The formation, transport and segregation of components in nuclear fuels fundamentally control their behavior, performance, longevity and safety. Most nuclear fuels enter service with a uniform composition consisting of a single phase with two or three components. Fission products form introducing more components. The segregation and transport of the components is complicated by the underlying microstructure consisting of grains, pores, bubbles and more, which is evolving during service. As they evolve, components and microstructural features interact such that composition affects microstructure and vice versa. The ability to predict compositional and microstructural evolution in 3D as a function of burn-up would greatly improve the ability to design safe, high burn-up nuclear fuels. We present a model that combines elements of Potts Monte Carlo, MC, and the phase-field model to treat coupled microstructural- compositional evolution. The evolution process demonstrated is grain growth and diffusion in a two-phase system. The hybrid model uses an equation of state, EOS, based on the microstructural state and composition. The microstructural portion uses the traditional MC EOS and the compositional portion uses the phase-field EOS: (Formula Presented) Ev is the bulk free energy of each site i and J is the neighbor interaction energy between neighboring sites i and j. The last term is the compositional interfacial energy as defined in the traditional phase-field model. The coupled microstructure-composition fields evolve by minimizing the free energy in a path dependent manner. An application of this modeling framework demonstrates the expected microstructural and phase coarsening, which is controlled by long-range diffusion.
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.
Legislated requirements and industry standards are replacing eutectic lead-tin (Pb-Sn) solders with lead-free (Pb-free) solders in future component designs and in replacements and retrofits. Since Pb-free solders have not yet seen service for long periods, their long-term behavior is poorly characterized. Because understanding the reliability of Pb-free solders is critical to supporting the next generation of circuit board designs, it is imperative that we develop, validate and exercise a solder lifetime model that can capture the thermomechanical response of Pb-free solder joints in stockpile components. To this end, an ASC Level 2 milestone was identified for fiscal year 2010: Milestone 3605: Utilize experimentally validated constitutive model for lead-free solder to simulate aging and reliability of solder joints in stockpile components. This report documents the completion of this milestone, including evidence that the milestone completion criteria were met and a summary of the milestone Program Review.
One of the tenets of nanotechnology is that the electrical/optical/chemical/biological properties of a material may be changed profoundly when the material is reduced to sufficiently small dimensions - and we can exploit these new properties to achieve novel or greatly improved material's performance. However, there may be mechanical or thermodynamic driving forces that hinder the synthesis of the structure, impair the stability of the structure, or reduce the intended performance of the structure. Examples of these phenomena include de-wetting of films due to high surface tension, thermally-driven instability of nano-grain structure, and defect-related internal dissipation. If we have fundamental knowledge of the mechanical processes at small length scales, we can exploit these new properties to achieve robust nanodevices. To state it simply, the goal of this program is the fundamental understanding of the mechanical properties of materials at small length scales. The research embodied by this program lies at the heart of modern materials science with a guiding focus on structure-property relationships. We have divided this program into three Tasks, which are summarized: (1) Mechanics of Nanostructured Materials (PI Blythe Clark). This task aims to develop a fundamental understanding of the mechanical properties and thermal stability of nanostructured metals, and of the relationship between nano/microstructure and bulk mechanical behavior through a combination of special materials synthesis methods, nanoindentation coupled with finite-element modeling, detailed electron microscopic characterization, and in-situ transmission electron microscopy experiments. (2) Theory of Microstructures and Ensemble Controlled Deformation (PI Elizabeth A. Holm). The goal of this Task is to combine experiment, modeling, and simulation to construct, analyze, and utilize three-dimensional (3D) polycrystalline nanostructures. These full 3D models are critical for elucidating the complete structural geometry, topology, and arrangements that control experimentally-observed phenomena, such as abnormal grain growth, grain rotation, and internal dissipation measured in nanocrystalline metal. (3) Mechanics and Dynamics of Nanostructured and Nanoscale Materials (PI John P. Sullivan). The objective of this Task is to develop atomic-scale understanding of dynamic processes including internal dissipation in nanoscale and nanostructured metals, and phonon transport and boundary scattering in nanoscale structures via internal friction measurements.
