标题： 均质形核的最小自由能路径从相场方程 显示英文标题

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

摘要： 最小自由能路径（MFEP）是在多维自由能表面上成核过程的最可能路径。 在本研究中，相场方程被用作数学工具来推导均匀成核的最小自由能路径（MFEP）。 我们使用一个简单的平方梯度自由能泛函，其中局部自由能函数为四次函数作为例子，并研究位于亚稳环境中单个晶核的时间演化。 相场方程的时间积分是通过数值高效的单元动力学方法进行的。 通过同时监测晶核尺寸和系统自由能的变化，我们可以轻松地推导出沿MFEP的自由能势垒作为亚临界和超临界晶核尺寸的函数。 显示英文摘要

摘要： 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.