Evaluation of thermophysical properties of the LiCl-KCl system via ab initio and experimental methods
}, volume={559}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2021.153414}, abstractNote={Molten Salt Reactors (MSRs) are envisioned as a potential pathway to safer, more economical nuclear electricity generation and supply of industrial heat. MSRs under consideration today are either solid-fueled salt-cooled designs or liquid-salt-fueled designs with chloride or fluoride based salts. A significant knowledge gap exists in the data for the fundamental properties relevant to fuels and coolants for MSRs that needs to be addressed in order to expedite the technical readiness level of the MSR design concepts. With the rapid development and improvement of computational materials science, computational methods such as Density Functional Theory (DFT) calculations and ab initio Molecular Dynamics (AIMD) simulations are widely used as an effective and reliable tool to investigate the atomic interaction in materials. In this article, the density of the LiCl-KCl system was determined via AIMD calculations and verified using new experimental analyses. AIMD was further utilized to calculate the compressibility, heat capacity, enthalpy of mixing, and Gibbs free energy of mixing. This work spans a wider range of compositions and temperatures than have previously been explored computationally for this pseudo-binary system and provides the basis for further advanced thermophysical property evaluation utilizing AIMD methods.}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Duemmler, Kai and Lin, Yuxiao and Woods, Michael and Karlsson, Toni and Gakhar, Ruchi and Beeler, Benjamin}, year={2022}, month={Feb} } @article{park_beeler_okuniewski_2021, title={An atomistic study of defect energetics and diffusion with respect to composition and temperature in gamma U and gamma U-Mo alloys}, volume={552}, ISSN={["1873-4820"]}, url={https://doi.org/10.1016/j.jnucmat.2021.152970}, DOI={10.1016/j.jnucmat.2021.152970}, abstractNote={Uranium-molybdenum (U-Mo) alloys are promising candidates for high-performance research and test reactors, as well as fast reactors. The metastable γ phase, which shows acceptable irradiation performance, is retained by alloying U with Mo with specific quenching conditions. Point defects contribute to the atomic diffusion process, defect clustering, creep, irradiation hardening, and swelling of nuclear fuels, all of which play a role in fuel performance. In this work, properties of point defects in γU and γU-xMo (x = 7, 10, 12 wt.%) were investigated. Vacancy and self-interstitial formation energies in γU and γU-xMo were calculated with molecular dynamics (MD) simulations using an embedded atom method interatomic potential for the U-Mo system. Formation energies of point defects were calculated in the temperature range between 400 K and 1200 K. The vacancy formation energy was higher than the self-interstitial formation energy in both γU and γU-xMo in the evaluated temperature range, which supports the previous results obtained via first-principles calculations and MD simulations. In γU-xMo, the vacancy formation energy decreased with increasing Mo content, whereas the self-interstitial formation energy increased with increasing Mo content in the temperature range of 400 K to 1200 K. The self-diffusion and interdiffusion coefficients were also determined in γU-xMo as a function of temperature. Diffusion of U and Mo atoms in γU-xMo were negligible below 800 K. The self-diffusion and interdiffusion coefficients decreased with increasing Mo concentration, which qualitatively agreed with the previous experimental observations. Point defect formation energies, self-diffusion coefficients, and interdiffusion coefficients in γU-xMo calculated in the present work can be used as input parameters in mesoscale and engineering scale fuel performance modeling.}, journal={JOURNAL OF NUCLEAR MATERIALS}, publisher={Elsevier BV}, author={Park, Gyuchul and Beeler, Benjamin and Okuniewski, Maria A.}, year={2021}, month={Aug} } @article{andersson_matthews_zhang_beeler_2021, title={Density functional theory calculations of the thermodynamic and kinetic properties of point defects in beta-U}, volume={557}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2021.153238}, abstractNote={Density functional theory (DFT) calculations of the thermodynamic and kinetic properties of point defects in the β phase of uranium are reported. Defect energies and entropies were calculated using 2×2×2 supercells and the Generalized Gradient Approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) for the exchange-correlation potential. Due to computational cost, calculations of the vibrational properties governing entropies were performed by only displacing atoms within (roughly) the 3rd or 4th nearest neighbor shell of the defect, which implicitly assumes that atoms beyond this distance are unaffected by the defect. Migration barriers were estimated by nudged elastic band (NEB) calculations. The low symmetry of the β-U phase (the unit cell is tetragonal and contains 30 atoms) results in many point defect configurations and even more migration pathways. A connectivity map, starting from the most stable point defects, was developed in order to identify the rate-limiting step controlling the net diffusion rate in each crystallographic direction. The uranium self-diffusivity tensor was calculated by combining the defect formation energies, entropies, migration barriers and attempt frequencies. The fastest diffusion rate was determined to be a vacancy mechanism in the z crystallographic direction. The predicted uranium self-diffusivity for this mechanism agrees well with available experimental data. The diffusion mechanisms and rates identified in this study will inform fuel performance models of swelling and gas evolution.}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Andersson, D. A. and Matthews, C. and Zhang, Y. and Beeler, B.