Spinodal Region Research Articles

Thermal chaos of charged-flat black hole via Rényi formalism

Charged-flat black holes in the Rényi extended phase space demonstrate phase structures akin to those of a van der Waals fluid in four-dimensional spacetime and mirror the behaviors of Reissner-Nordstrom-Anti-de-Sitter black holes within the standard Gibbs-Boltzmann extended phase space. This study delves into the dynamics of states initially positioned within the unstable spinodal region of the phase space associated with the charged-flat black hole when subjected to time-periodic thermal perturbations. Our analysis based on the Mel'nikov method reveals that chaos emerges when the δ parameter surpasses a critical threshold, δc. This critical quantity is dependent on the black hole charge; notably, a larger value of Q impedes the onset of chaos.Furthermore, we examine the effects of space-periodic thermal perturbations on its equilibrium state and find that chaos invariably occurs, irrespective of the perturbation amplitude. Hence, the chaotic dynamics observed in the analysis of charged-flat black holes under Rényi statistics exhibit resemblances to those of asymptotically AdS-charged black holes investigated via the Gibbs-Boltzmann formalism. This serves as yet another example of a potential and significant connection between the cosmological constant and the nonextensivity Rényi parameter.

Trade Off between Hydrodynamic and Thermodynamic Forces at the Liquid-Liquid Interface.

Viscous fingering (VF) instability has been investigated in the case of a partially miscible binary system by nonlinear numerical simulations. Partially miscible fluid systems offer the possibility of phase separation coupled with VF instability. The thermodynamics of such systems are governed by the Margules parameter (interaction parameter) as well as the fluid concentrations. Kinetics of the decomposition is also influenced by dynamical parameters such as the viscosity of the fluid, which incidentally also affects the hydrodynamic forces. Here, we explore the effects of concentration and Margules parameter in order to ascertain the trade-offs incurred between hydrodynamic and thermodynamic effects at the interface as well as the thermodynamics of the bulk. Based on the Gibb's free energy versus concentration curve, we select concentrations (i) outside spinodal and binodal regions, (ii) within binodal but outside the spinodal, and (iii) within the spinodal curve. We solve the modified Cahn-Hilliard-Hele-Shaw equation employing the COMSOL Multiphysics software. Applying high-resolution numerical simulations, we show a strong dependence of the thermodynamic forces on the concentration of the mixtures. Rapid phase separation and hence a faster rate of droplet formation have been found when the concentration lies inside the spinodal region. Further, we have investigated the correlation between the fractal dimension and dynamics of the system. The spatiotemporal studies presented in this work clearly illustrate the competition between hydrodynamic and thermodynamic forces and provide insights on the kinetics of decomposition and growth of interfacial instabilities.

Transport properties of asymmetric nuclear matter in the spinodal region

Transport properties of asymmetric nuclear matter in the spinodal region

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.

Effect of non-metallic silicon content on the microstructure and corrosion behaviour of AlCoCrFeNi high-entropy alloys

AlCoCrFeNi high-entropy alloys (HEAs) have shown excellent mechanical properties and high-temperature oxidation resistance but poor corrosion resistance owing to the high contents of the aluminium passivation film. In this study, Si was added to these alloys with the aim of improving the composition and stability of the passivation films. The microstructure and corrosion behaviour of AlCoCrFeNiSix (molar ratio x = 0, 0.1, 0.2, 0.3, and 0.4) HEAs were investigated. Dendritic and spinodal decomposition regions were observed in all five alloys. In the dendritic region, the dendritic structures transitioned from a petal shape to a dendritic shape with increasing Si content. Phase separation occurred in the spinodal decomposition region, which predominantly consisted of ordered body-centred cubic (B2) and disordered body-centred cubic (A2) phases. The size of the A2 phase decreased, and the amount of the A2 phase increased with increasing Si content. An optimised Si content could enhance the stability of Al and Cr passivation films, whereas excessive Si imposed an adverse effect by forming a Cr passivation film. The corrosion resistance of AlCoCrFeNiSi0.2 HEAs was optimum with a passive current density of 3.2 μA/cm2, which was 0.2 times that of the obtained AlCoCrFeNi HEAs without Si. The type of corrosion changed from local corrosion of AlCoCrFeNiSix (x ≤ 0.3) HEAs to general corrosion of AlCoCrFeNiSi0.4 HEAs. The corrosion mechanisms of the AlCoCrFeNi HEAs with various Si contents were elucidated.

