Interaction between point defects, diffusion

The nucleation behavior of transition metal particles is determined by the ratio between the thermal energy of the diffusing atoms and the interaction of the metal atoms at the various nucleation sites. To create very small particles or even single atoms, low temperatures and metal exposures have to be used. The metal was deposited as metal atoms impinging on the surface. The metal exposure is given as the thickness (in monolayer ML) of a hypothetical, uniform, close-packed metal layer. The interaction strength of the metals discussed here was found to rise in the series from Pd < Rh < Co ( Ir) < V [17,32]. Whereas Pd and Rh nucleate preferentially at line defects at 300 K and decorate the point defects at 90 K, point defects are the predominant nucleation center for Co and V at 300 K. At 60 K, Rh nucleates at surface sites between point defects [16,33]. 

Although this estimate of the interaction energy between defects is simplistic, it demonstrates that a fair number of defects may cluster together rather than remain as isolated point defects, provided, of course, that they can diffuse through the crystal. It is difficult, experimentally, to determine the absolute numbers of point defects present in a crystal, and doubly so to determine the percentage that might be associated rather than separate. It is in both of these areas that theoretical calculations are able to bear fruit. 

At r > Tr, the relaxation of a non-equilibrium surface morphology by surface diffusion can be described by Eq. 1 the thermodynamic driving force for smoothing smoothing is the surface stiffness E and the kinetics of the smoothing is determined by the concentration and mobility of the surface point defects that provide the mass transport, e.g. adatoms. At r < Tr, on the other hand, me must consider a more microscopic description of the dynamics that is based on the thermodynamics of the interactions between steps, and the kinetics of step motion [17]. 

The driving forces necessary to induce macroscopic fluxes were introduced in Chapter 3 and their connection to microscopic random walks and activated processes was discussed in Chapter 7. However, for diffusion to occur, it is necessary that kinetic mechanisms be available to permit atomic transitions between adjacent locations. These mechanisms are material-dependent. In this chapter, diffusion mechanisms in metallic and ionic crystals are addressed. In crystals that are free of line and planar defects, diffusion mechanisms often involve a point defect, which may be charged in the case of ionic crystals and will interact with electric fields. Additional diffusion mechanisms that occur in crystals with dislocations, free surfaces, and grain boundaries are treated in Chapter 9. 

At low temperatures, where diffusion in the solid state is unimportant, dislocations move principally by the process of slip (or glide) and may interact with other dislocations which move either in the same or in intersecting planes. Various kinds of lattice imperfections are introduced by such movement, and we shall discuss their identity in this subsection. At higher temperatures dislocation may anneal out by a process of annihilation resulting from slip. Moreover, since diffusion of individual species is now easier, important kinds of interaction between line and point defects are possible. These phenomena are also outlined below. 

---