Geometric model for the critical-value problem of nucleation phenomena containing the size effect of nucleating agent

Abstract

Nucleation is of great concern in many cases - for example, the production of artificial rainfall and the synthesis of advanced amorphous alloys. Although exact solutions have been well known to both homogeneous nucleation and heterogeneous nucleation occurring on a large flat container wall, yet in more general situations the actual nucleation takes place around finite-sized heterogeneous particles. The understanding of nucleation in such situations requires a more extended model which considers the size effect of nucleating agents. Partially motivated by our research on bulk metallic glasses, we construct such a geometric model. Also we derive an exact solution to the model and discuss briefly its physical implications. A previously presumed relation between the critical energy barrier (Ec) and the volumetric Gibbs free energy of the critical nucleus (Gc) - i.e., Ec= 1 2 Gc- is found to be not true for general cases, although it is correct for the limiting cases. © 2005 The American Physical Society.