Using the coverage grating-optical second-harmonic diffraction method, we have measured the diffusion rate of potassium on Re(001) in the coverage range of 0.6-1 ML. We observe a minimum in both the activation energy for diffusion and the diffusion preexponential at an initial potassium coverage of 0.75 ML. For potassium coverages of 0.93, 0.84, 0.73, and 0.59 ML, the activation energies for diffusion are determined to be 5.0+/-0.2, 3.9+/-0.71 3.6+/-0.2, and 5.0+/-1.0 kcal/mol, and D-0 is 5.6x10(-3+/-0.3), 3.5x10(-4+/-1.1), 5.8x10(-4+/-0.3), and 3.7x10(-1+/-1.9) cm(2)/s, respectively. The results are discussed in terms of electrostatic dipole-dipole repulsive interactions among neighboring adsorbates. (C) 1997 American Institute of Physics.