

The aging- or radiation-induced hardening of Cu/Mn/Ni precipitates in Fe alloys is one of property degradation mechanisms in structural materials in nuclear reactors. Experiments show that aging or radiation leads the formation of Cu-rich precipitates, and the addition of Mn or Ni elements enhances the precipitation kinetics. In this work, the phase-field model coupled with the constrained string method have been applied to investigate the thermodynamic properties of critical nuclei such as the minimum energy path of Cu/Mn/Ni precipitation in Fe-Cu-Mn and Fe-Cu-Ni ternary alloys. The chemical free energies used in the model are taken from CALPHAD. The simulation results show that the formation of Cu/Mn/Ni clusters needs to overcome an energy barrier, and the precipitate has a Core-Shell structure. The thermodynamic properties of the critical nucleus are influenced by temperature and Cu/Mn/Ni overall concentrations, which are in accordance with the simulation results as well as the experimental observations.

Pitting corrosion is one of the most destructive forms of corrosion that can lead to catastrophic failure of structures. This study presents a thermodynamically consistent phase field model for the quantitative prediction of the pitting corrosion kinetics in metallic materials. An order parameter is introduced to represent the local physical state of the metal within a metal-electrolyte system. The free energy of the system is described in terms of its metal ion concentration and the order parameter. Both the ion transport in the electrolyte and the electrochemical reactions at the electrolyte/metal interface are explicitly taken into consideration. The temporal evolution of ion concentration profile and the order parameter field is driven by the reduction in the total free energy of the system and is obtained by numerically solving the governing equations. A calibration study is performed to couple the kinetic interface parameter with the corrosion current density to obtain a direct relationship between overpotential and the kinetic interface parameter. The phase field model is validated against the experimental results, and several examples are presented for applications of the phase-field model to understand the corrosion behavior of closely located pits, stressed material, ceramic particles-reinforced steel, and their crystallographic orientation dependence. Stainless steel corrosion can be successfully simulated using a phase field model that takes into account anodic and cathodic reactions. A team led by San Qiang Shi at the Hong Kong Polytechnic University adapted a phase field method used for simulating metallic microstructure evolution to study corrosive pit growth in stainless steel immersed in mildly salted water. The authors developed equations taking into account the transport and concentration of ionic species and introduced a parameter to describe the changing corrosion interface. The resulting model simulated the corrosion process from the meso- to the macroscale, and successfully showed that two pits can coalesce to form a wider pit, while corrosion occurred preferentially along specific crystallographic planes. Successfully simulating complex corrosion situations may help us better understand them and lessen their impact.

This perspective focuses on the synthesis, characterization, and modeling of three classes of hierarchical materials with potential for sequestering radionuclides: nanoparticles, porous frameworks, and crystalline salt inclusion phases. The scientific impact of hierarchical structures and the development of the underlying crystal chemistry is discussed as laying the groundwork for the design, local structure control, and synthesis of new forms of matter with tailored properties. This requires development of the necessary scientific understanding of such complex structures through integrated synthesis, characterization, and modeling studies that can allow their purposeful creation and properties. The ultimate practical aim is to provide the means to create novel structure types that can simultaneously sequester multiple radionuclides. The result will lead to the creation of safe and efficient, long lasting waste forms for fission products and transuranic elements that are the products of nuclear materials ...

A quantitative phase-field model is developed for the investigation of crevice corrosion of iron in salt water. Six types of ionic species and some associated chemical reactions have been considered. In addition to the transient distributions of ion concentrations and electric potential in the electrolyte, some physical and chemical properties related to corrosion, such as overpotential, pH value and corrosion rate, under different metal potentials are studied. Benchmarking of the phase-field model against a sharp interface model is conducted. The corrosion rates predicted by the models are in the same order of magnitudes with experimental results.

Using ab initio calculations and the magnetic cluster expansion formula, a model with the magnetic effects on the energetic landscape of Fe–Cu was developed. The (partially) disordered local moment picture and Monte Carlo simulation method were combined to study the magnetically disordering effects on the thermodynamic properties in Fe–Cu alloys. The simulation results show nonlinear enhancements of Fe magnetism with increasing Cu concentration under varying magnetic ordering/disordering states, and the nonlinearity of the enhancement is more significant under the ferromagnetic state. It is also found that magnetism has subtle effects on the clustering of Cu because both the substitutional and binding energies could be affected but in different ways depending on the magnetic states. The results suggest that the alloying-induced enhancement of the Fe magnetism is a fundamental feature of Fe–Cu, which introduces difference on the concentration dependence of mixing, depending on the magnetic ordering/disordering states. In conjunction with the concentration dependence of short-range ordering, the enhancement of Fe magnetism also strongly affects the Curie temperatures in Fe–Cu.

