following is a summary of the most important of these processes: Hopping or jumping is conceptually the most basic mechanism for diffusion of adatoms. In this model, the adatoms reside on adsorption sites on the surface lattice. Motion occurs through successive jumps to adjacent sites, the number of which depends on the nature of the surface lattice. Figures 1 and 3 both display adatoms undergoing diffusion via the hopping process. Studies have shown the presence of metastable transition states between adsorption sites wherein it may be possible for adatoms to temporarily reside. Atomic exchange involves exchange between an adatom and an adjacent atom within the surface lattice. As shown in figure 4, after an atomic exchange event the adatom has taken the place of a surface atom and the surface atom has been displaced and has now become an adatom. This process may take place in both heterodiffusion (e.g. Pt adatoms on Ni) and self-diffusion (e.g. Pt adatoms on Pt). It is still unclear from a theoretical point of view why the atomic exchange mechanism is more predominant in some systems than in others. Current theory points towards multiple possibilities, including tensile surface stresses, surface relaxation about the adatom, and increased stability of the intermediate due to the fact that both atoms involved maintain high levels of coordination throughout the process. Tunneling diffusion is a physical manifestation of the quantum tunneling effect involving particles tunneling across diffusion barriers. It can occur in the case of low diffusing particle mass and low Ediff, and has been observed in the case of hydrogen diffusion on tungsten and copper surfaces. The phenomenon is unique in that in the regime where the tunneling mechanism dominates, the diffusion rate is nearly temperature-independent. Vacancy diffusion can occur as the predominant method of surface diffusion at high coverage levels approaching complete coverage. This process is akin to the manner in which pieces slide around in a "sliding puzzle". It is very difficult to directly observe vacancy diffusion due to the typically high diffusion rates and low vacancy concentration. Figure 5 shows the basic theme of this mechanism in an albeit oversimplified manner. Recent theoretical work as well as experimental work performed since the late 1970s has brought to light a remarkable variety of surface diffusion phenomena both with regard to kinetics as well as to mechanisms. Following is a summary of some of the more notable phenomena: