cluster’s center of mass. Individual mechanisms are those that involve movement of one atom at a time. Edge diffusion involves movement of adatoms or vacancies at edge or kink sites. As shown in figure 10, the mobile atom maintains its proximity to the cluster throughout the process. Evaporation-condensation involves atoms “evaporating” from the cluster onto a terrace accompanied by “condensation” of terrace adatoms onto the cluster leading to a change in the cluster’s center of mass. While figure 10 appears to indicate the same atom evaporating from and condensing on the cluster, it may in fact be a different atom condensing from the 2D gas. Leapfrog diffusion is similar to edge diffusion, but where the diffusing atom actually moves atop the cluster before settling in a different location from its starting position. Sequential displacement refers to the process involving motion one atom at a time, moving to free nearest-neighbor sites. Concerted mechanisms are those that involve movement of either sections of the cluster or the entire cluster all at once. Dislocation diffusion occurs when adjacent sub-units of a cluster move in a row-by-row fashion through displacement of a dislocation. As shown in figure 11(a) the process begins with nucleation of the dislocation followed by what is essentially sequential displacement on a concerted basis. Glide diffusion refers to the concerted motion of an entire cluster all at once (see figure 11(b)). Reptation is a snake-like movement (hence the name) involving sequential motion of cluster sub-units (see figure 11(c)). Shearing is a concerted displacement of a sub-unit of atoms within a cluster (see figure 11(d)). Size-dependence: the rate of cluster diffusion has a strong dependence on the size of the cluster, with larger cluster size generally corresponding to slower diffusion. This is not, however, a universal trend and it has been shown in some systems that the diffusion rate takes on a periodic tendency wherein some larger clusters diffuse faster than those smaller than them. Surface diffusion and heterogeneous catalysis Surface diffusion is a critically important concept in heterogeneous catalysis, as reaction rates are often dictated by the ability of reactants to "find" each other at a catalyst surface. With increased temperature adsorbed molecules, molecular fragments, atoms, and clusters tend to have much greater mobility (see equation 1). However, with increased temperature the lifetime of adsorption decreases as the factor kBT becomes large enough for the adsorbed species to overcome the barrier