The alloy U-10 wt% Mo was annealed at temperatures ranging from 700 °C to 900 °C for periods lasting up to 24 h. Annealed microstructures were examined using Electron Backscattered Diffraction (EBSD) to obtain average grain sizes and grain size distributions. From the temporal evolution of the average grain size, the activation energy of grain growth was determined to be 172.4 ± 0.961 kJ/mol. Grain growth over the annealing period stagnated after a period of 1–4 h. This stagnation is apparently caused by the pinning effect of second-phase particles in the materials. Back-scattered electron imaging (BSE) was used to confirm that these particles do not appreciably coarsen or dissolve during annealing at the aforementioned temperatures.

Pre-existing second phase particles can induce particle stimulated nucleation (PSN) and pinning effect on grain boundaries during DRX process of magnesium alloys. The interaction among pinning effect, PSN mechanism and strain-induced grain boundary migration (SIBM) nucleation mechanism imposes challenge in quantitative study of microstructure evolution. A phase field model that describes discontinuous dynamic recrystallization process considering second phase particles (PF-DDRX-SP) which mainly distribute along grain boundaries is developed. The second phase order parameter with diffusion interface is introduced to the free energy function. With considering the pinning effect of second phase particles on grain boundaries, the grain boundary energy couples the interaction between second phase and grains. The effect of second phase on dislocation density evolution is considered in the model, and the PSN and SIBM mechanism are both executed by limiting the nucleation position to the grain boundary and the second phase interface. For the validation, the initial topology consistent with initial microstructure is applied to the simulation of DRX kinetics and flow behavior of AZ80 magnesium alloy, and great reliability and accuracy of developed model is indicated. Furthermore, through the model, the microstructure evolution with different particle size and with different volume fraction of round particle during DRX process were simulated. The results show that particles with higher dispersion reduce the number of DRX nuclei, which indicate that second phase particles suppress the nucleation at grain boundaries because of the pinning effect. More importantly, the proposed model could also quantitatively predict the relationships between the parameters of second phase particles and DRX behaviors, and enable to optimize the initial second phase structure in a uniform grain structure during thermomechanical process.

Chemical dealloying beckons researchers both for scientific interest in corrosion failure of metallic materials and for the fabrication of nanoporous materials that have versatile applications due to their ultra-high surface area. Empirically, nanoporous structure evolves by the corrosion of less noble elements coupled with the rearrangement of more noble elements in the alloys. However, how topologically complex porous structures form and how environmental and material factors affect the dealloying kinetics are still unknown. This work develops a multi-phase-field model to demonstrate that a nucleation-growth mechanism can explain the formation of nanoporous structures under chemical attack. The evolution of nanoporous patterns from a binary alloy is examined as a function of the chemical content of the electrolyte, precursor alloy composition, dimensionality, and bulk and surface diffusion coefficients, which is validated with experimental observations. Two-phase composite dealloying and the effect of defect pre-existed in the precursor are also presented. The comprehensive model developed in this study provides a powerful tool to tailor made nanoporous metallic structures under chemical dealloying.

In this work, we developed a recrystallization model to study the effect of microstructures and radiation conditions on recrystallization kinetics in UMo fuels. The model integrates the rate theory of intragranular gas bubble and interstitial loop evolutions and a phase-field model of recrystallization zone evolution. A first passage method is employed to describe one-dimensional diffusion of interstitials with a diffusivity value several orders of magnitude larger than that of fission gas xenons. With the model, the effect of grain sizes on recrystallization kinetics is simulated. The results show that (1) recrystallization in large grains starts earlier than that in small grains, (2) the recrystallization kinetics (recrystallization volume fraction) decrease as the grain size increases, (3) the predicted recrystallization kinetics are consistent with the experimental results, and (4) the recrystallization kinetics can be described by the modified Avrami equation, but the parameters of the Avrami equation strongly depend on the grain size.

