Evidence for spinodal decomposition in nuclear multifragmentation

Multifragmentation of a "fused system" was observed for central collisions between 32 MeV/nucleon 129Xe and (nat)Sn. Most of the resulting charged products were well identified due to the high performances of the INDRA 4pi array. Experimental higher-order charge correlations for fragments show a weak but nonambiguous enhancement of events with nearly equal-sized fragments. Supported by dynamical calculations in which spinodal decomposition is simulated, this observed enhancement is interpreted as a "fossil" signal of spinodal instabilities in finite nuclear systems.     

Many-fragment correlations and possible signature of spinodal fragmentation

Abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation. Many-fragment correlations can be used to enlighten any extra production of events with specific fragment partitions. The high sensitivity of such correlation methods makes it particularly appropriate to look for small numbers of events as those expected to have kept a memory of spinodal decomposition properties and to reveal the dynamics of a first-order phase transition for nuclear matter and nuclei. This paper summarizes results obtained so far for both experimental and dynamical simulations data.     

Interplay between spinodal decomposition and glass formation in proteins exhibiting short-range attractions

We investigate the competition between spinodal decomposition and dynamical arrest using aqueous solutions of the globular protein lysozyme as a model system for colloids with short-range attractions. We show that quenches below a temperature Ta lead to gel formation as a result of a local arrest of the protein-dense phase during spinodal decomposition. The rheological properties of these gels allow us to use centrifugation experiments to determine the local densities of both phases and to precisely locate the gel boundary and the attractive glass line close to and within the unstable region of the phase diagram.     

New approach to the theory of spinodal decomposition

A new approach to the study of spinodal decomposition for a scalar field is proposed. The approach is based on treating this process as a relaxation of the one-time correlation function G(q,t)=∫d r<Φ (0, t)Φ (r,t)>exp(i q·r), which plays the role of an independent dynamical object (a unique two-point order parameter). The dynamical equation for G(q,t) (the Langevin equation in correlation-function space) is solved exactly in the one-loop approximation, which is the zeroth approximation in the approach proposed. This makes it possible to trace the asymptotic behavior of G(q,t) at long and intermediate times t (from the moment of onset of the spinodal decomposition). The values obtained for the power-law growth exponents for the height and position of the peak in G(q,t) at the intermediate stage is in satisfactory agreement with the data obtained by a number of authors through numerical simulation of the corresponding stochastic equations describing the relaxation of the local order parameter. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 432–437 (25 September 1997)     

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     

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.     

Isotropic averaging for cell-dynamical-system simulation of spinodal decomposition

Formulae have been developed for the isotropic averagings in two and three dimensions. Averagings are employed in the cell-dynamical-system simulation of spinodal decomposition for inter-cell coupling. The averagings used in earlier works on spinodal decomposition have been discussed.     

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.     

Elucidating the mechanism of nucleation near the gas-liquid spinodal

We have constructed a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. Close to the spinodal, the free energy, as a function of the size of the largest cluster, develops surprisingly a minimum at a subcritical cluster size. It is this minimum at intermediate size that is found to be responsible for the barrier towards further growth of the nucleus at large supersaturation. An alternative free energy pathway involving the participation of many subcritical clusters is found near the spinodal where the growth of the nucleus is promoted by a coalescence mechanism. The growth of the stable phase becomes collective and spatially diffuse, and the significance of a "critical nucleus" is lost for deeper quenches.     

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.     

Asymptotic behaviour of spinodal decomposition

We report a numerical study of the asymptotic regime of spinodal decomposition. Specifically, we find (a) that the characteristic pattern size shows a power-law growth with exponent 0.33; and (b) that the effect of noise is asymptotically irrelevant.     

From colloidal aggregation to spinodal decomposition in sticky emulsions

Aggregation mechanisms of emulsions at high initial volume fractions () is studied using light scattering. We use emulsion droplets which can be made unstable towards aggregation by a temperature quench. For deep quenches and , the aggregation mechanism is identified as diffusion-limited cluster aggregation (DLCA). An ordering of the clusters, which is reflected by a peak in the scattering intensity, is shown to result from the intercluster separation, exhibiting different scaling than that observed at lower volume fractions. This manifests an increasing similarity to spinodal decomposition observed as is increased. For and shallow quenches, different mechanisms, closer to spinodal decomposition, are observed. These results allow the subtle boundaries between DLCA and spinodal decomposition to be explored. Received: 7 April 1998 / Revised: 19 August 1998 / Accepted: 21 August 1998     

Model of spinodal decomposition of phases under hyperbolic diffusion

A model is proposed for the kinetics of spinodal decomposition at high diffusion rates described by a hyperbolic equation. The formation of new phases is described using a zero-radius nonlinear potential model. It is shown that a regular distribution in space of the phases during spinodal decomposition is initiated by suitable initial conditions for the concentration gradient with constant initial concentrations of the components. Fiz. Tverd. Tela (St. Petersburg) 41, 907–909 (May 1999)     

Phase field simulation of spinodal decomposition under external magnetic field

A computational model was developed to simulate the spinodal decomposition process of ferromagnetic alloys under an external magnetic field. In this model, the temporal evolution of the modulated structure was described by a phase field method, and the magnetic configuration was solved by using a micromagnetic method. The spinodal decomposition and coarsening processes of a single magnetic particle and an A-B hypothetical system under an external magnetic field were simulated using the proposed model. The simulation results show that the precipitated particles were elongated along the direction of the external magnetic field. The dependence of the modulated structure of an A-B hypothetic system on external magnetic field is much more sensitive than that of the single particle structure. The simulation results also demonstrate that the modulation of the external magnetic field is effective even if the spinodal decomposition has been completed and a stable modulated structure was formed.     

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.     

Model of surface structure formation by stabilized spinodal decomposition

A one-dimensional model of stabilized spinodal decomposition is proposed and investigated. In the model, a curvature field couples adiabatically to the order parameter field of standard nonlinear Cahn-Hilliard theory for spinodal decomposition on a membrane. A simple geometric interpretation of the specific coupling is given. Alternatively the theory can also be described by an additional nonlocal self coupling introduced into the usual Cahn-Hilliard theory. An exact stationary solution is found. It predicts a sinusoidal decomposition profile and a global curvature of the initially flat membrane which also develops long wavelength ripples. Stability of this solution against small fluctuations is investigated and conditions for stability are derived. The case of maximal effective coupling is studied in detail and the geometrical surface profile is evaluated analytically.