The sintering behavior of close-packed spheres

The sintering behavior and microstructural evolution of a powder compact is influenced strongly by initial properties, such as the relative density, the particle and pore size distribution, and the powder packing. While the influence of the former parameters on the microstructural evolution has been investigated in some detail, the impact of the initial packing of the powder has been mostly overlooked. However, research has shown that the sintering behavior of a powder can be significantly improved if the powder is regularly packed. This has been shown for monodisperse spherical TiO2 particles [1], which sintered 10 times faster and exhibited almost no grain growth compared to ordinary TiO2. Similar observations has been made for homogeneously packed Al2O3 [2], SiO2 [3], as well as a number of other materials [4]. Monodispersed spherical TiO2 particles have been shown to order in face-centered cubic (fcc) arrays, while the SiO2 powder forms stacked planes of hexagonal close-packed (hcp) particles. Close packing of monodispersed silica has also been observed [5]. Sintering of two-dimensional close packing cylinders has also been demonstrated experimentally [6–8] and numerically modeled [9,10], and the sintering of particle clusters in three dimensions has also been studied [11]

Numerical simulation of grain size distributions in liquid phase sintered materials

Many technologically important ceramics such as silicon nitride ceramics, alumina substrates and barium titanate electrical capacitors are liquid phase sintered. It is important to understand evolution of microstructural features generated by processes such as grain growth so that these materials may be engineered for their respective applications. Grain growth in liquid phase sintered materials by Ostwald ripening has been modeled extensively by both analytical and numerical techniques. However, all models make simplifying approximations to make the problem tractable and the approximations used in these models make them most accurate at very low solid fractions. A two-dimensional, Monte Carlo simulation technique based on the Potts model that makes no assumptions about solid fraction, grain shapes or diffusion fields around grains has been used to study grain growth in fully wetting, liquid phase sintered systems. The grain size distribution, GSD, was found to vary with solid fraction, becoming broader and more peaked with increasing solid fraction. The skewness was near zero at solid fraction of 0.41 and shifted to larger grain sizes with increasing solid fraction

Strain in the mesoscale kinetic Monte Carlo model for sintering

Shrinkage strains measured from microstructural simulations using the mesoscale kinetic Monte Carlo (kMC) model for solid state sintering are discussed. This model represents the microstructure using digitized discrete sites that are either grain or pore sites. The algorithm used to simulate densification by vacancy annihilation removes an isolated pore site at a grain boundary and collapses a column of sites extending from the vacancy to the surface of sintering compact, through the center of mass of the nearest grain. Using this algorithm, the existing published kMC models are shown to produce anisotropic strains for homogeneous powder compacts with aspect ratios different from unity. It is shown that the line direction biases shrinkage strains in proportion the compact dimension aspect ratios. A new algorithm that corrects this bias in strains is proposed; the direction for collapsing the column is determined by choosing a random sample face and subsequently a random point on that face as the end point for an annihilation path with equal probabilities. This algorithm is mathematically and experimentally shown to result in isotropic strains for all samples regardless of their dimensions. Finally, the microstructural evolution is shown to be similar for the new and old annihilation algorithms.Comment: 6 pages, 6 figure

Fabrication of Net-Shape Functionally Graded Composites by Electrophoretic Deposition and Sintering: Modeling and Experimentation

It is shown that electrophoretic deposition (EPD) sintering is a technological sequence that is capable of producing net-shape bulk functionally graded materials (FGM). By controlling the shape of the deposition electrode, components of complex shapes can be obtained. To enable sintering net-shape capabilities, a novel optimization algorithm and procedure for the fabrication of net-shape functionally graded composites by EPD and sintering has been developed. The initial shape of the green specimen produced by EPD is designed in such a way that the required final shape is achieved after sintering-imposed distortions. The optimization is based on a special innovative iteration procedure that is derived from the solution of the inverse sintering problem: the sintering process is modeled in the “backward movie” regime using the continuum theory of sintering incorporated into a finite-element code. The experiments verifying the modeling approach include the synthesis by EPD of Al2O3/ZrO2 3-D (FGM) structures. In order to consolidate green parts shaped by EPD, post-EPD sintering is used. The fabricated deposits are characterized by optical and scanning electron microscopy. The experimentally observed shape change of the FGM specimen obtained by EPD and sintering is compared with theoretical predictions

SIMULATION OF SINTERING OF LAYERED STRUCTURES

Abstract -An integrated approach, combining the continuum theory of sintering and Potts model based mesostructure evolution analysis, is used to solve the problem of hi-layered structure sintering. Two types of hi-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 hi-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.

A Phase-Field Model for Grain Growth

A phase-field model for grain growth is briefly described. In this model, a poly-crystalline microstructure is represented by multiple structural order parameter fields whose temporal and spatial evolutions follow the time-dependent Ginzburg-Landau (TDGL) equations. Results from phase-field simulations of two-dimensional (2D) grain growth will be summarized and preliminary results on three-dimensional (3D) grain growth will be presented. The physical interpretation of the structural order parameter fields and the efficient and accurate semi-implicit Fourier spectral method for solving the TDGL equations will be briefly discussed

Four electrons in a two-leg Hubbard ladder: exact ground states

In the case of a two-leg Hubbard ladder we present a procedure which allows the exact deduction of the ground state for the four particle problem in arbitrary large lattice system, in a tractable manner, which involves only a reduced Hilbert space region containing the ground state. In the presented case, the method leads to nine analytic, linear, and coupled equations providing the ground state. The procedure which is applicable to few particle problems and other systems as well is based on an r-space representation of the wave functions and construction of symmetry adapted orthogonal basis wave vectors describing the Hilbert space region containing the ground state. Once the ground state is deduced, a complete quantum mechanical characterization of the studied state can be given. Since the analytic structure of the ground state becomes visible during the use of the method, its importance is not reduced only to the understanding of theoretical aspects connected to exact descriptions or potential numerical approximation scheme developments, but is relevant as well for a large number of potential technological application possibilities placed between nano-devices and quantum calculations, where the few particle behavior and deep understanding are important key aspects to know.Comment: 19 pages, 5 figure