Spinodal Instability Research Articles

Finding the differences: Classical nucleation perspective on homogeneous melting and freezing of hard spheres.

By employing brute-force molecular dynamics, umbrella sampling, and seeding simulations, we investigate homogeneous nucleation during melting and freezing of hard spheres. We provide insights into these opposing phase transitions from the standpoint of classical nucleation theory. We observe that melting has both a lower driving force and a lower interfacial tension than freezing. The lower driving force arises from the vicinity of a spinodal instability in the solid and from a strain energy. The lower interfacial tension implies that the Tolman lengths associated with melting and freezing have opposite signs, a phenomenon that we interpret with Turnbull's rule. Despite these asymmetries, the nucleation rates for freezing and melting are found to be comparable.

Dynamical evolution of spinodal decomposition in holographic superfluids

We study the nonlinear dynamical evolution of spinodal decomposition in a first-order superfluid phase transition using a simple holographic model in the probe limit. We first confirm the linear stability analysis based on quasinormal modes and verify the existence of a critical length scale related to a gradient instability — negative speed of sound squared — of the superfluid sound mode, which is a consequence of a negative thermodynamic charge susceptibility. We present a comparison between our case and the standard Cahn-Hilliard equation for spinodal instability, in which a critical length scale can be also derived based on a diffusive instability. We then perform several numerical tests which include the nonlinear time evolution directly from an unstable state and fast quenches from a stable to an unstable state in the spinodal region. Our numerical results provide a real time description of spinodal decomposition and phase separation in one and two spatial dimensions. We reveal the existence of four different stages in the dynamical evolution, and characterize their main properties. Finally, we investigate the strength of dynamical heterogeneity using the spatial variance of the local chemical potential and we correlate the latter to other features of the dynamical evolution.

Composition Dependent Instabilities in Mixtures with Many Components.

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study phase ordering instabilities in a paradigmatic model that represents the complexity of-e.g., biological-mixtures via random second virial coefficients. Using tools from free probability theory we obtain the exact spinodal curve and the nature of instabilities for a mixture with an arbitrary composition, thus lifting an important restriction in previous work. We show that, by controlling the concentration of only a few components, one can systematically change the nature of the spinodal instability and achieve demixing for realistic scenarios by a strong composition imbalance amplification. This results from a nontrivial interplay of interaction complexity and entropic effects due to the nonuniform composition. Our approach can be extended to include additional systematic interactions, leading to a competition between different forms of demixing as density is varied.

Cubic silicon carbide under tensile pressure: Spinodal instability

Silicon carbide is a hard, semiconducting material presenting many polytypes, whose behavior under extreme conditions of pressure and temperature has attracted large interest. Here we study the mechanical properties of 3C-SiC over a wide range of pressures (compressive and tensile) by means of molecular dynamics simulations, using an effective tight-binding Hamiltonian to describe the interatomic interactions. The accuracy of this procedure has been checked by comparing results at T=0 with those derived from ab-initio density-functional-theory calculations. This has allowed us to determine the metastability limits of this material and in particular the spinodal point (where the bulk modulus vanishes) as a function of temperature. At T=300 K, the spinodal instability appears for a lattice parameter about 20% larger than that corresponding to ambient pressure. At this temperature, we find a spinodal pressure Ps=−43GPa, which becomes less negative as temperature is raised (Ps=−37.9GPa at 1500 K). These results pave the way for a deeper understanding of the behavior of crystalline semiconductors in a poorly known region of their phase diagrams.

