Future advanced nuclear energy systems are expected to place demands on structural materials that lie well beyond the capabilities of materials used in current designs. Structural materials in proposed fusion and many advanced fission reactor designs would be subject to significantly higher operating temperatures and much larger radiation doses than encountered to date. Nanostructured ferritic alloys (NFAs), which are a variant of oxide dispersion strengthened (ODS) steels, are a very promising candidate alloy class to meet these demanding requirements. The mechanical properties and radiation tolerance of NFAs rely on a dense population of nanometer-scale oxides, generally oxides based on Y and Ti. However, the structure and composition of these nanoprecipitates is still uncertain, as is their stability during extended service under high temperature applications. We address both these questions using ab initio based multiscale models in close collaboration with experiments.
To help clarify the nature of the smallest nanoprecipitates density functional theory calculations are used to investigate the most stable Ti, Y, and O nanocluster computational units in Fe.[1] Two distinct methods for searching for stable nanoclusters are proposed: one in which nanoclusters are restricted to the BCC Fe lattice and one in which the nanocluster structures are strained variants of bulk Ti and Y oxides. We discovered that nanoclusters that are structurally similar to bulk Ti and Y oxides are significantly more stable than nanoclusters that are restricted to the Fe lattice. Consequently, the most stable nanoprecipitates in Ti-Y-O NFAs are more likely to be small oxide phases than coherent solute-enriched clusters.
To understand the thermal stability of nanoprecipitates a model framework is developed for the thermodynamics and kinetics of Y-Ti oxide nucleation, growth and coarsening.[2] The model, which is based upon available thermodynamic and kinetic data as well as key density functional theory calculations, shows that nano-oxide nucleation and growth are highly driven and that pipe diffusion is the dominant mode of their coarsening, in agreement with previous analyses of experimental high temperature data. The model predicts that the nano-oxides are thermally stable for 80 or more years below 1175 K. This analysis also provides insights the effect of O and Ti on nano-oxide sizes, and optimizing the balance of alloy microstructure.
[1] L. Barnard, G. R. Odette, I. Szlufarska, and D. Morgan, An ab initio study of Ti-Y-O nanocluster energetics in nanostructured ferritic alloys, Acta Materialia 60, p. 935-947 (2012).
[2] L. Barnard, N. Cunningham, G. R. Odette, and D. Morgan, Thermodynamic and kinetic modeling of oxide precipitation in nanostructured ferritic alloys, Submitted for publication (2014).

The Oxide Dispersion Strengthened (ODS) steels are promising candidates for structural components of future fusion and advanced fission power plants. However, there are only few systematic studies that are dedicated to well understand oxide particle transformation behaviors (nucleation, growth, coarseninghellip;) in terms of the production processing parameters. It is thus a key issue to have a better control over the industrial production route (powder co-grinding and high-pressure thermo-mechanical treatment).
Ion implantation is a powerful technique to achieve the synthesis of particles in material under well-controlled conditions. It shows thus an alternative way to synthesize nano oxide particles and study their transformation behaviors through selected variation of implantation parameters, thus allowing a better understanding of their mechanisms of formation.
We report here the results of metallic oxide particles formation in high purity Fe-10wt.%Cr steel by ion implantation and subsequent thermal annealing (using JANNuS-Orsay facility, where two accelerators are linked to a Transmission Electron Microscope (TEM)). The nucleation of particles was observed just after ion implantation without any subsequent thermal annealing [1]. This unconventional phenomenon is suggested to be due to the enhanced diffusion of implanted atoms resulting from defects and pipe diffusion along dislocations created during ion implantation. The in situ thermal annealing at 500 °C was sequentially performed with a series of duration. Compositional and structural details of particles before/after thermal annealing have been analyzed by a range of TEM techniques (conventional TEM, high resolution TEM, energy-filtered TEMhellip;) combined with atom probe tomography (APT). The analysis of the experimental results gives also us the average size and number density of particles as a function of the in situ annealing duration. These experimental results are correlated with modeling data in order to clarify the mechanisms governing the formation of these oxide particles. Our study can be fed back into the optimization of the production processing of ODS steels.
[1] C. Zheng et al, Phil. Mag. 94 (2014) p.2937.
Mode of presentation: an oral contribution is highly preferred.

A variety of interesting and useful properties emerges in nano-grained materials because of their enormous grain boundary area. Nano-grained ceramics present excellent radiation tolerance because point defects (created upon radiation cascades) migrate to grain boundary and get absorbed, leaving the grain relatively defect-free. On the other hand, having large volume fraction of grain boundary area makes them closely approaching the enthalpy of amorphous phase. In that case, they become inherently unstable and prone to amorphization without radiation. Usage of dopants can promote nano-stability by reducing grain growth and still can result lower grain boundary energy. So dopant system can show improved radiation tolerance than undoped system.
We studied the effect of dopant (2mol%La) on grain boundary energy of 2La10YSZ and examined radiation tolerance behavior of 2mol%La doped 10mol% Yttria Stabilized Zirconia (2La10YSZ). Grain boundary energy of doped system (in the form of sintered pellets) has been determined by using Differential Scanning Calorimetry (DSC) technique. Scanning Transmission Electron Microscopy (STEM) and Electron Energy Loss Spectroscopy (EELS) has been used to determine grain size distribution and elemental mapping in grain boundary. Then, those pellets had been exposed to 400KeV Kr ion radiation. After radiation, radiation damage morphology is examined by X-ray diffraction and STEM imaging method.
Results indicate that grain growth and grain boundary energy have been reduced substantially with the addition of La. EELS mapping shows that there is segregation of La on the grain boundary of 2La10YS when heated for grain growth. Radiation damage morphology has changed compared to undoped system (10YSZ).

We use high-dose molecular dynamics simulations to study radiation-induced mixing and disordering. Our approach involves sequentially modeling multiple collision cascades to total doses as high as five displacements per atom (dpa). We apply these simulations to low-solubility Cu-Nb bilayers and to coherent Ni-Ni₃Al interfaces. The mixing parameters and disordering rates thereby obtained are in good agreement with low temperature experiments, where thermally activated recovery processes may be neglected. Implications of our findings for the stability of microstructures under irradiation will be discussed.
This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. 2008LANL1026 through the Center for Materials at Irradiation and Mechanical Extremes, an Energy Frontier Research Center at Los Alamos National Laboratory and by the Laboratory Directed Research and Development program at Los Alamos National Laboratory under Project No. 20130118DR, under DOE Contract DE-AC52-06NA253.

Much of the fundamental research on nuclear materials is focused on improving radiation tolerance, to enable both higher burnup in fission reactors as well as developing vessels that can contain the plasma for fusion reactors. One route that has been proposed is to go nano. The high density of interfaces in nanomaterials is expected to provide sinks for radiation-induced defects and thus enhance the tolerance of the material. However, despite extensive research over many years, there are still many fundamental questions about the interaction between interfaces and radiation-induced defects. Here, using Cu as a model material to probe these interactions, we use long-time simulations (including accelerated molecular dynamics and object kinetic Monte Carlo) to examine how grain boundaries influence radiation damage evolution in nanomaterials. We find that grain boundaries do not always promote enhanced tolerance and, in fact, may degrade tolerance for some cases. Further, we show that complex interactions can arise between damaged boundaries and residual defects, interactions that are not present for pristine boundaries. Finally, we examine defect mobility at grain boundaries and tie that mobility to the sink efficiency of the boundary. We find that in-boundary annihilation of defects, which is ultimately controlled by in-boundary defect mobility and depends on both the nature of the defect as well as the grain boundary character, has an important influence on the sink efficiency of the boundary. We discuss the ramifications of these results on the radiation tolerance of nanomaterials more generally.

The age hardening 6061-T6 aluminum alloy has been chosen for the confection of the core-vessel of the new Material Testing Reactor Jules Horowitz. The material is transparent to neutrons and displays good mechanical properties due to the precipitation of needle-shape nano-phases β&’&’-Mg₅Si₆. The alloy also contains submicronic intermetallic phases called Al(Cr,Fe,Mn)Si dispersoids which play a key role in controlling grain growth processes and recrystallization. The RJH core-vessel will be subjected to a high neutron flux. Thus it is crucial to study the effects of irradiation on the phases present in the alloy in order to understand the evolution of mechanical properties.
In this contribution, we present a study on the stability of the Al(Cr,Fe,Mn)Si dispersoids under irradiation by electrons and ions, analyzed by High-Resolution and Energy Filtered Transmission Electron Microscopy (HR- and EF-TEM). TEM samples were irradiated at room temperature by means of 1 MeV electrons and 2 MeV W³⁺ ions, so that the same dispersoids could be analyzed before and after irradiation. The irradiation damage reached 75 dpa (displacement per atom) for electron irradiation and 134 dpa for ion irradiation.
Before irradiation, dispersoids were identified to present a core/shell structure. Cr was observed to segregate towards the interface with the matrix whereas Mn and Fe were located preferentially at the center of the particle. After irradiation by 1 MeV electrons, this core/shell organization was observed to be enhanced, with a sharp interface separating the core from the shell. This result is discussed in terms of Radiation-Enhanced Diffusion (RED). Under electron irradiation, atomic mobility is more likely to result from point defects diffusion rather than from ballistic displacements. It is then proposed that radiation-enhanced diffusion favors the effect of unmixing forces and Cr interface segregation, allowing the system to relax toward the equilibrium core/shell structure. In order to assess the effect of atomic relocation distance on the core/shell stability, ion irradiations were performed. The dispersoid still appear to have a core/shell organization however the (Mn,Fe)/Cr interface is diffuse : (Mn,Fe) and Cr remain mixed on several nanometers at the core/shell interface. It is suggested that the unmixing forces driven by thermally activated diffusion enhance the core/shell organization of the dispersoids whereas ballistic effects prevent the formation of a sharp interface by unmixing forces.

Under heat treatment, maraging steels form coherent NiAl precipitates that can significantly increase the macroscopic strength of the material. The precipitates formed in these materials may act as sinks for defects, similar to oxide-dispersion strengthened steels (ODS). This talk presents computational work aimed at better understanding the role of coherent precipitates in increasing radiation tolerance. Interatomic potentials have been developed for the description of Fe-Ni-Al alloys, to simulate an ideal alloy of bcc iron with NiAl precipitates, and associated Fe/NiAl interfaces. Characteristics and energetics of the interfaces are analyzed, and, finally, radiation damage is induced in proximity to the interface whereafter the effect of the interface on defect accumulation is investigated.

Irradiation can lead to compositional patterning in immiscible alloy systems, resulting in a high density of interfaces that are dynamically stable under irradiation. These interfaces can facilitate point defect trapping and elimination, and thus provide greatly enhanced radiation resistance. Two types of compositional patterning have been investigated by modeling and by experiments, the first one relying on the dynamical competition between irradiation induced chemical mixing and irradiation enhanced diffusion, the second one relying on intracascade precipitation. In this presentation, we will first demonstrate how these reactions can be used to obtain complex nanostructured alloys that are highly resistant to coarsening under annealing and irradiation at elevated temperature. Predictions obtained from kinetic Monte Carlo simulations will be confronted with experimental results on model alloy systems. In the second part of the presentation, we will present our recent work on phase field modeling of alloys under irradiation, and on the derivation of quantitative kinetic transport coefficients that can be integrated into such phase field models in order to increase their predictive power.

Reactor materials must withstand irradiation to extremely high doses while under stress at high temperature and in aggressive environments. Cladding and structural materials in fast reactors and fusion reactors will reach 200 dpa, and concepts such as the Traveling Wave Reactor could reach in excess of 500 dpa. Ion irradiation has the potential to reach high dose levels in comparatively short amounts of time, at low cost and with minimal sample activation, providing an ideal path for studying microstructure evolution to high dose.
Evolution of the irradiated microstructure (dislocation loops, voids, and radiation-induced precipitates (RIP)) in ferritic-martensitic (F-M) steels T91, HT9 and HCM12A was studied using 5 MeV Fe⁺⁺ (self-ion)-irradiation to high doses (>100 dpa) in the temperature range 400-500°C with and without He pre-implantation. Samples for transmission electron microscopy and atom probe tomography were prepared by the focused ion beam (FIB) lift-out method and used to characterize dislocation microstructure, voids and precipitates.
Results showed that the dislocation microstructure developed rapidly and was relatively stable with increasing dose. However, precipitates and voids continued to evolve to high dose. Ni/Si/Mn-rich, Cu-rich precipitates, Cr-rich precipitates and chromium carbides all continue to evolve up through 250 dpa and their behaviors were sensitive to the alloy composition. Pre-implanted helium was found to promote void swelling at low doses by shortening the nucleation regime, and to retard void growth at doses in the transient regime by over-nucleation of the void microstructure. Swelling was found to peak at a temperature of 460°C. The primary effect of temperature was on the nucleation regime; nucleation regime was the shortest at 460°C compared to that at 440 and 480°C. The growth rate of voids was temperature-invariant. Steady state swelling was reached at 460^oC between 188 and 375 dpa at a rate of 0.02%/dpa.

