On a new approach for finding the non-steady state kinetic rate of phase formation

Abstract

In this study an expression is obtained for the non-steady state kinetic rate of phase formation by using elements of the probability theory. Its most important feature is that it is valid for various cluster sizes larger or equal to the critical (nucleus) size. The results from this expression are compared with the numerical solution of the basic kinetic equation of phase formation, known as Zeldovich's equation, and the coincidence is remarkable. Owing to its greater simplicity, the expression proposed here can be used instead of the numerical solution in a large number of cases. It is shown that some known expressions for the non-steady state kinetic rate valid for nucleus sizes can be used for various larger sizes when the induction period τ k can be determined for these sizes with sufficient accuracy. It is shown that these known expressions for nucleus size, as well as for larger sizes are less accurate than the expression proposed in this paper in view of closeness to the numerical solution.