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At least 325 records · Page 18

Phase-field simulation of irradiated metals Part II : Gas bubble kinetics.

The phase-field model developed in Part I of this work is expanded to include fission gas generation, diffusion, and segregation within bubbles nucleated both homogeneously and heterogeneously along grain boundaries. Illustrative results are presented that characterize bubble growth and shrinkage, as well as the bubble density, size and nucleation rate as a function of the irradiation conditions. Finally, intergranular bubble characteristics such as shape, pinning energy and bubble density are investigated.

36 MATERIALS SCIENCE↗

Understanding grain boundary segregation under irradiation: A mesoscale modeling study

Grain boundaries (GBs) are an important component in the design of irradiation resistant materials as they play a crucial role as point defect sinks for non-equilibrium vacancies and self-interstitials. However, in the presence of sustained point defect fluxes, the coupled transport of atomic components with inherently different diffusivities often leads to radiation-induced segregation (RIS), with undesired effects on properties such as intergranular corrosion and stress-assisted cracking. In this talk, we investigate the fundamental mechanisms leading to GB segregation in BCC FeCr-based alloys using multiscale modeling and experiments. A phase-field model is employed to account for both thermodynamic and kinetic segregation mechanisms. The full Onsager transport matrix is derived using kinetic Monte Carlo, molecular dynamics, and kinetic cluster expansion (KineCluE) calculations. The thermodynamics of GB segregation is described via an atomic density-based modification to the CALPHAD free energy. The modeling predictions are then compared against segregation data from atom probe characterization for various temperatures, compositions, and neutron irradiation conditions. We will conclude by discussing the utility of the multiscale modeling approach to shed light on the fundamental mechanisms leading to solute-GB interaction.

36 MATERIALS SCIENCE↗

Focused Ion Beam Tomography of Alloy 617 Corroded in Molten Chloride Salt

Materials qualification of reactor structural materials is a critical step in rapid implementation of advanced nuclear reactor technologies, particularly to assess the corrosion performance in these designs. Accelerated qualification of reactor structural materials requires incorporating powerful computational toolsets, such as phase field modelling in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, to predict the evolution of structural materials due to corrosion. Accordingly, computational toolsets will require experimental data generated at appropriate length scales to validate accuracy. Focused ion beam (FIB) provides a high degree of control over manipulation of materials for analytical purposes, including capturing data on the evolution in the microstructure and elemental composition of materials at the mesoscale, an appropriate length scale for phase field modelling of intergranular diffusion phenomena using the MOOSE framework. For instance, the FEI Helios G4 UX dual beam plasma FIB microscope at the Irradiated Materials Characterization Laboratory (IMCL) is capable of backscatter diffraction (EBSD) and energy-dispersive x-ray spectroscopy (EDS) documenting the evolution in the microstructure and elemental composition, respectively. The Helios can perform EDS and EBSD three-dimensionally (3D) using tomography, which is then combined using different software packages to visualize 3D volumes correlating elemental composition to microstructural data. The purpose of this investigation was to develop a streamlined characterization and data processing workflow for 3D tomography studies on the FEI Helios G4 plasma FIB. The investigation is segmented into three parts: 1) Optimizing the data collection workflow, 2) identifying appropriate data processing and visualization software (i.e. DREAM.3D, MIPAR, and VGStudioMax), and 3) establishing an infrastructure for public release. The optimization of the data collection workflow is in collaboration with members of the U220 department to setup formal training on the tomography operation of the G4, through ThermoFisher Scientific, and exploring DREAM.3D, MIPAR, and VGStudioMax data processing/visualization software packages. VGStudioMax currently demonstrates the most promise for future use. Optimization of the data collection and processing workflow is still ongoing. A collaboration with INL High Performance Computing (HPC) established an open-source license for expediting the public release of FIB tomography datasets through HPC. FIB tomography data generated by the G4 will provide comprehensive data for validating 3D phase field mesoscale modelling tools within the MOOSE framework for accelerated qualification of reactor structural materials.

Copeland-Johnson, Trishelle↗

Phase-field simulation of irradiated metals Part 1: Void kinetics.