Strong magnetic fields and pasta phases reexamined

In this work, we compute the structure and composition of the inner crust of a neutron star in the presence of a strong magnetic field, such as it can be found in magnetars. To determine the geometry and characteristics of the crust inhomogeneities, we consider the compressible liquid drop model, where surface and Coulomb terms are included in the variational equations, and we compare our results with previous calculations based on more approximate treatments. For the equation of state (EoS), we consider two non-linear relativistic mean-field models with different slopes of the symmetry energy, and we show that the extension of the inhomogeneous region inside the star core due to the magnetic field strongly depends on the behavior of the symmetry energy in the crustal EoS. Finally, we argue that the extended spinodal instability observed in previous calculations can be related to the presence of small amplitude density fluctuations in the magnetar outer core, rather than to a thicker solid crust. The compressible liquid drop model formalism, while in overall agreement with the previous calculations, leads to a systematic suppression of the metastable solutions, thus allowing a more precise estimation of the crust-core transition density and pressure, and therefore a better estimation of the crustal radius.

Finite-dimensional signature of spinodal instability in an athermal hysteretic transition

We study the off-equilibrium critical phenomena across a hysteretic first-order transition in disordered athermal systems. The study focuses on the zero temperature random field Ising model (ZTRFIM) above the critical disorder for spatial dimensions $d=2,3,$ and $4$. We use Monte Carlo simulations to show that disorder suppresses critical slowing down in phase ordering time for finite-dimensional systems. The dynamic hysteresis scaling, the measure of explicit finite-time scaling, is used to subsequently quantify the critical slowing down. The scaling exponents in all dimensions increase with disorder strength and finally reach a stable value where the transformation is no longer critical. The associated critical behavior in the mean-field limit is very different, where the exponent values for various disorders in all dimensions are similar. The non-mean-field exponents asymptotically approach the mean-field value ($\Upsilon \approx 2/3$) with increase in dimensions. The results suggest that the critical features in the hysteretic metastable phase are controlled by inherent mean-field spinodal instability that gets blurred by disorder in low-dimension athermal systems.

Identification of the seeding mechanism in the spinodal instability of dewetting liquids

HypothesisSpinodal dewetting is one of the basic processes inducing a spontaneous withdrawal of a liquid from a substrate surface. In the accepted theory, thickness fluctuations generated by thermally activated capillary waves are amplified by the competing actions of surface tension and disjoining pressure. Ubiquitous sub-nanometric substrate roughness also produces thickness fluctuations and may play a role analogous but even more efficient in seeding the process. ModellingAnalytic calculations valid at the early linear stage of the process and simulations extending the study to its whole non-linear development have been performed to compare features and the relative relevance of the two seeding mechanisms. FindingsCalculations and simulations have shown that substrate roughness can replace capillary waves in seeding spinodal dewetting. A typically larger amplitude and a steady nature compared to the transitory one of capillary waves allow us to conclude that, contrary to the common view, substrate roughness is the prevailing seed of the spinodal instability. The consequence of our statement is that spinodal dewetting loses most of its stochastic nature and becomes, in principle, a process that can be tuned by engineering substrate roughness.

Phase decomposition in nanoporous Au-Pt

This study explores microstructure and phase decomposition in nanoporous Au-Pt made by dealloying. The starting alloy, Ag75Au12.5Pt12.5, forms a uniform solid solution. Removing the Ag by dealloying at room temperature forms nanoporous equimolar Au-Pt with a ligament size as small as 4 nm. That alloy’s composition is in the Au-Pt phase diagram’s regime of spinodal instability. Surprisingly, in view of the instability and of the substantial atomic rearrangements accompanying dealloying, X-ray diffraction and transmission electron microscopy reveal a homogeneous single-phase state in the bulk of the nanoporous material. This can be traced back to enrichment of Pt at the surface, which depletes the bulk in Pt. The Pt-depleted bulk is in the metastable region of the alloy phase diagram, between the binodal and the spinodal. Annealing prompts curvature-driven coarsening by diffusion, diminishing the number of sites for Pt surface segregation. The ensuing enrichment of the bulk in Pt is accompanied by the formation first of crystallographically coherent, Pt-rich regions and later of semi-coherent regions of the Pt-rich phase. The morphology of the coherent regions is compatible with spinodal decomposition. Yet, the microstructure evolution pathway is nonstandard, since decomposition here concurs with rapid coarsening of the porous microstructure. Among the prospect of the nanoporous alloy are its high kinetic stability and the opportunity to tune the surface composition through the annealing temperature.

