General equations are derived for the description of correlations between average time 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 on 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 dynamic 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.
