Schematic model point defect

Point defects in solids make it possible for ions to move through the structure. Ionic conductivity represents ion transport under the influence of an external electric field. The movement of ions through a lattice can be explained by two possible mechanisms. Figure 25.3 shows their schematic representation. The first, called the vacancy mechanism, represents an ion that hops or jumps from its normal position on the lattice to a neighboring equivalent but vacant site or the movement of a vacancy in the opposite direction. The second one is an interstitial mechanism where an interstitial ion jumps or hops to an adjacent equivalent site. These simple pictures of movement in an ionic lattice, known as the hopping model, ignore more complicated cooperative motions. 

Fig. 31, Schematic of physicochemical processes that cwcur within a passive film according to the point defect model m = metal atom Mm = metal cation in cation site Oo = oxygen ion in anion site VjjJ = cation vacancy Vq = anion vaccancy Vm = vacancy in metal phase. During film growth, cation vacancies are produced at the film/solution interface, but are consumed at the metal/film interface. Likewise, anion vacancies are formed at the metal/film interface, but are consumed at the film/solution interface. Consequently, the fluxes of cation vacancies and anion vacancies are in the directions indicated. Note that reactions (i), (iii), and (iv) are lattice-conservative processes, whereas reactions (ii) and (v) are not. Reproduced from J. Electrochem, Sec. 139, 3434 (1992) by permission of the Electrochemical Society.

Figure 10 Schematic representation of HMM applications. In (a) simulation of a macroscopic process for which the constitutive relations have to be obtained from modeling at the microscale. The macroscopic system is solved using a grid xj ) and only a small region around each macroscopic-solver grid point is used for the atomistic calculation (the shaded area represents the atomic cell at grid point The time step (TS) used for the macroscopic calculations is much larger than the microscopic one (ts), and times, TS are necessary to equilibrate the atomistic calculations. In (b) and (c) isolated defect calculations, i.e., problems where the coupling with the microscale model is needed only in a limited part of the system (near the defect itself). If the time scale for the defect dynamics is much larger than the time scale for the relaxation of the defect structure (case b), then only a short time At TS is simulated using the atomistic model for each macroscopic time step, otherwise (case c) the whole time history of the defect should be computed atomistically.

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