Evolution of the structure factor in a hyperbolic model of spinodal decomposition

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. The memory effects are seen to affect the dynamics of phase transition at short times. The process of fast spinodal decomposition associated with a conserved order parameter - concentration is studied numerically. Details of a semi-implicit numerical scheme used to simulate the kinetics of spinodal decomposition and evolution of the structure factor are discussed. Analysis of the modeled structure factor predicted by a hyperbolic model of spinodal decomposition is presented in comparison with the parabolic model of Cahn and Hilliard. It is shown that during initial periods of decomposition the structure factor exhibits wave behavior. Analytical treatments explain such behavior by existence of damped oscillations in structure factor at earliest stages of phase separation and at large values of the wave-number. These oscillations disappear gradually in time and the hyperbolic evolution approaches the pure dissipative parabolic evolution of spinodal decomposition.     

Stochastic description of phase separation near the spinodal curve in alloys

The earlier-developed statistical methods for nonequilibrium alloys are applied to stochastically describe phase separation near the spinodal curve. An important parameter of the theory is the size of local equilibrium regions, which is estimated using simulations for the different values of this parameter. The simulations based on this approach reveal significant changes in the type of evolution from nucleation to spinodal decomposition under variation of concentration and temperature across the spinodal curve. The scale of these changes seems to be mainly determined by the difference of the properly defined supersaturation parameters.     

Van der waals limit and phase separation in a particle model with kawasaki dynamics

A one-dimensional interacting particle system with a stochastic dynamics is studied in the local mean field limit, extending the results of Lebowitz, Orlandi, and Presutti to processes which satisfy detailed balance (with respect to Gibbs measures). The behavior of the system below the critical temperature and inside the unstable (spinodal) region is then investigated by means of computer simulations. The experiments clearly indicate the presence of phase separation and confirm the validity of some conjectures on the dynamics of the spinodal decomposition.     

Density fluctuations in the presence of spinodal instabilities

Density fluctuations resulting from spinodal decomposition in a nonequilibrium first-order chiral phase transition are explored. We show that such instabilities generate divergent fluctuations of conserved charges along the isothermal spinodal lines appearing in the coexistence region. Thus, divergent density fluctuations could be a signal not only for the critical end point but also for the first-order phase transition expected in strongly interacting matter. We also compute the mean-field critical exponent at the spinodal lines. Our analysis is performed in the mean-field approximation to the Nambu-Jona-Lasinio model formulated at finite temperature and density. However, our main conclusions are expected to be generic and model independent.     

Phase-field study of spinodal decomposition under effect of grain boundary

Grain boundary directed spinodal decomposition has a substantial effect on the microstructure evolution and properties of polycrystalline alloys. The morphological selection mechanism of spinodal decomposition at grain boundaries is a major challenge to reveal, and remains elusive so far. In this work, the effect of grain boundaries on spinodal decomposition is investigated by using the phase-field model. The simulation results indicate that the spinodal morphology at the grain boundary is anisotropic bicontinuous microstructures different from the isotropic continuous microstructures of spinodal decomposition in the bulk phase. Moreover, at grain boundaries with higher energy, the decomposed phases are alternating α/β layers that are parallel to the grain boundary. On the contrary, alternating α/β layers are perpendicular to the grain boundary.     

Fluid-fluid demixing of off-critical colloid-polymer systems confined between parallel plates

We investigate the off-critical demixing of colloid-polymer systems confined between two parallel plates, where the surface potential is short ranged. We study the case where the minority phase completely wets the surfaces. We find that initially the sample separates as in bulk, until the size of the domains becomes sufficiently large such that further growth is restricted by the plate spacing. The behaviour of the droplets is then determined by the wettability of the walls. We furthermore explore a sample where the loss of wetting phase material to the surfaces causes a shift from a morphology associated with an unstable sample, showing spinodal decomposition, to that associated with a metastable sample. This underlines the importance of the rich interplay between the viscosity contrast and the local volume fraction on the observed morphologies.     

The Effect of Preparation Temperature on Phase Transitions of N-Isopropylacrylamide Gel

The spinodal decomposition of N-isopropylacrylamide (NIPA) gels prepared at various onset temperatures, T _on was studied by photon transmission. It was observed that the increase in turbidity is much faster in a gel prepared at higher T _on than at lower T _on values, which indicated that the NIPA-water system reaches the spinodal decomposition much faster for a gel prepared at high T _on. It is understood that a NIPA gel prepared at high T _on possesses more heterogeneities which are gained during gelation and has a low spinodal temperature, T _s. However, NIPA gels prepared at lower T _on values go to spinodal decomposition at higher T _s values.     

Anomalous Scenario for Termination of Metastable Melting in Simplified Coulomb Models in the Zero‐Temperature Limit

Two non‐standard scenarios of melting termination in deep metastable states are studied in the zero‐temperature limit on the base of two variants of modified one‐component Coulomb models. These additional scenarios supplement the previously studied standard case of “spinodal decomposition” (Iosilevskiy and Chigvintsev, arXiv:0609059) when liquid binodal of metastable freezing (liquidus) is terminated in intersection with gas‐liquid spinodal. In the first new scenario hypothetical unique crystal‐fluid global phase coexistence is realized as smooth superposition of melting and sublimation transitions (without gas‐liquid transition and corresponding critical point). The second new type of “spinodal decomposition” scenario is related to the situation when solid binodal of metastable melting (solidus) intersects spinodal of metastable isostructural crystal‐crystal phase transition. Modified one‐component Coulomb models allow one to investigate in details all features of such “spinodal decomposition” scenarios (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase separation in a chaotic flow

The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the presence-or absence-of Lagrangian chaos. A fully chaotic flow, in particular, limits the growth of domains, and for unequal volume fractions of the liquids, a characteristic exponential distribution of droplet sizes is obtained. The limiting domain size results from a balance between chaotic mixing and spinodal decomposition, measured in terms of Lyapunov exponent and diffusivity constant, respectively.     