}, year={2021}, month={Dec} } @article{beeler_mahbuba_wang_jokisaari_2021, title={Determination of Thermal Expansion, Defect Formation Energy, and Defect-Induced Strain of alpha-U Via ab Initio Molecular Dynamics}, volume={8}, ISSN={["2296-8016"]}, DOI={10.3389/fmats.2021.661387}, abstractNote={Uranium (U) is often alloyed with molybdenum (Mo) or zirconium (Zr) in order to stabilize its high-temperature body-centered cubic phase for use in nuclear reactors. However, in all metallic fuel forms, the α phase of U remains in some fraction. This phase decomposition due to temperature or compositional variance can play an outsized role on fuel performance and microstructural evolution. Relatively little is known about fundamental point defect properties in α-U at non-zero temperatures, from either computational or experimental studies. This work performs the first thorough evaluation of the α phase of U via ab initio molecular dynamics (AIMD). A number of thermophysical properties are calculated as a function of temperature, including equilibrium lattice parameters, thermal expansion, and heat capacity. These results indicate a two-region behavior, with the transition at 400 K. The thermal expansion/contraction in the a/b direction occurs rapidly from 100 up to 400 K, after which a more linear and gradual change in the lattice constant takes place. The volumetric expansion matches experiments quantitatively, but the individual lattice constant expansion only matches experiments qualitatively. Point defect formation energies and induced lattice strains are also determined as a function of temperature, providing insight on defect populations and the fundamentals of irradiation growth in α-U. Interstitials induce significantly more strain than vacancies, and the nature of that strain is highly dependent on the individual lattice directions. The direction of point defect-induced lattice strain is contrary to the irradiation growth behavior of α-U. This work shows that isolated point defects cannot be the primary driving force responsible for the significant irradiation-induced growth of α-U observed experimentally.}, journal={FRONTIERS IN MATERIALS}, author={Beeler, Benjamin and Mahbuba, Khadija and Wang, Yuhao and Jokisaari, Andrea}, year={2021}, month={Jun} } @article{mahbuba_beeler_jokisaari_2021, title={Evaluation of the anisotropic grain boundaries and surfaces of alpha-U via molecular dynamics}, volume={554}, ISSN={["1873-4820"]}, url={https://doi.org/10.1016/j.jnucmat.2021.153072}, DOI={10.1016/j.jnucmat.2021.153072}, abstractNote={Alloys based on uranium-zirconium are gaining renewed interest as fuels for the Versatile Test Reactor and a number of microreactor designs. Implementing metallic fuel in reactors creates the need for robust descriptive and predictive fuel performance modeling. The current state of metallic fuel performance modeling relies on empirical equations derived from historical experiments, which may be unreliable when applied outside of their temperature, power, and composition phase space. One area where such data is lacking is the irradiation behavior of α-U, specifically tearing and porosity formation at the early stages of irradiation. While grain boundaries likely play a key role in this fuel behavior, relatively little is known about grain boundaries in α-U. Thus, we evaluate the grain boundary, surface energy, and work of adhesion of α-U utilizing molecular dynamics. Symmetric tilt grain boundaries (STGBs) are analyzed with the tilt plane oriented along each major crystallographic axis, for a total of eighty unique grain boundaries. The effect of temperature, tilt plane, and misorientation angle on interfacial energies are analyzed. The interfacial energies typically increase with temperature and there is significant variance as a function of misorientation angle, irrespective of the tilt plane. At 500 K, the average surface energy (1.23 J/m2) is approximately 1.5 times the grain boundary energy (0.79 J/m2), and the work of adhesion is approximately twice the grain boundary energy (1.68 J/m2). Orientations for the likely formation of twins and likely failure planes are identified.}, journal={JOURNAL OF NUCLEAR MATERIALS}, publisher={Elsevier BV}, author={Mahbuba, Khadija and Beeler, Benjamin and Jokisaari, Andrea}, year={2021}, month={Oct} } @article{hu_beeler_2021, title={Gas Bubble Evolution in Polycrystalline UMo Fuels Under Elastic-Plastic Deformation: A Phase-Field Model With Crystal-Plasticity}, volume={8}, ISSN={["2296-8016"]}, DOI={10.3389/fmats.2021.682667}, abstractNote={In monolithic UMo fuels, the interaction between the Al cladding and large gas bubble volumetric swelling causes both elastic-plastic and creep deformation. In this work, a phase-field model of gas bubble evolution in polycrystalline UMo under elastic-plastic deformation was developed for studying the dynamic interaction between evolving gas bubble/voids and deformation. A crystal plasticity model, which assumes that the plastic strain rate is proportional to resolved shear stresses of dislocation slip systems on their slip planes, was used to describe plastic deformation in polycrystalline UMo. Xe diffusion and gas bubble evolution are driven by the minimization of chemical and deformation energies in the phase-field model, while evolving gas bubble structure was used to update the mechanical properties in the crystal plasticity model. With the developed model, we simulated the effect of gas bubble structures (different volume fractions and internal gas pressures) on stress-strain curves and the effect of local stresses on gas bubble evolution. The results show that 1) the effective Young’s modulus and yield stress decrease with the increase of gas bubble volume fraction; 2) the hardening coefficient increases with the increase of gas bubble volume fraction, especially for gas bubbles with higher internal pressure; and 3) the pressure dependence of Xe thermodynamic and kinetic properties in addition to the local stress state determine gas bubble growth or shrinkage. The simulated results can serve as a guide to improve material property models for macroscale fuel performance modeling.}, journal={FRONTIERS IN MATERIALS}, author={Hu, Shenyang and Beeler, Benjamin}, year={2021}, month={Jun} } @article{gamble_pastore_cooper_andersson_matthews_beeler_aagesen_barani_pizzocri_2021, title={Improvement of the BISON U3Si2 modeling capabilities based on multiscale developments to modeling fission gas behavior}, volume={555}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2021.153097}, abstractNote={Uranium silicide (U3Si2) is a concept explored as a potential alternative to UO2 fuel used in light water reactors (LWRs) since it may improve accident tolerance and economics due to its higher thermal conductivity and increased uranium density. U3Si2 has been previously used in research reactors in the form of dispersion fuel which operates at lower temperatures than commercial LWRs. The research reactor data illustrated that significant gaseous swelling occurs as the fuel burnup increases. Therefore, it is imperative to understand the fission gas behavior of U3Si2 under higher temperature LWR operating conditions. In this work, molecular dynamics and phase-field modeling techniques are used to reduce the uncertainty