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

TL;DR

This paper uses the phase-field equation to identify the most probable nucleation pathway by analyzing the free-energy landscape and nucleus evolution, providing insights into the energy barriers involved in homogeneous nucleation.

Contribution

It introduces a method to determine the minimum free-energy path of homogeneous nucleation using phase-field modeling and cell-dynamics simulation.

Findings

Successfully deduced free-energy barriers along the nucleation pathway.

Demonstrated the evolution of nucleus size and free energy during nucleation.

Provided a computational approach for analyzing nucleation processes.

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.