Numerical determination of the interfacial energy and nucleation barrier of curved solid-liquid interfaces in binary systems

摘要

The phase-field crystal (PFC) technique is a widely used approach for modeling crystal growth phenomena with atomistic resolution on mesoscopic time scales. We use a two-dimensional PFC model for a binary system based on the work of Elder et al. [Phys. Rev. B 75, 064107 (2007)] to study the effect of the curved, diffuse solid-liquid interface on the interfacial energy as well as the nucleation barrier. The calculation of the interfacial energy and the nucleation barrier certainly depends on the proper definition of the solid-liquid dividing surface and the corresponding nucleus size. We define the position of the sharp interface at which the interfacial energy is to be evaluated by using the concept of equimolar dividing surface (r(e)) and the minimization of the interfacial energy (r(s)). The comparison of the results based on both radii shows that the difference r(e) - r(s) is always positive and has a limit for large cluster sizes which is comparable to the Tolman length. Furthermore, we found the real nucleation barrier for small cluster sizes, which is defined as a function of the radius r(s), and compared it with the classical nucleation theory. The simulation results also show that the extracted interfacial energy as function of both radii is independent of system size, and this dependence can be reasonably described by the nonclassical Tolman formula with a positive Tolman length.