Through simulations with the moving finite element program GRAIN3D, we have studied the effect of anisotropic grain boundary energy on the distribution of boundary types in a polycrystal during normal grain growth. An energy function similar to that hypothesized for magnesia was used, and the simulated grain boundary distributions were found to agree well with measured distributions. The simulated results suggest that initially random microstructures develop nearly steady state grain boundary distributions that have local maxima and minima corresponding to local minima and maxima, respectively, of the energy function.

Simulation is becoming an increasingly important tool, not only in materials science in a general way, but in the study of grain growth in particular. Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Simulations must be accurate and at a scale large enough to have statistical significance. Moreover, they must be sufficiently flexible to use very general energies and mobilities. We introduce this theory and its discretization as a dissipative system in two and three dimensions. The approach has several interesting features. It consists in solving very large systems of nonlinear evolution equations with nonlinear boundary conditions at triple points or on triple lines. Critical events, the disappearance of grains and and the disappearance or exhange of edges, must be accomodated. The data structure is curves in two dimensions and surfaces in three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.

Measurements of the grain boundary character distribution in MgAl2O4 (spinel) as a function of lattice misorientation and boundary plane orientation show that at all misorientations, grain boundaries are most frequently terminated on 111 planes. Boundaries with 111 orientations are observed 2.5 times more frequently than boundaries with 100 orientations. Furthermore, the most common boundary type is the twist boundary formed by a 60$\,^\circ$ rotation about the [111] axis. 111 planes also dominate the external form of spinel crystals found in natural settings and this suggests that they are low energy and/or slow growing planes. The mechanisms that might lead to a high population of these planes during solid state crystal growth are discussed.

This brief review describes the major features of grain boundary mobility in metals and current limitations in our theoretical understanding. Although thermally activated exchange of atoms across boundaries provides a basic picture of grain boundary correct to within an order of magnitude, no refinement of this theory is available that account for the experimental characteristics of grain mobility as it depends on crystallographic type. An example is given of a simple extension involving density of kinks on the two surfaces that comprise a boundary to show that the resulting estimate of mobility is essentially different from the experimentally observed dependence.

Many issues in forming are influenced to some degree by the internal structure of the material which is commonly referred to by the materials science community as microstructure. Although the term microstructure is commonly only thought of in the context of grain size, it more properly encompasses all relevant aspects of internal material structure. For the purposes of forming, the most relevant features are the crystallographic orientations of the grains ( texture ) and the locations of the grain boundaries, or, equivalently, the size, topology and shape of the grains. In order to perform realistic simulations one needs to specify the initial state of the material, e.g. on a finite element mesh, with sufficient detail that all these features are reproduced. Measuring microstructure at the scale of individual grains is possible in the synchrotron but scarcely practicable for an analyst. Cross-sections or surfaces are easily evaluated through automated diffraction in the scanning electron microscope (SEM), however. Therefore this paper describes a set of methods for generating statistically representative 3D microstructures based on microscopy input for both single-phase and two-phase materials. Examples are given of application of the technique for generating input structures for recrystallization simulation, dynamic deformation and finite element modeling.

This article outlines the importance of anisotropic interfacial properties for microstructure evolution. The anisotropic properties of interfaces profoundly affect the development of microstructure during thin film deposition, sintering, grain growth and recrystallization, to name but a few processes. The properties of interfaces vary from mildly anisotropic, as for the energy of the solid-liquid interface, to strongly anisotropic as in the case of diffusion rates along grain boundaries. As a companion to this set of articles on interfacial anisotropy, this article demonstrates the connection between grain boundary anisotropy, primarily in mobility, and texture development during grain growth. A Monte Carlo model is used to investigate the evolution of the so-called cube texture component during grain growth of a polycrystal in which the texture is the result of prior deformation.

The grain boundary character distribution in commercially pure Al has been measured as a function of lattice misorientation and boundary plane orientation. The results demonstrate a tendency to terminate grain boundaries on low index planes with relatively low surface energies and large interplanar spacings. The most frequently observed grain boundary plane orientation is (1 1 1). However, there are also instances where boundaries terminated by higher index planes have significant populations. For example, certain twist configurations on 1 1 w planes, which correspond to symmetric [1 1 0] tilt boundaries, also have relatively high populations. The population of symirietric [1 1 0] tilt boundaries exhibits an inverse relationship with previously measured energies.

Techniques are described that have been used to create a statistically representative three-dimensional model microstructure for input into computer simulations using the geometric and crystallographic observations from two orthogonal sections through an aluminum polycrystal. Orientation maps collected on the observation planes are used to characterize the sizes, shapes, and orientations of grains. Using a voxel-based tessellation technique, a microstructure is generated with grains whose size and shape are constructed to conform to those measured experimentally. Orientations are then overlaid on the grain structure such that distribution of grain orientations and the nearest-neighbor relationships, specified by the distribution of relative misorientations across grain boundaries, match the experimentally measured distributions. The techniques are applicable to polycrystalline materials with sufficiently compact grain shapes and can also be used to controllably generate a wide variety of hypothetical microstructures for initial states in computer simulations.