Time of Formation of the First Supercritical Nucleus, Time‐lag, and the Steady‐State Nucleation Rate

General equations are derived for the description of correlations between average time of formation of the first supercritical nucleus, time‐lag in nucleation, and steady‐state nucleation rate. In their implementation, a set of representative equations is employed modeling the time‐dependence of the nucleation rate as proposed first by Zeldovich and advanced by a variety of other authors. The analysis is performed for both isothermal–isobaric and time‐dependent process conditions. It is shown that, in general, the time of formation of the first supercritical nucleus depends both on time‐lag and the average time of formation of a supercritical nucleus at steady‐state conditions. The conditions are specified at which one of these characteristic times may dominate. In contrast to alternative statements it is also demonstrated that for isothermal–isobaric conditions, due to the Poisson character of nucleation, steady‐state nucleation rates can be determined without having at one's disposal a detailed knowledge of the time‐lag and the kinetic laws of approach of steady‐state nucleation conditions. Results of molecular‐dynamics simulations of crystal nucleation in Lennard‐Jones liquids are presented for an illustration of the general conclusions. Several applications of the results to the interpretation of experimental data are discussed.