Xe gas bubble superlattice formation is observed in irradiated uranium–10 wt% molybdenum (U10Mo) fuels. However, the thermodynamic properties of the bubbles (the relationship among bubble size, equilibrium Xe concentration, and bubble pressure) and the mechanisms of bubble superlattice formation are not well known. In this work, the molecular dynamics (MD) method is used to study these properties and mechanisms. The results provide important inputs for quantitative mesoscale models of gas bubble evolution and fuel performance. In the MD simulations, the embedded-atom method (EAM) potential of U10Mo-Xe [1] is employed. Initial gas bubbles with a low Xe concentration (underpressured) are generated in a body-centered cubic (bcc) U10Mo single crystal. Then Xe atoms are sequentially added into the bubbles one by one, and the evolution of pressure and dislocation emission around the bubbles is analyzed. The relationship between pressure, equilibrium Xe concentration, and radius of the bubbles is established. It was found that an overpressured gas bubble emits partial dislocations with a Burgers vector along the direction and a slip plane of (11-2). Meanwhile, dislocation loop punch out was not observed. The overpressured bubble also induces an anisotropic stress field. A tensile stress was found along directions around the bubble, favoring the nucleation and formation of a face-centered cubic bubble superlattice in bcc U10Mo fuels.

A three-dimensional phase-field model was developed to study the effects of surface energy and diffusivity anisotropy on void growth behavior in irradiated Zr. The gamma surface energy function used in the phase-field model was developed with the surface energy anisotropy calculated from the molecular dynamics simulations. The model assumes that vacancies have larger mobility in the c-axis than in the a-axis and b-axis, whereas interstitials have larger mobility in the basal plane than in the c-axis. The equilibrium void morphology and the effect of defect concentrations and mobility anisotropy on void growth behavior were simulated using the developed model. The simulations demonstrated that (1) the developed phase-field model correctly reproduces the faceted void morphology predicted by the Wulff construction; (2) with isotropic diffusivity, the void prefers to grow on the basal plane; and (3) when the vacancy has large mobility along the c-axis and interstitial has a large mobility on the basal plane of hexagonal closed-packed Zr alloys, a platelet void grows in the c-direction and shrinks on the basal plane. These findings are in agreement with the observation of void morphology and growth behavior in irradiated Zr, and reveal that the strong mobility anisotropy of defects results in the anisotropic growth of voids in Zr.

Complex microstructure changes occur in nuclear fuel and structural materials due to the extreme environments of intense irradiation and high temperature. This paper evaluates the role of the phase field method in predicting the microstructure evolution of irradiated nuclear materials and the impact on their mechanical, thermal, and magnetic properties. The paper starts with an overview of the important physical mechanisms of defect evolution and the significant gaps in simulating microstructure evolution in irradiated nuclear materials. Then, the phase field method is introduced as a powerful and predictive tool and its applications to microstructure and property evolution in irradiated nuclear materials are reviewed. The review shows that (1) Phase field models can correctly describe important phenomena such as spatial-dependent generation, migration, and recombination of defects, radiation-induced dissolution, the Soret effect, strong interfacial energy anisotropy, and elastic interaction; (2) The phase field method can qualitatively and quantitatively simulate two-dimensional and three-dimensional microstructure evolution, including radiation-induced segregation, second phase nucleation, void migration, void and gas bubble superlattice formation, interstitial loop evolution, hydrate formation, and grain growth, and (3) The Phase field method correctly predicts the relationships between microstructures and properties. The final section is dedicated to a discussion of the strengths and limitations of the phase field method, as applied to irradiation effects in nuclear materials.

A three dimensional microstructure dependent swelling model is developed for studying the fission gas swelling kinetics in irradiated nuclear fuels. The model is extended from the Booth model [1] in order to investigate the effect of heterogeneous microstructures on gas bubble swelling kinetics. As an application of the model, the effect of grain morphology, fission gas diffusivity, and spatially dependent fission rate on swelling kinetics are simulated in UMo fuels. It is found that the decrease of grain size, the increase of grain aspect ratio for the grain having the same volume, and the increase of fission gas diffusivity (fission rate) cause the increase of swelling kinetics. Other heterogeneities such as second phases and spatially dependent thermodynamic properties including diffusivity of fission gas, sink and source strength of defects could be naturally integrated into the model to enhance the model capability.

