Binary Fluid Demixing: The Crossover Region

By performing lattice Boltzmann simulations of a binary mixture, we scrutinize the dynamical scaling hypothesis for the spinodal decomposition of binary mixtures for the crossover region, i.e., the region of parameters in the growth curve where neither inertia nor viscous forces dominate the coarsening process. Our results give no evidence for a breakdown of scaling in this region, as might arise if the process were limited by molecular scale physics at the point of fluid pinch-off between domains. A careful data analysis allows us to refine previous estimates on the width of the crossover region which is somewhat narrower than previously reported.     

A rigorous theory of finite-size scaling at first-order phase transitions

A large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered. The dependence of the finite-volume magnetizationM _per(h, L) in cubes of sizeL ^d under periodic boundary conditions on the external fieldh is analyzed. For the case where two phases coexist at the infinite-volume transition pointh _t , we prove that, independent of the details of the model, the finite-volume magnetization per lattice site behaves likeM _per(h _t )+M tanh[ML ^d (h–h_t)] withM _per(h) denoting the infinite-volume magnetization and M=1/2[M _per(h _t +0)–M _per(h _t –0)]. Introducing the finite-size transition pointh _m (L) as the point where the finite-volume susceptibility attains the maximum, we show that, in the case of asymmetric field-driven transitions, its shift ish _t –h _m (L)=O(L ^–2d ), in contrast to claims in the literature. Starting from the obvious observation that the number of stable phases has a local maximum at the transition point, we propose a new way of determining the pointh _t from finite-size data with a shift that is exponentially small inL. Finally, the finite-size effects are discussed also in the case where more than two phases coexist.On leave from: Institut für Theoretische Physik, FU-Berlin, D-1000 Berlin 33, Federal Republic of Germany.     

Nonequilibriurn discontinuous phase transitions in a fast ionic conductor model: Coexistence and spinodal lines

Two-dimensional lattice-gas models with attractive interactions and particle-conserving hopping dynamics under the influence of a very large external electric field along a principal axis are studied in the case of off-critical densities. We describe the corresponding nonequilibrium first-order phase transitions, evaluate coexistence and spinodal lines, and make some comparisons with experimental observations on fast ionic conductors.See Ref. 1 (henceforth referred to as II) for references.     

Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel

Smoluchowski's coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version wherec _t =c ₁ (t) is the concentration ofl-particle clusters at timet. We prove that for initial data satisfyingc ₁(0)>0 and the condition 0 c _l (0) <A (1+)^-l (A >0), the solutions behave asymptotically likec ₁ (t)t ^–2c(lt^–1) ast withlt ^–1 kept fixed. The scaling function c() is (1/gr), where , a conserved quantity, is the initial number of particles per unit volume. An analous result is obtained for the continuous version of Smoluchowski's coagulation equation wherec(v, t) is the oncentration of clusters of sizev.     

Stochastic models of firstorder nonequilibrium phase transitions in chemical reactions

The steady states of a simple nonlinear chemical system kept far from equilibrium are analyzed. A standard macroscopic analysis shows that the nonlinearity introduces an instability causing a transition analogous to a thermodynamic first-order phase transition. Near this transition the system exhibits hysteresis between two alternative steady states. Fluctuations are introduced into this model using a stochastic master equation. The solution of this master equation is unique, preventing two alternative exactly stable states. However, a quasi-hysteresis occurs involving transitions between alternative metastable steady states on a time scale that is longer than that of the fluctuations around the mean steady state values by a factor of the forme , where ø is the height of a generalized thermodynamic potential barrier between the two states. In the thermodynamic limit this time scale tends to infinity and we have essentially two alternative stable steady states.     

Characteristics of phase transitions via intervention in random networks

We present a percolation process in which the classical Erdo¨s–Re′nyi(ER) random evolutionary network is intervened by the product rule(PR) from some moment t0. The parameter t0is continuously tunable over the real interval [0, 1].This model becomes the random network under the Achlioptas process at t0= 0 and the ER network at t0= 1. For the percolation process at t0≤ 1, we introduce a relatively slow-growing point, after which the largest cluster begins growing faster than that in the ER model. A weakly discontinuous transition is generated in the percolation process at t0≤ 0.5.We take the relatively slow-growing point as the lower pseudotransition point and the maximum gap point of the order parameter as the upper pseudotransition point. The critical point can be approximately predicted by each fitting function of the two points about t0. This contributes to understanding the rapid mergence of the large clusters at the critical point.The numerical simulations indicate that the lower pseudotransition point and the upper pseudotransition point are equal in the thermodynamic limit. When t0> 0.5, the percolation processes generate a continuous transition. The scaling analyses of several quantities are presented, including the relatively slow-growing point, the duration of the relatively slow-growing process, as well as the relatively maximum strength between the percolation percolation at t0< 1 and the ER network about different t0. The presented mechanism can be viewed as a two-stage percolation process that has many potential applications in the growth processes of real networks.     