Microplasticity in inhomogeneous alloys

We report on a preliminary modelling effort to understand the influence of compositional inhomogeneity on alloy microplasticity from a dislocation dynamics perspective. We tackle this problem by multiscale simulations in three steps: (1) analysis of the 3D composition morphology in alloys with tendency to undergo spinodal instability both thermally and under irradiation, with bcc FeCrAl alloys as a model system, (2) atomistic simulation of the dislocation mobility as a function of the local alloy composition, and (3) using dislocation dynamics simulations to understand the impact of composition inhomogeneity on microplasticity. The dislocation dynamics model takes into consideration the coherency stress associated with composition inhomogeneity when computing the forces driving the dislocation motion and on cross slip. Our preliminary investigation shows that the stress-strain response of the alloy and the dislocation density evolution depend on the wavelength of the composition fluctuations. Our investigation also shows that the alloy inhomogeneity may alter the cross-slip activity, which, in turn, influences the dislocation density evolution. The dependence of the dislocation mobility and coherency stress on local composition and its variation, as well as the altered cross slip rates, cause the dislocation microstructure to differ relative to that in the homogeneous alloy of the same average composition.

Non-equilibrium dynamics of a scalar field with quantum backreaction

We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes. We renormalize the 2PI equations of motion in an on-shell scheme in terms of physical parameters. We present the Hartree-resummed renormalized effective potential at finite temperature and critically discuss the role of the effective potential in a non-equilibrium system. We follow the decay and thermalization of a scalar field from an initial cold state with all energy stored in the potential, into a fully thermalized system with a finite temperature. We identify the non-perturbative processes of parametric resonance and spinodal instability taking place during the reheating stage. In particular we study the unstable modes in the region where the vacuum 1PI effective action becomes complex and show that such spinodal modes can have a dramatic effect on the evolution of the one-point function. Our methods can be easily adapted to simulate reheating at the end of inflation.

Suppression of spinodal instability by disorder in an athermal system

We observed asymmetric critical slowing down and asymmetric dynamical scaling exponent in the superheating and supercooling kinetic processes during the thermally-induced metal-insulator transition of MnNiSn based Heusler alloy. During the transition to the insulator phase, the critical-like features get enhanced compared to the transition back to the metal phase. These experimental findings suggest that the metastable phase in the cooling branch of hysteresis has approached close to the spinodal instability. On the other hand, the extended disorder, generated over and above the intrinsic crystal defects during heating, triggers the excess heterogeneous nucleation before reaching the spinodal point. Zero-temperature random field Ising model (ZTRFIM) simulation, inscribed for the athermal martensitic transitions, supports the argument that the disorder smears the spinodal instabilities as the correlation length is bounded by the average distance between the disorder points.

Holographic approach of the spinodal instability to criticality

A smoking gun signature for a first-order phase transition with negative speed of sound squared {c}_s^2 is the occurrence of a spinodal instability. In the gauge/gravity duality it corresponds to a Gregory-Laflamme type instability, which can be numerically simulated as the evolution of unstable planar black branes. Making use of holography its dynamics is studied far from and near a critical point with the following results. Near a critical point the interface between cold and hot stable phases, given by its width and surface tension, is found to feature a wider phase separation and a smaller surface tension. Far away from a critical point the formation time of the spinodal instability is reduced. Across softer and harder phase transitions, it is demonstrated that mergers of equilibrated peaks and unstable plateaux lead to the preferred final single phase separated solution. Finally, a new atypical setup with dissipation of a peak into a plateau is discovered. In order to distinguish the inhomogeneous states I propose a new criterium based on the maximum of the transverse pressure at the interface which encodes phase-mixed peaks versus fully phase separated plateaux.

