Correlation factors for self-diffusion

So far, the diMision of atoms has been considered to occur in a random fashion throughout the crystal stracture. Each step was unrelated to the one before and the atoms were supposed to be jostled solely by thermal energy. However, diffusion of an atom in a solid may not be a truly random process and in some circumstances a given jump direction may depend on the direction of the previous jump. 

When these processes are considered over many jumps, the mean square displacement of the tracer will be less that that of the vacancy, even though both have taken the same number of jumps. Therefore, it is expected that the observed diffusion coefficient of the tracer will be less than that of the vacancy. In these circumstances, the random-walk diffusion equations need to be modified by the introduction of a correlation factor, /. The correlation factor is given by the ratio of the values of the mean square displacement of the tracer, ( )tracer t of the vacancy, if the 

Correlation factors for vacancy diffusion generally take values of between 0.5 and 0.8. 

In the case of interstitial diffusion, in which we have only a few difiusing atoms and many available empty interstitial sites, a correlation factor close to 1.0 would be expected. In effect, the interstitial atom moves in a sea of vacancies . In the case of interstitialcy diffusion, this will not be true because 

The diffusion of an impurity atom in a crystal, say K in NaCl, involves other considerations apart from those of a statistical nature. In such cases, the probability that the impurity will exchange with the vacancy will depend on factors such as the relative sizes of the impurity compared with the host atoms. In the case of ionic movement, the charge on the diffusing species will also play a part. These factors can can also be expressed in terms of the jump frequencies of the host and impurity atoms, in which case one is likely to be greater than the other. 

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