Density-functional theory of the kinetics of crystallization of hard-sphere suspensions: Single conserved order parameter

Abstract

A theoretical study is presented of the kinetics of crystallization of a hard-sphere-like colloidal suspension in a fixed volume based upon the use of time-dependent density-functional theory incorporating conserved particle dynamics. Distinguishing crystalline order by the particle density alone, we demonstrate that the constraints of fixed number and volume lead naturally to the appearance of a new nonuniform minimum in the free energy corresponding the equilibrium coexistence between crystalline order and disordered suspension. Using numerical integration, we follow the time dependence of a range of initial spherical crystallites. The normal and tangential osmotic pressure fields about these growing crystallites are presented and the growing crystallite is shown to be isolated from the higher pressure of the surrounding disordered suspension by the nonequilibrium depletion zone which surrounds it. These results are compared with recent light-scattering studies. ͓S1063-651X͑97͒06409-X͔

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

“…where ψ is the order parameter called phase field, F is the free-energy functional (grand potential) usually expressed by the square-gradient form 4,16,17 , and τ specifies the time scale of evolution. This phase-field equation is attractive as the kinetics of phase transformation is driven by the relative stability of each phase and by the topology of the associated free-energy surface F .…”

Multiphase solidification in multicomponent alloys

“…If the free energy density is of piecewise parabolic form, the Euler-Lagrange equation is linearized, and the solution can be found analytically. This method has been used to address such problems as crystal nucleation and growth in one-component liquids by Bagdassarian and Oxtoby [231] and Gránásy and Oxtoby [232], hard-sphere crystallization by Wild and Harrowell [233] and crystallization in the presence of metastable phases by Gránásy and Oxtoby [66]. A more complex single-order-parameter Cahn-Hilliard model relying on a quadratic free energy density has been recently used by Gránásy et al [234] to evaluate interfacial properties from nucleation experiments.…”

Nucleation and the Solid–Liquid Interfacial Free Energy

“…tion becomes linearized, and the solution can be found analytically. This method has been used to study crystal nucleation and growth in one-component liquids, 47,48 hardsphere crystallization, 49 and crystallization in the presence of metastable phases. 50 The density functional technique (DFT) offers a microscopic (molecular), rather than phenomenological, route to crystallization, which considers either the crystalline structure and/or molecular interactions.…”