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NASA NTRS1976

Summary of nozzle-exhaust plume flowfield analyses performed in support of space shuttle applications

Results are summarized of various analyses of the exhaust plumes of the space shuttle. Specific topics discussed included: the development of the two-phase plume flow field model, including finite rate chemistry and free molecular effects; analyses of exhaust plume simulation studies; verification of the analytical two-phase plume flow field model; and complete documentation of the two-phase plume computer code.

Smith, S. D.↗

DOE OSTI2024

Improving Additive Manufactured Component Performance through Multi-Scale Microstructure Simulation and Process Optimization

The purpose of this project was to utilize computational tools to understand the relationships between processing, microstructure, and properties for additively manufactured (AM) aluminum alloys for automotive applications, and to provide an engineering solution for helping to optimize process conditions. The project leverages ORNL developments in computational modeling, including AM process modeling, phase-field based microstructure evolution predictions, and data analytics techniques for mapping process conditions to material outcomes. The project utilized an Al-Cu-Mn-Zr alloy as a model material for studying formation of defects and microstructural features in response to variations in process conditions. Based on both pre-existing experimental data and simulation results, statistical process maps were constructed to identify regions of process space with minimal defect formation and advantageous microstructures and properties. The software tools used for this purpose were successful disseminated to GM, who were able to successful compile the relevant HPC codes within their own computing ecosystem and perform initial calculations to reproduce ORNL results.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Energy Frontier Research Center Center for Materials Science of Nuclear Fuels

Scientific Successes • The first phonon density of states (PDOS) measurements for UO2 to include anharmonicity were obtained using time-of-flight inelastic neutron scattering at the Spallation Neutron Source (SNS), and an innovative, experimental-based anharmonic smoothing technique has enabled quantitative benchmarking of ab initio PDOS simulations. • Direct comparison between anharmonicity-smoothed ab initio PDOS simulations for UO2 and experimental measurements has demonstrated the need for improved understanding of UO2 at the level of phonon dispersion, and, further, that advanced lattice dynamics simulations including finite temperatures approaches will be required for handling this strongly correlated nuclear fuel. • PDOS measurements performed on polycrystalline samples have identified the phonon branches and energy ranges most highly impacted by fission-product and hyper-stoichiometry lattice defects in UO2. These measurements have revealed the broad-spectrum impact of oxygen hyper-stoichiometry on thermal transport. The reduction in thermal conductivity caused by hyper-stoichiometry is many times stronger than that caused by substitutional fission-product impurities. • Laser-based thermo-reflectance measurements on UO2 samples irradiated with light (i.e. He) ions to introduce point defects have been coupled with MD simulations and lattice parameter measurements to determine the role of uranium and oxygen point defects in reducing thermal conductivity. • A rigorous perturbation theory treatment of phonon lifetimes in UO2 based on a 3D discretization of the Brillouin zone coupled with experimentally measured phonon dispersion has been implemented that produces improved predictions of the temperature dependent thermal conductivity. • Atom probe investigations of the influence of grain boundary structure on the segregation behavior of Kr in UO2 have shown that smaller amounts of Kr are present at low angle grain boundaries than at large angle grain boundaries due to the more dense dislocation arrays associated with large angle boundaries; this observation has potentially important ramifications for thermal transport in the high burn-up rim region of light water reactor fuel. • A variable charge interatomic potential has been developed that not only provides an accurate representation of the fluorite UO2 phase, it is further capable of describing continuous stoichiometry changes from UO2 to hyper-stoichiometric UO2+x, to U4O9 and U3O7, and possibly to orthorhombic U3O8. This is the first potential that features many-body effects in all possible interactions (U-U, U-O and O-O) combined with the variable charge. • A theoretical proof has been formulated showing that it is necessary to use the so-called model C phase field approach, consisting of Cahn-Hilliard and Allen-Cahn equations, to describe void evolution in irradiated materials. This work resolved a longstanding literature controversy regarding how to model voids at the mesoscale. • A novel cluster dynamics model has been developed for the nucleation of voids and loops in UO2 under irradiation. This model is important in understanding the defect state of UO2 after irradiation and, more importantly, reveals off-stoichiometric states of irradiated UO2 that are critical for understanding the impact of irradiation on thermal transport. Personnel Successes

36 MATERIALS SCIENCE↗

DOE OSTI2017

Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations

We study microstructure selection during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Lambda and tip radius rho. While rho shows a good agreement between experimental measurements and dendrite growth theory, with rho similar to V-1/2, Lambda is observed to increase with V (partial derivative Lambda/partial derivative V > 0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that partial derivative Lambda/partial derivative V <0. We show through simulations that this trend inversion for Lambda(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. We explain the observed inversion of partial derivative Lambda/partial derivative V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Co-Based superalloy morphology evolution: A phase field study based on experimental thermodynamic and kinetic data