Kinetics of phase separation in polymer mixtures

Characteristic features of the liquid-liquid phase separation process in polymer systems are presented, followed by a concise review of existing studies on phase-separation kinetics in polymer solutions and mixtures. Brief discussions have been made on two selective topics in this field, i.e., applicability of Cahn's linearized theory for spinodal decomposition to polymer mixtures and the scaling law in the late stage of phase separation.     

The role of elastic strains at non-ferroelastic displacive phase transitions

The role of elastic strains at structural phase transitions is illustrated within the Landau theory and its first-order corrections due to critical fluctuations and defects are described. The Landau theory is sufficient to demonstrate the impossibility of bulk nucleation in a supercooled symmetrical phase and the absence of heterophase fluctuations in solids. The critical fluctuations are known to convert a second-order transition in an Ising-like system in a solid to a first-order one. Close to the mean-field tricritical point the effect can be described, for displacive systems, within a first-order perturbation theory and takes place for the Heisenberg systems as well. The influence of defects on these transitions is mediated essentially by the elastic strains. Defects smear the transition. For the “random local field” defects and an incommensurate (Heisenberg-like) transition this effect is so strong that first-order perturbation theory leads to a divergence.     

Nucleation-and-growth problem in model lipid membranes undergoing subgel phase transitions is a problem of time scale

In this Rapid Note, we show that the problem of growth of molecular superlattice in a fully hydrated dipalmitoylphosphatidylcholine (DPPC) membrane during the gel-to-subgel phase transformation process is a problem of time scale. There are, in fact, two time scales. The first is an “integrated” or, in some sense, stagnant time scale, that reflects the well-known isotropic growth effect in the d-dimensional space, but assigns the problem to be still in a category of Debye relaxation kinetics. The fraction of old (parent) phase does not suit the Paley-Wiener criterion for relaxation functions, and the time behavior is exclusively due to the geometrical characteristics of the kinetic process. The second (multi-instantaneous) time scale, in turn, is recognised to be a “broken” (fractional time derivative) or memory-feeling (dynamic) scale, which carries some very essential physics of the phenomenon under study, and classifies the problem to be of non-Debye (viz., stretched exponential) nature. It may, in principle, contain all the important effects, like small scale coexistence, presence of collisions between domains, with possible annihilation and creation of domain boundaries, and/or a headgroup packing, hydration against lipid mobility behavior, and finally, a multitude of quasi-crystalline states. It turns out, that within the range of validity of the dynamic scale approximation proposed, the criterion for relaxation functions is very well fulfilled. Received 30 November 1998     

Modeling of fast phase transitions dynamics in metal target irradiated by pico- and femtosecond pulsed laser

We investigate laser pulse influence on aluminum target in irradiance range 10⁹ to 10¹⁶ W/cm², pulse duration between 10⁻⁸ and 10⁻¹⁵ s, Gaussian time profile with wavelength of 0.8 μm. For all computations energy density was 10 J/cm². Plasma in the evaporated material is generated at the energy density above 10 J/cm²as the modeling showed.Long and short laser pulses distinguish by the mechanisms of energy transformation. For short laser pulses there is volumetric energy absorption, together with rapid phase transitions it lead to overheating in solid and liquid states, overheated solid temperature rises up to (6-8)T_m. Under influence of the energy saved in overheated solid, duration of the phase transitions becomes nanosecond, which is several orders of magnitude longer than laser pulse.     

The role of dimensionality in the kinetic Ising model of spinodal decomposition: Evidence from zero-temperature quenches

We study a three-dimensional Ising lattice gas model with spin-exchange dynamics quenched from infinite to zero temperature. We consider a wide range of values of the binary composition (i.e., magnetization) and annealed vacancy concentration. We find that, as in two dimensions, the system freezes in a configuration very far from equilibrium, and that the interface energy per bond in the frozen state, which is very large, in all cases takes very nearly the same values as in two dimensions. We discuss the implications of these results regarding the irrelevance of dimensionality in this problem.     

