Enhanced Generic Phase-field Model of Irradiation Materials: Fission Gas Bubble Growth Kinetics in Polycrystalline UO2

Experiments show that inter-granular and intra-granular gas bubbles have different growth kinetics which results in heterogeneous gas bubble microstructures in irradiated nuclear fuels. A science-based model predicting the heterogeneous microstructure evolution kinetics is desired, which enables one to study the effect of thermodynamic and kinetic properties of the system on gas bubble microstructure evolution kinetics and morphology, improve the understanding of the formation mechanisms of heterogeneous gas bubble microstructure, and provide the microstructure to macroscale approaches to study their impact on thermo-mechanical properties such as thermo-conductivity, gas release, volume swelling, and cracking. In our previous report 'Mesoscale Benchmark Demonstration, Problem 1: Mesoscale Simulations of Intra-granular Fission Gas Bubbles in UO2 under Post-irradiation Thermal Annealing', we developed a phase-field model to simulate the intra-granular gas bubble evolution in a single crystal during post-irradiation thermal annealing. In this work, we enhanced the model by incorporating thermodynamic and kinetic properties at grain boundaries, which can be obtained from atomistic simulations, to simulate fission gas bubble growth kinetics in polycrystalline UO2 fuels. The model takes into account of gas atom and vacancy diffusion, vacancy trapping and emission at defects, gas atom absorption and resolution at gas bubbles, internal pressure in gas bubbles, elastic interaction between defects and gas bubbles, and the difference of thermodynamic and kinetic properties in matrix and grain boundaries. We applied the model to simulate gas atom segregation at grain boundaries and the effect of interfacial energy and gas mobility on gas bubble morphology and growth kinetics in a bi-crystal UO2 during post-irradiation thermal annealing. The preliminary results demonstrate that the model can produce the equilibrium thermodynamic properties and the morphology of gas bubbles at grain boundaries for given grain boundary properties. More validation of the model capability in polycrystalline is underway

Simulating Interface Growth and Defect Generation in CZT – Simulation State of the Art and Known Gaps

This one-year, study topic project will survey and investigate the known state-of-the-art of modeling and simulation methods suitable for performing fine-scale, fully 3-D modeling, of the growth of CZT crystals at the melt-solid interface, and correlating physical growth and post-growth conditions with generation and incorporation of defects into the solid CZT crystal. In the course of this study, this project will also identify the critical gaps in our knowledge of modeling and simulation techniques in terms of what would be needed to be developed in order to perform accurate physical simulations of defect generation in melt-grown CZT. The transformational nature of this study will be, for the first time, an investigation of modeling and simulation methods for describing microstructural evolution during crystal growth and the identification of the critical gaps in our knowledge of such methods, which is recognized as having tremendous scientific impacts for future model developments in a wide variety of materials science areas

PROGRESS ON GENERIC PHASE-FIELD METHOD DEVELOPMENT

In this report, we summarize our current collobarative efforts, involving three national laboratories: Idaho National Laboratory (INL), Pacific Northwest National Laboratory (PNNL) and Los Alamos National Laboatory (LANL), to develop a computational framework for homogenous and heterogenous nucleation mechanisms into the generic phase-field model. During the studies, the Fe-Cr system was chosen as a model system due to its simplicity and availability of reliable thermodynamic and kinetic data, as well as the range of applications of low-chromium ferritic steels in nuclear reactors. For homogenous nucleation, the relavant parameters determined from atomistic studies were used directly to determine the energy functional and parameters in the phase-field model. Interfacial energy, critical nucleus size, nucleation rate, and coarsening kinetics were systematically examined in two- and three- dimensional models. For the heteregoneous nucleation mechanism, we studied the nucleation and growth behavior of chromium precipitates due to the presence of dislocations. The results demonstrate that both nucleation schemes can be introduced to a phase-field modeling algorithm with the desired accuracy and computational efficiency

Investigation of Uranium Polymorphs

The UO3-water system is complex and has not been fully characterized, even though these species are common throughout the nuclear fuel cycle. As an example, most production schemes for UO3 result in a mixture of up to six or more different polymorphic phases, and small differences in these conditions will affect phase genesis that ultimately result in measureable changes to the end product. As a result, this feature of the UO3-water system may be useful as a means for determining process history. This research effort attempts to better characterize the UO3-water system with a variety of optical techniques for the purpose of developing some predictive capability for estimating process history in polymorphic phases of unknown origin. Three commercially relevant preparation methods for the production of UO3 were explored. Previously unreported low temperature routes to β- and γ-UO3 were discovered. Raman and fluorescence spectroscopic libraries were established for pure and mixed polymorphic forms of UO3 in addition to the common hydrolysis products of UO3. An advantage of the sensitivity of optical fluorescence microscopy over XRD has been demonstrated. Preliminary aging studies of the α and γ forms of UO3 have been conducted. In addition, development of a 3-D phase field model used to predict phase genesis of the system was initiated. Thermodynamic and structural constants that will feed the model have been gathered from the literature for most of the UO3 polymorphic phases