Nanocrystalline (NC) metals are stronger and more radiation-tolerant than their coarse-grained (CG) counterparts, but they often suffer from poor thermal stability as nanograins coarsen significantly when heated to 0.3 to 0.5 of their melting temperature (Tm). Here, we report an NC austenitic stainless steel (NC-SS) containing 1 at% lanthanum with an average grain size of 45 nm and an ultrahigh yield strength of ~2.5 GPa that exhibits exceptional thermal stability up to 1000 °C (0.75 Tm). In-situ irradiation to 40 dpa at 450 °C and ex-situ irradiation to 108 dpa at 600 °C produce neither significant grain growth nor void swelling, in contrast to significant void swelling of CG-SS at similar doses. This thermal stability is due to segregation of elemental lanthanum and (La, O, Si)-rich nanoprecipitates at grain boundaries. Microstructure dependent cluster dynamics show grain boundary sinks effectively reduce steady-state vacancy concentrations to suppress void swelling upon irradiation., Weaker ferritic/matensitic steels rather than stronger austenitic steels are usually candidates for nuclear reactors since they do not easily swell under irradiation. Here, the authors make an ultrastrong lanthanum-doped nanocrystalline austenitic steel that is thermally stable and radiation-tolerant.

Irradiation examination shows that gas bubble swelling kinetics are much faster after irradiation-induced recrystallization than that prior to recrystallization in U-10 wt% Mo alloy (UMo) fuels. These kinetics imply that gas bubbles in coarse grains and small recrystallized grains have different growth behavior. For the first time, researchers developed a phase-field model of gas bubble evolution integrating microstructure-dependent cluster dynamics to study the gas bubble swelling behavior in the recrystallization zone of UMo fuels. Generation, diffusion, reaction, sink, emission, and clustering of vacancies and interstitials are described by the cluster dynamics model while a phase-field model is used to describe the evolution of nonequilibrium gas bubbles including nucleation and growth. With the coupled model, the effect of defect generation rate, clustering rate, interstitial emission, and sink rates on grain boundaries on the gas bubble evolution are systematically simulated. A set of model parameters (defect generation rate, clustering rate, interstitial emission, and sink rates) is determined by comparing measured and simulated gas bubble swelling kinetics. The results demonstrate that interstitial clustering is one of the important physical mechanisms that results in fast gas bubble swelling kinetics in the recrystallization zone. The developed model can also be extended to study the associated growth of defect and second-phase precipitates often observed in irradiated materials.

Grain growth kinetics are known to deviate from the classical n = 2 behavior when particles in the microstructure impede grain boundary motion, and eventually halt as the driving force of grain boundary curvature approaches the pinning force exerted by the particles. Potts Model simulations were evaluated with respect to the non-physical Monte Carlo simulation temperature and theoretical predictions of grain growth behavior in the presence of second-phase particles. These simulations demonstrate that by modifying the simulation temperature, the pinned grain size will follow a selected inverse-linear relationship with respect to particle volume fraction. From these results, we suggest an approach for selecting Potts Model simulation temperature. Additionally, parameterizations of particle size, volume fraction, and simulation temperature in which the previously observed simulation phenomenon “Particle-Assisted Abnormal Grain Growth” (PA-AGG) occurred were recorded and discussed. The majority of this grain growth behavior occurred for simulation temperatures TS ≥ 1.5, particle diameters of less than six cells, and particle volume fractions smaller than 10%. However, PA-AGG was also observed in simulation for particle diameters of up to ten cells, particle volume fractions of twenty percent, and simulation temperatures as small as TS = 0.5. An analysis of the simulated grain size distributions showed that the occurrence of PA-AGG was not dependent on the abnormal grain reaching a critical relative grain size. The simulation domain size does not appear to have an influence on this effect.

Due to the large formation energy of vacancies and noble gas atoms at interstitial and/or substitutional sites in nuclear fuel (UO2), the thermodynamic equilibrium concentrations of these species are very low in the nuclear fuel matrix even at very high temperature, which imposes difficulties upon the quantitative study of bubble evolution via the phase-field method. In this study, a quantitative phase-field model is proposed to deal with this problem. The free energy density of the system is derived according to the principles of thermodynamics, with consideration of the elastic interaction and internal pressure of each gas bubble, and with the use of material parameters from experiments. The model enables one to study the kinetics of gas bubble growth with very dilute concentrations of vacancy and gas atoms in the matrix. With this model, the growth of a single bubble and multiple bubbles were simulated under different concentrations of vacancy and gas atoms and at different temperatures. The effect of elastic interaction energy and the generation rate of vacancies and gas atoms on bubble growth are analyzed.

