Nucleation pathway of core-shell composite nucleus in size and composition space and in component space

Abstract

The kinetics of nucleation of a core-shell composite nucleus that consists of a core of stable final phase surrounded by a wetting layer of intermediate metastable phase is studied using the kinetic theory of binary nucleation not only in the size and composition space but also in the component space. The steady-state solution of the Fokker-Planck equation is considered. Various formulas for the critical nucleus at the saddle point as well as for the postcritical nucleus are derived. The kinetics of nucleation at the saddle point is more appropriately characterized in the size and composition space, while the kinetics of the postcritical nucleus is more appropriately described in the component space. Although both the free-energy landscape and the reaction rates play decisive role to determine the kinetics of nucleation at the saddle point, the details of the free-energy landscape are irrelevant to the kinetics of the postcritical nucleus.

Characterizing the nucleation flux of linked-flux model for core-shell composite nucleus

“…where the factor n comes from the Jacobian ∂ (n 1 , n 2 ) /∂ (n, x) = n. Then, various analytical formulas [7] for the nucleation Àux at the critical point can be used even in the component space (n, x) [8]. Using these formulas, it is shown that the time scale of nucleation along the n-axis and x-axis can be characterized by the transformation rate κ + and the attachment rate α + , and can be discussed almost independently for our lined-Àux model.…”

“…In order to study the nucleation Àux for the core-shell composite nucleus, the linkedÀux model that consists of a spherical core of the stable new phase (number of molecules n 1 ) surrounded by an wetting layer of an intermediate metastable phase (number of molecules n 2 ) is considered [7,8,9]. The kinetics of nucleation is described by the Fokker-Planck equation in the two-dimensional space (n 1 , n 2 ) of stable and metastable components:…”

“…It is shown that each components changes linearly with time n n n ∝ t and they approach n 1 → ∞ and n 2 → 0 as the n 1 and n 2 correspond to the thermodynamically stable and metastable phase respectively. The growth velocity Ú n n n is determined from the relative stability of each phase characterized by the difference of the chemical potentials [8] from the metastable parent phase.…”

“…In the previous paper [6,7,8], we have studied the nucleation Àux of core-shell composite nucleus using a linked-Àux model of nucleation [9], which was used to study the nucleation Àux of nucleus that consists of a core of the ¿nal stable phase and a surrounding shell of the dense pre-nucleus [9]. In this report, we will review our previous study [6,7,8] and characterizes the nucleation Àux of core-shell composite nucleus.…”

“…In this report, we will review our previous study [6,7,8] and characterizes the nucleation Àux of core-shell composite nucleus. In particular, it is shown that the kinetics of critical nucleus at the saddle point is more appropriately characterized in the size and composition space, while the kinetics of the post-critical nucleus is more appropriately described in the component space.…”