Materials Degradation and Detection (MD2): Deep Dive Final Report

An effort is underway at Pacific Northwest National Laboratory (PNNL) to develop a fundamental and general framework to foster the science and technology needed to support real-time monitoring of early degradation in materials used in the production of nuclear power. The development of such a capability would represent a timely solution to the mounting issues operators face with materials degradation in nuclear power plants. The envisioned framework consists of three primary and interconnected “thrust” areas including 1) microstructural science, 2) behavior assessment, and 3) monitoring and predictive capabilities. A brief state-of-the-art assessment for each of these core technology areas is discussed in the paper

Mesoscale Benchmark Demonstration Problem 1: Mesoscale Simulations of Intra-granular Fission Gas Bubbles in UO2 under Post-irradiation Thermal Annealing

A study was conducted to evaluate the capabilities of different numerical methods used to represent microstructure behavior at the mesoscale for irradiated material using an idealized benchmark problem. The purpose of the mesoscale benchmark problem was to provide a common basis to assess several mesoscale methods with the objective of identifying the strengths and areas of improvement in the predictive modeling of microstructure evolution. In this work, mesoscale models (phase-field, Potts, and kinetic Monte Carlo) developed by PNNL, INL, SNL, and ORNL were used to calculate the evolution kinetics of intra-granular fission gas bubbles in UO2 fuel under post-irradiation thermal annealing conditions. The benchmark problem was constructed to include important microstructural evolution mechanisms on the kinetics of intra-granular fission gas bubble behavior such as the atomic diffusion of Xe atoms, U vacancies, and O vacancies, the effect of vacancy capture and emission from defects, and the elastic interaction of non-equilibrium gas bubbles. An idealized set of assumptions was imposed on the benchmark problem to simplify the mechanisms considered. The capability and numerical efficiency of different models are compared against selected experimental and simulation results. These comparisons find that the phase-field methods, by the nature of the free energy formulation, are able to represent a larger subset of the mechanisms influencing the intra-granular bubble growth and coarsening mechanisms in the idealized benchmark problem as compared to the Potts and kinetic Monte Carlo methods. It is recognized that the mesoscale benchmark problem as formulated does not specifically highlight the strengths of the discrete particle modeling used in the Potts and kinetic Monte Carlo methods. Future efforts are recommended to construct increasingly more complex mesoscale benchmark problems to further verify and validate the predictive capabilities of the mesoscale modeling methods used in this study

Millets across Eurasia: chronology and context of early records of the genera Panicum and Setaria from archaeological sites in the Old World

We have collated and reviewed published records of the genera Panicum and Setaria (Poaceae), including the domesticated millets Panicum miliaceum L. (broomcorn millet) and Setaria italica (L.) P. Beauv. (foxtail millet) in pre-5000 cal b.c. sites across the Old World. Details of these sites, which span China, central-eastern Europe including the Caucasus, Iran, Syria and Egypt, are presented with associated calibrated radiocarbon dates. Forty-one sites have records of Panicum (P. miliaceum, P. cf. miliaceum, Panicum sp., Panicum type, P. capillare (?) and P. turgidum) and 33 of Setaria (S. italica, S. viridis, S. viridis/verticillata, Setaria sp., Setaria type). We identify problems of taphonomy, identification criteria and reporting, and inference of domesticated/wild and crop/weed status of finds. Both broomcorn and foxtail millet occur in northern China prior to 5000 cal b.c.; P. miliaceum occurs contemporaneously in Europe, but its significance is unclear. Further work is needed to resolve the above issues before the status of these taxa in this period can be fully evaluated

Phase-field Model for Interstitial Loop Growth Kinetics and Thermodynamic and Kinetic Models of Irradiated Fe-Cr Alloys

Microstructure evolution kinetics in irradiated materials has strongly spatial correlation. For example, void and second phases prefer to nucleate and grow at pre-existing defects such as dislocations, grain boundaries, and cracks. Inhomogeneous microstructure evolution results in inhomogeneity of microstructure and thermo-mechanical properties. Therefore, the simulation capability for predicting three dimensional (3-D) microstructure evolution kinetics and its subsequent impact on material properties and performance is crucial for scientific design of advanced nuclear materials and optimal operation conditions in order to reduce uncertainty in operational and safety margins. Very recently the meso-scale phase-field (PF) method has been used to predict gas bubble evolution, void swelling, void lattice formation and void migration in irradiated materials,. Although most results of phase-field simulations are qualitative due to the lake of accurate thermodynamic and kinetic properties of defects, possible missing of important kinetic properties and processes, and the capability of current codes and computers for large time and length scale modeling, the simulations demonstrate that PF method is a promising simulation tool for predicting 3-D heterogeneous microstructure and property evolution, and providing microstructure evolution kinetics for higher scale level simulations of microstructure and property evolution such as mean field methods. This report consists of two parts. In part I, we will present a new phase-field model for predicting interstitial loop growth kinetics in irradiated materials. The effect of defect (vacancy/interstitial) generation, diffusion and recombination, sink strength, long-range elastic interaction, inhomogeneous and anisotropic mobility on microstructure evolution kinetics is taken into account in the model. The model is used to study the effect of elastic interaction on interstitial loop growth kinetics, the interstitial flux, and sink strength of interstitial loop for interstitials. In part II, we present a generic phase field model and discuss the thermodynamic and kinetic properties in phase-field models including the reaction kinetics of radiation defects and local free energy of irradiated materials. In particular, a two-sublattice thermodynamic model is suggested to describe the local free energy of alloys with irradiated defects. Fe-Cr alloy is taken as an example to explain the required thermodynamic and kinetic properties for quantitative phase-field modeling. Finally the great challenges in phase-field modeling will be discussed

