Transport in crystalline materials requires the motion of atoms away from their equilibrium posi­tions and, therefore, the role of point defects is sig­nificant.22 For example, vacancies provide the space into which neighboring atoms in the lattice can jump,27-29 although it is often the interstitial defects that provide the transport mechanism.22

Diffusion mechanisms refer to the way an atom can move from one position in the lattice to another, generally through an activated process that sees the ion move over an energy barrier. The beginning and end points to each jump may be symmetrically iden­tical, providing a contiguous pathway through the crystal, but this need not be so. In some cases, the contiguous migration pathway may involve a number of nonidentical steps. Nevertheless, in most materials, the motion of an atom is restricted to a few paths.

There are three main mechanisms that are rele­vant to most ceramic systems: the interstitial, the vacancy, and the interstitialcy mechanism. However, for completeness, we will also briefly describe the

collective and the interstitial-substitutional exchange mechanisms, which may be encountered in other classes of materials.22

In the interstitial mechanism, atoms at interstitial sites initially migrate by jumping from one interstitial site to a neighboring one (Figure 19). At the comple­tion of a single jump, there is no permanent displace­ment of the other ions, although, of course, in the process of diffusion, the extent of lattice relaxation is likely to have become greater to facilitate the saddle point configuration. In principle, it is a simple mech­anism as it does not require the existence of defects other than the interstitial ion, although it is possible that transient defects are produced if the lattice relaxation is great enough in the course of the jump. Interstitial diffusion is not common in ceramic mate­rials but does occur if the interstitial species is small.

In the vacancy mechanism, a host or substitutional impurity atom diffuses by jumping to a neighboring vacancy (Figure 20). Vacancy-mediated diffusion is common in a number of systems (particularly cera­mics with higher atomic density where interstitial defect energies are high). For example, the vacancy mechanism is important for the diffusion of substitu­tional impurities, for self-diffusion and the transport of я-type dopants in germanium,30,31 and for oxygen self-diffusion in a number of hypostoichiometric perovskite and fluorite-related systems.32 In the vacancy mechanism, the interaction, attractive or repulsive, between the species that undergo transport and the vacancy can be very important. Of course, the vacancy mechanism requires the presence of lattice vacancies and therefore, their concentration in the lattice will influence the kinetics.23

In the interstitialcy mechanism, an interstitial atom displaces an atom from its normal substitutional site (Figure 21). The displaced atom, in turn, moves

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Figure 19 The interstitial mechanism of diffusion. The red and blue atoms are lattice species.

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Figure 20 The vacancy mechanism of diffusion. The red and blue ions are lattice species.