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.
Interfaces are a critical determinant of the full range of materials properties, especially at the nanoscale. Computational and experimental methods developed a comprehensive understanding of nanograin evolution based on a fundamental understanding of internal interfaces in nanocrystalline nickel. It has recently been shown that nanocrystals with a bi-modal grain-size distribution possess a unique combination of high-strength, ductility and wear-resistance. We performed a combined experimental and theoretical investigation of the structure and motion of internal interfaces in nanograined metal and the resulting grain evolution. The properties of grain boundaries are computed for an unprecedented range of boundaries. The presence of roughening transitions in grain boundaries is explored and related to dramatic changes in boundary mobility. Experimental observations show that abnormal grain growth in nanograined materials is unlike conventional scale material in both the level of defects and the formation of unfavored phases. Molecular dynamics simulations address the origins of some of these phenomena.
Predicting and controlling the evolution of materials microstructure is one of the central challenges of materials science. The simulation of microstructural evolution requires a detailed knowledge of the properties, including energies and mobilities, of interfaces in the material. We present the results of molecular dynamics simulations of these interfacial properties for a large set of boundaries.
Like other interfaces, equilibrium grain boundaries are smooth at low temperature and rough at high temperature; however, little attention has been paid to roughening except for faceting boundaries. Using molecular dynamics simulations of face-centered cubic Ni, we studied two closely related grain boundaries with different boundary planes. In spite of their similarity, their boundary roughening temperatures differ by several hundred degrees, and boundary mobility is much larger above the roughening temperature. This has important implications for microstructural development during metallurgical processes.
As current experimental and simulation methods cannot determine the mobility of flat boundaries across the large misorientation phase space, we have developed a computational method for imposing an artificial driving force on boundaries. In a molecular dynamics simulation, this allows us to go beyond the inherent timescale restrictions of the technique and induce non-negligible motion in flat boundaries of arbitrary misorientation. For different series of symmetric boundaries, we find both expected and unexpected results. In general, mobility increases as the grain boundary plane deviates from (111), but high-coincidence and low-angle boundaries represent special cases. These results agree with and enrich experimental observations.
In the present work the authors describe the adaptation of a standard SEM into a flexible microjoining tool. The system incorporates exceptional control of energy input and its location, environmental cleanliness, part manipulation and especially, part imaging. Beam energetics, modeling of thermal flow in a simple geometry, significant effects of surface energy on molten pools and beam size characterization are treated. Examples of small to micro fusion welds and molten zones produced in a variety of materials (Ni, tool steel, Tophet C, Si) and sizes are given. Future directions are also suggested.
