Diffusion in Crystals Atomistic Approach

Let us now consider the crystal MO. If the diffusion takes place by migration of cationic vacancies, the number of atoms that undergo the process depends on the vacancy concentration [Vm] and the thermal state of single atoms M (the jump takes place only whenever atom M in the neighborhood of the vacancy has sufficient energy to perform it). The diffusion coefficient associated with the vacancy migration process is given by 

A similar relation holds for anionic vacancies and for diffusion through interstitial migration (replace [Vm] and TTym. nd so on). 

Because at high T the vacancy concentration depends exponentially on T, i.e. 

7 Vm = migration enthalpy of cationic vacancy = migration enthalpy of anionic vacancy /7m = migration enthalpy of cationic interstitial //xj = migration enthalpy of anionic interstitial 

Equation 4.75 finds its application in the region of intrinsic disorder (a similar equation can be developed for Frenkel defects), where Schottky and Frenkel defects are dominant with respect to point impurities and nonstoichiometry. 

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