Factual Revelation of Correlation Lengths Hierarchy in Micro- and Nanostructures by Scanning Probe Microscopy Data

Abstract

A new method is proposed to reveal the characteristic scales of substructures (in the case if they are present) in surface
structure represented by scanning probe microscopy (SPM) data. The method is based on processing the structural
functions (SF) of surface relief profiles to determine the positions of maxima of SF’s negative second derivative. New
approach is checked on model SFs, model structures and real SPM data (on LiF dissolution surfaces, track-etched
membranes and shungite rocks). It is shown that the positions correspond to the characteristic scales, or correlation
lengths, that can be related to objects having geometrical or physical sense. The use of the set of correlation lengths
instead of one effective length makes it possible to analyze in details a hierarchical structure of the objects under study.
This is extremely important when investigating the objects with complex many level hierarchical structures that are the
natural structures, structures of composite materials etc.