We present a phase-field model of void formation and evolution in irradiated metals by spatially and temporally evolving vacancy and self-interstitial concentration fields. By incorporating a coupled set of Cahn-Hilliard and Allen-Cahn equations, the model captures the processes of point defect generation and recombination, annihilation of defects at sinks, as well as void nucleation and growth in the presence of grain boundaries. Illustrative results are presented that characterize the rate of void growth or shrinkage due to supersaturated vacancy or interstitial concentrations, void nucleation and growth kinetics due to cascade-induced defect production, as well as void denuded and peak zones adjacent to grain boundaries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics

Under a pure tensile loading, cracks in brittle, isotropic, and homogeneous materials often propagate such that pure mode I kinematics are maintained at the crack tip. However, experiments performed on geo-materials, such as sedimentary rock, shale, mudstone, concrete and gypsum, often lead to the conclusion that the mode I and mode II critical fracture energies/surface energy release rates are distinctive. This distinction has great influence on the formation and propagation of wing cracks and secondary cracks from pre-existing flaws under a combination of shear and tensile or shear and compressive loadings. To capture the mixed-mode fracture propagation, a mixed-mode I/II fracture model that employs multiple critical energy release rates based on Shen and Stephansson, IJRMMS, 1993 is reformulated in a regularized phase field fracture framework. Here we obtain the mixed-mode driving force of the damage phase field by balancing the microforce. Meanwhile, the crack propagation direction and the corresponding kinematics modes are determined via a local fracture dissipation maximization problem. Several numerical examples that demonstrate mode II and mixed-mode crack propagation in brittle materials are presented. Possible extensions of the model capturing degradation related to shear/compressive damage, as commonly observed in sub-surface applications and triaxial compression tests, are also discussed.

42 ENGINEERING↗

Phase field benchmark problems for dendritic growth and linear elasticity

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem for solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.

36 MATERIALS SCIENCE↗

Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT

In this paper, we present a novel rapid phase-field model development capability using a modular free energy based approach in the finite element based MOOSE framework. The phase-field equations are implemented in a general form as separate code form the model specific data such as the thermodynamic free energy density and mobility functions. This isolates researchers from complicated code and allows them to focus on implementing new material models. In addition, using a native symbolic differentiation algorithm, all required derivatives of the free energy density are automatically determined, removing sources for potential human error, and guaranteeing optimally preconditioned equation systems through fully populated Jacobian matrices. Free energy terms contributing to a phase-field model are abstracted into self contained objects that can be combined at will at simulation run time. Combining multiple chemical and mechanical free energy contributions allows the construction of coupled phase-field, mechanics, and multiphase models. Through just-in-time compilation, we greatly reduce the computational time required to evaluate the differentiated expressions. Lastly, we demonstrate the new capability on a variety of example simulations.

97 MATHEMATICS AND COMPUTING↗

Nonequilibrium Thermodynamics of Hydrate Growth on a Gas-Liquid Interface

We develop a continuum-scale phase-field model to study gas-liquid-hydrate systems far from thermodynamic equilibrium. We design a Gibbs free energy functional for methane-water mixtures that recovers the isobaric temperature-composition phase diagram under thermodynamic equilibrium conditions. The proposed free energy is incorporated into a phase-field model to study the dynamics of hydrate formation on a gas-liquid interface. We elucidate the role of initial aqueous concentration in determining the direction of hydrate growth at the interface, in agreement with experimental observations. Our model also reveals two stages of hydrate growth at an interface—controlled by a crossover in how methane is supplied from the gas and liquid phases—which could explain the persistence of gas conduits in hydratebearing sediments and other nonequilibrium phenomena commonly observed in natural methane hydrate systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nano {gamma}'/{gamma}'' composite precipitates in Alloy 718

Nanoscale composite precipitates of Alloy 718 have been investigated with both high-resolution scanning transmission electron microscopy and phase field modeling. Chemical analysis via energy-dispersive x-ray spectroscopy allowed for the differentiation of {gamma}' and {gamma}'' particles, which is not otherwise possible through traditional Z-contrast methods. Phase field modeling was applied to determine the stress distribution and elastic interaction around and between the particles, respectively, and it was determined that a composite particle (of both {gamma}' and {gamma}'') has an elastic energy that is significantly lower than, for example, single {gamma}' and {gamma}'' precipitates which are non-interacting.

