Analyses of small facets imaged with scanning-probe microscopy

Two tools for the analysis of facets as detected by scanning-probe microscopy (SPM) images are proposed. One tool is an adaptation of the radial-histogram transform proposed by D. Schleef et al. in Phys. Rev. B. 55, 2535 (1997). In this article the local slopes in the SPM image are in the present version determined by Savitsky–Golay filters with variable lengths [A. Savitsky and M. J. E. Golay, Anal. Chem. 36, 1627 (1964)]. These variable length filters turn out to be important to suppress the influence of noise obscuring the possibility to detect facets and to analyze corrugations with different length scales in SPM images, e.g., surface reconstructions. The other tool allows the direct quantitative determination of the orientation (with a standard deviation) of user-specified parts of facets. It makes use of a Savitsky–Golay filter as well. Both tools were applied to an artificially constructed SPM image and several experimental SFM images showing (ionic) MnO precipitates protruding out of a (metallic) Cu surface. It is shown that the Miller indices of the facets can be derived experimentally