Reconsideration of the concept of critical nucleus and the Gibbs-Thomson equation

The concept of critical nucleus is reconsidered by taking a single component system as an example and it is found that the size n(k) of a cluster for which the probabilities of decay and growth balance is not equal to the size n* for which the reversible work of cluster formation takes its maximum value. n(k) is in general smaller than n* when n is treated as a continuous variable. There exist two values for n(k), the larger of the two is kinetically unstable but the smaller is stable. The difference between the larger n(k) and n* increases but the difference between the two values of n(k) decreases with the degree of supersaturation or supercooling, and in the critical state the two values of n(k) coincide and it diminishes to 8/27 of n* for three-dimensional homogeneous nucleation and to 1/4 of n* for two-dimensional nucleation on a substrate. Beyond this critical state n(k) does not exist and for a cluster with any size the probability of growth is higher than that of decay. Whenever the Gibbs-Thomson equation is employed to take into account the curvature effect in describing kinetic processes such as in the BCF theory of spiral growth or in the studies of morphological instability, it must be replaced by the relation between the larger n(k) and the degree of supersaturation or supercooling.