In Fe-Cr alloys under irradiation, the elimination of excess point defects at sinks, such as grain boundaries, free surfaces or dislocations, can lead to Radiation Induced Segregation (RIS) phenomena. RIS can oppose to or strengthen equilibrium segregation tendencies. Cases of Cr depletion or enrichments at grain boundaries have both been experimentally observed, depending on alloy compositions and irradiation conditions. Some observations of co-segregation of Cr and C atoms have been reported. Moreover, in supersaturated alloys, irradiation can considerably accelerate the phase separation between Fe-rich and Cr-rich phases (α-α&’ decomposition). We present atomistic Kinetic Monte Carlo simulations that take into account the mechanisms controlling the kinetics of RIS and precipitation: the formation and migration of Frenkel pairs, their recombination, and their annihilation at sinks. These simulations are used to measure the Lij coefficients of the Onsager Matrix, especially the non-diagonal terms that control the coupling between of Cr and point defect fluxes, and the enrichment or depletion tendencies. Their dependence on the alloy composition and temperature is analyzed. Simulations of radiation induced precipitation in undersaturated Fe-Cr solid solutions, as well as the interaction between segregation and precipitation in supersaturated alloys are presented. The effects of carbon on segregation and precipitation kinetics are considered.

High chromium ferritic-martensitic (F-M) steels are one of the promising structural material classes for future nuclear power plants. These steels are designed to combine corrosion resistance, conferred by chromium, with low swelling, high resistance to irradiation damage as well as to retain adequate toughness and elevated-temperature strength during service. However, the long-term use of these steels in intense neutron irradiation environments requires reliable predictions of the evolution of their microstructures and mechanical properties
In the present study, a series of six Fe-Cr alloys with nominal compositions between 3 and 18 at.%Cr were neutron-irradiated at 563K and to 1.8 dpa. Solute distributions revealed α#697; precipitation for alloys containing more than 9at.%Cr. Both the Cr concentration dependence of α#697; precipitation and the measured matrix compositions are in agreement with the recently published Fe-Cr phase diagrams. Clusters involving Si, P, Ni, and Cr, as well as Si and Cr segregated dislocation loops were also observed in the matrix. Complete analysis of the solute clusters and dislocations will be presented. In addition, the chemistries of grain boundaries were quantitatively compared between the as-received and the neutron irradiated alloys. Characterization after post-irradiation annealing is currently being conducted to assess the thermal stability of the solute clusters and observed Cr concentrations. The results will be compared with ion-irradiated Fe-Cr alloy and discussed in the context of equilibrium segregation, radiation-enhanced diffusion, and/or radiation induced segregation.

Irradiation creates excess point defects in materials which can be eliminated by mutual recombination, clustering, or annihilation into defect sinks such as surfaces, grain boundaries or dislocations. As a result, permanent irradiation induces permanent point defect fluxes toward these point defect sinks which lead, in case of preferential transport of one of the alloy components, to a local chemical redistribution in their vicinity. These radiation-induced segregation phenomena have important technological implications in particular because they are suspected to play a significant role in stress corrosion cracking mechanisms observed in austenitic steels.
In that context, kinetic and elastic properties need to be correctly described in order to simulate radiation-induced segregation. The purpose of that study is to combine density functional theory to calculate Onsager coefficients and phase field modeling which allows to solve Cahn-Hilliard equations by taking into account elasticity in the vicinity of defect sinks. This coupling allows simulating kinetics under irradiation at larger time and space scales than atomic scale simulations. In that study we focus on ferritic steels such as Fe-Cr and Fe-Cu alloys.

This presentation provides a review of recent models of the defect microstructure evolution in irradiated body-centered cubic materials, which provide good agreement with experimental measurements, and discusses outstanding challenges, which will require coordinated high-resolution characterization and modeling to resolve. It is well established that exposure of metallic structural materials to irradiation environments results in significant microstructural evolution, property changes and performance degradation, which limits the extended operation of current generation light water reactors and restricts the design of advanced fission and fusion reactors. Further, it has long been recognized that irradiation effects on materials microstructure and properties is a classic example of inherently multiscale phenomenon and that the mix of radiation-induced features formed and the corresponding property degradation depend on a wide range of material and irradiation variables. This inherently multiscale evolution emphasizes the importance of closely integrating models with high-resolution experimental characterization of the evolving radiation-damaged microstructure.

Recent applications of the Self-Consistent Mean Field (SCMF) kinetic theory provide the exact phenomenological coefficients Lij of dilute alloys, starting from vacancy, interstitial and split interstitial jump frequencies calculated ab initio [1]. Binding energies between the solute atom and the point defect at distances beyond the first nearest neighbor site distance are considered. The effect of a strain field and solute concentration on the migration energies and the resulting transport coefficients Lij can be considered as well [2]. Kinetic correlations are accounted for through a set of time-dependent effective interactions within a non-equilibrium distribution function. The contribution of multiple vacancies is taken into account and the mobilities of vacancy-solute clusters are calculated as well. In the case of strong binding energies between vacancy and substitutional or interstitial solute atoms, the kinetic correlations may lead to a drag of solute atoms by the vacancies from the bulk towards grain-boundaries. The resulting SCMF rate equations are then used to predict the radiation-induced segregation at grain boundaries in Fe-based model alloys. In the case of non uniform diffusion driving forces, a recent extension of the SCMF vacancy kinetic theory shows that the Onsager formalism is not valid: the effect of composition heterogeneities on the kinetic correlations and flux couplings has to be taken into account [3].
[1] L. Messina, M. Nastar, T. Garnier, C. Domain, P. Olsson, Phys. Rev. B 90, 104203 (2014).
[2] T. Garnier, V. R. Manga, D. R. Trinkle, M. Nastar, P. Bellon, Phys. Rev. B 88, 134108 (2013).
[3] M. Nastar, Phys. Rev. B 90, 144101 (2014).

Ferritic-martensitic stainless steels with high chromium content have been proposed as structural materials for fission and fusion nuclear reactors as they show good corrosion, temperature, and neutron resistance. However these alloys undergo a phase separation below 600^oC due to the FeCr well known miscibility gap of the iron-rich and chromium-rich phases. Development of FeCr models has become relevant to understand the cause and consequence of this phenomenon.
In this work, we present a non-lattice Object Kinetic Monte Carlo (OKMC) model for binary alloys capable of tracking the dynamical evolution of the phase distribution under irradiation damage and thermal aging. An OKMC approach is suitable since is capable of simulating the times and volumes relevant for these materials.
In the OKMC framework the volume is divided in cells that store, in a quasi-atomistic way, a counter with the number of Cr atoms within. Point defects (interstitials, vacancies and impurities) and defect clusters are defined as objects, that can migrate, interact with each other, transform into another type or move lattice atoms (Fe and Cr). Object properties (migration, interaction, etc...) depend on the alloy composition on each cell, and the cell composition depends on the Cr atom counter and a contribution of the adjacent cells based in a first neighbor and half of a second neighbor contribution. The model takes into account the properties of the coherent binary system by including the mixing energy contribution.
The model is not only capable of reproducing the stable phases predicted by the analytic derivation of the miscibility gap for the same energy, and the reported “vein-like” morphology of the FeCr, but also the time evolution of such transitions.
Finally, key experiments are selected and reproduced to validate the approach presented in this work. The experiments include aged sampled of compositions in the range of 15%Cr up to 32%Cr, and qualitative and quantitative data reported by these experiments are compared, in good agreement, with simulations.

Mechanical property degradation due to ordering phase transformation is of potential concern for alloys based on the Ni-Cr binary system (e.g., 690, 625), particularly in nuclear power applications where component lifetimes can exceed 40 years. In the present research, the disorder-order phase transformation has been studied in Ni-Cr model alloys with varying stoichiometry by a combined experimental and computational approach. The multiscale modeling framework utilizes grand canonical and kinetic Monte Carlo simulation techniques based upon density functional theory calculations to treat both the thermodynamic and kinetic aspects of the phase transformation. The simulation results are used to generate a simple model for the ordering kinetics based upon the Kolmogorov-Johnson-Mehl-Avrami equation. Experimental measurements of the change in lattice parameter and hardness as a function of aging time and temperature are obtained in order to assess the model accuracy.

Reduced activation high-chromium ferritic / martensitic steels are candidate materials for the generation IV fission and fusion reactors. Within these radiative environments, they will be exposed to high temperatures (~500 °C to 700 °C), high doses (> 100 dpa) and gas injection (He in particular). To gain knowledge about their radiation resistance in such environments, the first step is to study the Fe-Cr matrix of this material. For that purpose, self-ion irradiations up to high doses (> 100 dpa), with and without simultaneous He injection, were performed on a series of high purity Fe-Cr binary alloys [0-14wt. %] at 773 K in the triple-beam facility Jannus at CEA/Saclay. The study was focused on the the Cr evolution (RIS, RIP) at the point defects sinks and on Cr and He effects on the void swelling.
After irradiation, The TEM (transmission electron microscopy) analysis revealed some "displacement fringe contrast" inside the dislocation loops [1]. This was attributed to the presence of chromium enriched zones on their habit plane, which is a defect-free region for bcc Fe based alloys. A plausible mechanism will be discussed to explain the phenomenon, whose first step would be the radiation induced segregation (RIS) of chromium atoms on the dislocation loop core. As the loop grows under irradiation, the segregated areas are probably stabilized from re-dissolving by impurity elements like carbon. Energy dispersive X-ray spectroscopy in scanning TEM mode and atom probe tomography (APT) gave a coherent quantitative estimate of the chromium concentration in these enriched areas. APT study showed that the enrichment was heterogeneous on the loop plane.
Concerning the Cr effect on the void swelling, the FeCr alloys were irradiated with 2 MeV Fe ions and 2 MeV degraded He ions within the Jannus Saclay facility up to 128 dpa and 13 appmHe/dpa. Post-irradiation TEM examination on FIB (focused ion beam) thin foils revealed a strong void swelling suppression just by addition of 3 wt.%Cr in bcc Fe matrix. The trends indicted a minima close to 5 wt. % Cr and a maxima close to 10 wt.% Cr in agreement with the literature obtained in low-purity FeCr alloys and FeCr-based steels irradiated with neutrons. However, the amplitude of the void swelling is lower (close to one order of magnitude less), suggesting that the temperature of the peak swelling after ion irradiation would not be exactly 773K.
A detailed study of influence of helium on void swelling has also been performed. In this case, the material studied was a pure bcc Fe. An analysis of the microstructure by TEM on FIB thin foils revealed a strong swelling suppression when helium was co-implanted all along the damage depth. The result is in opposition with what is commonly admitted about the He effect on void swelling. Theoretical explanation for such a behavior will be given.
[1] A. Bhattacharya, E. Meslin, J. Henry, C. Pareige, B. Decamps, C. Genevois, D. Brimbal and A. Barbu, Acta
Mater. 78 (2014).

Gilsocarbon graphite produced by pressing or moulding is currently used in UK advanced gas-cooled reactors. It has a complex microstructure comprising filler particles, binder phase and 20% porosity as manufactured. The porosity includes open pores due to gas evolution, closed pores and various sizes of micro-cracks due to fabrication. During service, nuclear graphite is exposed to fast neutron irradiation which causes dimensional, thermal and mechanical changes in the material; and it loses mass to become more porous due to radiolytic oxidation.
When undertaken multi-scale computer modelling it is important to have input parameters at the correct length-scale. In the present work, the microstructure and mechanical properties of Gilsocarbon graphite have been characterised over a range of length-scales. Optical imaging, combined with 3D X-ray computed tomography and 3D high-resolution tomography based on focus ion beam milling has been adopted for microstructural characterisation. A range of small-scale mechanical testing approaches are applied including a novel in situ micro-cantilever technique based in a dualbeam workstation. It was found that pores ranging in size from nanometre to tens of micrometre in diameter are present which modify the deformation and fracture characteristics of the material. This multi-scale mechanical testing approach revealed the significant change of mechanical properties, for example flexural strength, of this graphite over the length-scale from a micrometre to tens of centimetres. Such differences emphasise why input parameters to numerical models have to be undertaken at the appropriate length-scale to allow predictions of the deformation, fracture and the stochastic features of the strength of the graphite with the required confidence.
A multi-scale microstructural computer model has been established to simulate the idealised key features quantified experimentally in virgin and irradiated Gilsocarbon graphite. These models are an input to the multi-scale finite element computer models which incorporate the experimentally determined mechanical properties to predict the evolution of deformation and damage in the material. The change of microstructure of the graphite with reactor environment is a convoluted complex process. In the present work, we focus on the evolution of porosity over service. A series of porosity up to 50% has been considered to represent an extreme case experienced by irradiated reactor core graphite towards the end of service life. It was found that the secondary porosity plays a role in reducing the strength and modifying the damage distribution of the material. The results are discussed with respect to the microstructural characterisation and measurement challenges and the output from the models particularly with respect to the ability to predict trends in the overall deformation and fracture that can be a value in assessing the integrity of graphite reactor core bricks.

The grain size of UO₂ significantly impacts the reactor fuel performance, influencing thermal conductivity, creep, fracture, and fission gas release. While the fuel pellets begin with a uniform average grain size across the pellet, this changes during reactor operation due to large temperature gradients. Grain growth within the fuel is also heavily impacted by defect generation due to radiation damage. In order to improve the predictive capability of fuel performance codes, we have developed a model that predicts the grain size throughout a UO₂ fuel pellet as a function of the temperature, sintered porosity, and fission gas bubble density. We have developed an analytical model, in which the critical mechanisms and parameter values have been determined using experimental data and multiscale simulations. Atomistic simulations have been used to determine the intrinsic grain boundary (GB) mobility and energy, as well as to investigate the temperature gradient driving force. Mesoscale phase field simulations using INL&’s MARMOT code have been used to evaluate the relative importance of different GB driving forces and to quantify the impact of GB pinning due to GB fission gas bubbles. The final model is being implemented in INL BISON fuel performance code.

