Publications

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U-Pu-Zr alloys are considered ideal metallic fuels for experimental breeder reactors because of their superior material properties and potential for increased burnup performance. However, significant constituent redistribution has been observed in these alloys when irradiated, or subject to a thermal gradient, resulting in inhomogeneity of both composition and phase, which, in turn, alters the fuel performance. The hybrid Potts-phase field method is reformulated for ternary alloys in a thermal gradient and utilized to simulate and predict constituent redistribution and phase transformations in the U-Pu-Zr nuclear fuel system. Simulated evolution profiles for the U-16Pu-23Zr (at. pct) alloy show concentric zones that are compared with published experimental results; discrepancies in zone size are attributed to thermal profile differences and assumptions related to the diffusivity values used. Twenty-one alloys, over the entire ternary compositional spectrum, are also simulated to investigate the effects of alloy composition on constituent redistribution and phase transformations. The U-40Pu-20Zr (at. pct) alloy shows the most potential for compositional uniformity and phase homogeneity, throughout a thermal gradient, while remaining in the compositional range of feasible alloys.

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Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bézier curves, which allow for the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. The model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.

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Additive manufacturing (AM) is of tremendous interest given its ability to realize complex, non-traditional geometries in engineered structural materials. However, microstructures generated from AM processes can be equally, if not more, complex than their conventionally processed counterparts. While some microstructural features observed in AM may also occur in more traditional solidification processes, the introduction of spatially and temporally mobile heat sources can result in significant microstructural heterogeneity. While grain size and shape in metal AM structures are understood to be highly dependent on both local and global temperature profiles, the exact form of this relation is not well understood. Here, an idealized molten zone and temperature-dependent grain boundary mobility are implemented in a kinetic Monte Carlo model to predict three-dimensional grain structure in additively manufactured metals. To demonstrate the flexibility of the model, synthetic microstructures are generated under conditions mimicking relatively diverse experimental results present in the literature. Simulated microstructures are then qualitatively and quantitatively compared to their experimental complements and are shown to be in good agreement.

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Under the sponsorship of the U.S. National Science Foundation, a workshop on emerging research opportunities in ceramic and glass science was held in September 2016. Reported here are proceedings of the workshop. The report details eight challenges identified through workshop discussions: Ceramic processing: Programmable design and assembly; The defect genome: Understanding, characterizing, and predicting defects across time and length scales; Functionalizing defects for unprecedented properties; Ceramic flatlands: Defining structure-property relations in free-standing, supported, and confined two-dimensional ceramics; Ceramics in the extreme: Discovery and design strategies; Ceramics in the extreme: Behavior of multimaterial systems; Understanding and exploiting glasses and melts under extreme conditions; and Rational design of functional glasses guided by predictive modeling. It is anticipated that these challenges, once met, will promote basic understanding and ultimately enable advancements within multiple sectors, including energy, environment, manufacturing, security, and health care.

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Using the kinetic Monte Carlo simulator, Stochastic Parallel PARticle Kinetic Simulator, from Sandia National Laboratories, a user routine has been developed to simulate mesoscale predictions of a grain structure near a moving heat source. Here, we demonstrate the use of this user routine to produce voxelized, synthetic, three-dimensional microstructures for electron-beam welding by comparing them with experimentally produced microstructures. When simulation input parameters are matched to experimental process parameters, qualitative and quantitative agreement for both grain size and grain morphology are achieved. The method is capable of simulating both single- and multipass welds. The simulations provide an opportunity for not only accelerated design but also the integration of simulation and experiments in design such that simulations can receive parameter bounds from experiments and, in turn, provide predictions of a resultant microstructure.

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In this report, we present a thermodynamic-­based model of hydride precipitation in Zr-based claddings. The model considers the state of the cladding immediately following drying, after removal from cooling-pools, and presents the evolution of precipitate formation upon cooling as follows: The pilgering process used to form Zr-based cladding imparts strong crystallographic and grain shape texture, with the basal plane of the hexagonal α-Zr grains being strongly aligned in the rolling-­direction and the grains are elongated with grain size being approximately twice as long parallel to the rolling direction, which is also the long axis of the tubular cladding, as it is in the orthogonal directions.