36 MATERIALS SCIENCE↗

Intrinsic space charge layers and field enhancement in ferroelectric nanojunctions

Conducting characteristics of topological defects in ferroelectric materials, such as charged domain walls, engendered a broad interest on their scientific merit and the possibility of novel applications utilizing domain engineering. At the same time, the problem of electron transport in ferroelectrics still remains full of unanswered questions and becomes yet more relevant over the growing interest in ferroelectric semiconductors and new improper ferroelectric materials. We have employed self-consistent phase-field modeling to investigate the physical properties of a local metal-ferroelectric (Pb(Zr{sub 0.2}Ti{sub 0.8})O{sub 3}) junction in applied electric field. We revealed an up to 10-fold local enhancement of electric field realized by large polarization gradient and over-polarization effects due to inherent non-linear dielectric properties of Pb(Zr{sub 0.2}Ti{sub 0.8})O{sub 3}. The effect is independent of bias polarity and maintains its strength prior, during and after ferroelectric switching. The observed field enhancement can be considered on similar grounds as increased doping level, giving rise to reduced switching bias and threshold voltages for charge injection, electrochemical and photoelectrochemical processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Phase-Field Method Tutorial Codes

This repository contains example implementations of phase-field codes primarily for educational purposes. These codes demonstrate how a simple phase-field models can be implemented as an introduction for researchers new to the area (students, new staff, collaborators from different domains, etc.). The computer code includes highly documented Jupyter notebooks that implement phase-field models and analyze the results.

DeWitt, Stephen [Oak Ridge National Laboratory (@O↗

Grain Growth and Bubble Evolution in U-Mo Alloy by Multiscale Simulations

Increased grain size in U-Mo dispersion fuel is believed to affect the fuel swelling at high fission density. In this work, a multiscale simulation approach combining first-principles calculation and phase-field modeling is used to investigate the grain growth behavior in U-Mo alloys. The material properties of U-Mo alloys predicted by first-principles calculations are incorporated into the mesoscale phase-field models to study the effect of annealing temperature, annealing time and the initial grain structures of fuel particles on the grain growth. The grain growth rate is evaluated and compared with experiment. Meanwhile, the gas bubble evolution kinetics in irradiated U-Mo alloy fuels is investigated to understand its effect on fuel swelling. We systematically examine the effect of Xe, vacancy, and SIA concentration, fission defect generation, and elastic interaction on the growth kinetics of gas bubble. The bubble size distribution and swelling of U-Mo are simulated and compared to experimental measurements.

Mei, Zhi-Gang↗

Multi-Scale Modeling of Swelling in Accident-Tolerant U 3 Si 2 Fuel

U 3 Si 2 is a promising candidate for use as an accident-tolerant fuel for light water reactors. A multi-scale computational approach was used to calculate swelling in pellet-form U 3 Si 2 fuel. Swelling was assumed to be equal to the volume fraction of fission gas bubbles in the fuel, and the evolution of bubble volume fraction was determined from phase-field simulations. To parameterize the phase-field model, density-functional theory and molecular dynamics simulations were performed. To enable molecular dynamics simulations, a new interatomic potential for the U-Si system was developed based on the modified embedded atom method. A new phase-field model based on a grand-potential functional was also developed. The model is applicable to both intergranular and intragranular bubbles. To calculate the volume fraction of bubbles, the microstructure was decomposed into regions consisting of only intragranular or intergranular bubbles based on a truncated octahedral grain structure, and growth of the bubbles in the two regions was simulated separately. The total swelling was then calculated based on a a weighted average of bubble volume fraction in the two regions. Total swelling was of the same order of magnitude, but larger than that predicted by the existing empirical swelling model used in BISON and a rate-theory based model. Limitations of the present approach and suggestions for improvement are presented.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Quantification and prediction of solidification textures under additive manufacturing conditions

