Spinodal decomposition of an ABv model alloy: Patterns at unstable surfaces

Abstract

We develop mean-field kinetic equations for a lattice gas model of a binary alloy with vacancies (ABv model) in which diffusion takes place by a vacancy mechanism. These equations are applied to the study of phase separation of finite portions of an unstable mixture immersed in a stable vapor. Due to a larger mobility of surface atoms, the most unstable modes of spinodal decomposition are localized at the vapor-mixture interface. Simulations show checkerboard-like structures at the surface or surface-directed spinodal waves. We determine the growth rates of bulk and surface modes by a linear stability analysis and deduce the relation between the parameters of the model and the structure and length scale of the surface patterns. The thickness of the surface patterns is related to the concentration fluctuations in the initial state.

Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration

“…Examples are the equations in Ref. [65], that describe the spinodal decomposition in ternary systems, the dewetting of nanoparticle suspensions in Ref. [70], the coupled demixing and dewetting of a binary mixture discussed in Ref.…”

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

“…Also, Plapp and Gouyet say in ref. 53 that, in their case with particle-vacancy dynamics only (where M = 2 and Arrhenius rates are used), numerical results indicate that qualitative phase-separation behaviour is unaffected by the attempt rate ratio w A0 /w B0 as long as it is not too far from unity.…”

“…60 This is as one would expect in a closed system, where there are no currents crossing boundaries. 53 We defer the derivation of the result dF/dt to Appendix A, which generalizes similar derivations discussed elsewhere in the literature 53 to include the case of direct particle-particle swapping.…”

“…no direct interchanges of particles are allowed), and one considers only the M = 2 case, then eqn (19) has the same form as eqn (27) in Plapp and Gouyet's work. 53 The only difference is that their expression for the homogeneous mobility is different from (20), as Plapp and Gouyet used Arrhenius jump rates. Their choice reflects the physical assumption for alloys that the elementary particle moves have an energy barrier effectively equivalent to removing a particle from the system.…”

Differential capacitance of liquid/liquid interfaces—A lattice gas model approach

“…Lattice gas models provide an adequate theoretical description of multicomponent systems such as fluid mixtures [12], alloys [13] as well as adsorption phenomena [14]. The isomorphism of the lattice gas models with the hierarchy of Ising models is well known [15].…”