in select modeling assumptions made in developing the fission gas behavior model for U3Si2 in the BISON fuel performance code. To support the implementation of a U3Si2 fission gas model in BISON, cluster dynamics simulations of irradiation enhanced Xe diffusion have been carried out. Similarly, MD simulations were used to predict the athermal contribution due to atomic mixing during ballistic damage cascades. By combining our results with literature DFT data for thermal equilibrium diffusion, Xe diffusivity has been described over a wide range of temperatures for in-reactor conditions. These lower length scale informed models are then utilized in the assessment of BISON U3Si2 modeling capabilities by simulating the ATF-1 experiments irradiated in the Advanced Test Reactor (ATR). Sensitivity analysis (SA) and uncertainty quantification (UQ) are included as part of the assessment process to identify where further experiments and lower length scale modeling would be beneficial. The multiscale modeling approach utilized in this work can be applied to new fuel concepts being explored for both LWRs and advanced reactors (e.g., uranium nitride, uranium carbide).}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Gamble, K. A. and Pastore, G. and Cooper, M. W. D. and Andersson, D. A. and Matthews, C. and Beeler, B. and Aagesen, L. K. and Barani, T. and Pizzocri, D.}, year={2021}, month={Nov} } @article{cooper_gamble_capolungo_matthews_andersson_beeler_stanek_metzger_2021, title={Irradiation-enhanced diffusion and diffusion-limited creep in U3Si2}, volume={555}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2021.153129}, abstractNote={U3Si2 is an advanced fuel candidate due to its relatively high fissile density and attractive thermal properties. Compared to standard UO2 fuel, there are significant data gaps for the thermophysical and thermomechanical properties of U3Si2. Point defect concentrations and mobilities under irradiation govern a number of important fuel performance properties, such as creep and fission gas release. In this work, we utilized density functional theory (DFT) data to inform a cluster dynamics framework to predict point defect concentrations in U3Si2 under irradiation. Molecular dynamics (MD) simulations were used to examine the contribution of atomic mixing during ballistic cascades to diffusion, as well as the diffusivity of U and Si at grain boundaries. These atomic scale models for diffusivity were then used to inform a creep model based on bulk (Nabarro-Herring) and grain boundary (Coble) diffusional creep, and climb-limited dislocation creep. The model compares well against available experimental data and has been implemented in the BISON fuel performance code. A demonstration case using simple power profiles has been carried out, showing that negligible creep occurs due to the low temperatures experienced by U3Si2 in-reactor, a consequence of its high thermal conductivity.}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Cooper, M. W. D. and Gamble, K. A. and Capolungo, L. and Matthews, C. and Andersson, D. A. and Beeler, B. and Stanek, C. R. and Metzger, K.}, year={2021}, month={Nov} } @article{beeler_andersson_jiang_zhang_2021, title={Ab initio molecular dynamics investigation of point defects in gamma-U}, volume={545}, ISSN={["1873-4820"]}, url={https://doi.org/10.1016/j.jnucmat.2020.152714}, DOI={10.1016/j.jnucmat.2020.152714}, abstractNote={Uranium (U) is often alloyed with molybdenum (Mo) or zirconium (Zr) in order to stabilize the high-temperature body-centered cubic γ phase of uranium for use in nuclear reactors. However, relatively little experimental or computational investigation has centered on γ-U, largely due to the mechanical instability of this phase at room temperature. This is particularly problematic for density functional theory calculations that typically investigate 0 K properties. However, ab initio molecular dynamics (AIMD) allows for quantum mechanical-based calculations to be performed at non-zero temperatures. In this work, AIMD simulations are performed to calculate the equilibrium volume for the γ phase of U from 900 K to 1400 K. Utilizing the volume at each temperature, the bulk modulus, the radial distribution function, the interstitial and vacancy formation energies, and the diffusion coefficients are determined.}, journal={JOURNAL OF NUCLEAR MATERIALS}, publisher={Elsevier BV}, author={Beeler, Benjamin and Andersson, David and Jiang, Chao and Zhang, Yongfeng}, year={2021}, month={Mar} } @article{beeler_casagranda_aagesen_zhang_novascone_2020, title={Atomistic calculations of the surface energy as a function of composition and temperature in gamma U-Zr to inform fuel performance modeling}, volume={540}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2020.152271}, abstractNote={Uranium-zirconium alloy fuels are candidates for advanced sodium cooled fast reactors due to their high uranium density, high thermal conductivity, inherent safety and ability to incorporate minor actinides into the fuel. Unlike traditional ceramic UO2 fuel, U–Zr alloys swell rapidly and substantially, but the actual mechanistic process of swelling, including the rate of swelling, is not well understood. Fuel performance models are being developed to describe the swelling process, but these models currently lack the requisite underlying physics and fundamental property data to be truly predictive. In this work, molecular dynamics simulations are utilized to investigate a number of bulk thermophysical properties in γU-Zr, the void surface energy as a function of temperature and composition, and the void free energy. Finally, the effect of surface energy on fuel swelling behavior is demonstrated via finite element based fuel performance simulations, emphasizing the importance of the inclusion of accurate fundamental material properties.