Understanding the microstructural evolution at the meso and atomic scales is critical for predictive modeling of fuel performance at the engineering scale. Currently, Idaho National Laboratory is developing a multiscale modeling toolkit for nuclear fuels where the meso-scale microstructure evolution is handled by the phase field code MARMOT with inputs from the atomic scale. One critical issue in modeling fuel performance is the evolving grain size which affects thermal conductivity, fission gas release, and mechanical stability of the fuel. The evolution in grain size depends on the grain boundary energies and mobilities; both can be highly anisotropic. Adopting a recently published model for fcc metals, in this work we aim to describe the grain boundary energies in UO₂ in a five-dimensional space in accordance to the five degrees of freedom. The continuum scale model is based on molecular dynamics calculations for grain boundary energies for parameter fitting and also verification, and it is capable of estimating the energy for any arbitrary grain boundary. Such a model is being implemented into MARMOT to allow for more accurate simulations of grain boundary migration and thus grain size evolution.

An atomistic level understanding of how varying types and numbers of irradiation induced defects affect thermal resistance in graphite is vital in designing accident tolerant fuels for next-generation nuclear reactors. A set of classical molecular dynamics (MD) calculations of a zoo of point defects has shown that the more energetically favorable clustering defects exhibit a significant increase in thermal resistance along the c-axis. These defects are also responsible for irradiation induced swelling along the c-axis, and both effects contribute to altering the thermal conductivity of polycrystalline graphite. Characterizing the changes in thermal conductivity as a function of defect type and number is accomplished by incorporating the phonon relaxation times computed with MD into a Boltzmann transport solver. With prescribed temperature boundary conditions, group velocities, relaxation times and specific heat, the Rattlesnake module of Idaho National Laboratory's MOOSE (Multi-physics Object Oriented Simulation Environment) is used to solve for the phonon intensity. Angular moments of this intensity yield the spatial distribution of temperature and heat flux, from which thermal conductivity can be calculated through Fourier's law. Clustering point defects have a marked influence on thermal conductivity in nuclear fuel, which is also affected by the presence of uranium, plutonium, and fission product isotopics. The project aim is to examine these induced changes in the lattice structure of nuclear fuel under irradiation in a nuclear reactor, and the effect they have on the thermal conductivity.

This research uses the atomistic framework to analyze interfaces and grain boundaries to help understand how they lead to the observed microstructure. Metallic uranium is important in the use for the new generation of fast reactors. Uranium is a transition metal with three stable solid phases, the α (face-centered orthorhombic) phase, the β (tetragonal) and the γ (body centered cubic) phase.
The α-uranium phase has low symmetry and twins easily with over 40 possible twinning modes. There have been a limited number of studies on the deformation mechanisms for uranium and even less on understanding them. This research hopes to study the energetics and the structure of the twinning process.
Little research has been done for both the α-uranium and γ-uranium grain boundaries. Molecular Statics (MS) and Molecular Dynamics (MD) allow for the characterization and the energetics of the grain boundaries to be analyzed. Research into the grain boundaries will help the understanding of observed microstructural characteristics.
Next, we investigate the solid-solid transitional hetero-phase interfaces of α-uranium against γ-uranium. These types of transitional hetero-phase interphases have not been previously studied and are not well understood. This research will allow for the new understanding of transitional interfaces on the atomistic scale.
Lastly, we examine the energetics and thermodynamics of the solid-liquid hetero-phase interfaces of the γ-uranium. This allows for a comprehensive study of the transition from the uranium liquid state to the α-uranium ground state.

The advanced ceramic fuel development program is exploring revolutionary ceramic fuels with the potential of “game-changing” impact on reactor operation & response to beyond design scenario. Key properties of advanced fuels include high thermal conductivity, oxidation resistance, high temperature mechanical properties, and thus improved accident tolerance. Composite ceramic fuels possess distinct advantages to fulfill these key requirements. On the other hand, the US Nuclear Energy Advanced Modeling and Simulation (NEAMS) program is developing science-based next generation fuel performance modeling capability as part its Fuel Product Line in order to facilitate the predictive capability of nuclear fuel performance and assist the design and analysis of reactor systems. Critical experimental data are needed to validate MARMOT models, particularly on effective thermal conductivity and fracture behavior and how microstructure features affect thermo-mechanical properties of fuels. The fabrication of sintered fuel pellets with well-controlled microstructure is prerequisite to establish the correlation of the microstructure feature and fuel behavior.
In this talk, recent advancements of using field-assisted sintering technologies, specifically spark plasma sintering (SPS), in fabricating advanced fuels and engineering fuel matrix as the target systems will be reviewed. The fuel behaviors are characterized with the focus on the thermal-mechanical properties and accident tolerance. The sintering fuels by SPS include monolithic UO₂ with well controlled microstructure, grain size and porosity across multiple length scales from nano-metered to micron-sizes, and the impact of the microstructure on the fuel properties is discussed within the context of the MARMOT predictions. In addition, the composite UO₂ fuels are also fabricated in which heterogeneous secondary phases are used as the additives to improve thermal conductivity and mechanical properties of the composite. The potential application of the composites as advanced fuels with enhanced accident tolerance will be discussed.

Metallic uranium alloys are candidate fuels for transmutation reactors. These transmutation fuels can be used to burn long-lived minor actinides and fission products in fast spectrum reactors. Metallic fuels possess a variety of beneficial characteristics, including high thermal conductivity, ease of fabrication, and high fissile density. In the past, the majority of research was focused on fuel performance experiments which required very high fluences. This research is centered on low fluence irradiations since this will serve as critical simulation input and validation data for the early stages of microstructural evolution in metallic fuels, including both uranium and uranium-zirconium alloys. These metallic fuels were irradiated from 0.003 to 1 dpa at approximately 690^oC within the hydraulic rabbit shuttle in the High Flux Isotope Reactor at Oak Ridge National Laboratory. The post-irradiation examination results will be discussed, including synchrotron x-ray diffraction, pair distribution function, positron annihilation spectroscopy, and electron microscopy analyses.

The widespread availability of 3^rd generation synchrotron sources provides unique opportunities for probing the microstructural behavior of nuclear materials under irradiation. This approach provides complimentary alternatives to existing characterization technologies as it utilizes time-resolved, in situ x-ray measurements to uniquely investigate the kinetics of materials degradation processes at the atomic-scale. We describe recent efforts utilizing high-resolution x-ray micro-diffraction (XRD) and x-ray absorption near edge spectroscopy (XANES), together with unique sample environments, to analyze the structural and chemical modifications in nuclear fuel materials (UO₂, ThO₂, UC, ThC, UN) induced by energetic heavy ions, characteristic of fission fragment radiation. These synchrotron techniques are particularly useful for characterizing irradiation effects such as the production of isolated defects, defect clusters, discontinuous damage domains, and structural transformations from multiple ion impacts. The use of a heatable high-pressure cell is also introduced as a new means to investigate the defect recovery behavior of irradiated nuclear materials under well-controlled high-temperature conditions (up to 10000C). Several sets of samples were irradiated at the GSI Helmholtz Center in Germany with swift heavy ions of energies up to 950 MeV and to fluences of up to 5×10¹³ ions/cm². Synchrotron powder XRD and XANES measurements were performed at the Advanced Photon Source. These recent studies demonstrate that the defect morphology and defect annealing kinetics in the nuclear materials are highly dependent on cation chemistry and the local structure of the irradiated materials. The experimental results provide precise benchmark data for first-principles modeling to potentially validate their use in multi-scale, multi-physics fuel performance codes. Lastly, recently developed experiments for characterizing the irradiated samples using neutron diffraction, which is complimentary to XRD, are discussed.

Spent nuclear fuel emits significant fluxes of low energy gammas, notably the 0.66 MeV decay channel of Cs-137. In the Swedish long-term repository programme, the spent fuel bundles will be encased in a cast iron frame protected by a copper shell. It has been noted that the damage induced by these gamma rays could induce hardening and possibly embrittlement of the cast iron matrix through radiation and temperature enhanced copper diffusion and clustering over the course of the first few hundred years of storage. We have revisited the theoretical foundations behind these conclusions, taking into account recent advances in the field of primary damage simulations. Furthermore, in order to estimate the effect of the irradiation induced vacancy supersaturation, an experiment where cast iron samples and a reference FeCu alloy were irradiated in an electron accelerator has been carried out. The aim was to accelerate the effects of the gamma induced damage. In order to better estimate the induced damage flux we have developed a Monte Carlo code to explicitly simulate electron scattering, damage deposition and attenuation in materials under electron irradiation. We apply a multi-scale modeling framework in order to carefully compare the electron irradiation experiment and the damage induced in the repository condition. Finally, the enhanced Cu-precipitation is investigated and compared to the experiments. The consequences for the deployment of the spent fuel repository are discussed.

In the severe reactor accidents, the cesium released from the core deposits on the surface of reactor coolant system (RCS). In steam environment, those deposits are supposed to be predominantly Cs₂MoO₄. However, the behavior of Cs₂MoO₄ and its interactions with the other components have yet to be understood. We have to understand the Cs-Mo complex oxides system in the complex conditions with temperature, steam contents and metal surfaces. Therefore, we study the deposition of Cs₂MoO₄ as well as their possible interactions with the stainless steel, which is used in primary coolant system in PWR. The effects of atmosphere and substrate were studied as well.
For the transpiration tests, Cs₂MoO₄ was placed in a platinum boat and heated at 1573 K. Either SUS304 or platinum plates were placed downstream at different distances corresponding to temperatures ranging from 1554 to 547 K. The carrier gas was Ar or Ar saturated with steam at 70°C. After the transpiration runs, the deposits were examined by the scanning electron microscope equipped with an energy dispersive X-ray spectroscopy (SEM/EDAX), micro-Raman spectroscopy and X-ray diffraction equipment.
In Ar+steam on Pt surface below about 1200 K, which is close to the melting point (1213 K) of Cs₂MoO₄, the deposits were predominantly Cs₂MoO₄. But at higher temperatures, they consisted of cesium polymolybdates, probably due to the formation of CsOH(g) in the gas phase. On the surface of SUS304, various reactions have happened, depend on the temperature and the atmosphere.
In dry Ar on SUS304, the deposits were mainly Mo metal at ~1500 K, then Cs₂Mo₂O₇ at ~1220 K, and Cs₂MoO₄ at further downstream.
In Ar+steam on SUS304, the reaction became even complicated due to the vaporization of CrO₂(OH)₂. We could not find cesium-containing species on SUS except for those found on the plates at the low temperatures below ~730 K, where Cs was found as Cs₂MoO₄. Molybdenum-containing species were found at higher temperatures. Thus, even if the vapor source was a single-phase Cs₂MoO₄, cesium polymolybdates and molybdenum oxides were found among deposits depending on the atmosphere and the substrate material. The results will be discussed with the thermodynamic analysis based on the Cs₂MoO₄-MoO₃ pseudo-binary phase diagram.

The atomic-level processes associated with void nucleation from isolated vacancies in UO₂ are analyzed from molecular dynamic simulations. Evaluation of energetics shows that isolated defects and voids interact through both elastic and electrostatic forces. Void growth mechanisms, Ostwald ripening and coalescence are identified and characterized, enabling an evolution map of void growth to be developed. The interactions of voids with a grain boundary, specifically the high-temperature interactions of a (310) Σ5 tilt GB structure, is also analyzed. We find that the GB tends to move towards the void when they are within a few nm of each other. Both GB pinning to the void and void dissolution at the GB take place.
The thermal conductivities of UO₂ single crystals containing nanoscale size voids and He gas bubbles are determined using non-equilibrium molecular dynamics as a function of void size and gas density in the bubble. As expected, the thermal conductivity decreases as void size increases, while the decrease in thermal conductivity is determined to be more substantial than the predictions of traditional analytical models. The thermal conductivity of UO₂ of the small voids considered here is reduced further when the void is filled with He gas. This surprising result is attributed to the penetration of the helium atoms into the lattice where they act as phonon scattering centers.

Some of the current fleet of nuclear power plants is poised to reach their end of life and will require an operating life time extension. Therefore, the main structural components, including the reactor pressure vessel (RPV), will be subject to higher neutron exposures than originally planned. These longer operating times raise serious concerns regarding our ability to predict the reliability of RPV steels at such high doses. In this study, several RPV steels were irradiated at high doses to study the degradation of the mechanical properties and related microstructural changes. It is well known that copper-enriched precipitates are key microstructural futures that are responsible for radiation hardening of RPV steels for high-copper welds. At high doses, (Ni-Mn)-enriched precipitates may start contribute to embrittlement process. In this study, the evolution of these different Cu- and (Ni-Mn) enriched precipitates is studied by means of SANS and compared to results of APT measurements.

Process path functions are continuous functions of microstructural evolution during thermo-mechanical processing. We develop process path functions in rolling and heat treating of the eutectoid Zr-18Nb alloy to determine texture evolution as a function of processing parameters. The eutectoid Zr-Nb alloys serves as a surrogate for the eutectoid transformation in several actinide alloys. Alloys are arc-melted and rolled at ambient and high temperatures. Rapid cooling after arc melting retains the cubic phase. X-ray diffraction and electron back scattered diffraction measurements are performed to obtain crystal structure, grain orientation and texture information. Crystallographic orientation and texture is expressed as a function of processing parameters using spherical harmonics functions. The evolution of microstructure in any thermo-mechanical process is investigated by following the modifications in Fourier coefficients for that specific process. Using this framework, we compare the influence of hot and cold rolling on the texture evolution of the metastable bcc phase as well as comment on the feasibility of using process path function in inverse process modeling wherein microstructural evolution may provide information about processing history. This latter consideration is of importance in the area of nuclear forensics where the microstructural analysis of interdicted uranium alloys may suggest processing paths leading to the establishment of the provenance of interdicted nuclear material.