Concentration-gradient-driven anisotropic spinodal decomposition kinetics: nitriding of metallic alloys

ABSTRACT The effect of crystallographically oriented, unidirectional concentration gradients on spinodal decomposition in cubic crystalline solids with elastic and interfacial energy anisotropy is discussed. Phase-field simulations reveal that the kinetics of spinodal decomposition occurring in such systems is dependent on the degree of misorientation between the direction of composition gradient and the preferred crystallographic orientation for growth of spinodal fluctuations; the larger is the misorientation, the slower the kinetics. This phenomenon has been used to explain the well-known grain-orientation-dependent N-uptake kinetics observed during nitriding of metallic alloys. Several plausible causes have been proposed in the literature for the grain-orientation-dependent N-uptake kinetics during nitriding. However, this study reveals that this phenomenon is observed exclusively and without exception in alloy systems having a spinodal instability. The N-uptake kinetics in such systems is known to be dependent on the kinetics of spinodal decomposition. Consequently, anisotropic spinodal decomposition kinetics occurring owing to the presence of a surface-directed N-composition gradient in poly-crystalline metals has been shown to be a more fundamental cause for the phenomenon.

Thermal effects in hot and dilute homogeneous asymmetric nuclear matter

We present a comprehensive analysis of hot and dilute isospin-asymmetric nuclear matter employing the temperature-dependent effective-relativistic mean-field theory (E-RMF). The E-RMF is applied to study the effect of $\delta$ and $\omega-\rho$ meson cross-coupling on the thermal properties of asymmetric nuclear matter using two recently developed IOPB-I and G3 parameter sets. These sets are known to reproduce the nuclear matter properties in agreement with various experimental and observational constraints. We consider the nuclear matter to be homogeneous and study the equation of state (EoS) for densities, temperature and asymmetry which are relevant for astrophysical simulations such as supernovae explosion. The effect of temperature is investigated in reference to the density-dependent free symmetry energy and its higher-order derivatives using the well known parabolic approximation. The larger value of $\lambda_\omega$ cross-coupling in G3 in addition to the $\delta$ meson coupling in G3 smoothen the free symmetry energy. Thermal effects on various state variables are examined at fixed temperature and isospin asymmetry by separating their T=0 and the finite-T expressions. The thermal effects are mainly governed by effective mass with larger effective mass estimating larger thermal contribution. The effect of temperature on isothermal and isentropic incompressibility is discussed which is in harmony with various available microscopic calculations. The liquid-gas phase transition properties are examined in asymmetric matter with two conserved charges in the context of different slope parameter and comparable symmetry energy in IOPB-I and G3 set. The spinodal instability, binodal curve and critical properties are found to be influenced by the slope parameter $L_{sym}$.

Crossing a large-N phase transition at finite volume

The existence of phase-separated states is an essential feature of infinite-volume systems with a thermal, first-order phase transition. At energies between those at which the phase transition takes place, equilibrium homogeneous states are either metastable or suffer from a spinodal instability. In this range the stable states are inhomogeneous, phase-separated states. We use holography to investigate how this picture is modified at finite volume in a strongly coupled, four-dimensional gauge theory. We work in the planar limit, N → ∞, which ensures that we remain in the thermodynamic limit. We uncover a rich set of inhomogeneous states dual to lumpy black branes on the gravity side, as well as first- and second-order phase transitions between them. We establish their local (in)stability properties and show that fully non-linear time evolution in the bulk takes unstable states to stable ones.

