The interaction of potassium atoms on top of Cr 2 O 3 ͑0001͒/Cr͑110͒ has been studied using work-function ͑⌬⌽͒, temperature programmed desorption ͑TPD͒, and optical second-harmonic generation ͑SHG͒ measurements. Potassium grows via the completion of a first layer, followed by a second layer in the form of two-dimensional ͑2D͒ islands, and at higher coverage 3D clusters are formed. This growth model is supported by and consistent with the results obtained from all three methods. Work-function data suggest that annealing at temperatures above 350 K results in the formation of a surface potassium oxide compound, provided the potassium coverage is higher than 0.5 monolayers ͑ML͒. Diffusion of alkali-metal atoms on an oxide surface is reported here over distances of several micrometers. This was measured using optical SH diffraction from coverage gratings that were generated by laser-induced thermal desorption. The activation energy for surface diffusion of potassium on Cr 2 O 3 ͑0001͒/Cr͑110͒ has been determined to be 11Ϯ0.5 kcal/mol with a preexponential factor D 0 ϭ10 5 cm 2 /sec in the coverage range of 1.5-2.5 ML, dropping to 9 kcal/mol and D 0 ϭ3 ϫ10 3 cm 2 /sec at a coverage of 3.0 ML. These results are consistent with the diffusion of atoms in the third layer, on top of two-dimensional potassium islands in the second layer, the activation energy represent the barrier for descending from the 2D islands.