Nitride fuels are considered as an alternative to oxide fuels for both conventional light water reactors and GEN IV fast reactors due to their thermo-mechanical properties: high thermal conductivity and high density among others. However, they still need to undergo licensing and to be proven safe before they can be used. Experiments and fuel performance codes should be used together in order to accelerate this process while keeping the costs at a reasonable level.
A model for nitride fuels has been created for nitride fuels and implemented in the TRANSURANUS fuel performance code developed by JRC-ITU. In particular, special attention is given to the fission gas release module, for which a model based on the open porosity has been developed. The fission gas release results are compared to experiments. The NIMPHE irradiation experiment is used for the validation of the full model. This work is a first step and a better prediction of the porosity and open porosity as well as a more precise determination of diffusion coefficients should be pursued.

Residual resistivity in isochronal annealing is a very powerful experimental technique that can be used to provide quantitative data on single point defect migration energies and estimates on point defect - solute binding energies. Here we present systematic first principles calculations of the residual resistivity of point defects and solutes in metals. The resistivity is calculated both in the framework of Boltzmann transport theory and using linear response, based on density functional theory. The validity of the superposition principle that is used when performing resistivity recovery experiments such as isochronal annealing is investigated. We will here discuss the implications of having a more physics based appreciation of the effect that clustering has on the residual resistivity.

Understanding solute-defect flux coupling in alloys is crucial for modeling several ageing and irradiation-induced diffusion phenomena, such as clustering or radiation induced segregation (RIS). The flux coupling tendencies can be fully predicted if all transport coefficients (the elements of the Onsager matrix) of the alloy are known. They can be calculated in a mean field framework starting from the microscopic atomic jump frequencies, which can be obtained for instance by means of density functional theory (DFT) calculations. The transport coefficients depend on temperature and solute concentration, but also on the strain fields possibly affecting the material. An example of an irradiated system where flux coupling phenomena are significant are the ferritic-martensitic alloys of reactor pressure vessels, where for instance the coupling between interstitials and P and Mn atoms is strong and lead to segregation at grain boundaries and dislocations. The calculation of the Onsager matrix in these alloys allow for an accurate low-temperature prediction of diffusion coefficients and RIS tendencies.
Self-Consistent Mean Field theory represents a fully-developed mean-field analytical model that allows for an accurate calculation of the Onsager matrix, its reliability being benchmarked by the very good agreement with Monte Carlo simulations [1]. In this work, the theory developed for interstitial-mediated solute transport in [2] is extended to include solute-defect interactions at an arbitrary nearest neighbor distance. The analytical solution is found by means of an automatic routine, which is developed at the moment for dilute alloys only. This code is applied to the analysis of externally-applied anisotropic strain effects onto interstitial-transport properties in model iron-based binary alloys. The effect of strain on microscopic jump frequencies is obtained by coupling DFT calculations and linear elasticity theory [3], and the sensitivity on different exchange-correlation functionals is tested. The results are used to investigate the effect of strain on the RIS tendencies in RPV steels.
References:
[1] M. Nastar, Philos. Mag. 85 (32), 3767 (2005).
[2] V. Barbe and M. Nastar, Philos. Mag. 87 (11), 1649 (2007).
[3] C. Varvenne et al., Phys. Rev. B 88, 134102 (2013).

This work has as objective to evaluate the sputtering in a biphasic surface under severe irradiation conditions of 80 and 380 dpa due this level of irradiation is similarly of the irradiation conditions of the next generation of nuclear reactors. The hypereutectic alloy was selected, Ni-22 at% Si due that exist a difference of 15 atomic percent on the concentration of silicon between the phases, α-Ni and Ni3Si at the irradiation temperature, this difference in silicon concentration promoted that exist a difference of 130 eV/nm on the energy deposited between regions with different content of silicon. The hypereutectic microstructure allowed us to evaluate the sputtering yield of monophasic regions, dendritic structure formed by the intermetallic phase Ni₃Si, and biphasic regions, eutectic α-Ni-Ni₃Si. The experimental results showed that the sputtering yield was higher on the biphasic regions than on the monophasic regions, other changes detected on the biphasic region were the formation of a pattern regular of V grooves and the reduction of the rugosity, this change it is directly related with the increase of irradiation dose. Previous results of mathematical simulation indicated that the sputtering yield of α-Ni phase is higher than of the Ni3Si phase, this fact is not sufficient to explain the experimental observations, therefore phenomenological models are proposed to explain the experimental observations, these models take in count the local variation of ion beam incident angle and the preferential sputtering between regions and phases. The main result of this work is that the alternance of lamella with different concentration of silicon promote the formation of regular patron of V grooves and that this patron has the potential of increased the sputtering yield of the biphasic region. This high sputtering yield promotes the formation of a 75 nm edge between the monophasic and biphasic regions for the above facts; we conclude that this type of surface will have underperformance under the irradiation conditions that were used on this work.

Nickel and Nickel based superalloy with complex microstructures are the most widely used and attractive materials for high temperature application especially in aerospace industries and nuclear industries, owing to good combination of high strength, ductility and corrosion resistance. Aerospace industry has experienced unexpected hydrogen embrittlement (HE) problems for many years. Hydrogen embrittlement is the delayed failure mechanisms due to loss of ductility to the presence of hydrogen in the material. The hydrogen may enters the material from internal manufacturing sources such as welding, electroplating etc. and this phenomena is known as internal hydrogen embrittlement. The hydrogen may enter the material from environmental during service period and this phenomenon is known as environmental hydrogen embrittlement. This work focused on the role of microstructure in internal hydrogen embrittlement on nickel and nickel based material associated with electroplating and welding process. And the development of industrially applicable multiscale approach from atomic to component level in experimental & virtual testing from material characterization to modelling in order to investigate the HE problem in aerospace industries.

Thermal conductivity is a critical property of oxide fuels. Many factors can affect this property, such as fission products, microstructure, temperature, stoichiometry, and radiation damage. Some solid fission products can form oxides and their cations have different ionic radii and charges. Here we use five different trivalent cations doped CeO₂ as model systems to study the effects of ionic radius and their accompanying off-stoichiometry on the thermal transport in oxide fuels. As these cations have the same charge state and they induce the same amount of oxygen vacancies, the effects of ionic radius can be isolated. Using non-equilibrium molecular dynamics simulations, we calculate the thermal conductivities of different doped systems under various conditions. We found that the bulk thermal conductivity decreases as ionic radius increases and the correlation can be approximated with a linear relationship. However, compared to accompanying off-stoichiometry induced by these trivalent cations, the effect of ionic radius on thermal transport is much smaller. When these doped cations segregate to grain boundaries, they increase the grain boundary thermal resistance and the magnitude of change also correlates strongly with the ionic radius. Finally, using these atomistic results as inputs for an analytical model, we compare how the segregation of these cations to grain boundaries affects the overall thermal conductivity of polycrystals at different grain sizes.

We report experimental measurements of the thermal conductivity on oriented stoichiometric uranium dioxide single crystals from 4 K to above 300 K. Since uranium dioxide is a cubic compound and thermal conductivity is a second-rank tensor, it has always been assumed to be isotropic. However, our results indicate anisotropy for the thermal conductivity, which is unexpected due to the lack of non-cubic distortions in diffraction. This contradiction is reconciled by invoking interaction between an applied temperature gradient and the electric moments on uranium ions to slightly break cubic symmetry of excited states that are active in resonant phonon scattering processes. The interaction is hypothesized to be mediated by the small electric fields induced by the thermoelectric effect. Specifically, the temperature gradient or electric field gives rise to small changes in the properties of spin excitations linked to the dynamical Jahn-Teller distortions in UO₂. The dynamical Jahn-Teller distortions split the triplet ground state of the uranium ion into three singlets, which are in the appropriate energy range for interaction with phonons and give rise to significant phonon-spin scattering in the paramagnetic phase. This is emphasized by comparing our results to literature data for diamagnetic ThO₂. The experimental results are also compared to molecular dynamics simulations of the UO₂ thermal conductivity using the direct method. The effect of spin scattering is added based on analysis of the single crystal experiments in order to make accurate predictions for the reduction of UO₂ thermal conductivity due to fission gases and fission products.

Better understanding the influence of isotope and fission products on thermophysical properties of UO₂ is essential to predict fuel performance and design new fuel types. In this work, we present results of a comprehensive density-functional theory study of the influence of isotope and magnetization on phonon and thermophysical properties of the strongly correlated UO₂ system, and compare with results of recent experimental studies. Phonon properties will include the phonon density of states, phonon dispersion curves, Debye temperature, and phonon relaxation time. Thermophysical properties will cover thermal expansion coefficient, free energy, entropy, specific heat capacities of C_v and C_p, mode Gruneisen parameters and thermal conductivity. Temperature ranges from 10 to 2000 K. This work is supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program funded by the U.S. Department of Energy, Office of Nuclear Energy.

The nature of primary damage produced by ion and neutron irradiation
of materials starts to be well understood thanks to decades of
experimental and molecular dynamics computer simulation studies. For a
while, we thought quantitative reliability had been achieved in widely
studied materials like Fe and W, for which well-characterized
interatomic potentials are available. However, recently we realized
that the way the low-energy limit of electronic stopping, or
alternatively the electron-phonon coupling, is handled in the
simulations can affect the results on damage production by as much as
a factor of two. In this talk, I will present results on this issue
in W, and how the issue affects not only total number of Frenkel
pairs, but also clustering. I will show that some combinations of an
interatomic potential and low-energy stopping limit can be ruled out
as disagreeing with experiments, but that there some uncertainty of
the results still remains after that. I will finally discuss possible
ways by which the uncertainty could be reduced.

The production of fission gas products, namely xenon and krypton, in irradiated nuclear fuel elements leads to a variety of phenomena that directly influence fuel performance. Central to the retention and release of fission gases is the evolution of bubbles existing on grain boundaries and grain triple junctions. This presentation will highlight progress specifically regarding the modeling and simulation of intergranular bubble nucleation, growth, percolation, and gas release as it relates to Light Water Reactor (LWR) fuel elements. This effort has included various simulation methodologies ranging from the atomistic to the fuel pellet length scales. In particular, we have developed and implemented a Random Walk Monte Carlo method to model bubble nucleation, the Phase Field method to model intergranular bubble growth and percolation, and a Network Percolation method to model the longer-range interconnection on a grain boundary network allowing predictions of Fission Gas Release (FGR). We focus our simulations on trying to quantify and understand how the variability in bubble percolation amongst different GBs initiates at the nucleation stage, continues during the bubble growth stages, and ultimately affects fission gas release. This research was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program within the US-DOE.

The ability to predict the onset and extent of internal corrosion in fuel pins is needed for safe and economical nuclear reactor operation. GERMINAL V2 is a fuel performance code developed by CEA, EDF, and Areva dedicated to simulating the behavior of mixed oxide (MOX) fuel under irradiation in sodium cooled fast reactors (SFRs). In order to improve the current internal corrosion prediction capabilities, efforts are made to develop and implement a new model based on thermodynamic properties of compounds consisting of certain fission products suspected to play a role in the corrosion process of the cladding material. Using ab initio simulations in the framework of density functional theory, formation enthalpies, entropies, and heat capacities have been computed in order to improve the corrosion model. The focus has been on compounds formed by oxygen and the fission products molybdenum, tellurium, cesium, and iodine.

Conventional density functional theory modeling of actinides presents limitations, as such, due to the importance of correlation and relativistic effects. One way to address these problems is to add a correlation correction, fitted on certain experimental results. Doing so can, however, lead to the system converging into a metastable state [Meredig]. Different schemes have been proposed to avoid, or at least limit, the occurrences of these metastable states: for instance ramping and occupation matrix control (OMC).
A study of the fission gas in an actinide nitride matrix is carried out in order to better determine the diffusion coefficients. The ground state is found using the OMC scheme and the incorporation and migration energy of fission products are investigated. This is the first step in a study that will lead to an improved model of the fission gas release in a fuel performance code.
[Meredig] Meredig, Thompson, Hansen, Wolverton, van de Walle, “Method for locating low-energy solutions within DFT plus U”, PHYSICAL REVIEW B, 2010, Vol 82, Iss 19

We report diffusion properties of xenon (Xe) fission gas atoms in UO₂ nuclear fuel for a range of non-stoichiometry (i.e. UO_2±x), under both out-of-pile or instrinsic (no irradiation) and in-pile (irradiation) conditions. The results were obtained from a combination of density functional theory (DFT) and empirical potential calculations. First, analytical models for the diffusion activation energy were derived, which account for the type of trap site that the fission gas atoms occupy, the charge state of these defects and the chemistry controlling the equilibrium state. Next, DFT calculations were used to estimate migration barriers and internal energy contributions to the thermodynamic properties and calculations based on empirical potentials were used to estimate defect formation and migration entropies (i.e. pre-exponentials). The predictions were compared to available experimental data. The importance of the large Xe_U3O cluster (a Xe atom in a uranium + oxygen vacancy trap site with two bound uranium vacancies) is emphasized, which is a consequence of its high mobility and high binding energy. Further investigation of the diffusion properties were carried by solving the complete set of coupled reaction-diffusion equations describing defect evolution and Xe diffusion in UO₂ under irradiation, as compared to the simplified analytical model referred to above. The MARMOT phase field code was used to solve the reaction-diffusion equations and Xe diffusivities were calculated for a range of irradiation and microstructure conditions. We find that the Xe_U3O cluster gives Xe diffusivities that are higher for intrinsic conditions than under irradiation over a wide range of temperatures. Under irradiation the fast-moving Xe_U3O cluster recombines quickly with irradiation induced interstitial U ions, while this mechanism is less important for intrinsic conditions. The net result is higher concentration of the Xe_U3O cluster for intrinsic conditions than under irradiation. We speculate that differences in the irradiation conditions and their impact on the Xe_U3O cluster can explain the wide range of diffusivities reported in experimental studies. However, all vacancy-mediated mechanisms underestimate the Xe diffusivity compared to the empirical radiation-enhanced model used in most fission gas release models. We investigate the possibility that diffusion of small fission gas bubbles may give rise to the observed radiation-enhanced diffusivity.