Crystallographic textures are a major determinant of the macroscale anisotropic properties of polycrystalline metallic alloys produced in a wide range of additive manufacturing (AM) processes. Here, we introduce a statistical method that can accurately quantify the degree of orientational order of textures despite the large random fluctuations in the orientation of individual grains inherent in AM processes. The method, demonstrated for laser and resolidification of AlSi thin films, extends Z-scoring to a dynamical regime to assess the statistical significance of observed textures compared to randomly generated ones at different stages of solidification. We further show that, combined with phase-field modeling, this method can be used to infer fundamental anisotropic properties of the solid-liquid interface that are essential for texture prediction, and are compared here to the results of atomistic simulations. In addition, phase-field modeling reveals that, even at rapid AM solidification rates, the observed 〈110〉-dominated textures in the AlSi thin films are controlled predominantly by the anisotropy of the interface free-energy and sheds light on the physical mechanism of grain competition. These results significantly enhance both the existing tools for the quantification and prediction of AM crystallographic textures and our basic understanding of their formation.

36 MATERIALS SCIENCE↗

Grain growth in U–7Mo alloy: A combined first-principles and phase field study

Grain size is an important factor in controlling the swelling behavior in irradiated U-Mo dispersion fuels. Increasing the grain size in U-Mo fuel particles by heat treatment is believed to delay the fuel swelling at high fission density. In this work, a multiscale simulation approach combining first-principles calculation and phase field modeling is used to investigate the grain growth behavior in U-7Mo alloy. The density functional theory based first-principles calculations were used to predict the material properties of U-7Mo alloy. The obtained grain boundary energies were then adopted as an input parameter for mesoscale phase field simulations. The effects of annealing temperature, annealing time and initial grain structures of fuel particles on the grain growth in U-7Mo alloy were examined. The predicted grain growth rate was compared well with the empirical correlation derived from experiments.

Mei, Zhi-Gang↗

Phase-field simulations of fission gas bubbles in high burnup UO2 during steady-state and LOCA transient conditions

To improve the economics of commercial nuclear energy generation, U.S. utilities are currently seeking licensing approval to operate UO2 fuel to higher burnups. One significant safety issue that must be addressed to obtain approval is the potential for fine fragmentation/pulverization of the fuel during a loss-of-coolant accident (LOCA). It has been hypothesized this is caused by the rapid increase of pressure in fission gas bubbles in the high burnup region of the fuel. To better understand this phenomenon, a novel phase-field model of the fission gas bubble microstructure in UO2 has been developed and implemented in Idaho National Laboratory's Marmot application for phase-field simulation of nuclear materials. Simulations of bubble growth in the high burnup region during steady-state conditions showed that initially overpressurized bubbles decreased in pressure during growth, but still remained above equilibrium pressure. During a LOCA transient, simulations of bubbles in the high burnup region showed that bubble size did not change significantly, and the pressure increase due to the transient was calculated and passed to a phase-field model of fracture.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

In situ measurement and modelling of the growth and length scale of twins in α -uranium

Twinning is an important deformation mechanism in crystalline materials. Twins nucleate, then grow, forming a discrete pattern of deformation bands with a certain thickness. The mechanism for twin growth is not completely understood. We present a simple phase field model which captures the physics of twin growth and reproduces the details observed during in situ electron backscatter diffraction experiments on α-uranium. The interaction between residual dislocations at twin interfaces and mobile dislocations in untwinned regions increases the stress needed for twin growth. This is described by a nonlocal term in the proposed constitutive equations: the nucleation stress of a twin increases proportionally to the twin phase field in a neighborhood. Competition between slip and twinning favors the nucleation of a new twin rather than the growth of a preexisting twin. The phase field model is coupled with a crystal plasticity finite element solver that includes the plastic deformation due to twinning. Simulations are able to reproduce the number of twins and their thicknesses as a function of the strain observed during in situ electron backscatter diffraction experiments. The stress-strain curve is also reproduced. This comparison allows the values of the nucleation stress and the interaction strength between residual and mobile dislocations to be found. It also gives an estimation of the density of residual dislocations that is consistent with the observed twin thickness. Finally, this model can be applied to understand microstructural effects in materials using twinning as a strengthening mechanism.

36 MATERIALS SCIENCE↗