Kinetic expressions derived for interface advance reactions

1 KINETIC EXPRESSIONS DERIVED FOR INTERFACE ADVANCE REACTIONS 

Rate equations of the form f(a) = kt are derived through integrations of specific forms of the generalized expression [ 28] representing the summation of the growth of all nuclei, so that the volume of product at time f, V(t), is given by 

This may (at least in principle) be integrated for any combination of a law of nucleation [the (dJV/df) term] and a law of growth. A nucleus formed at time occupies a volume V(t, tj) at time t and 

Those special cases of integration of eq. (1), which have found the most widespread application in the development of rate equations for reactions of solids, are discussed below. 

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