The diffusivity of the solid fission products (FPs) Zr (Zr⁴⁺ ), Ru (Ru⁴⁺ , Ru³⁺ ), Ce (Ce⁴⁺ ), Y (Y³⁺ ), La (La³⁺ ), Sr (Sr²⁺ ) and Ba (Ba²⁺ ) in UO₂ by a vacancy mechanism has been calculated, using a combination of density functional theory (DFT) and empirical potential (EP) calculations. Direct and indirect migration mechanisms were considered. Most solid fission products diffuse with rates similar to U self-diffusion. However, Ru, Ba and Sr exhibit significantly faster diffusion than the other solid FPs. The diffusivities correlate with the fission product solubility in UO₂ , and the tendency to from metallic and oxide second phase inclusions, and are compared to recent results on the diffusion of Xe fission gas atoms.

Within the current safety assessment of the underground final repository for spent nuclear fuel planned for Sweden an in-depth analysis of the chemistry of H₂O at Cu surfaces is being carried out. In this work we report results of an investigation of the interactions between H₂O and Cu. Employing density functional theory (DFT), we investigated the possible oxidation of Cu(110) by H₂O in anoxic conditions. Starting from a monolayer of molecularly adsorbed H₂O at the Cu(110) surface, we sequentially dehydrogenated the H₂O molecules until a monolayer of O atoms was formed. We evaluated the Gibbs free energies for each of the steps of this sequential dehydrogenation considering the different symmetries available for disposition of the surface products. A comparison between this chemistry occurring at a dry surface was done with the same reactions described incorporating a continuous solvation model and also when an additional layer of H₂O molecules is at the surface. We found that the oxidation of Cu(110) driven solely by H₂O is not spontaneous even when both solvation is included and explicit H₂O molecules are assisting this chemical process. Though, the spontaneous formation of H₂ (g) from adsorbed H₂O leading to a partially hydroxylated Cu(110) surface is possible. Additionally, the analysis of the surface relaxation that takes place during dehydrogenation of H₂O revealed that the presence of an additional H₂O layer has a large impact on the extension and direction of the surface relaxation. The relaxation of the surface is dependent on the fine balance between the Coulomb attraction that occurs between the water molecules and the Cu surface, the Coulomb repulsion occurring between the O atoms of H₂O and the hydrogen bonding network that takes place between the H₂O molecules.

The philosophy that models guide experiment and experiments inform models, and that both inspire each other, has been the foundational guiding principle of our research for more than three decades. This integrated approach totally contrasts with the ill-informed notion that the extremes of bottom up fundamental models need only be validated by experiment, or that empirical data fits are reliable for extrapolations. Here we describe how early 1990&’s model-based predictions of irradiation enhanced Mn-Ni(-Si) (MNS) rich precipitates, or so-called late blooming phases (LBP), led first to experimental searches for their existence; and recently to developing a new predictive thermo-kinetic precipitation model and supporting databases that are needed for RPV life extension. Notably MNS LBP form only at high fluence and are not accounted for in current regulatory embrittlement models.
A hierarchical master model relates interacting material and irradiation variable combinations to nano-structural evolutions, which are then coupled to mesoscale dislocation based models of changes in the irradiated steel&’s constitutive law, that are in turn related to changes in continuum transition temperature shifts. Here we develop a new precipitation model to replace the classical treatment of nanostructural evolutions, heretofore based on two or three independently evolving features. The new model incorporates a unified treatment of the development chemically complex nano-features that previously ranged from cascade induced solute-defect cluster complexes (previously so called matrix features) to well developed Cu-enriched precipitates (CRP) alloyed with Mn, Ni and Si. However, the new model recognizes that there is a continuum of features that have now been extended to include Mn-Ni-Si (MNS) intermetallic phases, that eventually form in both Cu bearing and free steels. The new models include coupling empirically based thermodynamics (e.g., CALPHAD), augmented by first principles calculations, to Monte Carlo and cluster dynamics simulations of precipitation kinetics that are used to support reduced order Avrami-type models that are fit very large embrittlement databases.
We also emphasize the importance of coupling of advanced methods, including radiation scattering, atom probe tomography, transmission electron microscopy, positron annihilation spectroscopy and other nanoanalytical techniques to more fully characterize the nanofeatures. We also show how these methods can give direct insight on the relation between bulk alloy and precipitate chemistry and mole fractions. The nanoscale characterization results are combined with large coupled mechanical property databases. The irradiation experiments span about 6 orders of magnitude in displacement damage rates. The talk concludes with the status of treating rate effects that will permit accurate predictions of embrittlement for low flux-high fluence extended end of life conditions.

For operation of existing nuclear power plants (NPPs) beyond their design lifetime (up to 80 years), one of the main issues is the assessment of the performance of its structures, systems and components (SSC) during the period of extended operation. The reactor pressure vessel (RPV) being one of the components that determine the lifetime of a NPP, it is important to be able to predict the mechanical properties of irradiated RPV&’s steel using small pieces of irradiated material. Neutron irradiation at the temperature of operation of the nuclear reactors facilitates the chemical equilibrium of the alloying elements of the RPV steels, especially copper, while producing nanoscale precipitates (Cu, Mn-Ni-Si, and ~M₆C carbides) that leads to embrittlement [1-4]. The goal is to take into account such effects in neutron embrittlement prediction models. It is expected that prolonged thermal ageing of RPV steels should promote such chemical equilibrium and should be able to contribute to a deeper understanding of what happens at high neutron fluences.
The results of thermal ageing treatments (450°C, 500°C and 550°C) performed in a A533 Cl.1 (JRQ) steel during 0.5 to 1000 hours are presented in this paper. JRQ steel has a bainitic microstructure, but well separated ferrite and bainite islands are observed at high magnification. The hardness evolution of such islands as a function of the thermal ageing treatment is correlated with the number of precipitates present after thermal ageing as well as with the chemical evolution in these microconstituents.
References
1. C. Lemaignan, “Structural Materials under irradiation”, in notes of “The 2006 Fréderic Joliot & Otto Hann summer School on Nuclear Reactors: challenges and Innovation for light water reactors”, Cadarache, France 23 august- 1 september 2006.
2. G.R. Odette, “On the dominant mechanism of irradiation embrittlement of reactor pressure vessel steels”, Scr. Metall., 17 (1983) 1183- 1188.
3. Peter B. Wells, Takuya Yamamoto, Brandon Miller, Tim Milot, James Cole, Yuan Wu, G. Robert Odette, “Evolution of manganese-nickel-silicon-dominated phases in highly irradiated reactor pressure vessel steels”, Acta Mater., 80 (2014) 205-219.
4. T. Toyama a, N. Tsuchiya, Y. Nagai, A. Almazouzi, M. Hatakeyama, M. Hasegawa, T. Ohkubo, E. van Walle, R. Gerard, “Irradiation-induced changes of the atomic distributions around the interfaces of carbides in a nuclear reactor pressure vessel steel”, JNM 405 (2010) 177-180.

Formation of Mn-Ni-Si rich precipitates in ferrite under irradiation is likely to be one of the main sources of embrittlement in reactor pressure vessel (RPV) steels under life extension conditions. Due to their small size and slow formation, the phases and clustering kinetics are still not well understood. Recently, it has been predicted by CALPHAD modeling that Mn₆Ni₁₆Si₇ and Mn(Ni,Si)₂ are two possible phases that will form under irradiation. Here we report on the precipitation kinetics of these phases. A multi-phase simulation of the kinetics of formation of Mn-Ni-Si precipitates was performed using a cluster dynamics model with both homogeneous and cascade induced heterogeneous nucleation mechanisms. Thermodynamic data obtained from CALPHAD was used to assess the chemical potentials of the solutes in the matrix and precipitates. Good agreements are obtained for predicted composition, number densities, mean radius and size distribution of clusters between the simulation and available experimental results. The model shows that while homogeneous nucleation dominates for high solute alloys, heterogeneous nucleation dominates for low solute alloys under irradiation. The results also highlight that the evolution of these precipitates is very sensitive to the local composition of the steels and the irradiation temperature.

The ageing and the evolution of mechanical properties of pressure vessel steels under radiation has been correlated with the formation of more or less dilute solute clusters. In the dilute Fe alloys, tomographic atom probe analysis show that these clusters are mainly enriched in Cu, Ni, Mn, Si, P. The evolution of these features is governed by the migration of the individual point defects. Understanding the mechanisms responsible requires the use of atomistic simulation of the diffusion and agglomeration of both point defects and solute atoms. Atomistic kinetic Monte Carlo (AKMC) models developed to provide the microstructure state obtained after irradiation require simulations very heavy in terms of computing time. Furthermore, as several substitutional elements (Cu, Ni, Mn, Si, P) and foreign interstitials (C, N) need to be taken into account to describe the alloy, the possible microstructural objects that can form in the alloys are numerous and complex (from clusters to dislocation loops mixed with solutes), their evolution follow very different time scales, when one compares in particular, times associated to local rearrangement of the clusters or their migration. In this work, some optimization methods and strategies that we develop in our AKMC simulations will be presented and discussed. In addition, some recent Density Functional Theory calculation results on the interaction of solutes and carbon with different extended defects (such as small interstitial loops) will be examined, and their use to improve the energetical model of the KMC will be presented.

In this research we have studied dislocation - obstacle interactions over a wide range of obstacle types, environmental and microstructural parameters with the main objectives focused on the direct comparison with available and future experiments. Conventional range of parameters such as obstacle size, temperature range and dislocation speed effects was considered together with the specific output from “computer modeling experiment”.This includes stress-strain behavior, critical resolved shear stress (CRSS) temperature dependence and a complete analysis of the interaction mechanisms and their temperature behavior.For the mechanism analysis we used a recently developed new dislocation characterization and visualization technique that allowed us to define the dislocation line direction and the local Burgers vector with an unachievable so far accuracy.This new technique allows us to have a direct comparison with in situ deformation TEM experiments and especially with the recently developed 3D TEM tomography.
This work was supported by the US Department of Energy Office of Fusion Energy Sciences.

Iron based alloys serve as critical infrastructure for various energy applications, many of which require these structural alloys to work in challenging conditions. For instance, iron-based alloys have been considered as candidates of structural component for next-generation fission and fusion energy system, demanding improved radiation resistance and mechanical properties. To better understand the effects of complex composition profile on the electronic structure of these materials and their corresponding influence on the mechanical properties, we have determined the ideal shear strength (ISS) of the body center cubic (bcc) iron-chromium and the face centered cubic (fcc) iron-nickel random alloys using density functional theory. The ISS is the minimum stress needed to plastically deform an infinite dislocation free crystal but offers an upper bound to the strength of a real crystal. We have performed spin polarized DFT calculations for the {110}<111> and {211}<111> slip systems for the bcc Fe-Cr, and the {111}<110> and {111}<211> slip systems for the fcc Fe-Ni compounds. The ISS for both slip system have been determined and the relationship between composition and ISS as well as elastic constants has been established as a function of alloy compositions. The focus of this study is the change in electronic structure caused by the alloying composition, which may provide further fundamental insights on how to improve the mechanical properties of these strategically important iron-based alloys.
This material is based upon work supported as part of the Center for Defect Physics, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number ERKCS99.

We present a Green&’s function formulation for the climb of curved dislocations and multiple dislocations in three-dimensions. In this new dislocation climb formulation, the dislocation climb velocity is determined from the Peach-Koehler force on dislocations through vacancy diffusion in a non-local manner. The long-range contribution to the dislocation climb velocity is associated with vacancy diffusion rather than from the climb component of the well-known, long-range elastic effects captured in the Peach-Koehler. Both long-range effects are important in determining the climb velocity of dislocations. Analytical and numerical examples show that the widely used local climb formula, based on straight infinite dislocations, is not generally applicable, except for a small set of special cases. We also present a numerical discretization method of this Green&’s function formulation appropriate for implementation in discrete dislocation dynamics (DDD) simulations. In DDD implementations, the long-range Peach-Koehler force is calculated as is commonly done, then a linear system is solved for the climb velocity using these forces.

