Effect of Planar Interfaces on Nucleation in Melting and Crystallization

Abstract

The effect of planar interfaces on nucleation (namely, on the work of critical cluster formation and their shape) is studied both for crystallization and melting. Advancing an approach formulated about 150 years ago by J. W. Gibbs for liquid phase formation at planar liquid–liquid interfaces, we show that nucleation of liquids in the crystal at crystal–vapor planar interfaces proceeds as a rule with a much higher rate compared to nucleation in the bulk of the crystal. Provided the surface tensions crystal–liquid (σcl), liquid–vapor (σlv), and crystal–vapor (σcv) obey the condition σcv=σcl+σlv, the work of critical cluster formation tends to zero; in the range σcv<σcl+σlv, it is less than one half of the work of critical cluster formation for bulk nucleation. The existence of a liquid–vapor planar interface modifies the work of critical cluster formation in crystal nucleation in liquids to a much less significant degree. The work of critical crystal cluster formation is larger than one half of the bulk value of the work of critical cluster formation, reaching this limit at σcv=σcl+σlv. The shape of the critical clusters can be described in both cases by spherical caps with a radius, R, and a width parameter, h. This parameter, h, is the distance from the cutting plane (coinciding with the crystal–vapor and liquid–vapor planar interface, respectively) to the top of the spherical cap. It varies for nucleation of a liquid in a crystal in the range (h/R)≤1 and for crystal nucleation in a liquid in the range 2≥(h/R)≥1. At σcv=σcl+σlv, the ratio (h/R) of the critical cluster for nucleation in melting tends to zero ((h/R)→0). At the same condition, the critical crystallite has the shape of a sphere located tangentially to the liquid–vapor interface inside the liquid ((h/R)≅2). We present experimental data which confirm the results of the theoretical analysis, and potential further developments of the theoretical approach developed here are anticipated.