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The elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn3m polymorph of δ-ZrH1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P42/mcm polymorph. Elastic moduli predicted with the Voigt-Reuss-Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pugh's and Poisson's ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted for γ-ZrH, δ-ZrH1.5 and ε-ZrH2 are D = 299.7, 415.6 and 356.9 K, respectively, while D = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.

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In this study, we introduce a simplification to the previously demonstrated hybrid Potts–phase field (hPPF), which relates interfacial energies to microstructural sharp interfaces. The model defines interfacial energy by a Potts-like discrete interface approach of counting unlike neighbors, which we use to compute local curvature. The model is compared to the hPPF by studying interfacial characteristics and grain growth behavior. The models give virtually identical results, while the new model allows the simulator more direct control of interfacial energy.

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This report documents the development, demonstration and validation of a mesoscale, microstructural evolution model for simulation of zirconium hydride {delta}-ZrH{sub 1.5} precipitation in the cladding of used nuclear fuels that may occur during long-term dry storage. While the Zr-based claddings are manufactured free of any hydrogen, they absorb hydrogen during service, in the reactor by a process commonly termed ‘hydrogen pick-up’. The precipitation and growth of zirconium hydrides during dry storage is one of the most likely fuel rod integrity failure mechanisms either by embrittlement or delayed hydride cracking of the cladding. While the phenomenon is well documented and identified as a potential key failure mechanism during long-term dry storage (NUREG/CR-7116), the ability to actually predict the formation of hydrides is poor. The model being documented in this work is a computational capability for the prediction of hydride formation in different claddings of used nuclear fuels. This work supports the Used Fuel Disposition Research and Development Campaign in assessing the structural engineering performance of the cladding during and after long-term dry storage. This document demonstrates a basic hydride precipitation model that is built on a recently developed hybrid Potts-phase field model that combines elements of Potts-Monte Carlo and the phase-field models. The model capabilities are demonstrated along with the incorporation of the starting microstructure, thermodynamics of the Zr-H system and the hydride formation mechanism.

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Most materials microstructural evolution processes progress with multiple processes occurring simultaneously. In this work, we have concentrated on the processes that are active in nuclear materials, in particular, nuclear fuels. These processes are coarsening, nucleation, differential diffusion, phase transformation, radiation-induced defect formation and swelling, often with temperature gradients present. All these couple and contribute to evolution that is unique to nuclear fuels and materials. Hybrid model that combines elements from the Potts Monte Carlo, phase-field models and others have been developed to address these multiple physical processes. These models are described and applied to several processes in this report. An important feature of the models developed are that they are coded as applications within SPPARKS, a Sandiadeveloped framework for simulation at the mesoscale of microstructural evolution processes by kinetic Monte Carlo methods. This makes these codes readily accessible and adaptable for future applications.

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Microstructural evolution during sintering can be simulated using the Potts kinetic Monte Carlo model. This model simulates detailed evolution of the powder particles, pore shapes, neck growth, and other microstructural features with sufficient resolution over a sufficiently large compact so that interfacial energies and curvatures of a statistically representative sample of surfaces in a complex compact can be obtained from the simulations. In this work, we present a technique based on measuring curvature of surfaces to obtain sintering stress of sintering powder compacts with arbitrarily complex geometries of powder size and powder shape distributions. The method is applied to three distinct powder compacts with very different sintering behavior to obtain sintering stress for each of these cases. The sintering stress for the three simulated cases were distinct and dependent on the geometric microstructural details of the powder compacts. © 2012 The American Ceramic Society.