}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Beeler, Benjamin and Casagranda, Albert and Aagesen, Larry and Zhang, Yongfeng and Novascone, Stephen}, year={2020}, month={Nov} } @article{hu_setyawan_beeler_gan_burkes_2020, title={Defect cluster and nonequilibrium gas bubble associated growth in irradiated UMo fuels – A cluster dynamics and phase field model}, volume={542}, url={https://doi.org/10.1016/j.jnucmat.2020.152441}, DOI={10.1016/j.jnucmat.2020.152441}, abstractNote={Irradiation examination shows that gas bubble swelling kinetics are much faster after irradiation-induced recrystallization than that prior to recrystallization in U-10 wt% Mo alloy (UMo) fuels. These kinetics imply that gas bubbles in coarse grains and small recrystallized grains have different growth behavior. For the first time, researchers developed a phase-field model of gas bubble evolution integrating microstructure-dependent cluster dynamics to study the gas bubble swelling behavior in the recrystallization zone of UMo fuels. Generation, diffusion, reaction, sink, emission, and clustering of vacancies and interstitials are described by the cluster dynamics model while a phase-field model is used to describe the evolution of nonequilibrium gas bubbles including nucleation and growth. With the coupled model, the effect of defect generation rate, clustering rate, interstitial emission, and sink rates on grain boundaries on the gas bubble evolution are systematically simulated. A set of model parameters (defect generation rate, clustering rate, interstitial emission, and sink rates) is determined by comparing measured and simulated gas bubble swelling kinetics. The results demonstrate that interstitial clustering is one of the important physical mechanisms that results in fast gas bubble swelling kinetics in the recrystallization zone. The developed model can also be extended to study the associated growth of defect and second-phase precipitates often observed in irradiated materials.}, journal={Journal of Nuclear Materials}, publisher={Elsevier BV}, author={Hu, Shenyang and Setyawan, Wahyu and Beeler, Benjamin W. and Gan, Jian and Burkes, Douglas E}, year={2020}, month={Dec}, pages={152441} } @article{cheniour_tonks_gong_yao_he_harp_beeler_zhang_lian_2020, title={Development of a grain growth model for U3Si2 using experimental data, phase field simulation and molecular dynamics}, volume={532}, ISSN={0022-3115}, url={http://dx.doi.org/10.1016/j.jnucmat.2020.152069}, DOI={10.1016/j.jnucmat.2020.152069}, abstractNote={The purpose of this work is to develop a model for normal grain growth in U3Si2. The average grain boundary energy was determined from previously published molecular dynamics simulations. The grain growth kinetics were quantified at various temperatures by annealing nanocrystalline samples. The mobility was determined by comparing phase field grain growth simulations to the experimental data. From these various methods, we found that the average grain size D in U3Si2 can be estimated over time t using the equation D2−D02=2αMγt, where D0 is the initial average grain size, the geometry factor α=0.96, the average grain boundary mobility M=6.30×10−18e−0.33[eV]kbTm4/(Js) with the Boltzmann constant kb and temperature T, and the average grain boundary energy has been found as a function of temperature, e.g. γ¯=0.83 J/m2 at 673 K.}, journal={Journal of Nuclear Materials}, publisher={Elsevier BV}, author={Cheniour, Amani and Tonks, Michael R. and Gong, Bowen and Yao, Tiankai and He, Lingfeng and Harp, Jason M. and Beeler, Benjamin and Zhang, Yongfeng and Lian, Jie}, year={2020}, month={Apr}, pages={152069} } @article{mei_ye_yacout_beeler_gao_2020, title={First-principles study of the surface properties of uranium carbides}, volume={542}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2020.152257}, abstractNote={Uranium carbides have attracted renewed interest as advanced nuclear fuels for Generation IV reactors. As an important property required for gas bubble modeling in nuclear fuels, the surface energy of uranium carbides is scarce in literature. In this work, we study the surface properties of uranium carbides by first-principles density functional theory calculations. Surface orientations with maximum Miller index up to 3, 2 and 2 are investigated for UC, U2C3 and α-UC2, respectively. By studying the effects of surface termination and chemical potential on surface energy, we identify the factors that determines the surface stability. From the calculated surface energies, the surface properties of uranium carbide single crystals are obtained from Wulff construction, including equilibrium morphology, dominant surface orientation and area weighted surface energy.}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Mei, Zhi-Gang and Ye, Bei and Yacout, Abdellatif M. and Beeler, Benjamin and Gao, Yipeng}, year={2020}, month={Dec} } @article{aagesen_andersson_beeler_cooper_gamble_miao_pastore_tonks_2020, title={Phase-field simulations of intergranular fission gas bubble behavior in U3Si2 nuclear fuel}, volume={541}, url={https://doi.org/10.1016/j.jnucmat.2020.152415}, DOI={10.1016/j.jnucmat.2020.152415}, abstractNote={U3Si2 is a potential accident-tolerant fuel that shows promise due to its high thermal conductivity and higher uranium density relative to UO2. However, its swelling and fission gas release behavior in light water reactor (LWR) conditions is relatively unknown. To provide mechanistic insight and determine parameters for engineering-scale fuel performance modeling of pellet-form U3Si2, phase-field simulations of the growth, interconnection, and venting of intergranular fission gas bubbles were performed. The fractional coverage of the grain boundary and the fraction of bubble area that is vented were calculated as a function of time. From the simulation data, the fractional grain boundary coverage at saturation, an important parameter needed in engineering-scale modeling of swelling and fission gas release, was determined. Multiple simulations were run to determine the uncertainty in the calculated value. The effect of model assumptions and input parameters that are not well known was evaluated. Simulation results are compared to related theoretical and computational work. Based on the simulation results, a value of 0.60 for the fractional grain boundary coverage at saturation is recommended for U3Si2 fuel.}, journal={Journal of Nuclear Materials}, publisher={Elsevier BV}, author={Aagesen, Larry K. and Andersson, David and Beeler, Benjamin W. and Cooper, Michael W.D. and Gamble, Kyle A. and Miao, Yinbin and Pastore, Giovanni and Tonks, Michael R.}, year={2020}, month={Dec}, pages={152415} } @article{beeler_cooper_mei_schwen_zhang_2021, title={Radiation driven diffusion in γU-Mo}, volume={543}, url={https://doi.org/10.1016/j.jnucmat.2020.152568}, DOI={10.1016/j.jnucmat.2020.152568}, abstractNote={A monolithic fuel design based on a U-Mo alloy has been selected as the fuel type for conversion of the U. S. High-Performance Research Reactors. A critical phenomenon of interest regarding U-Mo monolithic fuel is the large amount of swelling that takes place during operation, particularly at high fission densities. The accurate prediction of fuel evolution under irradiation requires implementation of correct thermodynamic and kinetic properties into mesoscale and engineering fuel performance modeling codes. One such property where there exists incomplete data is the diffusion of relevant species under irradiation. Fuel performance swelling predictions rely on an accurate representation of diffusion in order to determine the rate of fission gas swelling and the local microstructural evolution. In this work, we present molecular dynamics simulations of the radiation driven diffusion of U, Mo, and Xe in U-Mo nuclear fuels. Diffusion coefficients for each species are determined over a range of temperatures and compositions. Updated diffusion coefficients are presented that are applicable under irradiation and incorporate both intrinsic and radiation driven diffusion.