Publications

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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.