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In this project, we performed a preliminary set of sintering experiments to examine nanocrystal-enabled diffusion bonding (NEDB) in Ag-on-Ag and Cu-on-Cu using Ag nanoparticles. The experimental test matrix included the effects of material system, temperature, pressure, and particle size. The nanoparticle compacts were bonded between plates using a customized hot press, tested in shear, and examined post mortem using microscopy techniques. NEDB was found to be a feasible mechanism for low-temperature, low-pressure, solid-state bonding of like materials, creating bonded interfaces that were able to support substantial loads. The maximum supported shear strength varied substantially within sample cohorts due to variation in bonded area; however, systematic variation with fabrication conditions was also observed. Mesoscale sintering simulations were performed in order to understand whether sintering models can aid in understanding the NEDB process. A pressure-assisted sintering model was incorporated into the SPPARKS kinetic Monte Carlo sintering code. Results reproduce most of the qualitative behavior observed in experiments, indicating that simulation can augment experiments during the development of the NEDB process. Because NEDB offers a promising route to low-temperature, low-pressure, solid-state bonding, we recommend further research and development with a goal of devising new NEDB bonding processes to support Sandia's customers.

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Simulating the detailed evolution of microstructure at the mesoscale is increasingly being addressed by a number of methods. Discrete element modeling and Potts kinetic Monte Carlo have achieved success in capturing different aspects of sintering well. Discrete element cannot treat the details of neck formation and other shape evolution, especially when considering particles of arbitrary shapes. Potts kMC treats the micorstructural evolution very well, but cannot incorporate complex stress states that form especially during differential sintering. A model that is capable of simulating microstructural evolution during sintering at the mesoscale and can incorporate differential stresses is being developed. This multi-physics model that can treat both interfacial energies and the inter-particle stresses will be introduced. It will be applied to simulate microstructural evolution while resolving individual particles and the stresses that develop between them due to local shrinkage. Results will be presented and the future development of this model will be discussed.

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The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.

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The Global Nuclear Energy Partnership fuels development program is currently developing metallic, oxide, and nitride fuel forms as candidate fuels for an Advanced Burner Reactor. The Advance Burner Reactor is being designed to fission actinides efficiently, thereby reducing the long-term storage requirements for spent fuel repositories. Small fuel samples are being fabricated and evaluated with different transuranic loadings and with extensive burnup using the Advanced Test Reactor. During the next several years, numerous fuel samples will be fabricated, evaluated, and tested, with the eventual goal of developing a transmuter fuel database that supports the down selection to the most suitable fuel type. To provide a comparative database of safety margins for the range of potential transmuter fuels, this report describes a plan to conduct a set of early transient tests in the Annular Core Research Reactor at Sandia National Laboratories. The Annular Core Research Reactor is uniquely qualified to perform these types of tests because of its wide range of operating capabilities and large dry central cavity which extents through the center of the core. The goal of the fuels testing program is to demonstrate that the design and fabrication processes are of sufficient quality that the fuel will not fail at its design limit--up to a specified burnup, power density, and operating temperature. Transient testing is required to determine the fuel pin failure thresholds and to demonstrate that adequate fuel failure margins exist during the postulated design basis accidents.