Influence of evaporation on the morphology of a thin film of a partially miscible binary mixture

In this paper, we develop numerical, theoretical and experimental analyses of the different morphologies that can be created by the phase separation phenomena that are induced by solvent evaporation in a thin film of a partially miscible binary mixture. Disregarding hydrodynamic effects, the Cahn–Hilliard–Cook and temperature equations are used to describe the thermodynamics of non-isothermal phase separation in a 2D thin film. Numerical simulations are performed to investigate the interplay between evaporation and phase separation and we examine the effect on the morphology of the film of several parameters such as the initial thickness of the layer, or the initial temperature and concentration of the mixture. Interestingly, the competition between evaporation and phase separation is shown to be the main determinant of the choice between a lamellar or a lateral pattern in the beginning of phase separation. For moderate evaporation rate, the spinodal instability takes place close to the evaporating interface and a lateral structure is formed. For stronger evaporation, the spinodal instability does not occur and a lamellar structure is created. In addition, the mid- or long- term evolution of the system is also considered. The thickness of the film is an important parameter in this analysis and possible modifications of the pattern over time are emphasized. Detailed physical and theoretical interpretations are proposed for the results and experiments in a Hele-Shaw cell that nicely confirm our predictions are presented.

Spinodal instabilities of spin-polarized asymmetric nuclear matter

We analyze the spinodal instabilities of spin polarized asymmetric nuclear matter at zero temperature for several configurations of the neutron and proton spins. The calculations are performed with the Brueckner--Hartree--Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential plus a three-nucleon force of Urbana type. An analytical parametrization of the energy density, which reproduces with good accuracy the BHF results, is employed to determine the spinodal instability region. We find that, independently of the of the orientation of the neutron and proton spins, the spinodal instability region shinks when the system is polarized, being its size smaller smaller when neutron and proton spins are antiparallel than when they are oriented in a parallel way. We find also that the spinodal instability is always dominated by total density fluctuation independently of the degree of polarization of the system, and that restoration of the isospin symmetry in the liquid phase, {\it i.e.,} the so-called isospin distillation or fragmentation effect, becomes less efficient with the polarization of the system.

Spinodal instability at the onset of collective expansion in nuclear collisions

Using transport theory to model central Au + Au collisions in the energy region of 20–110 MeV/u, at impact parameters b≤5 fm, we predict a measurable impact of the spinodal instability as the collective expansion sets in with energy. Two transport models are employed, the pBUU model, solving a Boltzmann-Uehling-Uhlenbeck equation, and the Brownian Motion (BM) model, solving a set of Langevin equations to describe the motion of individual nucleons in a noisy nuclear medium. We find without ambiguity, for the first time, that a combination of delayed equilibration, onset of collective expansion and the spinodal instability produces a pair of transient ring structures, made of the projectile and target remnants, with spectator nucleons predicted to end in the entities reminiscent of stones in jewelry, on the rings. The ring structures, calculated in the configuration space and mapped onto the velocity space, could be detected in experimental collective flow data.

Polarization Spinodal at Ferroelectric Morphotropic Phase Boundary.

Here, we report a new phenomenon of uniform and continuous transformation of a single polarization domain into alternating nanodomains of two polarization vectors with the same magnitude but different directions at ferroelectric morphotropic phase Boundary (MPB). The transformation is fully reversible and could enhance the piezoelectric coefficient d_{33}. Further free energy calculations illustrate that such a polarization "decomposition" process occurs within the region on the Landau free energy curve with respect to the polarization direction where the second derivative becomes negative, which is similar to spinodal instability in phase transformations such as spinodal ordering or isostructural phase separation (e.g., spinodal decomposition). This "polarization spinodal" uncovers a new mechanism of polarization switching that may account for the ultrahigh ahysterestic piezoelectric strain at the MPB. This work could shed light on the development of phase transition theory and the design of novel ferroelectric memory materials.

Finite Dimensional Vestige of Spinodal Criticality above the Dynamical Glass Transition.

Finite dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally activated processes that also limit how close the instability can be approached. We combine numerical tools to directly observe vestiges of the spinodal criticality in finite dimensional glass formers. We use the swap MonteCarlo algorithm to efficiently thermalize configurations beyond the mode-coupling crossover, and analyze their dynamics using a scheme to screen out activated processes, in spatial dimensions ranging from d=3 to d=10. We observe a strong softening of the mean-field square-root singularity in d=3 that is progressively restored as d increases above d=8, in surprisingly good agreement with perturbation theory.