Adam Morawiec

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 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 {1 0 0} 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.

Polycrystal orientation maps from TEM

Determination of topography of crystallite orientations is an important technique of investigation of polycrystalline materials. A system for creating orientation maps using transmission electron microscope (TEM) Kikuchi patterns and Convergent beam electron diffraction patterns is presented. The orientation maps are obtained using a step-by-step beam scan on a computer-controlled TEM equipped with a CCD camera. At each step, acquired diffraction patterns are indexed and orientations are determined. Although, the approach used is similar to that applied in SEM/electron back scattered diffraction (EBSD) orientation imaging setups, the TEM-based system considerably differs from its SEM counterpart. The main differences appear due to specific features of TEM and SEM diffraction patterns. Also, the resulting maps are not equivalent. On these generated by TEM, the accuracy of orientation determination can be better than 0.1 degrees. The spatial resolution is estimated to be about 10nm. The latter feature makes the TEM orientation mapping system an important tool for studies at fine scale unreachable by SEM/EBSD systems. The automatic orientation mapping is expected to be a useful complement of the conventional TEM contrast images. The new technique will be essential for characterization of fine structure materials. To illustrate that, example maps of an aluminum sample produced by severe plastic deformation are included.

Automatic orientation determination from Kikuchi patterns

Some formal aspects of crystal orientation determination from Kikuchi patterns are discussed, with respect to writing general and fast algorithms for automatic indexing of the patterns and orientation determination. The geometry of the problem is presented in a general form which is also suitable for channeling patterns or X-ray Kossel patterns. Moreover, geometrical ambiguities and other reliability issues are considered. Some strategies designed to handle artifacts of automatic pattern analysis are presented. Finally, the reliability and the accuracy of the described procedures and the sensitivity of the results to the errors of the basic measurement parameters were tested on computer-generated patterns.

Method to calculate the grain boundary energy distribution over the space of macroscopic boundary parameters from the geometry of triple junctions

Abstract Details of a numerical method for reconstructing the grain boundary energy distribution over the complete space of macroscopic boundary parameters are presented. The reconstruction is based on the analysis of the dihedral angles between homophase grain boundaries of polycrystalline triple junctions. Instead of the Herring equilibrium condition, the procedure uses the Hoffman–Cahn formalism of the capillarity vector. This turns the reconstruction into the problem of solving a homogeneous system of algebraic linear equations. A numerical example demonstrating a reasonably good performance of the method is also given.

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.

Crystallographic orientation inhomogeneity and crystal splitting in biogenic calcite

The calcitic prismatic units forming the outer shell of the bivalve Pinctada margaritifera have been analysed using scanning electron microscopy–electron back-scatter diffraction, transmission electron microscopy and atomic force microscopy. In the initial stages of growth, the individual prismatic units are single crystals. Their crystalline orientation is not consistent but rather changes gradually during growth. The gradients in crystallographic orientation occur mainly in a direction parallel to the long axis of the prism, i.e. perpendicular to the shell surface and do not show preferential tilting along any of the calcite lattice axes. At a certain growth stage, gradients begin to spread and diverge, implying that the prismatic units split into several crystalline domains. In this way, a branched crystal, in which the ends of the branches are independent crystalline domains, is formed. At the nanometre scale, the material is composed of slightly misoriented domains, which are separated by planes approximately perpendicular to the c-axis. Orientational gradients and splitting processes are described in biocrystals for the first time and are undoubtedly related to the high content of intracrystalline organic molecules, although the way in which these act to induce the observed crystalline patterns is a matter of future research.

A note on mean orientation

The procedure of calculating the mean orientation considered by Humbert et al. [J. Appl. Cryst. (1996), 29, 662–666] is reformulated in terms of quaternions of unit magnitude. The problem is reduced to the calculation of an eigenvector of a certain symmetric 4 × 4 matrix.

Orientation mapping by transmission-SEM with an on-axis detector.

Conventional orientation mapping in a scanning electron microscope (SEM) is a valuable technique for characterizing crystalline materials, but its application to ultrafine or nano-grain materials is limited by its spatial resolution. The resolution can be increased by collecting transmission diffraction patterns in SEM. In previous works, such patterns were collected using off-axis detectors in nearly vertical position. To avoid some drawbacks of such arrangement, a new configuration was devised in which the scintillator is located underneath the thin foil on the optical axis of the microscope, and the light is reflected towards the camera by a mirror. This simple configuration gives intense patterns even at very low probe currents, and can be potentially used for collecting maps of relatively high spatial resolution. Example maps reveal details with dimensions of about 5nm. Because of its resolution and geometric simplicity, the proposed configuration will open new opportunities in SEM-based characterization of nanocrystalline materials.

Models of uniformity for grain boundary distributions

Progress in experimental methods of serial sectioning and orientation determination opens new opportunities to study inter-crystalline boundaries in polycrystalline materials. In particular, macroscopic boundary parameters can now be measured automatically. With sufficiently large data sets, statistical analysis of interfaces between crystals is possible. The most basic and interesting issue is to find out the probability of occurrence of various boundaries in a given material. In order to define a boundary density function, a model of uniformity is needed. A number of such models can be conceived. It is proposed to use those derived from an assumed metric structure of the interface manifold. Some basic metrics on the manifold are explicitly given, and a number of notions and constructs needed for a strict definition of the boundary density function are considered. In particular, the crucial issue of the impact of symmetries is examined. The treatments of homo- and hetero-phase boundaries differ in some respects, and approaches applicable to each of these two cases are described. In order to make the abstract matter of the paper more accessible, a concrete boundary parameterization is used and some examples are given.