2009/06/04 by Masao Iwamatsu
Earth and Planetary Sciences · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Classical mechanics #Computer science #Energy (signal processing) #Field (mathematics) #Fluid Dynamics and Thin Films #Function (biology) #Mathematics #Metastability #Nucleation #Path (computing) #Phase (matter) #Physics #Quantum mechanics #Solidification and crystal growth phenomena #Statistical physics #Thermodynamics #cond-mat.mtrl-sci #nanoparticles nucleation surface interactions
paper · pdf · doi:10.1063/1.3158471
8 pages, 5 figures, Journal of Chemical Physics accepted for publication
arxiv created 2009/06/04 · openalex publication_date 2009/06/28 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 supercritical nucleus along the MFEP.