Load-dependent studies of the frictional properties of mica and germanium sulfide were performed by friction force spectroscopy in air and in argon atmosphere. Well-defined spherical tips made from amorphous carbon were used to profile the surface at low loads. In air, the frictional force (Formula presented) as a function of the normal force (Formula presented) for GeS follows an (Formula presented) behavior with good agreement, as is predicted by contact mechanical theories for a Hertz-type contact with small tip radius, with not too soft tip and sample materials, and with low surface energies involved. The friction of mica, however, deviates significantly in many cases from the (Formula presented) law due to its higher surface energy. In argon, chemical reactions between clean sample and tip material prevent the observation of wearless friction on in situ prepared samples. These effects were partially suppressed by an ex situ cleavage of the mica or germanium sulfide samples.