Kinetics of spinodal decomposition in the Ising model with vacancy diffusion

Quantitative analysis of phase formation and growth in ternary mixtures upon evaporation of one component

We perform a quantitative analysis of Monte Carlo simulation results of phase separation in ternary blends upon evaporation of one component. Specifically, we calculate the average domain size and plot it as a function of simulation time to compute the exponent of the obtained power law. We compare and discuss results obtained by two different methods, for three different models: two-dimensional (2D) binary-state model (Ising model), 2D ternary-state model with and without evaporation. For the ternary-state models, we study additionally the dependence of the domain growth on concentration, temperature and initial composition. We reproduce the expected 1/3 exponent for the Ising model, while for the ternary-state model without evaporation and for the one with evaporation we obtain lower values of the exponent. It turns out that phase separation patterns that can form in this type of systems are complex. The obtained quantitative results give valuable insights towards devising computable theoretical estimations of size effects on morphologies as they occur in the context of organic solar cells.

Phase diagram and aggregation dynamics of a monolayer of paramagnetic colloids

We have developed a tunable colloidal system and a corresponding theoretical model for studying the phase behavior of particles assembling under the influence of long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and a rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle θ of the rotating magnetic field. For a purely in-plane field, θ=90^{∘}, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles 50^{∘}≲θ≲55^{∘}, the two-body interaction gives a short-range attractive and long-range repulsive interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We further characterize the anomalous regime by measuring the time-dependent cluster size distribution.

The mechanism of morphogenesis in a phase-separating concentrated multicomponent alloy

What determines the morphology of a decomposing alloy? Besides the well-established effect of the nucleation barrier, we demonstrate that, in a concentrated multicomponent Ni(Al,Cr) alloy, the details of the diffusion mechanism strongly affect the kinetic pathway of precipitation. Our argument is based on the combined use of atomic-scale observations, using three-dimensional atom-probe tomography (3D APT), lattice kinetic Monte Carlo simulations and the theory of diffusion. By an optimized choice of thermodynamic and kinetic parameters, we first reproduce the 3D APT observations, in particular the early-stage transient occurrence of coagulated precipitates. We then modify the kinetic correlations among the atomic fluxes in the simulation, without altering the thermodynamic driving force for phase separation, by changing the vacancy-solute interactions, resulting in a suppression of coagulation. Such changes can only be quantitatively accounted for with non-zero values for the off-diagonal terms of the Onsager matrix, at variance with classical models.

Application of the Bethe-Peierls approximation to a lattice-gas model of adsorption on mesoporous materials

We calculate adsorption and desorption isotherms in models of several classes of porous materials using a lattice-gas model solved in the Bethe-Peierls (quasichemical) approximation. Isotherms and fluid density profiles from the Bethe-Peierls and Bragg-Williams approximations are compared with grand-canonical Monte Carlo simulation results. The Bethe-Peierls approximation produces both more accurate adsorption and desorption isotherms and more realistic fluid density profiles than the Bragg-Williams approximation. Details of the application of the Bethe-Peierls approximation applied to a three-dimensionally inhomogeneous system are given. We show that the numerical solution of this theory can be accomplished using a self-consistent iterator very similar to that currently used in studies employing the Bragg-Williams approximation. This iterative scheme is substantially more efficient than the numerical optimization method used in many previous studies of lattice-gas models in the quasichemical approximation. We find that use of the Bethe-Peierls approximation is only slightly more computationally demanding than the Bragg-Williams approximation, and thus recommend it for use in future work on this class of models.

Autocorrelation functions for phase separation in ternary mixtures

We present numerical and analytical results for the autocorrelation functions which characterize domain growth in ternary mixtures. The numerical results are obtained from Monte Carlo simulations of the spin-1 Blume-Emery-Griffiths model with spin-exchange kinetics. Further, we model the autocorrelation functions using an approach based on the continuous-time random walk formalism. The aging property of these functions is related to the time dependence of the domain-size distribution. Our analytical results are found to be in good agreement with the numerical data.