Percolation theory is now standard in the analysis of polycrystalline materials where the grain boundaries can be divided into two distinct classes, namely 'good' boundaries that have favorable properties and 'bad' boundaries that seriously degrade the material performance. Grain-boundary engineering (GBE) strives to improve material behavior by engineering the volume fraction c and arrangement of good grain boundaries. Two key percolative processes in GBE materials are the onset of percolation of a strongly connected aggregate of grains, and the onset of a connected path of weak grain boundaries. Using realistic polycrystalline microstructures, we find that in two dimensions the threshold for strong aggregate percolation c{sub SAP} and the threshold for weak boundary percolation c{sub WBP} are equivalent and have the value c{sub SAP} = c{sub WBP} = 0.38(1), which is slightly higher than the threshold found for regular hexagonal grain structures, c{sub RH} = 2 sin({pi}/18) = 0.347. In three dimensions strong aggregate percolation and weak boundary percolation occur at different locations and we find c{sub SAP} = 0.12(3) and c{sub WBP} = 0.77(3). The critical current in high T{sub c} materials and the cohesive energy in structural systems are related to the critical manifold problem in statistical physics. We develop a theory of critical manifolds in GBE materials, which has three distinct regimes: (1) low concentrations, where random manifold theory applies, (2) critical concentrations where percolative scaling theory applies, and (3) high concentrations, c > c{sub SAP}, where the theory of periodic elastic media applies. Regime (3) is perhaps most important practically and is characterized by a critical length L{sub c}, which is the size of cleavage regions on the critical manifold. In the limit of high contrast {open_square} {yields} 0, we find that in two dimensions L{sub c} {proportional_to} gc/(1-c), while in three dimensions L{sub c} {proportional_to} g exp[b{sub 0}c/(1-c)]/[c(1-c)]{sup 1/2}, where g is the average grain size, {open_square} is the ratio of the bonding energy of the weak boundaries to that of the strong boundaries, and b{sub 0} is a constant which is of order 1. Many of the properties of GBE materials can be related to L{sub c}, which diverges algebraically on approach to c=1 in two dimensions, but diverges exponentially in that limit in three dimensions. We emphasize that GBE percolation processes and critical manifold behavior are very different in two dimensions as compared to three dimensions. For this reason, the use of two dimensional models to understand the behavior of bulk GBE materials can be misleading.
Biological systems create proteins that perform tasks more efficiently and precisely than conventional chemicals. For example, many plants and animals produce proteins to control the freezing of water. Biological antifreeze proteins (AFPs) inhibit the solidification process, even below the freezing point. These molecules bond to specific sites at the ice/water interface and are theorized to suppress solidification chemically or geometrically. In this project, we investigated the theoretical and experimental data on AFPs and performed analyses to understand the unique physics of AFPs. The experimental literature was analyzed to determine chemical mechanisms and effects of protein bonding at ice surfaces, specifically thermodynamic freezing point depression, suppression of ice nucleation, decrease in dendrite growth kinetics, solute drag on the moving solid/liquid interface, and stearic pinning of the ice interface. Stearic pinning was found to be the most likely candidate to explain experimental results, including freezing point depression, growth morphologies, and thermal hysteresis. A new stearic pinning model was developed and applied to AFPs, with excellent quantitative results. Understanding biological antifreeze mechanisms could enable important medical and engineering applications, but considerable future work will be necessary.
The purpose of microstructural control is to optimize materials properties. To that end, they have developed sophisticated and successful computational models of both microstructural evolution and mechanical response. However, coupling these models to quantitatively predict the properties of a given microstructure poses a challenge. This problem arises because most continuum response models, such as finite element, finite volume, or material point methods, do not incorporate a real length scale. Thus, two self-similar polycrystals have identical mechanical properties regardless of grain size, in conflict with theory and observations. In this project, they took a tiered risk approach to incorporate microstructure and its resultant length scales in mechanical response simulations. Techniques considered include low-risk, low-benefit methods, as well as higher-payoff, higher-risk methods. Methods studied include a constitutive response model with a local length-scale parameter, a power-law hardening rate gradient near grain boundaries, a local Voce hardening law, and strain-gradient polycrystal plasticity. These techniques were validated on a variety of systems for which theoretical analyses and/or experimental data exist. The results may be used to generate improved constitutive models that explicitly depend upon microstructure and to provide insight into microstructural deformation and failure processes. Furthermore, because mechanical state drives microstructural evolution, a strain-enhanced grain growth model was coupled with the mechanical response simulations. The coupled model predicts both properties as a function of microstructure and microstructural development as a function of processing conditions.
The Microsystems Subgrid Physics project is intended to address gaps between developing high-performance modeling and simulation capabilities and microdomain specific physics. The initial effort has focused on incorporating electrostatic excitations, adhesive surface interactions, and scale dependent material and thermal properties into existing modeling capabilities. Developments related to each of these efforts are summarized, and sample applications are presented. While detailed models of the relevant physics are still being developed, a general modeling framework is emerging that can be extended to incorporate evolving material and surface interaction modules.