Computer Simulation of Nonequilibrium Growth of Crystals in a Two-Dimensional Medium with a Phase-Separating Impurity

Two-dimensional nonequilibrium growth of crystals (quasistable faceted and dendritic) in the presence of a phase separating impurity is studied by computer simulation. It is shown that there is a gradual modification in this system from quasistable faceted growth to the formation of dendrites when the impurity concentration increases. If there is dendritic growth in the presence of a phase-separating impurity, the cyclic changes in the morphology, expressed through the periodic occurrence of tertiary branches of a dendrite, are observed when the phase-separating impurity concentration is raised. This behavior of the morphology is considered as a reentrant nonequilibrium phase transition.     

Raman study of phase transitions in double orthophosphates of lutetium and potassium

This study by Raman spectrometry of double orthophosphates of lutetium and potassium consists of a systematic analysis of double orthophosphates of the potassium and lanthanide family. In the 10-300 K temperature range three solid-solid phase transitions in this compound are obtained which demonstrate the application of Raman spectrometry to the study of the nature and mechanism of such transitions.     

Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalism

We investigate the superposition of multifractals in the generalized thermodynamic formalism. It is shown analytically that phase transitions of first and second order are obtained and that the topology of the corresponding critical lines endows bicritical behavior. We demonstrate that these phase transitions can be observed in the spectrum of fractal dimensions and in the spectra of related quantities. Therefore, the obtained results are of importance for the interpretation of experimental systems.     

A characterization of first-order phase transitions for superstable interactions in classical statistical mechanics

We give bounds on finite-volume expectations for a set of boundary conditions containing the support of any tempered Gibbs state and prove a theorem connecting the behavior of Gibbs states to the differentiability of the pressure for continuum statistical mechanical systems with long-range superstable potentials. Convergence of grand canonical Gibbs states is also studied.     

Influence on the phase transitions of barium titanate of the manganese valency,introduced as a substituant in the titanium site

A small amount of manganese introduced in BaTiO₃ modifies strongly the vibrational and electronic properties of the pure compound. Dielectric response and EPR measurements are reported in order to study the influence of the manganese valency on the ferroelectric-paraelectric phase transition.     

The effect of clamped and free boundaries on long range strain coupling in structural phase transitions

In ferroelastic structural phase transitions, the atomic ordering in one cell creates a local strain field which is propagated elastically throughout the material, resulting in an effective or indirect coupling J(R _ij ) between the ordering in cells i and j. With free boundaries on the sample, the J(R _ij ) contains a Zener-Eshelby term J _Z of infinite range, which largely determines the transition temperature T _c. The present paper shows what happens when the boundaries are clamped. On cooling from a high temperature an anomaly takes place at more or less the same temperature as the phase transition for free boundaries. Cooling results in an irregular pattern of domains with positive and negative order parameter whose long range strains cancel. Two cases are distinguished. In the “tweed” case coherent domain boundaries form easily and result in fine lamellar domains. When coherent domain boundaries are not possible (the “non-Sapriel”) case, larger less regular domains are formed. In either case the macroscopic net strain adds up to zero.     

On the surface configuration of solids in relation to the surface free enthalpy excess and its consequences in phase transitions

Summary In previous studies the average number of neighbors (n _avrg) of an atom in the surface phase was found to increase by about (5÷20)% between 0 K and the melting temperature for all solid chemical elements in the periodic table. This increment makes the solid surface “geometrically impossible” to exist at the melting temperature. The latter results in the collapse of crystal structure, beginning with the formation of liquid in the surface layers. Ratio of critical and melting temperature is also discussed.     

Crystal growth and phase transitions of solid solutions in [N(CH3)4]2MX4 isomorph class

Abstract

Homogeneous single crystals of tetramethylammonium tetrahalogenometallate solid solutions have been grown: a temperature difference growth method with thermally enforced convection was used during the material transport from an equilibrated feed material to the growing crystals. The smallest crystals were mostly studied by differential scanning calorimetry and X-ray crystallography. Some bigger crystals were available for dielectric measurements and Raman scattering. The temperature-concentration phase diagrams of solid solutions look like the temperature-pressure phase diagrams of pure tetramethylammonium salts. The progressive substitution seems equivalent to a change of the pressure, and is understood as a distortion of the metal-halide tetrahedron and a change of interactions with the first, second and third neighbours. The structure instabilities seem to have their origin within the b?c layers, and the increase of pressure (or equivalent concentration) should correspond to a hardening of the Layer-Shift Mode.