Possible local structures of K ions in the tunnel of a hollandite superstructure KxMg(8 + x)/3Sb(16 (-) O-x)/3(16) (x approximate to 1.76) were presented, and the validity of the models was confirmed by the structure refinement using single-crystal X-ray diffraction data. Additional constraint conditions were introduced in refinements so that the average structure obtained from the refinement is consistent with assumed microscopic pictures. Joint-probability density functions were calculated for specific K ions concerning the hopping process between neighboring cavities, and converted to the one-particle potentials. Three types of the energy barrier for the hopping process were seen, which were uniformly reduced applying the anharmonic atomic displacement parameters. (C) 2011 Elsevier B.V. All rights reserved.