Cobalt-based superalloys with two phase $\gamma$/$\gamma '$ microstructures offer great promise as candidates for next-generation high-temperature alloys for applications, such as turbine blades. It is essential to understand the thermodynamic and kinetic factors that influence the microstructural evolution of these alloys in order to optimize the alloy compositions and processing steps with a goal to improve their coarsening, creep and rafting behavior. We are using a continuum phase field approach to study the diffusion process and to predict the equilibrium shapes of Co-Al-W $\gamma '$ precipitates. In order to obtain quantitatively predictive capabilities, we extract chemical free energies for the $\gamma$/$\gamma '$ phases based on CALculation of PHAse Diagrams (CALPHAD) thermodynamic data and diffusion mobilities for Co alloys based on CALPHAD kinetic data. We also use experimental or first-principles data for other quantities, such as misfit strain and interface information, for the parameterization of our model. A particular focus of our study is to understand how different energy balances, misfit strain and kinetics affect the coarsening and rafting behavior of $\gamma '$ precipitates, and the sensitivity of the final precipitate shape to materials parameters. Here, we find that the equilibrium shape of the precipitate results from a delicate competition between chemical, interfacial, and elastic energies, and it is very sensitive to changes in model parameters. Here, we examine how modeling input parameters affect the equilibrium shape of precipitates and relate these parameters to experimentally available values.

36 MATERIALS SCIENCE↗

DOE OSTI2011

Phase Field Simulations of Elastic Deformation-Driven Grain Growth in 2D Copper Polycrystals

In this work, a phase field grain growth model coupled with a spectral stress calculation method is used to investigate the effect of applied elastic deformation on grain growth in 2D copper polycrystals with isotropic grain boundary properties. The applied deformation accelerates the grain growth compared to a relaxed polycrystal, though the effect of the deformation decreases rapidly with time. The softest grain orientations with respect to the applied deformation grow at the expense of other orientations, though they have higher elastic energy density. Due to a rapid decrease in the elastic energy stored in the system, the GB energy eventually dominates the growth leading to a linear change in the average grain area with time. Increasing the magnitude of the applied deformation accelerates the growth, while increasing the temperature accelerates the growth but decreases the effect of the applied deformation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

A mechanistic, multiscale model for predicting Pd penetration in TRISO fuels using BISON

TRistructural ISOtropic (TRISO) particles use silicon carbide (SiC) as the primary structural member and barrier against metallic fission product (FP) release. palladiums (PDs), produced by fission in the fuel kernel, can diffuse to and chemically interact with the SiC layer, degrading its structural integrity and ability to contain radioactive FPs. Existing temperature-dependent correlations for predicting Pd penetration rely on experimental data with significant scatter due to varying conditions, potentially complicating ongoing fuel qualification and licensing efforts for advanced reactors that would subject TRISO fuels to operating conditions outside of those examined in the experiments. A mechanistic model of Pd production, transport, and reaction is developed in this work to better understand and predict PD attack of SiC in TRISO particles. molecular dynamicss (MDs) simulations are utilized to calculate the Pd diffusivity in SiC grain bulk and grain boundaries. A mesoscale phase-field diffusion model, informed by the MD diffusivities, is used to develop a reduced order model (ROM) for the effect of SiC microstructure on the Pd penetration rate. The engineering scale BISON model calculates Pd production and transport, utilizing the ROM to predict penetration rates consistent with experimental data. This novel mechanistic ROM captures the effect of temperature, microstructure, and irradiation history on Pd penetration. In conclusion, these new capabilities are expected to support ongoing qualification and licensing efforts associated with near-term TRISO-fueled reactor applications.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

3D interface size effects on slip transfer in Ti/Nb nanolaminates

Two-phase nanolaminates are well-renowned for achieving extraordinarily high strengths but at the sacrifice of reduced toughness and strain to failure. Recently ”thick” interfaces, or so called 3D interfaces, in Cu/Nb nanolaminates were experimentally shown to improve both of these mechanical properties. Here, in this work, we study the effect of 3D interfaces in the hexagonal close packed (HCP)/body centered cubic (BCC) Ti/Nb nanolaminate system. Nanoindentation hardness testing suggests increased strength with the introduction of a 3D Ti–Nb interface and a positive size effect with increases in 3D interface thickness from 5 nm to 20 nm. To understand this effect from a single dislocation perspective, we present a phase-field dislocation dynamics (PFDD) model for multi-phase HCP/BCC systems. We employ the model to simulate stress-driven transfer of single dislocations across 3D Ti/Nb interfaces of various thicknesses. Our results show that the critical stress for slip transfer increases with the thickness of the interface. This positive size effect is stronger for transfer from basal or prismatic dislocations in the Ti layer to 110$\langle$111$\rangle$ dislocations in the Nb layer than the reverse. For this Ti/Nb system, a critical thickness of 2 nm is identified at which the asymmetry in slip transfer is minimized. This work showcases 3D interfaces as a beneficial microstructure modification to strengthen as well as reduce anisotropy in nanocrystalline materials containing HCP phases.