Nano-gas bubble superlattices are often observed in irradiated UMo nuclear fuels. However, the formation mechanism of gas bubble superlattices is not well understood. A number of physical processes may affect the gas bubble nucleation and growth; hence, the morphology of gas bubble microstructures including size and spatial distributions. In this work, a phase-field model integrating a first-passage Monte Carlo method to investigate the formation mechanism of gas bubble superlattices was developed. Six physical processes are taken into account in the model: 1) heterogeneous generation of gas atoms, vacancies, and interstitials informed from atomistic simulations; 2) one-dimensional (1-D) migration of interstitials; 3) irradiation-induced dissolution of gas atoms; 4) recombination between vacancies and interstitials; 5) elastic interaction; and 6) heterogeneous nucleation of gas bubbles. We found that the elastic interaction doesn’t cause the gas bubble alignment, and fast 1-D migration of interstitials along 〈110〉 directions in the body-centered cubic U matrix causes the gas bubble alignment along 〈110〉 directions. It implies that 1-D interstitial migration along [110] direction should be the primary mechanism of a fcc gas bubble superlattice which is observed in bcc UMo alloys. Simulations also show that fission rates, saturated gas concentration, and elastic interaction all affect the morphology of gas bubble microstructures.

Low-enriched U-22at% Mo (U–10Mo) alloy has been considered as an alternative material to replace the highly enriched fuels in research reactors. For the U–10Mo to work effectively and replace the existing fuel material, a thorough understanding of the microstructure development from as-cast to the final formed structure is required. The as-cast microstructure typically resembles an inhomogeneous microstructure with regions containing molybdenum-rich and -lean regions, which may affect the processing and possibly the in-reactor performance. This as-cast structure must be homogenized by thermal treatment to produce a uniform Mo distribution. The development of a modeling capability will improve the understanding of the effect of initial microstructures on the Mo homogenization kinetics. In the current work, we investigated the effect of as-cast microstructure on the homogenization kinetics. The kinetics of the homogenization was modeled based on a rigorous algorithm that relates the line scan data of Mo concentration to the gray scale in energy dispersive spectroscopy images, which was used to generate a reconstructed Mo concentration map. The map was then used as realistic microstructure input for physics-based homogenization models, where the entire homogenization kinetics can be simulated and validated against the available experiment data at different homogenization times and temperatures.

Phase field models are developed to study the gas bubble migration in uranium dioxide nuclear fuel in which a large temperature gradient exists during the operation. In this work, thermal diffusion mechanism for nanosized gas bubbles and vapor transport process for micron-sized gas bubbles are considered, respectively. In both cases, gas bubbles migrate to the high-temperature area. Due to the velocity difference between leading and trailing edges of the gas bubbles, nanosized gas bubbles are elongated along the temperature gradient direction when thermal diffusion is dominated. Micron-sized gas bubbles are either compressed along temperature gradient direction to form lenticular shape bubbles or elongated along temperature gradient direction, depending on the location of the gas bubbles within the fuel pellet. Initial gas bubble radius has no significant effect on the gas bubble migration velocity for both thermal diffusion and vapor transport mechanisms. We notice that the shape change of the gas bubble due to vapor transport mechanism has no significant effect on the migration velocity. Furthermore, the center cavity formation is also captured by our model which is due to the migration and accumulation of lenticular gas bubbles at the center of the fuel pellet. The modeling results compare well with experimental observations and theoretical analysis in the literature.

A phase field model of discontinuous dynamic recrystallization (PF-DDRX) was employed to investigate grain structure evolution and its impact on mechanical response during thermomechanical processing of magnesium alloys. A set of isothermal compression experiments were conducted by thermo-mechanical simulator and used to calibrate the PF-DDRX model parameters such as the critical stress of recrystallization, the activation energy coefficient of dislocation, grain boundary mobility and recrystallization grain nucleation. The grain structure features of polycrystalline magnesium alloys were used to generate the initial grain structure for DDRX simulations. Simulation results show that 1) the ‘necklace’ microstructures, which are often observed in DDRX, form at the earlier stage of recrystallization; and 2) both predicted grain structure and mechanical response are in a reasonable agreement with experimental data. More importantly, the results demonstrate that the proposed methods enable one to establish the relationships between PF-DDRX model parameters and material properties for quantitative prediction and design of grain microstructures and material properties with thermomechanical processes.

In this work, we combined phase field method and crystal plasticity to study the effects of initial grain structures, recrystallized grain orientation, and strain rates on dynamic recrystallization and deformation behavior under stress states typical of the Shear Assisted Processing and Extrusion (ShAPE) process. The geometrically necessary dislocation density was used as the nucleation criterion for recrystallization, and the minimization of the deformation energy drove the growth of the recrystallized grains. With the set of material properties and model parameters, the simulation results demonstrate that (1) a polycrystalline structure with the texture observed in ShAPE process has the lowest yield stress under the ShAPE stress conditions, (2) the recrystallized grains with the texture observed in ShAPE process largely soften the materials, and (3) higher shear strain rate or rotation speed results in larger magnitude of material softening.