}, journal={Journal of Nuclear Materials}, publisher={Elsevier BV}, author={Beeler, Benjamin and Cooper, Michael W.D. and Mei, Zhi-Gang and Schwen, Daniel and Zhang, Yongfeng}, year={2021}, month={Jan}, pages={152568} } @article{beeler_hu_zhang_gao_2020, title={A improved equation of state for Xe gas bubbles in gamma U-Mo fuels}, volume={530}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2019.151961}, abstractNote={A monolithic fuel design based on a U–Mo alloy has been selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). An issue with U–Mo monolithic fuel is the large amount of swelling that takes place during operation. The accurate prediction of fuel evolution under irradiation requires implementation of correct thermodynamic properties into mesoscale and continuum level fuel performance modeling codes. However, the thermodynamic properties of the fission gas bubbles (such as the relationship among bubble size, equilibrium Xe concentration, and bubble pressure) are not well known. This work studies Xe bubbles in γU-Mo from a diameter of 3 nm up to 8.5 nm and from 400 K up to 700 K. The energetic relationship of Xe bubbles with regard to voids and Xe substitutional atoms is described. The transition is also determined for when a bubble becomes over-pressurized. Finally, an equation of state is fit to the pressure as a function of molar volume and temperature.}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Beeler, Benjamin and Hu, Shenyang and Zhang, Yongfeng and Gao, Yipeng}, year={2020}, month={Mar} } @article{dacus_beeler_schwen_2019, title={Calculation of threshold displacement energies in UO2}, volume={520}, ISSN={["1873-4820"]}, DOI={10.1016/j.jnucmat.2019.04.002}, abstractNote={Despite the extensive utilization of uranium dioxide (UO2) as a fuel in commercial nuclear reactors, there is only minimal information regarding the fundamental nature of radiation damage at high temperatures, such as those experienced by the fuel under operation. In this work, molecular dynamics simulations have been performed to determine the threshold displacement energy (Ed) for oxygen and uranium in UO2 at 1500 K. Three definitions of displacement energy were employed to fully study the nature of low energy radiation damage: 1) the probability of having the primary knock-on atom (PKA) leave its original lattice site, 2) the probability that the PKA will permanently displace atoms from their original lattice site, and 3) the probability of forming a stable Frenkel pair. Additionally, four unique interatomic potentials were utilized to investigate uncertainties associated with potential choice in high temperature radiation damage studies in UO2. This work provides critical insight into the high temperature behavior of radiation damage in UO2, as well as the variation in behavior between oxygen and uranium PKAs.}, journal={JOURNAL OF NUCLEAR MATERIALS}, author={Dacus, Benjamin and Beeler, Benjamin and Schwen, Daniel}, year={2019}, month={Jul}, pages={152–164} } @article{beeler_baskes_andersson_cooper_zhang_2017, title={A modified Embedded-Atom Method interatomic potential for uranium-silicide}, volume={495}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85027967820&partnerID=MN8TOARS}, DOI={10.1016/j.jnucmat.2017.08.025}, abstractNote={Uranium-silicide (U-Si) fuels are being pursued as a possible accident tolerant fuel (ATF). This uranium alloy fuel benefits from higher thermal conductivity and higher fissile density compared to uranium dioxide (UO2). In order to perform engineering scale nuclear fuel performance simulations, the material properties of the fuel must be known. Currently, the experimental data available for U-Si fuels is rather limited. Thus, multiscale modeling efforts are underway to address this gap in knowledge. In this study, a semi-empirical modified Embedded-Atom Method (MEAM) potential is presented for the description of the U-Si system. The potential is fitted to the formation energy, defect energies and structural properties of U3Si2. The primary phase of interest (U3Si2) is accurately described over a wide temperature range and displays good behavior under irradiation and with free surfaces. The potential can also describe a variety of U-Si phases across the composition spectrum.}, journal={Journal of Nuclear Materials}, author={Beeler, B. and Baskes, M. and Andersson, D. and Cooper, M.W.D. and Zhang, Y.}, year={2017}, pages={267–276} } @inproceedings{beeler_baskes_andersson_zhang_2017, title={A modified embedded-atom method interatomic potential for U-Si}, volume={116}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85033481319&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Beeler, B. and Baskes, M. and Andersson, D. and Zhang, Y.}, year={2017}, pages={407–409} } @book{aagesen_ahmed_beeler_schwen_zhang_andersson_2017, title={Multi-Scale Modeling of Swelling in Accident-Tolerant U3Si2 Fuel}, url={https://doi.org/10.2172/1472119}, DOI={10.2172/1472119}, abstractNote={U3Si2 is a promising candidate for use as an accident-tolerant fuel for light water reactors. A multi-scale computational approach was used to calculate swelling in pellet-form U3Si2 fuel. Swelling was assumed to be equal to the volume fraction of fission gas bubbles in the fuel, and the evolution of bubble volume fraction was determined from phase-field simulations. To parameterize the phase-field model, density-functional theory and molecular dynamics simulations were performed. To enable molecular dynamics simulations, a new interatomic potential for the U-Si system was developed based on the modified embedded atom method. A new phase-field model based on a grand-potential functional was also developed. The model is applicable to both intergranular and intragranular bubbles. To calculate the volume fraction of bubbles, the microstructure was decomposed into regions consisting of only intragranular or intergranular bubbles based on a truncated octahedral grain structure, and growth of the bubbles in the two regions was simulated separately. The total swelling was then calculated based on a a weighted average of bubble volume fraction in the two regions. Total swelling was of the same order of magnitude, but larger than that predicted by the existing empirical swelling model used in BISON and a rate-theory based model. Limitations of the present approach and suggestions for improvement are presented.