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.
Computational materials simulations have traditionally focused on individual phenomena: grain growth, crack propagation, plastic flow, etc. However, real materials behavior results from a complex interplay between phenomena. In this project, the authors explored methods for coupling mesoscale simulations of microstructural evolution and micromechanical response. In one case, massively parallel (MP) simulations for grain evolution and microcracking in alumina stronglink materials were dynamically coupled. In the other, codes for domain coarsening and plastic deformation in CuSi braze alloys were iteratively linked. this program provided the first comparison of two promising ways to integrate mesoscale computer codes. Coupled microstructural/micromechanical codes were applied to experimentally observed microstructures for the first time. In addition to the coupled codes, this project developed a suite of new computational capabilities (PARGRAIN, GLAD, OOF, MPM, polycrystal plasticity, front tracking). The problem of plasticity length scale in continuum calculations was recognized and a solution strategy was developed. The simulations were experimentally validated on stockpile materials.
The minimum expended energy for fracture is the free energy required to form two new surfaces. For intergranular fracture, the minimum surface formation energy is complicated by the rough fracture surface, with area greater than the specimen cross-section. We utilize network optimization algorithms (max-flow/min-cut) to determine the minimum surface formation energies and surfaces for intergranular fracture in 3D polycrystals. For equiaxed grains and uniform boundary strength, the minimum energy fracture area is independent of grain size and is 45% larger than the specimen cross-section, and intergranular fracture will occur when surface energy is less than 1.6 times the grain boundary energy. The 3D fracture area is larger than projected from 2D systems. In systems with microcracked boundaries, the fracture surface deviates to preferentially include microcracked boundaries, creating interlocking grain configurations. Two-dimensional percolation of microcracks occurs at about 80% microcracked boundaries.
The origin of recrystallization nuclei is reviewed with particular emphasis on materials in which well-developed cells are present in the deformed state. Nucleation is discussed in terms of coarsening of the subgrain network that develops on annealing and an analogy is made with abnormal grain growth. The results of a theoretical analysis of abnormal growth are summarized. The Monte Carlo model for grain growth is adapted for variable grain boundary energy and mobility in order to investigate the behavior of individual grains with special properties. The simulation results show that both energy and mobility affect abnormal growth as expected from the theoretical analysis. The results are discussed in terms of the stability that subgrain networks may exhibit depending on their mean misorientation.
The application of computer simulation to grain growth and recrystallization was strongly stimulated in the early 80s by the realization that Monte Carlo models could be applied to problems of grain structure evolution. By extension of the Ising model for domain modeling of magnetic domains to the Potts model (with generalized spin numbers) it was then possible to represent discretely grains (domains) by regions of similarly oriented sets of material (lattice) points. In parallel with this fascinating development, there also occured notable work on analytical models, especially by Abbruzzese and Bunge, which has been particularly useful for understanding the variation of texture (crystallographic preferred orientation) during grain growth processes. Geometric models of recrystallization, worked on most recently and productively by Nes et al., have been useful in connection with grain size prediction as a result of recrystallization. Also, mesh-based models have been developed to a high degree by Kawasaki, Fradkov and others, and, rather recently, by Humphreys to model not just grain growth but also the nucleation process in recrystallization. These models have the strength that they deal with the essential features of grains, i.e. the nodes, but have some limitations when second phases must be considered. These various approaches to modeling of recrystallization processes will be reviewed, with a special emphasis on practical approaches to implementing the Potts model. This model has been remarkably successful in modeling such diverse phenomena as dynamic recrystallization, secondary recrystallization (abnormal grain growth), particle-inhibited recrystallization, and grain structure evolution in soldering and welding. In summary, the application of mesoscopic simulation to the phenomenon of recrystallization has yielded much new insight into some longstanding deficiencies in our understanding.
