Minimum free-energy path of homogenous nucleation from the phase-field equation

Abstract

The minimum free-energy path (MFEP) is the most probable route of the nucleation process on the multidimensional free-energy surface. In this study, the phase-field equation is used as a mathematical tool to deduce the minimum free-energy path (MFEP) of homogeneous nucleation. We use a simple square-gradient free-energy functional with a quartic local free-energy function as an example and study the time evolution of a single nucleus placed within a metastable environment. The time integration of the phase-field equation is performed using the numerically efficient cell-dynamics method. By monitoring the evolution of the size of the nucleus and the free energy of the system simultaneously, we can easily deduce the free-energy barrier as a function of the size of the sub- and the super-critical nucleus along the MFEP.

8 pages, 5 figures, Journal of Chemical Physics accepted for publication

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• Steady-state nucleation rate and flux of composite nucleus at saddle point
• Nucleation pathway of core-shell composite nucleus in size and composition space and in component space
• Stability of critical bubble in stretched fluid of square-gradient density-functional model with triple-parabolic free energy