Determination of in-plane surface directions in scanning probe microscopy images.

We describe an approach to determine the in-plane crystallographic surface directions in scanning probe microscopy (SPM) images. This method is based on a one-time characterization of the SPM instrument with an appropriate test sample and is exemplified by the analysis of non-contact atomic force microscopy (NC-AFM) images on surfaces whose natural cleavage occurs along {111} planes. We introduce a two-dimensional rotation matrix relating the crystallographic surface directions known from an analysis of the macroscopic crystal to the directions in the NC-AFM images. The procedure takes into account rotations and mirror axes resulting from sample mounting, the SPM scanner rotation, the choice of scan direction, as well as data processing, storage, and display. We demonstrate the practicability of the approach by determining the [112̄] direction in topographic images of a CeO2(111) film grown on a Si(111) wafer and atomic resolution images of CaF2(111) with an instrument based on the beetle-type scanner.