On Frequencies of Occurrence of Geometrically Characteristic Grain Boundaries

Abstract

Development of spatial microstructure imaging techniques (e.g. of automated serial sectioning) has made it possible to collect five macroscopic grain boundary parameters for sets of boundaries large enough for carrying out statistical studies. As a point of reference for future analysis of experimentally measured boundary data, various aspects of estimating the frequencies of occurrence of geometrically characteristic boundaries among random grain boundaries for the cases of cubic Oh, hexagonal D6h and tetragonal D4h point groups are discussed. Example frequencies, in particular for symmetric and improperly quasi-symmetric boundaries, are presented. Two approaches for verification whether a given boundary has a tilt or twist character are confronted, i.e. a method based on a distance function defined in the boundary parameter space and the widely known decomposition of a boundary into its tilt and twist components. The frequencies for tilt and twist boundaries calculated using both methods are compared.