  The (111) surface of CaF$_2$ has been intensively studied with
large-amplitude frequency-modulation atomic force microscopy and atomic
contrast formation is now well understood. It has been shown that the apparent
contrast patterns obtained with a polar tip strongly depend on the tip
terminating ion and three sub-lattices of anions and cations can be imaged.
Here, we study the details of atomic contrast formation on CaF$_2$(111) with
small-amplitude force microscopy utilizing the qPlus sensor that has been shown
to provide utmost resolution at high scanning stability. Step edges resulting
from cleaving crystals in-situ in the ultra-high vacuum appear as very sharp
structures and on flat terraces, the atomic corrugation is seen in high clarity
even for large area scans. The atomic structure is also not lost when scanning
across triple layer step edges. High resolution scans of small surface areas
yield contrast features of anion- and cation sub-lattices with unprecedented
resolution. These contrast patterns are related to previously reported
theoretical results.
