Mass Transfer in Defect Solids

The usual differential equation of diffusion processes is due to Pick 

When for the same solid the ionic migration is studied, it is found for the purely ionic conductivity that 

We see immediately that for the same ion in the same crystal there is a relation between D and o- of the kind 

If the defect is of the Schottky type in a stoichdioinetric crystal we have (2.1 (i)) 

The examples discussed here are the simplest possible and real systems are usually more complicated. Moreover, we have used simplified models for example, v is the characteristic frequency of the interstitial ion or an ion adjacent to a vacant lattice position it will be diflerent from the characteristic lattice frequency and will not be the same for Schottky and Frenkel defects. However, the general principles of the transfer of matter through a crystalline solid are as they have been given here. 

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