Using a helium cooled field ion microscope (FIM), it has been possible to observe individual platinum atoms on Pt(111) surfaces and clusters without affecting atomic behavior. Pt atoms diffuse at temperatures T greater than or equal to 80 K, and occupy fee sites exclusively; hcp sites are filled only by depositing atoms on a cold Pt(111) surface (T similar to 20 K). The two different binding sites are readily identifiable by the characteristic orientation of the triangular image spot produced by the adatom, even though the distribution of intensity over the image spot is sensitively dependent upon the voltage. Observations of the motion of Pt atoms on top of clusters reveal behavior much more interesting than assumed in theories of crystal growth. At temperatures T less than or equal to 95 K, Pt atoms diffusing over the central region of platinum clusters are prevented from reaching the cluster edges. The zone close to the cluster edges similar to 3 nearest-neighbor spacings wide can only be penetrated at higher temperatures. At these temperatures, Pt adatoms rapidly diffuse to the edge, where they are trapped, leaving this outer zone empty of atoms. Along the edges, platinum atoms diffuse quite rapidly at temperatures much below those required for incorporation into the crystal.