Improved representations of misorientation information for grain boundary science and engineering

For every class of polycrystalline materials, the scientific study of grain boundaries as well as the increasingly widespread practice of grain boundary engineering rely heavily on visual representation for the analysis of boundary statistics and their connectivity. Traditional methods of grain boundary representation drastically simplify misorientations into discrete categories such as coincidence vs. non-coincidence boundaries, special vs. general boundaries, and low- vs. high-angle boundaries. Such rudimentary methods are used either because there has historically been no suitable mathematical structure with which to represent the relevant grain boundary information, or, where there are existing methods they are extremely unintuitive and cumbersome to use. This review summarizes recent developments that significantly advance our ability to represent a critical part of the grain boundary space: the misorientation information. Two specific topics are reviewed in detail, each of which has recently enjoyed the development of an intuitive and rigorous framework for grain boundary representation: (i) the mathematical and graphical representation of grain boundary misorientation statistics, and (ii) colorized maps or micrographs of grain boundary misorientation. At the outset, conventions for parameterization of misorientations, projections of misorientation information into lower dimensions, and sectioning schemes for the misorientation space are established. Then, the recently developed hyperspherical harmonic formulation for the description of orientation distributions is extended to represent grain boundary statistics. This allows an intuitive representation of the distribution functions using the axis-angle parameterization that is physically related to the boundary structure. Finally, recently developed coloring schemes for grain boundaries are presented and the color legends for interpreting misorientation information are provided. This allows micrographs or maps of grain boundaries to be presented in a colorized form which, at a glance, reveals all of the misorientation information in an entire grain boundary network, as well as the connectivity among different boundary misorientations. These new and improved methods of representing grain boundary misorientation information are expected to be powerful tools for grain boundary network analysis as the practice of grain boundary engineering becomes a routine component of the materials design paradigm. (c) 2012 Elsevier Ltd. All rights reserved.