On the quantitative evaluation of characteristic length scales of interior and surface structure

In the present paper we use a simple method for the quantitative evaluation of characteristic length scales of some dislocation and surface topographical structures in mechanically deformed metals by means of linear integral transforms (in particular, the Fast Hartley Transform, FHT). The method also provides valuable information about the point symmetry group of a given microstructural pattern thereby allowing one to distinguish between different types of patterning (e.g. "Isotropic rotationally invariant" vs highly directional "crystallographic"). Such information, if combined with the proven techniques of modern stereology and quantitative metallography, can provide added insight into the nature of spatial coupling in those systems of non-linear governing equations that describe the formation and evolution of microstructure, and how these systems can be applied to a variety of technological applications. Several concrete examples of dislocation and topographical structures are considered, and results of a "computational diffraction analysis" of each example are discussed.