EXTENSION OF KIRSTE-POROD LAW IN THE CASE OF ANGULOUS INTERFACES

A preceding paper handled, by way of application, the usefulness of Po rod's law extended to the second nonoscillating term. The h-6 term all ows the structure of the phases to be better characterized. This paper is mainly concerned with the setting up of the main equations used in this preceding paper. The h-6 term is analysed from the correlation f unction gamma(r) and related to the 'stick probability function'. It c an be positive or negative. The positive case appears in smooth phases and has been previously analysed by Kirste & Porod. The negative case occurs in the presence of linear edges resulting from the meeting of surfaces that are planar in the vicinity of their intersection. More p recisely, it is shown that the h-6 negative term results from the fini te length of the edge. Its magnitude depends on the dihedral angles at the vertex defined by the limited sharp edges. The smaller the dihedr al angles, the greater the h-6 term amplitude. The new concept of angu losity, theta, a pure number characterizing the geometry of the phase, is introduced. In this way, it is possible to develop similar equatio ns for a specific surface, angularity and angulosity. Some simple-geom etry examples are developed. The region where the extended Kirste-Poro d law is useful in analysing small-angle scattering curves is discusse d.