This presentation describes in situ measurements of irradiation-induced compression creep on amorphous (a-) Cu₅₆Ti₃₈Ag₆, Zr₅₂Ni₄₈, Si, and SiO₂ micropillars bombarded with ~2 MeV Ne⁺, Ar⁺, and Kr⁺ ions at room temperature. We have employed a custom mechanical testing apparatus¹ which is composed of a nanopositioner, a doubly-clamped silicon beam transducer, and an interferometric laser displacement sensor. The apparatus has a displacement resolution of 1 nm and force resolution of 1 mu;N. Amorphous Cu₅₆Ti₃₈Ag₆ samples were prepared by ball milling and single crystal Si microposts were fabricated by deep reactive-ion etching. Amorphous Zr₅₂Ni₄₈ and SiO₂ were deposited on Si microposts through magnetron sputtering and plasma enhanced chemical vapor deposition. Silicon samples were amorphized by pre-irradiation. The micropillars of 1 mu;m diameter and 2 mu;m height were milled by using a focused ion beam, and amorphous structure of the samples were verified by electron diffraction and X-ray diffraction analyses.
We have observed Newtonian flow in the stress range 50-600 MPa and determined that for point defect mediated creep, irradiation-induced fluidity is asymp;3 GPa^-1dpa^-1 irrespective of the material and bombarding ion. When the electron mobility of the material is low and electronic stopping power is above a certain threshold, stress relaxation through thermal spikes can also contribute to creep, increasing the fluidity. Measurements on Ar⁺ and Ne⁺ irradiated a-SiO₂ have resulted in fluidities of 35 and 83 GPa^-1dpa^-1, demonstrating the additional effect of thermal spikes. Measurement results corresponding to point defect mediated creep are in very good agreement with molecular dynamics simulation predictions² and previous stress relaxation measurements³. We quantitatively explain the additional contribution of electronic stopping by using a previous model of stress relaxation in thermal spikes⁴. MeV heavy ion irradiation of micron-sized specimens results in unique combinations of electronic and nuclear stopping and provides an effective approach to the analysis of irradiation-induced creep.
¹ S. Özerinccedil;, R.S. Averback, and W.P. King, J. Nucl. Mater. 451, 104 (2014).
² S.G. Mayr, Y. Ashkenazy, K. Albe, and R.S. Averback, Phys. Rev. Lett. 90, 055505 (2003).
³ E. Snoeks, T. Weber, A. Cacciato, and A. Polman, J. Appl. Phys. 78, 4723 (1995).
⁴ H. Trinkaus and A.I. Ryazanov, Phys. Rev. Lett. 74, 5072 (1995).

Recent electron microscope observations of defects produced in collision cascades in the limit of very low irradiation dose provide evidence that, even at the moment of production, clusters of defects strongly interact [1]. Dislocation loops and vacancy clusters formed in a cascade are separated by distances comparable with their size, resulting in elastic interaction energies on the scale given by the product of the shear modulus and atomic volume. Direct evaluation of such energies from electron microscope images show that they often exceed one or several electron volts. Such an energy scale is comparable with the height of energy barriers characterising thermally activated motion of individual defects, for example vacancies, giving rise to fairly complex dynamical evolution, where thermally activated migration and interaction between defects manifest themselves over similar temperature intervals and timescales. We review recent experimental data and simulation results [2,3] illustrating the part played by elastic interaction between radiation defects, and explaining the origin of the observed complexity of microstructural evolution under ion and neutron irradiation.
[1] D.R. Mason, X. Yi, M.A. Kirk, S.L. Dudarev, J. Phys.: Condens. Matter 26 (2014) 375701; [2] S.L. Dudarev, K. Arakawa, X. Yi et al., J. Nucl. Mater. 455 (2014) 16; [3] S.L. Dudarev, M.R. Gilbert, K. Arakawa et al., Phys. Rev. B81 (2010) 224107

Using the MMonCa Object Kinetic Monte Carlo code we have studied the impact of carbon content on the evolution of dislocation loops in iron-carbon.
In this study we have introduced explicitly, and for the first time, the carbon atomic features, i.e, the number and position of C atoms, plus their interactions with vacancies to form clusters and with the loops. Carbon migration, and emission from loops and carbon vacancy clusters is also included. Parametrization of the carbon vacancy clusters is based on ab-initio calculations. The treatment of the interactions of C interstitials and loops, and of the loops themselves, is based on molecular dynamics results, and includes a) a detailed description of the interacion of carbon with loops and loops themselves, b) the 1D migration of some dislocation loops, c) the emission, and growth of such loops by interstitial atoms, and d) the explicit treatment of carbon vacancies complexes (formation and dissolution).
Part of this treatment is the assumption that mobile dislocation loops become immobile when decorated with carbon, and the existence of two types of dislocation loops, <111> and <100>, plus small interstitial clusters, where only the first and last time diffuse, in 1 and 3D respectively.
We demonstrate that saturated loop density strongly depends on carbon content and temperature, in good agreement with in-situ irradiation microscopy studies. Finally, we rationalize the physical processes responsible for the accumulation and long range migration of the loops, and their implications for the low dose rate neutron irradiation of the nanostructural evolution in commercial steels.

Oxide Dispersion Strengthened (ODS) alloys based on a Fe-Cr ferritic or ferritic-martensitic matrix (chromium content is about 9~ 18%), are good candidates for structural components in the new generation of nuclear reactors (fission and fusion) where they will be submitted to high operating temperatures (T>550°C) and high neutron irradiation damage . ODS steels are fabricated using mechanical alloying and their good properties depend on the composition, the size and the homogeneous dispersion of nanometric oxide (very often made of Y-Ti- O) particles. But their formation mechanism is not yet clarified. The excess vacancy defects introduced in ODS fabrication process, during mechanical alloying, have been considered to be one of the key points for oxide composition and formation mechanism. By combining the techniques of positron annihilation spectroscopy (PAS) and secondary ion mass spectrometry (SIMS), we aim to obtain information about the interaction between vacancy defects and impurities such as Y, Ti, and O in Fe and Fe-Cr alloy.
In this work we focus our studies on the Oxygen-vacancy couple. High purity Fe samples (99.99%) have been implanted with oxygen ions at 2 energies (285 and 560 keV) and 3 fluences (from 4.6x10¹⁴ to 2.7x10¹⁵cm^-2) and room temperature. A slow positron beam coupled to a Doppler broadening spectrometer allowed to characterize the vacancy defects induced by oxygen implantation and the oxygen depth profile has been measured using SIMS. Measurements are perfomed after implantation and after annealing in different conditions.
The vacancy defects depth distribution is heterogeneous and can be modeled with at least 2 layers: In a first region close to the surface vacancy clusters were detected, and their concentration and size is reduced in a second one. The thickness of these two layers depends on the energy and fluence of the implanted ions. At low fluence, the first layer stops at about 170 nm for the lowest energy to about 300 nm for the highest. The second layer where the detected vacancy cluster concentration and size is reduced correspond to implantation peak as measured with SIMS. It indicates that O atoms are involved in the processes that lead to the defect distribution. The vacancy and oxygen depth profiles evolve after room temperature storage and annealing performed between 100 to 550°C under vacuum. The evolutions are discussed in regards with the theoretical data on the properties (migration, binding, hellip;) of the vacancy and oxygen.

Under irradiation, a large amount of vacancies (V) are produced. They strongly interact with interstitial solutes (X) such as carbon (C), nitrogen (N) and oxygen (O) atoms, which are always present in steels, either as alloying elements or as impurities. The V-X attraction influences the mobility of both the solutes and the vacancies. On one hand, a decrease of the vacancy mobility has been revealed experimentally in the presence of carbon and nitrogen, most likely due to the trapping of vacancies at small vacancy-solute complexes [1, 2]. On the other hand, however, it is not clear whether vacancies always reduce the mobility of the interstitial elements.
Density Functional Theory (DFT) calculations have been performed to study the energetic and kinetic properties of V_nX_m clusters. Low-energy configurations of small V_nX_m have been determined. It has been revealed that vacancies enhance the clustering of solutes. Moreover, a systematic comparison of C, N and O - neighbors in the Periodic Table - shows different behaviors of the solutes in the neighborhood of vacancies as a function of the electronic band filling.
The mobility of the V_nX_m clusters has been carefully studied. We especially focused on the V_nX clusters as it has been shown that V₂ and V₃ are even more mobile than a monovacancy in α-Fe [3]. As a result, all the V₃X have been found to be very mobile. In particular, some clusters can be as mobile as the isolated solutes. Therefore, vacancies may be efficient to drag the interstitial solutes towards sinks such as grain boundaries, dislocations and free surfaces. Also, the result found on the mobility of small V_nN clusters may explain the apparent discrepancy between the resistivity recovery experiments and the DFT data [2]. The interpretation of such experiments may be worth revisiting in the light of the present DFT prediction.
The obtained DFT data have been used to parameterize a Cluster Dynamics model, based on the Rate Theory, which allows to predict the time evolution of the clusters concentration. The consequences of small highly mobile clusters on the kinetic properties of vacancies and solutes under various irradiation conditions have been explored using this model.
This work is supported by the joint program "CPR ODISSEE" funded by AREVA, CEA, CNRS, EDF and Mécachrome under contract n°070551.
[1] S. Takaki et al., Rad. Eff. 79, 87 (1983).
[2] A. L. Nikolaev et al., J. Nucl. Mater. 414, 374 (2011).
[3] C.-C. Fu et al., Nature Mater. 4, 68 (2005).

Solute diffusion in alloys is predominantly mediated by defect-driven mechanisms. Especially in irradiated materials, the defect concentrations can be considerably larger than in thermal equilibrium and solute diffusion can be strongly enhanced or even induced. In a recent work [1] it was shown that, in Fe-based dilute binary alloys, solute atoms such as Cu, Mn, Ni, P and Si are characterized by a strong correlation with the vacancy flux, and vacancy-driven diffusion occurs below the Curie temperature mostly through vacancy drag, in which a vacancy and a solute atom diffuse together as a small cluster. This has great impact on the alloy microstructural evolution, especially on the formation of embrittling nanofeatures and on the radiation induced segregation tendencies in reactor pressure vessel (RPV) steels, whose operational temperature is considerably lower than the threshold at which drag disappears.
The aformentioned species show, at different extents, the same drag tendency as function of temperature, and are all characterized by an attractive interaction with vacancies at first and second nearest neighbor (nn). However, among the transition metals three classes can be distinguished, depending on the solute-vacancy binding interaction in an iron matrix: (i) binding; (ii) binding at 1nn and repulsive at 2nn; (iii) binding at 2nn only [2]. This can lead a priori to different drag tendencies, as the vacancy drag depends not only on the binding energy, but also on the combination of several vacancy-jump frequencies around the solute atom. In this work we perform a systematic investigation of the several drag trends that can be found in Fe-X binary alloys, with X being any transition metal, by applying the same ab initio-mean field approach used in [1]. We will discuss the consequences of the calculated drag tendencies in terms of solute diffusion and radiation-induced segregation tendencies, in particular for the minor impurities that are found in RPV steels.
References:
[1] L. Messina et al., Phys. Rev. B 90, 104203 (2014).
[2] P. Olsson et al., Phys. Rev. B 81, 054102 (2010).

The multiscale modeling scheme that is typically envisioned covers a range of computation methods; these include: ab initio electronic structure methods at the finest scale and the highest accuracy, atomistic methods such as molecular dynamics, mean-field models based on reaction rate theory, and continuum models or finite element approaches at the coarsest scale. Currently there is little direct integration of these methods, rather information is passed in some fashion between scales. For example, ab initio calculations are used to develop empirical potentials for use in molecular dynamics simulations, and the results from MD simulations can be used to parameterize Monte Carlo models. Increasing computing capability has enabled larger scale ab initio and atomistic simulations, but the limits for both remain well below the scale of most experimental measurements. Moreover, advanced computing capabilities have done little to extend the time scale accessible by these more accurate methods. Recent development and application of on-the-fly atomistic kinetic Monte Carlo methods provide the most promising approach to reaching the longer time scales required to investigate evolution of radiation-induced defects while maintaining fidelity to the underlying physical processes. Together with molecular dynamics, these methods play a crucial role in our still-developing understanding of microstructutal evolution under irradiation. The central role of atomistic simulations in the multiscale modeling scheme will be discussed and illustrated with several examples from recent research.

