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)     

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.     

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.     

False vacuum decay after inflation

Inflation is terminated by a non-equilibrium process which finally leads to a thermal state. We study the onset of this transition in a class of hybrid inflation models. The exponential growth of tachyonic modes leads to decoherence and spinodal decomposition. We compute the decoherence time, the spinodal time, the size of the formed domains and the homogeneous classical fields within a single domain.     

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.     

Relevance of the Cahn-Hilliard-Cook theory at early times in spinodal decomposition

We analyse Cook's equation for spinodal decomposition and compare its predictions with computer-simulation data to conclude its formal consistency with the observations at early times. We thus provide a simple reference for the analysis of experiments at early, observable times and for the development of theory at late times.     

Phase diagrams and kinetics of phase transitions in protein solutions

The phase behavior of proteins is of interest for fundamental and practical reasons. The nucleation of new phases is one of the last major unresolved problems of nature. The formation of protein condensed phases (crystals, polymers, and other solid aggregates, as well as dense liquids and gels) underlies pathological conditions, plays a crucial role in the biological function of the respective protein, or is an essential part of laboratory and industrial processes. In this review, we focus on phase transitions of proteins in their properly folded state. We first summarize the recently acquired understanding of physical processes underlying the phase diagrams of the protein solutions and the thermodynamics of protein phase transitions. Then we review recent findings on the kinetics of nucleation of dense liquid droplets and crystals. We explore the transition from nucleation to spinodal decomposition for liquid-liquid separation and introduce the new concept of solution-to-crystal spinodal. We review the two-step mechanism of protein crystal nucleation, in which mesoscopic metastable protein clusters serve as precursors to the ordered crystal nuclei. The concepts and mechanisms reviewed here provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.     

Entropy of a Two-phase Mixture

The isentropic expansion of a blob of nuclear matter towards the two-phase instability region is studied by considering two extreme conditions: the instantaneous development of the phase transition and the spinodal decomposition. We show that the experimentally observed entropy values of light clusters give evidence for the onset of a liquid-gas phase transition in heavy ion and proton induced reactions, but to be more conclusive the disassembly of relatively cold nuclear systems has experimentally to be investigated in more detail.     

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.     

Characterization of the spinodal decomposition of Fe−Cr alloys by Mössbauer spectroscopy

Addition of 5%Ni to an Fe?28%Cr alloy causes a transition of the aging behavior from the nucleation and growth to the spinodal decomposition. Very rapid increase in the average internal magnetic field and a broadening of the internal magnetic field distribution occur in the spinodal decomposition. Mössbauer spectra are synthesized by assuming a rectangular and a sinusoidal wave for the composition fluctuation, and the internal magnetic field distributions obtained from those are compared with the experimental results to estimate a time evolution of the amplitude of the composition wave.     

Modulated K structures in the supercritical region of existence of peeling solid solutions

The conditions under which solid solutions can exist in the spinodal region have been considered. It is shown that, in the absence of effective kinetic mechanisms implementing decomposition processes, modulated K structures can be formed in a solid solution, which are a particularly ordered impurity distributions in a high-temperature phase.     

Volume effects in the theory of equilibrium and quasiequilibrium states of multicomponent solid solutions

A phenomenological theory of equilibrium and quasiequilibrium states of multicomponent solid solutions is constructed taking account of volume effects. Quasiequilibrium states are characterized by the fact that only some of the conditions for thermal dynamic equilibrium of the system are satisfied. The short-range parts of the interatomic interactions are taken into account by introducing the proper volumes of the atoms based on a generalized lattice model. The long-range parts of the potentials are taken into account in the effective-field approximation. The equations for the quasiequilibrium components in the solutions are introduced taking account of the nonuniformity in the distributions of the less mobile nonequilibrium components. The conditions for spinodal decomposition of a solid solution with an arbitrary number of components in the equilibrium and quasiequilibrium cases are obtained. An equation for equilibrium spinodal decomposition of a three-component microheterogeneous solid solution is found. Fiz. Tverd. Tela (St. Petersburg) 41, 1609–1613 (September 1999)     

On the theory of spinodal decomposition in solid and liquid binary mixtures

The kinetics of phase separation is discussed with emphasis on the transition between spinodal decomposition and nucleation. A reanalysis of the theory of Langer, Baron and Miller shows that it exhibits a spinodal line somewhat closer to the coexistence curve than the meanfield spinodal. There the same (as we think unphysical) critical singularities occur as in Cahn-Hilliard theory. The precise location of this spinodal line depends on the cell size of the coarse graining. For concentrations less than the spinodal one the structure factorS(k, t) converges then towards the structure factor of the metastable onephase state, implying an infinite lifetime of the latter.In order to include the effects of nucleation and growth we hence present an alternative treatment, extending our previous work on cluster dynamics. From a simple approximation for the radial concentration distribution function of clustersS(k, t) is computed numerically. Even at rather low concentrations the time evolution ofS(k, t) is then similar to what Langer et al. find at high concentrations, implying a very gradual transition from nucleation and growth to spinodal decomposition, at least for parameter values appropriate to the Ising model. This treatment, which is consistent with Lifshitz-Slyozov's coarsening law at late times, is extended to the early stages of phase separation in liquid mixtures.     

Spinodal decomposition: An alternate mechanism of phase conversion

The scenario of homogeneous nucleation is investigated for a first-order quark-hadron phase transition in a rapidly expanding background of quark gluon plasma. It is found that significant supercooling is possible before hadronization begins. This study also suggests that spinodal decomposition competes with nucleation and may provide an alternative mechanism for phase conversion.     

First-order amorphous-amorphous transformation in silica

Molecular simulations predict that a first-order amorphous-amorphous transformation occurs in SiO2 under pressure, analogous to the first-order amorphous-amorphous transformation known to occur in H2O. At low temperatures the first-order transformation is kinetically hindered, and an amorphous-amorphous transformation occurs instead by gradual spinodal decomposition at higher pressures. We suggest that previous experiments have observed the spinodal decomposition pathway in SiO2 and that the predicted first-order transformation will be observed in experiments carried out at higher temperatures.     

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.     

Isospin fractionation: Equilibrium versus spinodal decomposition

This paper focuses on the isospin properties of the asymmetric nuclear-matter liquid–gas phase transition analyzed in a mean-field approach, using Skyrme effective interactions. We compare two different mechanisms of phase separation for low-density matter: equilibrium and spinodal decomposition. The isospin properties of the phases are deduced from the free-energy curvature, which contains information both on the average isospin content and on the system fluctuations. Some implications on experimentally accessible isospin observables are presented.