}, institution={Office of Scientific and Technical Information (OSTI)}, author={Aagesen, Larry and Ahmed, Karim and Beeler, Benjamin and Schwen, Daniel and Zhang, Yongfeng and Andersson, David}, year={2017}, month={Sep} } @book{zhang_beeler_aagesen_jiang_ahmed_yu_schwen_andersson_baskes_cooper_et al._2017, title={Progress update on lower length scale research and development on U3Si2 fuel and FeCrAl cladding}, url={https://doi.org/10.2172/1472101}, DOI={10.2172/1472101}, abstractNote={This report summarizes the lower length scale model development and studies in regards to two accident tolerant (ATF) concepts, U3Si2 and FeCrAl. U3Si2 is proposed to replace UO2 fuel for its high thermal conductivity and higher uranium density. FeCrAl alloys are proposed to replace Zr based cladding for their high mechanical strength and good corrosion resistance. Before applying them in reactors, sufficient data are needed to establish their predictable in-pile performance, but largely missing, and they are costly and time consuming to obtain by experimental approaches. Under the NEAMS ATF high-impact-problem (HIP), multiscale modeling and simulations are used to develop atomistic and mesoscale tools, obtain fundamental material properties, and assess the behaviors of these two ATF concepts. The accomplishments in FY17 are briefly introduced in this report including the development of interatomic potentials, assessment of swelling in U3Si2, and Cr precipitation in FeCrAl alloys.}, institution={Office of Scientific and Technical Information (OSTI)}, author={Zhang, Yongfeng and Beeler, Benjamin and Aagesen, Larry and Jiang, Chao and Ahmed, K. and Yu, J. and Schwen, D. and Andersson, D. and Baskes, M. and Cooper, M. and et al.}, year={2017}, month={Sep} } @article{beeler_asta_hosemann_gr?nbech-jensen_2016, title={Effect of strain and temperature on the threshold displacement energy in body-centered cubic iron}, volume={474}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84963585213&partnerID=MN8TOARS}, DOI={10.1016/j.jnucmat.2016.03.017}, abstractNote={The threshold displacement energy (TDE) is the minimum amount of kinetic energy required to displace an atom from its lattice site. The magnitude of the TDE displays significant variance as a function of the crystallographic direction, system temperature and applied strain, among a variety of other factors. It is critically important to determine an accurate value of the TDE in order to calculate the total number of displacements due to a given irradiation condition, and thus to understand the materials response to irradiation. In this study, molecular dynamics simulations have been performed to calculate the threshold displacement energy in body-centered cubic iron as a function of strain and temperature. With applied strain, a decrease of the TDE of up to approximately 14 eV was observed. A temperature increase from 300 K to 500 K can result in an increase of the TDE of up to approximately 9 eV.}, journal={Journal of Nuclear Materials}, author={Beeler, B. and Asta, M. and Hosemann, P. and Gr?nbech-Jensen, N.}, year={2016}, pages={113–119} } @article{moore_beeler_deo_baskes_okuniewski_2015, title={Atomistic modeling of high temperature uranium-zirconium alloy structure and thermodynamics}, volume={467}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84946780407&partnerID=MN8TOARS}, DOI={10.1016/j.jnucmat.2015.10.016}, abstractNote={A semi-empirical Modified Embedded Atom Method (MEAM) potential is developed for application to the high temperature body-centered-cubic uranium–zirconium alloy (γ-U–Zr) phase and employed with molecular dynamics (MD) simulations to investigate the high temperature thermo-physical properties of U–Zr alloys. Uranium-rich U–Zr alloys (e.g. U–10Zr) have been tested and qualified for use as metallic nuclear fuel in U.S. fast reactors such as the Integral Fast Reactor and the Experimental Breeder Reactors, and are a common sub-system of ternary metallic alloys like U–Pu–Zr and U–Zr–Nb. The potential was constructed to ensure that basic properties (e.g., elastic constants, bulk modulus, and formation energies) were in agreement with first principles calculations and experimental results. After which, slight adjustments were made to the potential to fit the known thermal properties and thermodynamics of the system. The potentials successfully reproduce the experimental melting point, enthalpy of fusion, volume change upon melting, thermal expansion, and the heat capacity of pure U and Zr. Simulations of the U–Zr system are found to be in good agreement with experimental thermal expansion values, Vegard's law for the lattice constants, and the experimental enthalpy of mixing. This is the first simulation to reproduce the experimental thermodynamics of the high temperature γ-U–Zr metallic alloy system. The MEAM potential is then used to explore thermodynamics properties of the high temperature U–Zr system including the constant volume heat capacity, isothermal compressibility, adiabatic index, and the Grüneisen parameters.}, journal={Journal of Nuclear Materials}, author={Moore, A.P. and Beeler, B. and Deo, C. and Baskes, M.I. and Okuniewski, M.A.}, year={2015}, pages={802–819} } @inproceedings{beeler_asta_hosemann_gr?nbech-jensen_2015, title={Effect of interfaces on radiation damage accumulation in FeNiAl maraging steels}, volume={112}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84988891995&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Beeler, B. and Asta, M. and Hosemann, P. and Gr?nbech-Jensen, N.}, year={2015}, pages={328–329} } @article{beeler_asta_hosemann_grønbech-jensen_2015, title={Effects of applied strain on radiation damage generation in body-centered cubic iron}, volume={459}, DOI={10.1016/j.jnucmat.2014.12.111}, abstractNote={Radiation damage in body-centered cubic (BCC) Fe has been extensively studied by computer simulations to quantify effects of temperature, impinging particle energy, and the presence of extrinsic particles. However, limited investigation has been conducted into the effects of mechanical stresses and strain. In a reactor environment, structural materials are often mechanically strained, and an expanded understanding of how this strain affects the generation of defects may be important for predicting microstructural evolution and damage accumulation under such conditions. In this study, we have performed molecular dynamics simulations in which various types of homogeneous strains are applied to BCC Fe and the effect on defect generation is examined. It is found that volume-conserving shear strains yield no statistically significant variations in the stable number of defects created via cascades in BCC Fe. However, strains that result in volume changes are found to produce significant effects on defect generation.