Aging and equilibrium fluctuations for domain growth in ternary mixtures

We present numerical and analytical results for the autocorrelation functions which characterize domain growth in ternary mixtures. The numerical results are obtained from Monte Carlo studies of the spin-1 Blume-Emery-Griffiths model with spin-exchange kinetics. We formulate a stochastic model, which accounts for both aging and equilibrium contributions to the autocorrelation functions.

Kinetics of phase transformation on a Bethe lattice in the presence of spin exchange

Kinetics of phase transformation on a Bethe lattice governed by single-spin-flip Glauber and spin-exchange Kawasaki dynamics is examined. For a general Glauber dynamics for which all processes (splitting and coagulation, growth and decay of clusters, as well as creation and annihilation of single-spin clusters) take place, the addition of the Kawasaki dynamics accelerates the transformation process without changing the qualitative behavior. In the growth-decay regime of the Glauber dynamics, regime in which the splitting and coagulation, and creation and annihilation processes due to single-spin flips are negligible, the Kawasaki dynamics strongly increases the fraction of transformed phase because of the splitting and coagulation of clusters induced by the spin-exchange processes. Acting alone, the Kawasaki dynamics leads to the growth of the clusters of each of the phases after the quenching of the temperature to a lower value. When the final temperature T(f) is smaller than a certain temperature T(f0), the average cluster radius grows linearly with time during both the initial and intermediate stages of the kinetic process, and diverges as log(2)(t(d)-t)(-1) when the time t approaches the value t(d) at which infinite clusters arise. It is shown that, among the various spin-exchange processes involved in Kawasaki dynamics, the main contribution is provided by those which decrease or increase the number of clusters by unity.

Phase transformation in a lattice system in the presence of spin-exchange dynamics

A joint action of the Glauber single-spin-flip and the Kawasaki spin-exchange mechanisms upon the processes of phase transformation is examined in the framework of the one-dimensional kinetic Ising model. It is shown that the addition of the Kawasaki dynamics to that of Glauber accelerates the process of phase transformation in the initial stage, but slows it down in later stages. For the truncated form of Glauber dynamics, which excludes the processes of splitting and coagulation of clusters, the addition of the Kawasaki dynamics always accelerates the phase transformation process. Acting alone, the Kawasaki mechanism provides a cluster growth proportional to t(1/2) (where t is the time) in the initial stage and proportional to t(1/3) (Lifshitz-Slyozov-Wagner law) in the intermediate stage. In the final stage, a cluster size approaches exponentially its equilibrium value.

Spinodal decomposition, power laws, and wetting at a triple point

We study numerically the dynamics of phase separation in ternary mixtures at a triple point. For the full range of compositions and for different interaction parameters, the long time growth is in accord with a universal law. The early time behavior is governed by the structure of the spinodal region, including the possibility of a two step separation and decomposition originating at a surface and propagating into the bulk. The appearance of the domains is governed by the wetting properties of the mixture and the growth of a wetting layer follows again the universal law; a result that we can interpret with a simple phenomenological model.

Kinetics of phase separation in ternary mixtures

We present detailed results from Monte Carlo simulations of the kinetics of phase separation in ternary mixtures. We focus on the case of ABV mixtures (where V denotes a vacancy) and investigate segregation kinetics resulting from V-mediated dynamics. We provide heuristic arguments for the existence of different morphologies in various parameter regimes. Furthermore, we present comprehensive numerical results for various characteristic features of the domain growth process, e.g., real-space correlation functions, domain-size distribution functions, and growth laws.

Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions

We investigate the domain growth and phase separation of hydrodynamically correct binary immiscible fluids of differing viscosity as a function of minority phase concentration in both two and three spatial dimensions using dissipative particle dynamics. We also examine the behavior of equal-viscosity fluids and compare our results to similar lattice-gas simulations in two dimensions.