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All ceramics and powder metals, including the ceramics components that Sandia uses in critical weapons components such as PZT voltage bars and current stacks, multi-layer ceramic MET's, ahmindmolybdenum & alumina cermets, and ZnO varistors, are manufactured by sintering. Sintering is a critical, possibly the most important, processing step during manufacturing of ceramics. The microstructural evolution, the macroscopic shrinkage, and shape distortions during sintering will control the engineering performance of the resulting ceramic component. Yet, modeling and prediction of sintering behavior is in its infancy, lagging far behind the other manufacturing models, such as powder synthesis and powder compaction models, and behind models that predict engineering properties and reliability. In this project, we developed a model that was capable of simulating microstructural evolution during sintering, providing constitutive equations for macroscale simulation of shrinkage and distortion during sintering. And we developed macroscale sintering simulation capability in JAS3D. The mesoscale model can simulate microstructural evolution in a complex powder compact of hundreds or even thousands of particles of arbitrary shape and size by 1. curvature-driven grain growth, 2. pore migration and coalescence by surface diffusion, 3. vacancy formation, grain boundary diffusion and annihilation. This model was validated by comparing predictions of the simulation to analytical predictions for simple geometries. The model was then used to simulate sintering in complex powder compacts. Sintering stress and materials viscous module were obtained from the simulations. These constitutive equations were then used by macroscopic simulations for simulating shrinkage and shape changes in FEM simulations. The continuum theory of sintering embodied in the constitutive description of Skorohod and Olevsky was combined with results from microstructure evolution simulations to model shrinkage and deformation during. The continuum portion is based on a finite element formulation that allows 3D components to be modeled using SNL's nonlinear large-deformation finite element code, JAS3D. This tool provides a capability to model sintering of complex three-dimensional components. The model was verified by comparing to simulations results published in the literature. The model was validated using experimental results from various laboratory experiments performed by Garino. In addition, the mesoscale simulations were used to study anisotropic shrinkage in aligned, elongated powder compacts. Anisotropic shrinkage occurred in all compacts with aligned, elongated particles. However, the direction of higher shrinkage was in some cases along the direction of elongation and in other cases in the perpendicular direction depending on the details of the powder compact. In compacts of simple-packed, mono-sized, elongated particles, shrinkage was higher in the direction of elongation. In compacts of close-packed, mono-sized, elongated particles and of elongated particles with a size and shape distribution, the shrinkage was lower in the direction of elongation. We also explored the concept of a sintering stress tensor rather than the traditional sintering stress scalar concept for the case of anisotropic shrinkage. A thermodynamic treatment of this is presented. A method to calculate the sintering stress tensor is also presented. A user-friendly code that can simulate microstructural evolution during sintering in 2D and in 3D was developed. This code can run on most UNIX platforms and has a motif-based GUI. The microstructural evolution is shown as the code is running and many of the microstructural features, such as grain size, pore size, the average grain boundary length (in 2D) and area (in 3D), etc. are measured and recorded as a function of time. The overall density as the function of time is also recorded.

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Sintering is one of the oldest processes used by man to manufacture materials dating as far back as 12,000 BC. While it is an ancient process, it is also necessary for many modern technologies such a multilayered ceramic packages, wireless communication devices, and many others. The process consists of thermally treating a powder or compact at a temperature below the melting point of the main constituent, for the purpose of increasing its strength by bonding together of the particles. During sintering, the individual particles bond, the pore space between particles is eliminated, the resulting component can shrinks by as much as 30 to 50% by volume, and it can distort its shape tremendously. Being able to control and predict the shrinkage and shape distortions during sintering has been the goal of much research in material science. And it has been achieved to varying degrees by many. The object of this project was to develop models that could simulate sintering at the mesoscale and at the macroscale to more accurately predict the overall shrinkage and shape distortions in engineering components. The mesoscale model simulates microstructural evolution during sintering by modeling grain growth, pore migration and coarsening, and vacancy formation, diffusion and annihilation. In addition to studying microstructure, these simulation can be used to generate the constitutive equations describing shrinkage and deformation during sintering. These constitutive equations are used by continuum finite element simulations to predict the overall shrinkage and shape distortions of a sintering crystalline powder compact. Both models will be presented. Application of these models to study sintering will be demonstrated and discussed. Finally, the limitations of these models will be reviewed.

Microstructural evolution during simple solid-state sintering of two-dimensional compacts of elongated particles packed in different arrangements was simulated using a kinetic, Monte Carlo model. The model used simulates curvature-driven grain growth, pore migration by surface diffusion, vacancy formation, diffusion along grain boundaries, and annihilation. Only the shape of the particles was anisotropic; all other extensive thermodynamic and kinetic properties such as surface energies and diffusivities were isotropic. We verified our model by simulating sintering in the analytically tractable cases of simple-packed and close-packed, elongated particles and comparing the shrinkage rate anisotropies with those predicted analytically. Once our model was verified, we used it to simulate sintering in a powder compact of aligned, elongated particles of arbitrary size and shape to gain an understanding of differential shrinkage. Anisotropic shrinkage occurred in all compacts with aligned, elongated particles. However, the direction of higher shrinkage was in some cases along the direction of elongation and in other cases in the perpendicular direction, depending on the details of the powder compact. In compacts of simple-packed, mono-sized, elongated particles, shrinkage was higher in the direction of elongation. In compacts of close-packed, mono-sized, elongated particles and of elongated particles with a size and shape distribution, the shrinkage was lower in the direction of elongation. The results of these simulations are analyzed, and the implication of these results is discussed.