Dislocations↗

DOE OSTI2020

Effect of transport mechanism on the coarsening of bicontinuous structures: A comparison between bulk and surface diffusion

Here, coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to t 1/4 for surface diffusion and t 1/3 for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Experimentally validated multiphysics modeling of fracture induced by thermal shocks in sintered UO 2 pellets

Uranium Dioxide (UO 2 ) fuel powers almost all commercial Nuclear Power Plants (NPPs) worldwide, generating carbon-free energy and contributing to the fight against climate change. UO 2 fuel incurs damage and fractures due to large thermal gradients that develop across the fuel pellet during normal and transient operating conditions. A comprehensive understanding of the underlying mechanisms by which these processes take place is still lacking. A combined experimental and computational approach is utilized here to quantify the behavior of UO 2 fuel fracture induced by thermal shock. Here, this work introduces both (1) an experimental study to understand the fuel fracturing behavior of sintered UO 2 pellets when exposed to thermal shock, and (2) a Multiphysics phase-field fracture model capable of simulating this process. Parametric studies were conducted to evaluate the effects of uncertainties in fracture properties on the fracture behavior of UO 2 due to thermal shocking. A set of energy release rate (or equivalently fracture toughness) and contract area (the part of the fuel pellet in direct contact with the cold bath) were able to capture the overall fracture trends of the corresponding experimental data. Our combined approach presents a new method for accounting for the effects of microstructure and sample size on the energy release rate/fracture toughness. The experimental data were collected from multiple experiments that exposed UO 2 pellets to high-temperature conditions (589–676 °C) followed by a quench in sub-zero water. This work demonstrates that joint experimental and computational efforts are able to advance the understanding of thermal fracture in the primary fuel source for existing and future NPPs.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Demonstrating the Temperature Gradient Impact on Grain Growth in UO2 Using the Phase Field Method

Grain boundaries (GBs) are driven to migrate up a temperature gradient. In this work, we use a phase field (PF) model to investigate the impact of temperature gradients on normal grain growth. GB motion in 2D UO2 polycrystals is predicted under increasing temperature gradients. We find that the temperature gradient does not significantly impact the average grain growth behavior, because the curvature driving force is dominant. However, it does cause significant local migration of the individual grains. In addition, the change in the GB mobility due to the temperature gradient results in larger grains in the hot portion of the polycrystal.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient

We extend the Ginzburg-Landau (GL) theory of atomically rough bcc-liquid interfaces outside of equilibrium. We use this extension to derive an analytical expression for the kinetic coefficient, which is the proportionality constant μ(nˆ) between the interface velocity along a direction nˆ normal to the interface and the interface undercooling. The kinetic coefficient is expressed as a spatial integral along the normal direction of a sum of gradient square terms corresponding to different nonlinear density wave profiles. Anisotropy arises naturally from the dependence of those profiles on the angles between the principal reciprocal lattice vectors K → i and nˆ. Values of the kinetic coefficient for the (100), (110), and (111) interfaces are compared quantitatively to the prediction of linear Mikheev-Chernov (MC) theory and previous molecular dynamics (MD) simulation studies of crystallization kinetics for a classical model of Fe. Additional MD simulations are carried out here to compute the relaxation time of density waves in the liquid in order to make this comparison free of fit parameters. The GL theory predicts an expression for μ similar to the MC theory but yields a better agreement with MD simulations for both its magnitude and anisotropy due to a fully nonlinear description of density wave profiles across the solid-liquid interface. In particular, the overall magnitude of μ predicted by GL theory is an order of magnitude larger than predicted by the MC theory. GL theory is also used to derive an inverse relation between μ and the solid-liquid interfacial free energy. Here, the general methodology used here to derive an expression for μ(nˆ) also applies to amplitude equations derived from the phase-field-crystal model, which only differ from GL theory by the choice of cubic and higher order nonlinearities in the free-energy density.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Microstructure prediction for Ti-22Al-25Nb in laser powder bed fusion