The crystalline defects, which are produced under irradiation, aggregate in clusters and play an important role in the microstructural evolution of materials. Large time-space scale simulations for radiation embrittlement of fusion materials, based on radiation-induced defects and dislocation microstructure, generated by ions and/or neutrons, require valuable inputs for the growth of point-defect clusters. The dislocation loops at nanometric size are too small to be characterized by the experiment or too big to be investigated by a reliable energetic model as ab-initio. Empirical potentials give a good basis for self-interstitial clusters but the reliability of these potentials is continuously revised with the last advancements in the field of ab-initio electronic structure calculations [1-4]. In this presentation, we propose the development of an energetic model for the self-interstitial clusters in body centered cubic metals which is able to predict the relative stability of large self-interstitials clusters up to nanometric-size directly from ab initio calculations performed on small clusters. We will apply this model in the case of Fe and W. We will give particular attention to the relative stability of the traditional dislocation loops with <100> and ½<111> orientations in W as well as the C15 clusters, recently predicted by the DFT in Fe [5]. The theoretical findings will be compared with recent experiments in W [6].
[1] C. C. Fu, F. Willaime, and P. Odrejon, laquo; Stability and mobility of mono- and di-interstitials in alpha-Fe raquo;, Phys. Rev. Lett., 92,175503, (2004).
[2] D. A. Terentyev, T. P. C. Klaver, P. Olsson, M.-C. Marinica, F. Willaime, C. Domain, and L. Malerba, laquo; Self-Trapped Interstitial-Type Defects in Iron raquo;, Phys. Rev. Lett., 100, 145503, (2008).
[3] L. Malerba, M. C. Marinica, N. Anento, C. Björkas, H. Nguyen, C. Domain, F. Djurabekova, P. Olsson, K. Nordlund, A. Serra, D. Terentyev, F. Willaime, and C. S. Becquart, laquo; Comparison of empirical interatomic potentials for iron applied to radiation damage studies raquo;, Journal of Nuclear Materials, 406, 19, (2010).
[4] M.-C. Marinica, L. Ventelon, M. R. Gilbert, L. Proville, S. L. Dudarev, J. Marian, G. Bencteux, and F. Willaime, laquo; Interatomic potentials for modelling radiation defects and dislocations in tungsten raquo;, Journal of Physics: Condensed Matter, 25, 395502, (2013).
[5] M.-C. Marinica, F. Willaime, and J.-P. Crocombette, laquo; Irradiation-Induced Formation of Nanocrystallites with C15 Laves Phase Structure in bcc Iron raquo;, Phys. Rev. Lett., 108, n025501, (2012).
[6] X. Yi, M. L. Jenkins, M. Briceno, S. G. Roberts, Z. Zhou, and M. A. Kirk, laquo; In situ study of self-ion irradiation damage in W and W-5Re at 500 °C raquo;, Philosophical Magazine, 93, 1715, (2013).

The development of radiation-induced lattice damage in steels has been identified as one of the primary causes for material degradation in the structural materials of light-water-reactors. As a commonly observed configuration for interstitial clusters in Fe-based alloys, the formation mechanisms of <100> prismatic loops has remained unclear. Combining molecular dynamics simulations and elasticity, this work reveals a new mechanism for the formation of prismatic loops in body-centered-cubic iron, via direct transformation from C15 phase self-interstitial clusters. Both molecular dynamics simulations and elasticity theory analysis show a crossover in the relative stabilities between different interstitial cluster configurations, including the C15 phase structure and prismatic loops. Within a certain size threshold (~ 30 interstitials), C15 clusters are found to be more stable than loops, but the relative stabilities are reversed beyond this range. Consistent with the crossover in relative stabilities, C15 clusters can grow by absorbing individual interstitials at small sizes and transform into loops at large sizes. Both <100> and <111>/2 loops are possible transformation products. The transformation takes place by nucleation and subsequent reaction of multiple <111>/2 segments. These results explain why the theoretically-predicted C15 phase interstitial clusters have never been observed in previous experiments. More importantly, this finding reveals a new formation mechanism for <100> loops which does not require prior formation of <111>/2 loops, in contrast to many previous studies.

To predict the microstructural evolution in metals upon irradiation, we require accurate understandings of structures and dynamic behaviors of radiation-produced lattice defects, such as atomic-size point defects (self-interstitial atoms (SIAs) and vacancies) and nanometer-sized point-defect clusters (dislocation loops, cavities, etc.). We have been examining the dynamics of these small defects using transmission electron microscopy (TEM), which is one of the most hopeful experimental techniques for directly detecting dynamics of defects. Actually, we have directly traced dynamics of individual loops [1, 2]. In addition, we recently extracted dynamic properties of even fast-migration point defects, which cannot be directly traced even using cutting-edge TEM.
In the present talk, our results on the dynamics of point defects and their clusters are shown, such as diffusivity of loops, migration dimension of SIAs, etc. These results are compared with those obtained by recent simulation studies.
[1] Arakawa, K. et al., “Changes in the Burgers Vector of Perfect Dislocation Loops without Contact with the External Dislocations,” Phys. Rev. Lett., 96 (2006) 125506.
[2] Arakawa, K. et al., “Observation of the One-Dimensional Diffusion of Nanometer-Sized Dislocation Loops,” Science, 318 (2007) 956.

There is a long standing controversy regarding the formation of <100> and ½ <111> loops in a-Fe and FeCr alloys under irradiation. The formation of these loops, the ratio of one type vs. the other and even their nature depends strongly on the type of irradiation (electron, ions or neutrons), temperature and the sample thickness. For the case of self-interstitial loops, the mechanism of formation of <100> loops is still under debate.
In this work we combine results from molecular dynamics simulations and density functional theory (DFT) calculations into an object kinetic Monte Carlo [1] to study damage accumulation and microstructure evolution in a-Fe thin films under irradiation. Firstly, the damage produced by the ion is simulated with molecular dynamics considering the presence of the surface. These calculations show that the primary damage in thin films is very different from the primary damage in the bulk material. For example, large vacancy clusters are produced under ion implantation more frequently than in the bulk, most of them of <100> type.
To study the evolution of the damage under implantation we compare two different models for the formation of <100> self-interstitial loops. In one of the models we consider that ½ <111> loops interact to produce <100> loops following the results from molecular dynamics simulations by Marian et al. [2] and the SEAKMC simulations by Terentyev et al [3]. The second model assumes that two populations of loops are formed in the collision cascade, mobile <111> loops and immobile self-interstitial clusters. These immobile clusters are considered to be the ones that evolve towards <100> self-interstitial loops. This model is based on the observation of stable immobile clusters from DFT calculation [4]. In this work we compare the population of loops formed as a function of dose for conditions used experimentally [5] and discuss the validity of the models and the influence of different parameters.
[1] I. Martin-Bragado, et. al., MMonCa: An Object Kinetic Monte Carlo simulator for damage irradiation evolution and defect diffusion. Computer Physics Communications (2013).
[2] J. Marian, Brian Wirth and J. Manuel Perlado, Phys. Rev. Lett. 88, 25 (2002).
[3] Haixuan Xu, Roger E. Stoller, Yuri N. Osetsky and Dmitry Terentyev, Phys. Rev. Lett. 110, 265503 (2013).
[4] M.-C. Marinica, F. Williaime, J.-P. Crocombette, Phys. Rev. Lett. 108, 025501 (2012).
[5] Z. Yao, M. Hernández Mayoral, M. L. Jenkins, M. A. Kirk, Phil. Mag. 88 (2008) 2851.

We investigate the structure and ion-conducting properties of the defect-fluorite ring structure formed around amorphous ion-tracks in swift heavy ion irradiation of pyrochlore-Gd₂Ti₂O₇. Using high angle annular dark field (HAADF) imaging, we show that the ring structure has relatively larger cation-cation interspacing than that in the bulk pyrochlore. From our density functional theory (DFT) calculations, we find that the transformation from pyrochlore to defect fluorite could be achieved by straining the bulk pyrochlore, thus stabilizing the defect-fluorite structure. Using static pair-potential calculations, we also find that planar tensile strain lowers oxygen vacancy migration barriers. This strain-induced lowering of migration barriers has been widely observed recently in other materials such as ZrO₂, CeO₂, etc. In view of these results, we suggest that strain engineering could be possibly used to stabilize the defect-fluorite structure, and gain control over its high ion-conducting properties.
This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.

Amorphous silicon oxycarbides (SiOC) are a promising class of radiation-resistant materials. We present a multi-scale modeling investigation of unit displacement damage processes in these materials using classical potentials and density functional theory (DFT). 0.1keV primary knock-on atoms (PKAs) are modeled in SiO₂ and SiOC following the construction of reliable atomic structures for SiOC. Comparisons of responses of SiO₂ and SiOC with different C distributions are performed to reveal the role of C plays in the performance of SiOC, such as defect formation, atomic structure evolutions, and internal energy changes.
This work was funded by the DOE Office of Nuclear Energy, Nuclear Energy Enabling Technologies, Reactor Materials program, under contract No. DE-NE0000533. Computational support was provided by DOE-NERSC and NSF XSEDE-TACC.

The evolution of radiation defects after cascade thermalization plays the dominant role in the formation of stable radiation disorder in most nuclear materials. However, our current understanding of such defect dynamic processes remains limited. Here, we develop a pulsed-ion-beam method to gain insight into defect interaction dynamics and apply it to Si and SiC. We measure the effective time constant of defect interaction by studying the dependence of damage on the passive part of the beam duty cycle, while the effective defect diffusion length is estimated from the dependence of damage on the active part of beam cycle. We further study how these dynamic parameters depend on the average density of collision cascades, the maximum instantaneous defect generation rate, and sample temperature.
This work was performed under the auspices of the U.S. DOE by LLNL under Contract DE-AC52-07NA27344.

ZrC, ZrN and SiC possess excellent physical and thermochemical properties, which could be exploited for fuel encapsulation in the new generation nuclear reactors that will work at higher temperatures than the present ones. To study their properties, thin films were grown on (100) Si substrates by the pulsed laser deposition (PLD) technique using a KrF excimer laser. The deposited films were ion-irradiated at room temperature by 800 keV Ar ions to qualitatively simulate disorder induced by neutron irradiation at the micrometer-scale. The maximum damage for the highest irradiation dose was estimated to be around 50 dpa (displacements per atoms). X-ray reflectivity and diffuse scattering investigations were used to estimate the mass density and surface and interface roughness, while glancing incidence X-ray diffraction investigations were used to assess the structure of the films and modifications induced by the ion irradiation. X-ray photoelectron spectroscopy investigations using hard X-ray allowed for sampling a deeper region than that obtained by using the usual Al or Mg K alpha radiation. Therefore, information about the chemical bonding in the irradiated region was collected without the need of Ar ion sputtering. Also, modifications of the chemical bonding in the irradiated volume was investigated by performing Raman scattering investigations. Nanoindentation tests and optical reflectance measurements were employed to assess changes of the mechanical and optical properties of the films after irradiation.
Results showed that after irradiation at a dose of around 10¹⁴ at/cm² the structural modifications were relatively small, whereas the mechanical properties were slightly poorer with respect to the as-deposited ones. After irradiation at doses around 10¹⁵ at/cm², the lattice parameters increased by several percentages, the mass density decreased and chemical modifications of the atoms bonding were clearly observed. The mechanical properties sharply decreased, roughly by more than 30-40 % of the as-deposited values.

Time dependent density functional theory, TD-DFT, provides a framework to study the ion-electron interaction in computer simulations of radiation damage by energetic ions on solids. It gives a quantitative value for the damping term that can be used in the Langevin equations of motion for the ions. This term represents a viscous damping of ionic motion, i. e. is proportional to the ion velocity.
Several empirical models have been proposed for the dependence of this viscous term on the host electronic density. In this work, we explore the density dependence given by TD-DFT aiming at providing a single framework that could account for the electron-phonon interaction regime, at very low ion motion energy, and the electronic stopping regime, at much higher energies.
Work at LANL supported by the DOE Office of Basic Energy Science Energy Frontier Research Center Energy Deposition to Defect Evolution, and at LLNL by the Laboratory Directed Research and Development Program.

In order to investigate short-term radiation damage accumulation, an integrated atomistic model has been developed that combines successive applications of displacement cascade simulations generated by molecular dynamics (MD) with long-time aging performed using the kinetic Activation-Relaxation Technique (k-ART), an atomistic off-lattice kinetic Monte Carlo algorithm. Under ion irradiation conditions, waiting times between successive cascades in the same volume reach times of the order of one second; simulating defect evolution for such times is completely out-of-reach for classical MD. Although high-temperature MD is sometimes used to accelerate aging, entropic effects involved by this procedure might drastically modify the outcome of the simulations. To resolve this issue, a powerful adaptive Monte Carlo algorithm, k-ART, is used to simulate the defect evolution during the time between successive cascades in a given volume. In order to compare with recent experimental data, the simulations have been performed in fcc metals and alloys: Ni, NiCo, NiFe and NiPd. Embedded-atom-method-based classical potentials have been used with a mixing procedure for the binary alloys that is based on the enthalpy of solution. The results are compared to experimental measurements of damage accumulation after ion-bombardment at various fluences and provide an atomistic explanation for the dose-dependent behavior of these systems. The work was supported as part of the “Energy Dissipation to Defect Evolution”, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science.

Irradiation induced swelling is one of the primary issues in development of new types of nuclear power plants. This effect on structural materials can severely restrict the lifetime of a reactor. It was recognized that the microstructure of the material after the irradiation is the key for understanding the phenomenon. In addition, the microstructural evolution, such as the growth of voids, the formation and migration of dislocation loops, are of importance. Much research has been done and models have been developed to explain the variety of phenomena observed. One of the widely recognized parameters used in those models is the dislocation bias. Dislocation bias describes the preference of dislocation on self-interstitials than on vacancies. This bias is regarded as the intrinsic driving force in the standard rate theory model² and an integral part of production bias model (PBM)³. Nevertheless, the parameter is either obtained by fitting certain experiments with a model or calculated analytically with the first order size interaction between point defects and dislocations.
A systematic study of dislocation bias has been performed using a method that combines atomistic and analytical dislocation-point defect interaction models with a numerical solution of the diffusion equation with a drift term. Cooper, nickel and aluminum model lattices are used in this study to represent a range of elastic constants and stacking fault energies. It is found that the dominant parameter for the dislocation bias in fcc materials is the distance between the split partial dislocations. The different elastic properties do not have large impacts on the dislocation bias calculation. As a result of this analysis, the dislocation bias of an austenitic alloy model is predicted to be about 5% at 815K with a dislocation density of 10¹⁴ m^-2 by comparing its properties with the sample model lattices.