}, journal={Journal of Nuclear Materials}, publisher={Elsevier BV}, author={Beeler, Benjamin and Asta, Mark and Hosemann, Peter and Grønbech-Jensen, Niels}, year={2015}, month={Apr}, pages={159–165} } @article{miao_beeler_deo_baskes_okuniewski_stubbins_2015, title={Defect structures induced by high-energy displacement cascades in γ uranium}, volume={456}, DOI={10.1016/j.jnucmat.2014.09.016}, abstractNote={Abstract Displacement cascade simulations were conducted for the γ uranium system based on molecular dynamics. A recently developed modified embedded atom method (MEAM) potential was employed to replicate the atomic interactions while an embedded atom method (EAM) potential was adopted to help characterize the defect structures induced by the displacement cascades. The atomic displacement process was studied by providing primary knock-on atoms (PKAs) with kinetic energies from 1 keV to 50 keV. The influence of the PKA incident direction was examined. The defect structures were analyzed after the systems were fully relaxed. The states of the self-interstitial atoms (SIAs) were categorized into various types of dumbbells, the crowdion, and the octahedral interstitial. The voids were determined to have a polyhedral shape with {1 1 0} facets. The size distribution of the voids was also obtained. The results of this study not only expand the knowledge of the microstructural evolution in irradiated γ uranium, but also provide valuable references for the radiation-induced defects in uranium alloy fuels.}, journal={Journal of Nuclear Materials}, publisher={Elsevier BV}, author={Miao, Yinbin and Beeler, Benjamin and Deo, Chaitanya and Baskes, Michael I. and Okuniewski, Maria A. and Stubbins, James F.}, year={2015}, month={Jan}, pages={1–6} } @inproceedings{moore_beeler_baskes_okuniewski_deo_2013, title={Atomistic ordering in body centered cubic Uranium-Zirconium alloy}, volume={1514}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84888074338&partnerID=MN8TOARS}, DOI={10.1557/opl.2013.517}, abstractNote={ABSTRACTThe metallic binary-alloy fuel Uranium-Zirconium is important for the use of the new generation of advanced fast reactors. Uranium-Zirconium goes through a phase transition at higher temperatures to a (gamma) Body Centered Cubic (BCC) phase. The BCC high temperature phase is particularly important, since the BCC phase corresponds to the temperature range in which the fast reactors will operate. A semi-empirical MEAM (Modified Embedded Atom Method) potential is presented for Uranium-Zirconium. The physical properties of the Uranium-Zirconium binary alloy were reproduced using Molecular Dynamics (MD) simulations and Monte Carlo (MC) simulations with the MEAM potential. This is a large step in making a computationally acceptable fuel performance code.}, booktitle={Materials Research Society Symposium Proceedings}, author={Moore, A.P. and Beeler, B. and Baskes, M. and Okuniewski, M. and Deo, C.S.}, year={2013}, pages={27–35} } @inproceedings{beeler_deo_baskes_okuniewski_2013, title={Atomistic investigations of intrinsic and extrinsic point defects in bcc uranium}, volume={1547 STP}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84875784961&partnerID=MN8TOARS}, DOI={10.1520/STP104141}, abstractNote={Metallic alloys of uranium show great potential as transmutation fuels that could be used to burn long-lived and high-heat-producing minor actinides and fission products in nuclear reactors. In fuels, fission and radiation damage result in the production of a large number of intrinsic point defects and extrinsic fission atoms. Radiation damage and diffusion (processes heavily dependent on point defects), as well as fission product behavior, are important to the understanding of the behavior of these metallic fuel alloys. Of the fission products, fission gases Xe, Kr, and the decay product He are of special importance, as they migrate and form bubbles detrimentally affecting fuel properties. In this work, several systems of body-centered-cubic (gamma) U are examined through a semi-empirical interatomic potential based on the modified embedded-atom method. The vacancy formation energy is analyzed as a function of pressure and is used to determine the stable vacancy formation energy at ambient conditions. The vacancy formation energy as a function of temperature is analyzed for high-temperature systems. Interatomic potentials are developed and implemented in the investigation of He, Xe, and Kr point defects in the gamma phase of uranium. For all fission gases studied, the most energetically favorable location is the substitutional position, with helium having the lowest formation energies of the species investigated.}, booktitle={ASTM Special Technical Publication}, publisher={ASTM International}, author={Beeler, Benjamin and Deo, Chaitanya and Baskes, Michael and Okuniewski, Maria}, year={2013}, pages={231–247} } @article{beeler_deo_baskes_okuniewski_2012, title={Atomistic properties of γ uranium}, volume={24}, DOI={10.1088/0953-8984/24/7/075401}, abstractNote={The properties of the body-centered cubic γ phase of uranium (U) are calculated using atomistic simulations. First, a modified embedded-atom method interatomic potential is developed for the high temperature body-centered cubic (γ) phase of U. This phase is stable only at high temperatures and is thus relatively inaccessible to first principles calculations and room temperature experiments. Using this potential, equilibrium volume and elastic constants are calculated at 0 K and found to be in close agreement with previous first principles calculations. Further, the melting point, heat capacity, enthalpy of fusion, thermal expansion and volume change upon melting are calculated and found to be in reasonable agreement with experiment. The low temperature mechanical instability of γ U is correctly predicted and investigated as a function of pressure. The mechanical instability is suppressed at pressures greater than 17.2 GPa. The vacancy formation energy is analyzed as a function of pressure and shows a linear trend, allowing for the calculation of the extrapolated zero pressure vacancy formation energy. Finally, the self-defect formation energy is analyzed as a function of temperature. This is the first atomistic calculation of γ U properties above 0 K with interatomic potentials.