Temperature Variation and Intrinsic Diffusion

In most ordinary solids, bulk diffusion is dominated by the impurity content, the number of impurity defects present. Any variation in D0 from one sample of a material to another is accounted for by the variation of the impurity content. However, the impurity concentration does not affect the activation energy of migration, Ea, so that Arrhenius plots for such crystals will consist of a series of parallel lines (Fig. 5.21a). The value of the preexponential factor D0 increases as the impurity content increases, in accord with Eq. (5.13). 

In very pure crystals, the number of intrinsic defects may be greater than the number of defects due to impurities, especially at high temperatures. Under these circumstances, the value of D0 will be influenced by the intrinsic defect population and may contribute to the observed value of the activation energy. 

Suppose that vacancy diffusion is the principal mechanism involved in atom transport. An expression for the fraction of vacancies in a pure crystal is [Eq. (2.6)] 

The activation energy is now made up of two parts, one part being the Gibbs energy to create a vacancy, —AGv, and the other to surmount the energy barrier, — AGm. The entropy terms can be incorporated into the geometrical factor to give 

The same analysis can be applied to more complex situations. Suppose that cation vacancy diffusion is the predominant migration mechanism, in a sodium chloride structure crystal, of formula MX, which contains Schottky defects as the major type of intrinsic defects. The relevant defect concentration [ii] is [Eq. (2.11)] 

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