A monolithic fuel design based on a U–Mo alloy has been selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). An issue with U–Mo monolithic fuel is the large amount of swelling that takes place during operation. The accurate prediction of fuel evolution under irradiation requires implementation of correct thermodynamic properties into mesoscale and continuum level fuel performance modeling codes. However, the thermodynamic properties of the fission gas bubbles (such as the relationship among bubble size, equilibrium Xe concentration, and bubble pressure) are not well known. This work studies Xe bubbles in γU-Mo from a diameter of 3 nm up to 8.5 nm and from 400 K up to 700 K. The energetic relationship of Xe bubbles with regard to voids and Xe substitutional atoms is described. The transition is also determined for when a bubble becomes over-pressurized. Finally, an equation of state is fit to the pressure as a function of molar volume and temperature.

The Potts Model was used to simulate the post-recrystallization grain growth behavior of U-10 wt% Mo (U–10Mo). The fabrication process for monolithic U–10Mo fuels involves multiple stages of rolling, during which spatially heterogeneous distributions of second phase particles form in the alloy microstructure. These particles can strongly affect the post-recrystallization grain growth process. Absent particle dissolution effects, U–10Mo grain growth has been observed stagnating at increasing grain size with increasing annealing temperature. In this work, we simulate this effect in the Potts Model by making adjustments to the non-physical Monte Carlo temperature. This modification was used to account for the weakening pinning effect of the second phases with elevated annealing temperature. Simulated average grain sizes and grain size distributions were compared with experimentally obtained results for 700 °C, 800 °C, and 900 °C anneals of duration up to 240 h. These simulations achieved reasonable agreement with experimentally observed grain growth behavior, but showed narrower grain size distributions. It is believed that this disagreement originates from the formation of bands of second-phase particles during rolling. These results demonstrate the capability to evaluate the post-recrystallization grain growth behavior for U–10Mo as a function of previous homogenization, rolling, and annealing treatments.

In nuclear pressure vessel steels, some alloy elements, such as Mn, Ni and Cr, can improve the mechanical and radiation resistance performances. Experiments have shown, however, that these elements will segregate and lead to clusters in the matrix after neutron/ion radiation. These segregation/clusters will reduce the toughness in the material. In this work, we simulated the radiation-induced segregation (RIS) along the ion path in bcc Fe–1.4at.%Mn–0.7at.%Ni alloys and Fe–1.7%Cr–3.3%Ni alloys currently according to RPV steel, to study the ion irradiation induced segregation of Cr/Mn and Ni, using the framework of reaction rate-theory modeling. The simulation results are compared with experiment results and demonstrated that Cr, Mn, Ni segregate along the ion irradiation path. These results are consistent with both the theoretical simulation and experimental observations.

This work presents a numerical method to assess the relative impact of various microstructural features including grain sizes, nanometer scale intragranular gas bubbles, and larger intergranular gas bubbles in irradiated U–Mo metallic fuels on the effective thermal conductivity. A phase-field model was employed to construct a three-dimensional polycrystalline U–Mo fuel alloy with a given crystal morphology and gas bubble microstructures. An effective thermal conductivity “concept” was taken to capture the effect of polycrystalline structures and gas bubble microstructures with significant size differences on the thermal conductivity. The thermal conductivity of inhomogeneous materials was calculated by solving the heat transport equation. The obtained results are in reasonably good agreement with experimental measurements made on irradiated U–Mo fuel samples containing similar microstructural features. The developed method can be used to predict the thermal conductivity degradation in operating nuclear fuels if the evolution of microstructures is known during operation of the fuel.

As a candidate material for fusion reactor applications, silicon carbide (SiC) undergoes transmutation reactions under high-energy neutron irradiation with magnesium as the major metallic transmutant; the others include aluminum, beryllium and phosphorus in addition to helium and hydrogen gaseous species. The impact of these transmutants on SiC structural stability is currently unknown. This study uses ion implantation to introduce Mg into SiC. Multiaxial ion-channeling analysis of the as-produced damage state suggests that there are preferred Si interstitial splits. The microstructure of the annealed sample was examined using high-resolution scanning transmission electron microscopy. The results show a high concentration of likely non-faulted tetrahedral voids and possible stacking fault tetrahedra near the damage peak. In addition to lattice distortion, dislocations and intrinsic and extrinsic stacking faults are also observed. Magnesium in 3C-SiC prefers to substitute for Si and it forms precipitates of cubic Mg2Si and tetragonal MgC2. The diffusion coefficient of Mg in 3C-SiC single crystal at 1573 K has been determined to be 3.8±0.4×10e-19 m2/sec.