This work presents a physics-informed framework for predicting solidification morphology and defect susceptibility in additively manufactured Ti–22Al–25Nb across a broad processing space. The framework integrates solidification microstructure selection (SMS) analysis with a single-track defect-based printability map to establish a unified methodology linking processing parameters to both interfacial morphology and manufacturability. Thermal gradients G and solidification rates R are first computed using the Thermo-Calc Additive Manufacturing (TC-AM) module, a finite-interface-dissipation (FID) phase-field (PF) model coupled with CALPHAD method is then employed to systematically distinguish planar and dendritic regimes as functions of $G$ and $R$. By superimposing the printability map onto the morphology projections, a comprehensive process–structure framework is obtained. Across most processing conditions, the predicted microstructure is predominantly dendritic, while planar growth emerges only under selected laser power $P$ and scan speed $v$ combinations. In addition to morphology classification, the framework quantifies the dendritic area fraction and introduces a width-based morphology descriptor to characterize the spatial extent of planar/dendritic regions within the melt pool. It provides mechanistic insight into the interplay between solidification physics and defect formation, offering practical guidance for parameter selection and microstructural control in Ti–22Al–25Nb additive manufacturing (AM).

36 MATERIALS SCIENCE↗

DOE OSTI2025

Mesoscale Modeling of Dislocation Cell Structure Evolution and Radiation-Induced Segregation in Additively Manufactured Austenitic Stainless Steel

Structural alloys under irradiation develop radiation-induced segregation (RIS) at point defect sinks, which lead to undesired changes in the alloy's properties. Additively manufactured austenitic stainless steels are expected to yield a distinct response to irradiation damage owing to their unique as-printed dislocation cell structure. In this talk, we present the development of a mesoscale model for dislocation cell structure evolution coupled with RIS using the MOOSE framework. The evolution of network dislocations within spatially distinct cells and cell walls are modeled using climb-mediated edge annihilation and generation processes. Starting with initial microstructures of as-printed non-equilibrium segregations at dislocation cell walls, our 2D and 3D simulations explore the effects of irradiation temperature, dose rate, dislocation sink bias, and specimen thickness on microstructure evolution. The results will be compared against experimental characterizations of in-situ and ex-situ ion-irradiated samples, and the implications of evolving cell structure on irradiation damage response will be discussed.

additive manufacturing↗

DOE OSTI2025

In situ irradiation of spent nuclear fuels

To improve the economics of commercial nuclear reactors, nuclear vendors and utilities are seeking approval for increased burnup usage of the existing nuclear fleet. This is especially critical for meeting the clean energy initiative by the United States Government, Department of Energy (DOE). However, one of the key challenges the nuclear industry faces in this regard is that the regions exposed to high burnup and low temperatures exhibit a fine-grained microstructure with large bubbles known as high-burnup structure (HBS) [1]. The formation of HBS has been correlated to the diminished performance of the reactor, as well as fuel fragmentation and pulverization during transient and accidental conditions [2]. Therefore, it is paramount to understand the mechanisms for HBS formation along with its impact on the properties and performance of nuclear fuels. While existing programs, such as Nuclear Energy Advanced Modeling and Simulation (NEAMS) and Advanced Fuel Campaign (AFC) are focusing on evaluating the performance impact of HBS, the physical mechanisms contributing to HBS formation are still not fully understood. In addition, having predictive capabilities and sound understanding of the microstructural evolution of nuclear fuel is essential for accelerated development, qualification, and deployment of new nuclear materials and novel reactor designs for advanced nuclear reactors. There is a lack of consensus among researchers regarding the mechanisms leading to such restructuring observed in HBS. Grain subdivision due to polygonization versus recrystallization, continuous versus discrete recrystallization occurring in tandem or conjunction, etc., have been proposed and debated. In general, it is hypothesized that defect accumulation and dislocation interaction within the grains cause the realignment of dislocations into grain boundaries, leading to the new subgrain formation, which over time transforms into new grains. However, due to the lack of transient data, the importance of fission rate, irradiation, thermal, and stress history of the fuel on the restructuring could not be assessed. In situ microstructural evolution under various irradiation conditions is desired to bridge this gap. Alternatively, phase-field-based models have been developed to capture HBS formation via discrete recrystallization utilizing the classical nucleation approach [3–5]. However, in these models, the grain nucleation criteria are often defined based on empirical relations for burnup and fission gas density leading to dislocation density change. A mechanistic approach to capture the dislocation interaction with the microstructural features leading to grain subdivision is lacking.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Density functional theory for carbon dioxide crystal

We present a density functional approach to describe the solid−liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