}, number={7}, journal={J. Phys.: Condens. Matter}, publisher={IOP Publishing}, author={Beeler, Benjamin and Deo, Chaitanya and Baskes, Michael and Okuniewski, Maria}, year={2012}, month={Feb}, pages={075401} } @inproceedings{beeler_deo_baskes_okuniewski_2012, title={Calculation of the displacement energy in b.c.c. U at 800 K}, volume={106}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84876400924&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Beeler, B. and Deo, C. and Baskes, M. and Okuniewski, M.}, year={2012}, pages={1214–1215} } @article{beeler_deo_baskes_okuniewski_2013, title={First principles calculations of the structure and elastic constants of α, β and γ uranium}, volume={433}, DOI={10.1016/j.jnucmat.2012.09.019}, abstractNote={This study analyzes structural and elastic properties of five uranium crystal structures: the face centered orthorhombic A20 (α phase), the tetragonal D8b (β phase), body centered tetragonal (bct), body centered cubic (γ phase) and face centered cubic structures. Calculations are performed within the density functional theory framework employing the Projector Augmented Wave method and the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE–GGA) of the exchange correlation. The elastic constants are used to compute polycrystalline elastic moduli, Poisson's ratio and the Debye temperature for all five structures. The α and γ phase properties are compared with theoretical and experimental results. The complex tetragonal 30 atom beta phase is examined in detail. Representation of the β phase by a bct structure is examined; we find that the structure of the β phase is significantly different from the bct phase but exhibits similar elastic properties. This is the first comprehensive investigation into the elastic constants of uranium utilizing the PBE–GGA.}, number={1-3}, journal={Journal of Nuclear Materials}, publisher={Elsevier BV}, author={Beeler, Benjamin and Deo, Chaitanya and Baskes, Michael and Okuniewski, Maria}, year={2013}, month={Feb}, pages={143–151} } @article{hayward_beeler_deo_2012, title={Multiple hydrogen trapping at monovacancies}, volume={92}, DOI={10.1080/09500839.2012.657702}, abstractNote={Novel structures for multiple hydrogen atoms trapped at a monovacancy are discussed. Using atomistic simulations based on semiempirical interatomic potentials and density functional theory, we find low-energy configurations for four, five, and six hydrogen atoms around a monovacancy different than those that have been previously studied in the literature. The energetics of hydrogen binding are compared to results, both theoretical and experimental, previously published in the literature. We argue that up to four hydrogen atoms may be exothermically bound to monovacancy.}, number={5}, journal={Philosophical Magazine Letters}, publisher={Informa UK Limited}, author={Hayward, Erin and Beeler, Benjamin and Deo, Chaitanya}, year={2012}, month={May}, pages={217–225} } @article{beeler_good_rashkeev_deo_baskes_okuniewski_2012, title={First-principles calculations of the stability and incorporation of helium, xenon and krypton in uranium}, volume={425}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84860435889&partnerID=MN8TOARS}, DOI={10.1016/j.jnucmat.2011.08.014}, abstractNote={While metallic fuels have a long history of reactor use, their fundamental physical and thermodynamic properties are not well understood. Many metallic nuclear fuels are body-centered cubic alloys of uranium that swell under fission conditions, creating fission product gases such as helium, xenon and krypton. In this paper, helium, xenon, and krypton point defects are investigated in the α and γ phases of metallic uranium using first principles calculations. A density functional theory (DFT) framework is utilized with projector augmented-wave (PAW) pseudopotentials. Formation and incorporation energies of He, Xe, and Kr are calculated at various defect positions for the prediction of fission gas behavior in uranium. In most cases, defect energies follow a size effect, with helium incorporation and formation energies being the smallest. The most likely position for the larger Xe and Kr atoms in uranium is the substitutional site. Helium atoms are likely to be found in a wide variety of defect positions due to the comparable formation energies of all defect configurations analyzed. This is the first detailed study of the stability and incorporation of fission gases in uranium.}, number={1-3}, journal={Journal of Nuclear Materials}, author={Beeler, B. and Good, B. and Rashkeev, S. and Deo, C. and Baskes, M. and Okuniewski, M.}, year={2012}, pages={2–7} } @article{beeler_good_rashkeev_deo_baskes_okuniewski_2010, title={First principles calculations for defects in U}, volume={22}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78649825146&partnerID=MN8TOARS}, DOI={10.1088/0953-8984/22/50/505703}, abstractNote={Uranium (U) exhibits a high temperature body-centered cubic (bcc) allotrope that is often stabilized by alloying with transition metals such as Zr, Mo, and Nb for technological applications. One such application involves U–Zr as nuclear fuel, where radiation damage and diffusion (processes heavily dependent on point defects) are of vital importance. Several systems of U are examined within a density functional theory framework utilizing projector augmented wave pseudopotentials. Two separate generalized gradient approximations of the exchange-correlation are used to calculate defect properties and are compared. The bulk modulus, the lattice constant, and the Birch–Murnaghan equation of state for the defect free bcc uranium allotrope are calculated. Defect parameters calculated include energies of formation of vacancies in the α and γ allotropes, as well as self-interstitials, Zr interstitials, and Zr substitutional defects for the γ allotrope. The results for vacancies agree very well with experimental and previous computational studies. The most probable self-interstitial site in γ-U is the ⟨110⟩ dumbbell, and the most probable defect location for dilute Zr in γ-U is the substitutional site. This is the first detailed study of self-defects in the bcc allotrope of U and also the first comprehensive study of dilute Zr defects in γ-U.}, number={50}, journal={Journal of Physics Condensed Matter}, author={Beeler, B. and Good, B. and Rashkeev, S. and Deo, C. and Baskes, M. and Okuniewski, M.}, year={2010} }