Chapter 8 - Diffusion in Crystals

Abstract

Diffusion in crystals is governed by atomic jumping among well-defined positions on the crystalline matrix or interstitial positions. The four primary atomic mechanisms for atomic diffusion in crystals are the ring, vacancy, interstitial, and interstitialcy mechanisms. Of these, only the ring mechanism does not involve the presence of a point defect. Since the (defect-free) ring mechanism requires a cooperative motion of atoms, it is less efficient than the other defect-mediated mechanisms. With the vacancy mechanism, atoms diffuse by single-particle jumping into a vacancy site. Hence, the atomic diffusion coefficient can be interpreted in terms of a diffusivity of the vacancies. The interstitial and interstitialcy mechanisms for diffusion involve atomic jumping into interstitial sites. The difference is that with the interstitialcy mechanism, the atoms jump into interstitials from their normal lattice positions. This is in contrast to the interstitial mechanism, where dopant atoms jump directly between interstitial sites, squeezing between neighboring atoms on the lattice. Unlike random walk diffusion, diffusion in real crystals typically has memory of the preceding state and thus exhibits a correlated walk. To account for these correlations between successive jumps, a geometry-dependent correlation factor is included in the atomic jumping models. Diffusion in ionic crystals is more complicated than in metals, since local charge neutrality of the species must be satisfied. Intrinsic defects in ionic crystals are generated by Schottky and Frenkel defect reactions. In the presence of both intrinsic and extrinsic defects, defect-mediated diffusion will display two distinct regimes, dominated by extrinsic defects at low temperatures and by intrinsic defects at high temperatures.