David M. Saylor

Distribution of grain boundaries in magnesia as a function of five macroscopic parameters

Abstract A semi-automated method has been used to measure all five macroscopically observable parameters of 4.1×10 6 boundary plane segments making up 5.4 mm 2 of boundary area in a hot-pressed magnesia polycrystal. The observations allow a complete description of the distribution of crystal orientations, grain boundary misorientations, and the crystallographic orientations of grain boundary planes. Among the low misorientation angle grain boundaries, there is a preference for tilt boundaries, especially those with boundary plane normals in the direction. At all fixed misorientations, there is a preference for boundaries with a boundary plane normal in the direction. These boundaries are generally asymmetric and occur at least twice as frequently as the average boundary for each fixed misorientation.

The Distribution of Internal Interfaces in Polycrystals

Recent advances both in experimental instrumentation and computing power have made it possible to interrogate the distribution of internal interfaces in polycrystals and the three dimensional structure of the grain boundary network with an unprecedented level of detail. The purpose of this paper is to review techniques that can be used to study the mesoscopic crystallographic structure of grain boundary networks and to summarize current findings. Recent studies have shown that grain surfaces within dense polycrystals favor the same low energy planes that are found on equilibrium crystal shapes and growth forms of crystals in contact with another phase. In the materials for which comprehensive data exists, the distribution of grain boundaries is inversely correlated to the sum of the energies of the surfaces of the grains on either side of the boundary.

The relative free energies of grain boundaries in magnesia as a function of five macroscopic parameters

Abstract Using measurements of the geometric and crystallographic characteristics of approximately 10 4 triple junctions in a MgO polycrystal, the relative grain boundary energy has been determined as a function of five macroscopic parameters. The relative energy of a particular grain boundary is inversely correlated with its frequency of occurrence. At all misorientations, grain boundaries with {1u20080u20080} interface planes have relatively low energies. For low misorientation angle grain boundaries, the results are consistent with the predictions of dislocation models. At high misorientation angles, the population and energy are correlated to the sum of the energies of the free surfaces that comprise the boundary.

Extracting Grain Boundary and Surface Energy from Measurement of Triple Junction Geometry

Measurement of the geometry of triple junctions between grain boundaries in polycrystalline materials generates large sets of dihedral angles from which maps of the grain boundary energy may be extracted. A preliminary analysis has been performed for a sample of magnesia based on a three-parameter description of grain boundaries. An extended form of orientation imaging microscopy (OIM) was used to measure both triple junction geometry via image analysis in the SEM and local grain orientation via electron back scatter diffraction. Serial sectioning with registry of both in-plane images and successive sections characterizes triple junction tangents from which true dihedral angles are calculated. We apply Herrings relation at each triple junction, based on the assumption of local equilibrium at the junction. By limiting grain boundary character to a (three parameter) specification of misorientation for the preliminary analysis, we can neglect the torque terms and apply the sine law to the three boundaries. This provides two independent relations per triple junction between grain boundary energies and dihedral angles. Discretizing the misorientation and employing multiscale statistical analysis on large data sets allows (relative) grain boundary energy as a function of boundary character to be extracted from triple junction geometry. A similar analysis of thermal grooves allows the anisotropy of the surface energy to be measured in MgO.

Misorientation Dependence of the Grain Boundary Energy in Magnesia

Geometric and crystallographic data obtained from a well annealed magnesia polycrystal have been used to specify the five macroscopic degrees of freedom for 4665 grain boundaries. The results indicate, that for this sample, the five parameter grain boundary character space is fully occupied. A finite series of symmetrized spherical harmonics has been used to approximate the misorientation dependence of the relative grain boundary energy. Best fit coefficients for this series were determined by assuming that the interfacial tensions at each triple junction are balanced. The grain boundary energy function shows Read-Shockley behavior at small misorientations and a broad minimum near the Σ3 misorientation. Furthermore, misorientations about the ‹100› axis create boundaries with relative energies that are less than those created by misorientations about the ‹110› or ‹111› axes.