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A kinetic, three-dimensional Monte Carlo model for simulating grain growth in the presence of mobile pores is presented. The model was used to study grain growth and pore migration by surface diffusion in an idealized geometry that ensures constant driving force for grain growth. The driving forces, pore size, and pore mobilities were varied to study their effects on grain-boundary mobility and grain growth. The simulations captured a variety of complex behaviors, including reduced grain-boundary velocity due to pore drag that has been predicted by analytical theories. The model is capable of treating far more complex geometries, including polycrystals. We present the capabilities of this model and discuss its limitations.

Prediction of the evolution of microstructures in weapons systems is critical to meeting the objectives of stockpile stewardship in accordance with the Nuclear Weapons Test Ban Treaty. For example, accurate simulation of microstructural evolution in solder joints, cermets, PZT power generators, etc. is necessary for predicting the performance, aging, and reliability both of individual components and of entire weapons systems. A recently developed but promising approach called the ''Phase-Field Model'' (PFM) has the potential of allowing the accurate quantitative prediction of microstructural evolution, with all the spatial and thermodynamic complexity of a real microstructure. Simulating with the PFM requires solving a set of coupled nonlinear differential equations, one for each material variable (e.g., grain orientation, phase, composition, stresses, anisotropy, etc.). While the PFM is versatile and is able to incorporate the necessary complexity for modeling real material systems, it is very computationally intensive, and it has been a difficult and major challenge to formulate an efficient algorithmic implementation of the approach. We found that second order in space algorithm is more stable and leads to more accurate results. However, the computational requirements still remain high, so we have developed a single field algorithm to reduce the computations by 2 orders of magnitude. We have created a 3-D parallel version of the basic phase-field (PF model) and benchmarked it performance. Preliminary results indicate that we will be able to run very large problems effectively with the new parallel code. Microstructural evolution in a diffusion couple was simulated using PFM to simultaneously simulate grain growth, diffusion and phase transformation. Solute drag in a variable composition material, a process no other model can simulate, was successfully simulated using the phase-field model. The phase field model was used to study the evolution of fractal high curvature structures to show that these structures have very different morphological and kinetic behaviors than those of equi-axed structures.

An integrated approach, combining the continuum theory of sintering and Potts model based mesostructure evolution analysis, is used to solve the problem of bi-layered structure sintering. Two types of bi-layered structures are considered: layers of the same material with different initial porosity, and layers of two different materials. The effective sintering stress for the bi-layer powder sintering is derived, both at the meso- and the macroscopic levels. Macroscopic shape distortions and spatial distributions of porosity are determined as functions of the dimensionless specific time of sintering. The effect of the thickness of the layers on shrinkage, warpage, and pore-grain structure is studied. Ceramic ZnO powders are employed as a model experimental system to assess the model predictions.

An integrated approach, including a continuum theory of sintering and mesostructure evolution analysis, is used for the solution of the problem of bi-layered structure sintering. Two types of bi-layered structures are considered: layers of the same material different by initial porosity, and layers of two different materials. The effective sintering stress and the normalized bulk modulus for the bi-layer powder sintering are derived based on mesoscale simulations. The combined effect of the layers' porosity and differences in sintering rate on shrinkage and warpage is studied for both sintering on a rigid substrate and free sintering.

A lattice-Monte Carlo approach was developed to simulate ferroelectric domain behavior. The model utilizes a Hamiltonian for the total energy that includes electrostatic terms (involving dipole-dipole interactions, local polarization gradients, and applied electric field), and elastic strain energy. The contributions of these energy components to the domain structure and to the overall applied field response of the system were examined. In general, the model exhibited domain structure characteristics consistent with those observed in a tetragonally distorted ferroelectric. Good qualitative agreement between the appearance of simulated electrical hysteresis loops and those characteristic of real ferroelectric materials was found.