Dynamical spinodal: The transition between nucleation and spinodal decomposition

The nonclassical regime in the two phase region between nucleation and spinodal decomposition of a binary model with medium range interaction has been investigated. The Monte Carlo results indicate a dynamical spinodal. At this dynamical spinodal a transient percolating structure occurs. However, the mean droplet size remains finite there.     

多晶凝固及后续调幅分解过程的晶体相场法模拟

采用晶体相场模型,模拟了二元合金多晶凝固及后续调幅分解全过程.结果表明,晶体相场模型可完整再现包括形核、生长、粗化、晶界形成等多晶生长过程以及圆满完成从凝固到调幅分解的多相变过程. 关键词： 晶体相场模型 多晶凝固 调幅分解 组织演化     

On the kinetics of spinodal decomposition

We discuss the kinetics of phase separation based on the mechanism of spinodal decomposition. The starting point is Boltzmann's transport equation. A perturbation theory will be developed leading to a hierarchy of differential equations for the local density. The first member of this hierarchy is a nonlinear wave-type equation, which linearized version will be solved in order to discuss the behaviour of the amplification factor. Additionally, we compare our results with those of standard diffusion-type approximations and molecular dynamics calculations.Research supported in part by National Science Foundation, Grant ENG-7 515 882-A01     

Static and time-dependent properties of polymer gels around the volume phase transition

Recent progress in the study of the volume phase transition of polymer gels is reviewed. The phenomenological theories of swelling equilibrium and phase transition of gels are summarized, and some basic experimental results on poly-N-isopropylacrylamide (NIPA) gels are compared with the prediction from these theories. Special attention is paid to the elastic properties of the gel network near the volume phase transition. The effect of external stresses on the swelling and the phase transition is analyzed. Some anomalous and unique characteristics revealed in NIPA gels such as shape- and size-dependent swelling and phase transition properties, curious phase coexistence, and domain structure are presented. Experimental results on some time-dependent phenomena such as phase separation, spinodal decomposition, and pattern formation are also presented and discussed. Some problems inherent to gels from biological bodies are briefly discussed.     

Experimental small-angle X-ray scattering investigation of initial stages of the spinodal decomposition in model sodium silicate glasses

The kinetics of the initial stages of the spinodal decomposition in model glasses of the Na₂O-SiO₂ system has been investigated in situ. It has been demonstrated that there is a quantitative agreement of the experimental results obtained in the framework of the Stephenson theory with the basic principles of modern theories and the data on direct determination of the viscosity, mobility, and diffusion. It has been found that the spatial-temporal evolution of the heterogeneous structure has a multistage character during spinodal decomposition. The characteristic size of the phase regions at each stage varies with time according to the power law. The sequence of stages and the values of exponents for the spinodal decomposition are as follows: 1/20, 1/4, 1/2, and 1/3.     

On the nucleation of hadronic domains in the quark-hadron transition

We present numerical results on bubble profiles, nucleation rates and time evolution for a weakly first-order quark-hadron phase transition in different expansion scenarios. We confirm the standard picture of a cosmological first-order phase transition, in which the phase transition is entirely dominated by nucleation. We also show that, even for expansion rates much lower than those expected in heavy-ion collisions nucleation is very unlikely, indicating that the main phase conversion mechanism is spinodal decomposition.     

Spinodal decomposition of tungsten-containing phases in functional coatings obtained via high-energy implantation processes

We have studied structural and phase transformations in tungsten-containing functional coatings of carbon steels obtained during the high-energy processes of implanting tungsten carbide micropowders by the method of complex pulse electromechanical processing and micropowders of tungsten by technology of directed energy of explosion based on the effect of superdeep penetration of solid particles (Usherenko effect). It has been shown that, during thermomechanical action, intensive steel austenization occurs in the deformation zone with the dissolution of tungsten carbide powder, the carbidization of tungsten powder, and the subsequent formation of composite gradient structures as a result of the decay of supercooled austenite supersaturated by tungsten according to the diffusion mechanism and the mechanism of spinodal decomposition. Separate zones of tungsten-containing phases of the alloy are in the liquid-phase state, as well as undergo spinodal decomposition with the formation of highly disperse carbide phases of globular morphology.     

Morphological characterization of spinodal decomposition kinetics

The time evolution of the morphology of homogeneous phases during spinodal decomposition is described using a family of morphological measures known as Minkowski functionals. They provide the characteristic length scale L of patterns in a convenient, statistically robust, and computationally inexpensive way. They also allow one to study the scaling behavior of the content, shape, and connectivity of spatial structures and to define the crossover from the early stage decomposition to the late stage domain growth. We observe the scaling behavior with , , and depending on the viscosity of the fluid. When approaching the spinodal density , we recover the prediction for the early time spinodal decomposition. Received 3 March 1998