One of the challenges of multiscale modelling is the development of computational tools capable of simulating the experimentally observed nanostructural evolution of materials subjected to irradiation, based on physical mechanisms parameterised on information coming from more fundamental approaches. Object kinetic Monte Carlo (OKMC) methods are a suitable tool to tackle this challenge. In OKMC the production of defects by irradiation and their evolution via migration, clustering, recombination and dissolution of clusters, as well as absorption at sinks, is quite realistically simulated in a given volume, spontaneously allowing for any spatial correlation effect. The input of the model are the probabilities for all the relevant events, that must be acceptably assessed. OKMC methods are very flexible: since the defects occupy precise positions in the volume in which they evolve, the implementation of physical mechanisms such as one-dimensional migration or repulsion due to specific nanostructural features, is achieved in a relatively straightforward way. The method does not generally explicitly include atoms in the system, but rather their effect on defect evolution, thereby remaining computationally more efficient than, e.g., atomistic KMC models. The main limitations come from: (1) the still non-negligible computational load, which de facto limits the simulations to doses < 1 dpa and temperatures < 350°C (in Fe alloys), if the volume has to be statistically representative; (2) the large amount of parameters that is needed to correctly express all the relevant probabilities, especially if the real system to be simulated exhibits a degree of chemical complexity. While the solution to the former problem relies on advances in computer power or development of suitable algorithms to speed up the simulation, the latter requires not only extensive calculations using atomistic techniques to calculate parameters, but also, unavoidably, physical insight to identify suitable approximations for the specific system to be studied.
In this presentation we overview recent work of development of OKMC models to successfully simulate nanostructural evolution in irradiated and annealed iron alloys, showing how the effect of interstitial and substitutional elements can be incorporated to obtain acceptable predictions of experimental results, with the added value of identifying the key mechanisms that drive the evolution. Fe-C-Mn-Ni alloys and Fe-C-Cr alloys will be specifically addressed, as model materials for, respectively, reactor pressure vessel steels and ferritic/martensitic steels. In the case of the latter, progress in describing simultaneously, within the same OKMC model, both radiation defect evolution and precipitation of phases, will be reported.

During operation of future fusion reactors, it is expected that energetic neutrons arising from fusion reactions will generate primary knock-on atoms (PKA) with energies as high as MeV in materials surrounding the plasma such tungsten or steels. In turn, these PKAs will trigger numerous collisions in materials, displacing a large amount of atoms from their lattice sites. The defects thus formed during collision cascades will then evolve and migrate during long time, eventually leading to hardening or embrittlement, which may strongly affect macroscopic properties of irradiated materials. Therefore, it is essential to accurately predict the formation of defects during collision cascades in order to precisely simulate their subsequent evolution. On one hand, Molecular Dynamics (MD) allows to simulate the motion of each atom of the system, given an interatomic potential. The advantage of MD is that it accounts for complex processes such as the emission of phonons and interaction and recombination of defects during the cooling phase of the cascade. However, the computational cost strongly increases as the PKA energy does since the system to simulate quickly reaches several hundreds million atoms. On the other hand, the Binary Collision Approximation (BCA) is significantly more efficient than MD since the motion of atoms in their equilibrium position in the lattice is ignored and only displaced atoms are followed. Between two collisions, the trajectory of a projectile is assumed to be rectilinear but the energy loss can be taken into account through the electronic stopping power. However, the BCA is only valid during the ballistic phase of the cascade, i.e. while the velocity of the projectile is higher than the velocity of lattice atoms. When the velocity of the projectile is in the order of the velocity of the sound in the material, the BCA breaks down since the collective movement of atoms must be taken into account. Furthermore, the BCA does not take into account the interaction or recombination of defects during the cooling phase of the cascade since it does not take into account the long-range interatomic potential between atoms. Therefore, the BCA is not able to predict the size or morphology of defects that form in dense cascades.
In this work, we propose a hybrid approach combining both advantages of MD and BCA. BCA is first used to simulate the high-energy part of cascades, until a predefined criterion is reached. Then, coordinates, velocities and energy of atoms in movement, as well as coordinates of vacancies, are used as input in the MD model. MD model is then used to simulate final stages of the cascades, accounting for collective movement of atoms and the formation of stable defects. Results obtained with this hybrid approach are studied as a function of different criteria and compared to results obtained with pure MD simulations. The speedup achieved with this hybrid approach as a function of the PKA energy is also discussed.

Recently, high entropy alloys (HEAs) have received lots of attention as a candidate material for extreme environments due to their superior properties. According to traditional thermodynamic point of view, it is difficult to make single solid solution with multicomponent alloy systems, because of Gibbs phase rule. However, HEAs exhibit unique single solid solution with multi-constituents by forming single solid solution in high temperature range at once and by keeping their structure to room temperature due to sluggish diffusion. Therefore, HEAs can be considered as metastable single solid solution which is stable in high temperature. High pressure torsion (HPT) is a type of severe plastic deformation experiment inducing severe plastic shear deformation to the materials, which is a useful method to evaluate stability/safety of metallic materials in extreme environments. In this study, we report the effects of HPT on structural changes in AlxCoCrFeNi HEAs, which have different crystal structures depending on Al contents. BCC-type HEAs exhibit higher phase stability than FCC-type HEAs under severe deformation. This result would offer a guideline to design a new type of next generation nuclear materials under harsher environments.

The nucleation, growth and diffusion of helium bubbles and voids, as well as dislocation loops, will significantly affect the global evolution of microstructures and consequently degrade the mechanical properties of materials. Development of advanced steels for reactor components requires an understanding of the kinetics of helium atoms, voids and dislocation loops, including the their formation, mobilities and interactions with microstructural features in materials, which is inherently a multiscale phenomenon.
A steady-state accelerated molecular dynamics (SSAMD) method is developed to model infrequent atomic-scale events, which is applicable to the events on a rugged free-energy surface. In this method, the total displacement of a system in its equilibrium state can be determined for a given temperature, and is used to construct a boost-potential to accelerate molecular dynamics simulations. The boost-potential is slowly increased, allowing the system to evolve from a steady state to another, and thus, leading to a state transition. This approach is self-evolving and can be applied to the coupled motion of fast and slow dynamics. We have applied the SSAMD method to investigate the evolution of He-V clusters in times on the order of ~10² s in Fe. A helium-rich He-V cluster migrates by an interstitial-assisted mechanism, which contrasts with the vacancy-assisted migration mechanism found for a vacancy-rich He-V cluster. The SSCMD approach is also applied to study the growth of a nano He-V cluster from small clusters, and it is found that Ostwald ripening is responsible for cluster evolution by mass transport from one cluster to another. In addition, SSCMD method has been applied to study the nucleation and growth of voids, as well as the directional changes of dislocation loops from <111> to another <111> or from <111> to <100> in Fe.

Zirconium alloys are utilized in the nuclear energy industry for nuclear fuel cladding. The formation of hydrides during reactor operation degrades the mechanical behavior of the cladding due to the brittleness of hydrides. The shape, spatial distribution, and orientation of the hydrides are critical to determining the fracture initiation. Therefore, understanding the hydride precipitate microstructure is a crucial step toward the accurate prediction of life-time of cladding. The hydride nucleation and precipitation is driven by many factors, often competing. In this presentation, we present a phase-field model for simulating #61556;#61544;#61541;#61472;nucleation and growth of the d-hydride precipitate microstructure involving both hydrogen diffusion and the structural transformation in single- and polycrystalline Zr alloys. In particular, the model incorporates solute-grain boundary interactions and the elastic inhomogeneity arising from different grain orientations. We discuss the habit plane orientation, effects of grain orientations and grain boundaries, and influences of an external load on the morphological evolution of hydrides and compare our predictions to experimentally observed microstructures.

Microstructural changes associated with radiation damage mechanisms are fundamental factors influencing the lifetime of structural materials used in nuclear reactors. Reactor materials in service simultaneously experience displacement cascades and transmutation reactions that produce significant quantities of helium. The synergetic effect of helium production and displacement damage on defect structure evolution is, as of today, poorly understood.
In this study, in-situ Transmission Electron Microscope (TEM) characterization is performed on nanocrystalline nickel samples under self-ion irradiation, He implantation, and both simultaneously. Such experimental observations provide insights on the active mechanisms impacting microstructural changes under separate and combined effects.
The experimental setup utilizes a dual-beam ion irradiation system at Sandia National Laboratories, where a 6 MV Tandem accelerator and a 10kV Colutoron ion accelerator are connected to a Transmission Electron Microscope (TEM). Nanocrystalline free-standing nickel thin films were produced by pulse laser deposition. In-situ self-ion irradiation with and without simultaneous helium implantation was performed in the TEM at several temperatures up to 600#730;C. The evolution of radiation-induced defect structures under dual-beam irradiations are monitored in real time through video recordings.
In this study, experimental observations uncovering different active mechanisms during self-ion irradiation and He implantation at different temperatures are reported and compared to other existing observations and models of radiation damage in FCC microstructures. For He⁺ implantation (10 keV He⁺ at doses up to 10²⁰He⁺/m²) at room temperature, no visible voids could be observed. During post irradiation in-situ annealing up to 600#730; C, voids were found to grow and coarsen to observable sizes, with the largest formed bubbles reaching a diameter of 20 nm. For He⁺ implanted to the same dose but at higher temperatures (up to 600#730;C), void size was seen to increase with increasing implantation temperature. The nickel foils were also irradiated with 3 MeV Ni³⁺ at various temperatures with and without simultaneous helium implantation. Ni³⁺ irradiation resulted in clearly visible displacement damage, while dual-beam irradiation resulted in both damage and voids at room temperature at a dose around 10²⁰ He⁺/m² and a total damage of approximately 2 dpa.
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy&’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Nuclear power plants are a major source of energy production in France and account for about 75% of the country's total electricity. In France all the operational nuclear reactors are PWRs, for which nickel base alloys and stainless steels are used in the construction of the steam generator tubes (A600, A690) and reactor internal components (SS316L). Under operating conditions, these components are exposed to a high temperature (HT)-high pressure environment. The corrosion process in this environment promotes the formation of hydrogen by the cathodic reaction that may be absorbed by the alloy [1,2]. Once absorbed, the H can become trapped in the crystallographic defects, or trap sites (TS), present in the material [3-6]. This trapping phenomenon may play an important role in material degradation processes, such as stress corrosion cracking, which may lead to premature component failure.
Since the diffusion and trapping kinetics may be different at HT, it is crucial to determine the kinetic trapping/release constants in order to extrapolate and eventually model what happens at HT during the oxidation process from a dynamic point of view. In order to characterize these H-material interactions TDS has been used. TDS methods generally involve first charging a material with H, or an isotopic tracer, then monitoring its desorption flux during a temperature ramp or at an isotherm. Literature states that information concerning the total H concentration in the material, the amount of H occupying TS, and the respective TS detrapping activation energies can be determined from these spectra [7-10]. In order to access this information, a well adapted spectral analysis technique must be used, but the analytical methods found in literature impose many simplifying hypotheses. It is for this reason the McNabb & Foster equations[11] coupled with experimentally acquired TDS spectra on "model materials" will be used to analyze hydrogen trapping in industrial alloys and derive the associated kinetic constants by using of a numerical routine described elsewhere [12,13]. These kinetic constants are then compared to those found in literature using the common analytical methods. This iterative approach provides the basis for more accurate TDS spectrum analysis and a more comprehensive understanding of complex H-material interactions. Furthermore these constants can be compiled and injected into a more general simulation code which couples several corrosion mechanisms.
[1] F. Jambon, et al, J. Nucl. Mater. (2011)
[2] M. Dumerval, et al, Corr. Sci.(2014)
[3] A. Brass, et al, Mater. Sci. Eng., A (1998)
[4] F. Lecoester, et al, Mater. Sci. Eng., A (1999)
[5] G. Pressouyre, Metall. Trans. A (1979)
[6] W. Choo, et al, Metall. Mater. Trans. A (1982)
[7] T. Kasuya, et al, J. Appl. Phys. (1998).
[8] R. Oriani, Acta Mater. (1970)
[9] A. McNabb, et al, AIME (1963)
[10] C. Hurley, et al, OCAS, 2014.
[11] C. Hurley, et al, under review.

We have explored the nature of helium-helium interaction in metals using a first-principles method. Our findings suggest that the dissolution of helium in metals can be popularly considered as electrophobic: The high electron density plays a key role in the poor solubility of helium in metals, and the significant decrease of local electron density induced by the helium-helium synergistic damaged to metal lattice drives helium atoms to preferably get together in a metallic environment, which reveals the origin of the helium self-trapping in metals.

Self trapping and trap mutation (i.e. the emission of one self interstitial atom (SIA) along with the creation of one vacancy from a vacancy-helium or pure helium cluster) are important mechanisms impacting on the kinetics of helium-bubble nucleation and growth. We have evaluated the thermal stability of helium-vacancy clusters (nHe.mv) as well as pure interstitial helium clusters in tungsten using density functional theory calculations and Molecular Dynamics (MD) using empirical potential. The stability of such objects results from a competitive process between thermal emission of vacancies, SIAs and helium, depending on the helium-to-vacancy ratio in mixed clusters or helium number in pure interstitial helium clusters. We have determined the ground state configurations for self trapping and trap mutation and evaluated the activation barrier for self trapping using MD and nudge elastic band (NEB) calculations. Self trapping is thermally activated and Arrhenius plots of self trapping events observed by MD gave activation energies that have been compared to the ones obtained by the NEB calculations.