Three Dimensional Microstructures: Statistical Analysis of Second Phase Particles in AA7075-T651

This paper describes some aspects of reconstruction of microstructures in three dimensions. A distinction is drawn between tomographic approaches that seek to characterize specific volumes of material, either with or without diffraction, and statistical approaches that focus on particular aspects of microstructure. A specific example of the application of the statistical approach is given for an aerospace aluminum alloy in which the distributions of coarse constituent particles are modeled. Such distributions are useful for modeling fatigue crack initiation and propagation.

Thermal-elastic response of marble polycrystals: Influence of grain orientation configuration

Abstract Two-dimensional, microstructure-based finite element simulations were used to elucidate the influence of grain orientation configuration on the thermal-elastic response of polycrystalline ceramic materials. The two main constituent minerals of marbles, calcite and dolomite, were considered. The crystallographic configuration of the grains is described in terms of the distribution of grain orientations and grain-boundary misorientations. To probe the influence of grain orientation configuration, we first generated the geometry of a hypothetical microstructure. Next, crystallographic orientations were assigned to each grain in the microstructure such that the grain orientations and grain-boundary misorientations matched predefined distributions. By varying the predefined distributions, we generated 45 unique microstructures covering a wide range of crystallographic configurations. After assigning thermal-elastic properties to each structure, corresponding to either calcite or dolomite, finite-element simulations were performed. The simulations demonstrated that both the orientation and misorientation distributions have a substantial impact on the thermal-elastic response of microstructures with the same material properties: varying the crystallographic configuration results in variations of stored elastic strain energy density from 10 kJ m−3 to 39 kJ m−3 for a 100 °C temperature change. Further, the ratio of the bulk coefficient of thermal expansion in the two principal directions varies from − 0.17 to 1.46. Surprisingly, the grain-boundary misorientations alone had a substantial impact on the thermal-elastic response of the system. By simply rearranging a fixed set of crystallographic orientations to obtain different nearest-neighbor misorientation configurations, we observed variations in strain energy density from 10 kJ m−3 to 39 kJ m−3 and variations in thermal expansion ratio from 0.06 to 0.90. The results suggest that to predict accurately the thermal-elastic response of polycrystalline ceramics, it is critical to consider both the distribution of grain-boundary misorientations as well as the distribution of grain orientations.

Evaluating Anisotropic Surface Energies Using the Capillarity Vector Reconstruction Method

By measuring the geometry and crystallography of the three interfaces that meet at grain boundary thermal grooves, it is possible to determine the anisotropy of the surface free energy. Previously, the surface energy of MgO at 1400°C in air was approximated by a truncated double Fourier series with coefficients that were determined by fitting the observations to Herrings condition for local equilibrium at a triple junction. The purpose of this paper is to describe an alternative analysis of the same data set that is not limited by an assumed functional form of the surface energy. In this case, the space of surface characters is discretized and each orientation is associated with a capillarity vector (according to the Cahn–Hoffmann definition). The set of capillarity vectors that most closely satisfies the condition for local equilibrium at each triple junction is then determined by an iterative method. The relative surface free energies derived from this analysis are more anisotropic than those derived from the series fit and more consistent with the observed faceting of MgO in air at 1400°C. The relative surface energies of the low index planes are γ110/γ100 = 1.07±0.04 and γ111/γ100 = 1.17±0.04.

Crystallographic Distribution of Internal Interfaces in Spinel Polycrystals

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° 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.

Distribution of Grain Boundary Planes at Coincident Site Lattice Misorientations

The grain boundary plane distributions in MgO, SrTiO3, MgAl2O4, and Al are compared at lattice misorientations with a coincident site density of greater than or equal to 1/9. In most situations, the most frequently adopted grain boundary orientation is a habit plane of low index and low surface energy that depends on the particular material. Cases where the most common boundary orientation is a plane of high planar coincident site density instead of a characteristic habit plane are rare. In fact, in most cases, the distributions of grain boundary planes at misorientations with high lattice coincidence are not substantially different from the distributions at other, more general misorientations. The results indicate that a model for grain boundary energy and structure based on grain surface relationships is more appropriate than the widely accepted models based on lattice orientation relationships.