Density functional theory (DFT) is used to calculate the thermodynamic and kinetic properties of transmutant Mg in 3C–SiC due to high-energy neutron irradiation associated with the fusion nuclear environment. The formation and binding energies of intrinsic defects, Mg-related defects, and clusters in 3C–SiC are systematically calculated. The minimum energy paths and activation energies during point defect migration and small cluster evolution are studied using a generalized solid-state nudged elastic band (G-SSNEB) method with DFT energy calculations. Stable defect structures and possible defect migration mechanisms are identified. The evolution of binding energies during Mg2Si formation demonstrates that the formation of Mg2Si needs to overcome a critical nucleus size and nucleation barrier. It is found that C vacancies promote the formation of the Mg2Si nucleus, and formation of which results in a compressive stress field around the nucleus. These data are important inputs in meso- and macro-scale modeling and experiments to understand and predict the impact of Mg on phase stability, microstructure evolution, and performance of SiC and SiC-based materials during long-term neutron exposures.

Nonlinear ultrasonic technique is one of several promising nondestructive evaluation methods for monitoring the evolution of nanosized defects such as radiation-induced defects in nuclear materials. In this work, a microstructure-based phase-field model of dynamic deformation in elastically nonlinear materials has been developed for investigating the dynamic interaction between distributed defects and a propagating longitudinal sound wave. With the model, the effect of second phase precipitates’ size and properties on the nonlinearity parameter β that describes the magnitude of the 2nd harmonic wave was simulated. The results showed that (1) the nonlinearity parameter β increases as the elastic inhomogeneity increases regardless of whether the precipitates are softer or harder than the matrix; (2) β linearly increases with the increase of lattice mismatch strain; and (3) for a given volume fraction of second phase precipitates, β strongly depends on the precipitate size. The predicted precipitate size dependence of β agrees with the experimental data. These results demonstrate that the developed model enables one to predict the contributions of different nonlinear sources to β, to explain the signal physics behind the measured nonlinear ultrasonic response, and to guide the development of nonlinear ultrasound nondestructive detection of material defects in nuclear reactor materials.

The diffusion properties of He interstitials and He clusters in the bulk and grain boundaries (GBs) of α-Fe have been studied using molecular dynamics with a newly developed Fe–He potential. The low migration energy barrier for a single He interstitial in the bulk is consistent with that obtained using ab initio methods. Small He clusters can migrate at low temperatures, but at higher temperatures they will kick out a self-interstitial atom (SIA) and become trapped by the vacancy, forming an He-vacancy complex. It is of great interest to note that small He n -vacancy clusters ( n n clusters ( n ∼ 1–10) can easily kick out an SIA, and become trapped by the vacancy, while the SIA quickly diffuses away from the clusters, disappearing into the GB, such that de-trapping of the He clusters by absorbing an SIA is less likely to occur. This suggests that small He clusters may be treated as relatively immobile defects in GBs. The different behavior of He clusters in the bulk compared to their behavior in GBs may explain the different He bubble sizes experimentally observed in the bulk and in GBs in reduced activation ferritic/martensitic steels that have been simultaneously neutron irradiated and He implanted.

There is increased interest in improved methods for in situ non-destructive interrogation of materials for nuclear reactors in order to ensure reactor safety and quantify material degradation (particularly embrittlement) prior to failure. Therefore, a prototypical ferritic/martensitic alloy, HT-9, of interest to the nuclear materials community was investigated to assess microstructure effects on micromagnetics measurements (Barkhausen noise emission, magnetic hysteresis measurements, and first order reversal curve analysis) for samples undergoing three different heat treatments. Microstructural and physical measurements consisted of high precision density, resonant ultrasound elastic constant, Vickers microhardness, grain size, and texture determination. These were varied in the HT-9 alloy samples and related to various magnetic signatures. In parallel, a mesoscale microstructure model was created for α-iron and the effects of polycrystallinity and the demagnetization factor were explored. It was observed that Barkhausen noise emission decreased with increasing hardness and decreasing grain size (lath spacing), while coercivity increased. The results are discussed in terms of the use of magnetic signatures for the non-destructive interrogation of radiation damage and other microstructural changes in ferritic/martensitic alloys.