Phase-field Model for Interstitial Loop Growth Kinetics and Thermodynamic and Kinetic Models of Irradiated Fe-Cr Alloys

Microstructure evolution kinetics in irradiated materials has strongly spatial correlation. For example, void and second phases prefer to nucleate and grow at pre-existing defects such as dislocations, grain boundaries, and cracks. Inhomogeneous microstructure evolution results in inhomogeneity of microstructure and thermo-mechanical properties. Therefore, the simulation capability for predicting three dimensional (3-D) microstructure evolution kinetics and its subsequent impact on material properties and performance is crucial for scientific design of advanced nuclear materials and optimal operation conditions in order to reduce uncertainty in operational and safety margins. Very recently the meso-scale phase-field (PF) method has been used to predict gas bubble evolution, void swelling, void lattice formation and void migration in irradiated materials,. Although most results of phase-field simulations are qualitative due to the lake of accurate thermodynamic and kinetic properties of defects, possible missing of important kinetic properties and processes, and the capability of current codes and computers for large time and length scale modeling, the simulations demonstrate that PF method is a promising simulation tool for predicting 3-D heterogeneous microstructure and property evolution, and providing microstructure evolution kinetics for higher scale level simulations of microstructure and property evolution such as mean field methods. This report consists of two parts. In part I, we will present a new phase-field model for predicting interstitial loop growth kinetics in irradiated materials. The effect of defect (vacancy/interstitial) generation, diffusion and recombination, sink strength, long-range elastic interaction, inhomogeneous and anisotropic mobility on microstructure evolution kinetics is taken into account in the model. The model is used to study the effect of elastic interaction on interstitial loop growth kinetics, the interstitial flux, and sink strength of interstitial loop for interstitials. In part II, we present a generic phase field model and discuss the thermodynamic and kinetic properties in phase-field models including the reaction kinetics of radiation defects and local free energy of irradiated materials. In particular, a two-sublattice thermodynamic model is suggested to describe the local free energy of alloys with irradiated defects. Fe-Cr alloy is taken as an example to explain the required thermodynamic and kinetic properties for quantitative phase-field modeling. Finally the great challenges in phase-field modeling will be discussed

Enhanced Generic Phase-field Model of Irradiation Materials: Fission Gas Bubble Growth Kinetics in Polycrystalline UO2

Experiments show that inter-granular and intra-granular gas bubbles have different growth kinetics which results in heterogeneous gas bubble microstructures in irradiated nuclear fuels. A science-based model predicting the heterogeneous microstructure evolution kinetics is desired, which enables one to study the effect of thermodynamic and kinetic properties of the system on gas bubble microstructure evolution kinetics and morphology, improve the understanding of the formation mechanisms of heterogeneous gas bubble microstructure, and provide the microstructure to macroscale approaches to study their impact on thermo-mechanical properties such as thermo-conductivity, gas release, volume swelling, and cracking. In our previous report 'Mesoscale Benchmark Demonstration, Problem 1: Mesoscale Simulations of Intra-granular Fission Gas Bubbles in UO2 under Post-irradiation Thermal Annealing', we developed a phase-field model to simulate the intra-granular gas bubble evolution in a single crystal during post-irradiation thermal annealing. In this work, we enhanced the model by incorporating thermodynamic and kinetic properties at grain boundaries, which can be obtained from atomistic simulations, to simulate fission gas bubble growth kinetics in polycrystalline UO2 fuels. The model takes into account of gas atom and vacancy diffusion, vacancy trapping and emission at defects, gas atom absorption and resolution at gas bubbles, internal pressure in gas bubbles, elastic interaction between defects and gas bubbles, and the difference of thermodynamic and kinetic properties in matrix and grain boundaries. We applied the model to simulate gas atom segregation at grain boundaries and the effect of interfacial energy and gas mobility on gas bubble morphology and growth kinetics in a bi-crystal UO2 during post-irradiation thermal annealing. The preliminary results demonstrate that the model can produce the equilibrium thermodynamic properties and the morphology of gas bubbles at grain boundaries for given grain boundary properties. More validation of the model capability in polycrystalline is underway