Atomistic simulations of the nucleation of He clusters and bubbles in bcc iron at 800 K have been carried out using the newly developed Fe–Fe interatomic potential, along with Ackland potential for the Fe–Fe interactions. Microstructure changes were analyzed in detail. We found that a He cluster with four He atoms is able to push out an iron interstitial from the cluster, creating a Frenkel pair. Small He clusters and self-interstitial atom (SIA) can migrate in the matrix, but He-vacancy (He-V) clusters are immobile. Most SIAs form clusters, and only the dislocation loops with a Burgers vector of b = 1/2 appear in the simulations. SIA clusters (or loops) are attached to He-V clusters for He implantation up to 1372 appm, while the He-V cluster–loop complexes with more than one He-V cluster are formed at the He concentration of 2057 appm and larger.

A phase-field model is developed to investigate the influence of microstructure, thermodynamic and kinetic properties, and charging conditions on charged particle transport in nanocomposite electrodes. Two sets of field variables are used to describe the microstructure. One is comprised of the order parameters describing size, orientation and spatial distributions of nanoparticles, and the other is comprised of the concentrations of mobile species. A porous nanoparticle microstructure filled with electrolyte is taken as a model system to test the phase-field model. Inhomogeneous and anisotropic dielectric constants and mobilities of charged particles, and stresses associated with lattice deformation due to Li-ion insertion/extraction are considered in the model. Iteration methods are used to find the elastic and electric fields in an elastically and electrically inhomogeneous medium. The results demonstrate that the model is capable of predicting charge separation associated with the formation of a double layer at the electrochemical interface between solid and electrolyte, and the effect of microstructure, inhomogeneous and anisotropic thermodynamic and kinetic properties, charge rates, and stresses on voltage versus current density and capacity during charging and discharging.

Early experimental data on void swelling in electron-irradiated materials disagree with the dislocation bias models based on the dislocation-point defect elastic interactions. Later, this became one of the factors that prompted the development of models based on production bias (PBM) as the main driver for swelling, which assumed that the dislocation bias was much lower than that predicted by theoretical analyses of dislocation bias. However, the PBM in its present form fails to account for important and common observations, namely, the indefinite void growth often observed under cascade irradiation and the swelling saturation observed under high-dose irradiation and in void lattices. In this paper, we show that these contradictions can be naturally resolved in the framework of the rate theory that accounts for the radiation-induced vacancy emission from extended defects, such as voids, dislocations and grain boundaries. This modification introduces a new bias type in the theory, namely, the emission bias. This modified rate theory agrees well with the experimental data and demonstrates that the original dislocation bias should be used in rate theory models along with the emission bias in different irradiation environments. The modified theory predictions include, but are not limited to, the radiation-induced annealing of voids, swelling saturation under high-dose irradiation, generally, and in void lattices, in particular.

The purpose of this document is to provide a theoretical framework for (1) estimating uranium carbide (UC) volume fraction in a final alloy of uranium with 10 weight percent molybdenum (U-10Mo) as a function of final alloy carbon concentration, and (2) estimating effective 235U enrichment in the U-10Mo matrix after accounting for loss of 235U in forming UC. This report will also serve as a theoretical baseline for effective density of as-cast low-enriched U-10Mo alloy. Therefore, this report will serve as the baseline for quality control of final alloy carbon content

Rational design of silicon and carbon nanocomposite with a special topological feature has been demonstrated to be a feasible way for mitigating the capacity fading associated with the large volume change of silicon anode in lithium ion batteries. Although the lithiation behavior of silicon and carbon as individual components has been well understood, lithium ion transport behavior across a network of silicon and carbon is still lacking. In this paper, we probe the lithiation behavior of silicon nanoparticles attached to and embedded in a carbon nanofiber using in situ TEM and continuum mechanical calculation. We found that aggregated silicon nanoparticles show contact flattening upon initial lithiation, which is characteristically analogous to the classic sintering of powder particles by a neck-growth mechanism. As compared with the surface-attached silicon particles, particles embedded in the carbon matrix show delayed lithiation. Depending on the strength of the carbon matrix, lithiation of the embedded silicon nanoparticles can lead to the fracture of the carbon fiber. These observations provide insights on lithium ion transport in the network-structured composite of silicon and carbon and ultimately provide fundamental guidance for mitigating the failure of batteries due to the large volume change of silicon anodes.