Spinodal enhancement of fluctuations in nucleus-nucleus collisions

Subensemble Acceptance Method (SAM) [1, 2] is an essential link between measured event-by-event fluctuations and their grand canonical theoretical predictions such as lattice QCD. The method allows quantifying the global conservation law effects in fluctuations. In its basic formulation, SAM requires a sufficiently large system such as created in central nucleus-nucleus collisions and sufficient space-momentum correlations. Directly in the spinodal region of the First Order Phase Transition (FOPT) different approximations should be used that account for finite size effects. Thus, we present the generalization of SAM applicable in both the pure phases, metastable and unstable regions of the phase diagram [3]. Obtained analytic formulas indicate the enhancement of fluctuations due to crossing the spinodal region of FOPT and are tested using molecular dynamics simulations. A rather good agreement is observed. Using transport model calculations with interaction potential we show that the spinodal enhancement of fluctuations survives till the later stages of collision via the memory effect [4]. However, at low collision energies the space-momentum correlation is not strong enough for this signal to be transferred to second and third order cumulants measured in momentum subspace. This result agrees well with recent HADES data on proton number fluctuations at √SNN = 2.4 GeV which are found to be consistent with the binomial momentum space acceptance [5].

Phase separation of a magnetic fluid: Asymptotic states and nonequilibrium kinetics.

We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model, which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the nonequilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms-a diffusive growth law ℓ(t)∼t^{1/3} in the nucleation regime and hydrodynamics-driven inertial growth law ℓ(t)∼t^{2/3} in the spinodal regimes. [ℓ(t) is the average size of the condensate at time t after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected nonconserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile, and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a Janus particle to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.

Effect of Ferrite/Austenite Phase Transformation on 475 °C Embrittlement in Duplex Stainless Steel Weld

The change in hardness due to 475°C embrittlement was investigated in the melt-run GTA welds of type 329J4L duplex stainless steel. A ferritic phase was hardened with ageing at 673-773K due to the phase decomposition into Fe-rich and Cr-rich phases, while an austenitic phase was barely hardened with ageing. Hardness in a ferritic phase was rapidly increased with ageing in the base metal (BM) region, and the hardening rate was reduced in the order of BM, weld metal (WM) and heat affected zone (HAZ). The ferrite/austenite fractions in HAZ and WM were higher than that in BM, furthermore, Cr content in a ferritic phase was lowered and Ni content in it was contrarily heightened in the same order of BM, WM and HAZ. A computed phase diagram suggested that the chemical composition of a ferritic phase in each region was located in the nucleation/growth region not spinodal decomposition region, which was situated between the spinodal and binodal lines. Computer simulation of phase decomposition phenomena in a ferritic phase using phase field model revealed that phase decomposition was accelerated with an increase in Cr content and a decrease in Ni content. It followed that Cr would enhance the 475°C embrittlement and Ni would inhibit it, because of the increased/decreased driving force of the phase decomposition. The difference in 475°C embrittlement behaviour at each region could be attributed to the difference in the chemical composition of a ferritic phase caused by the ferrite/austenite phase transformation during welding.

Unexpected spinodal decomposition in as-cast eutectic high entropy alloy Al30Co10Cr30Fe15Ni15

By integrating calculation of phase diagram (CALPHAD) simulations, ab initio molecular dynamics (AIMD) and experimental validation, we shed light on the unexpected spinodal decomposition in as-cast Al30Co10Cr30Fe15Ni15 alloy, as opposed to the eutectic BCC/B2 microstructure predicted by CALPHAD. We showed that the eutectic high entropy alloy (EHEA) and spinodal decomposition (SD) may be correlated with each other. A shift from as-cast EHEA to SD can be triggered by the strong short-range ordering in the EHEA liquid phase and high configuration entropy of the metastable phase. CALPHAD showed that the low eutectic temperature of Al30Co10Cr30Fe15Ni15 alloy is stabilized by the short-range and topological ordering (SRO), rendering a small undercooling ΔT for partitionless solidification of the metastable B2 phase. AIMD calculations showed that the particular metastable-like liquid preordering might reduce interface energy between the eutectic liquid and saturated B2, facilitating metastable saturated phase formation even with a small undercooling and suppressing the eutectic reaction. The single B2 phase might have solidified in the spinodal region of the phase diagram resulting in a shift from as-cast EHEA to SD. The interplay between SD and EHEAs presents an alternative route to explore spinodal HEAs by simple as-casted samples without lengthy heat treatments for homogenization.

An inspection into the unexpected gamma precipitation in supersaturated U-13 at.% Nb subjected to aging

Phase separation of the U-Nb (13 at.%) alloy at an aging temperature of 723 K was investigated through transmission electron microscopy. Chemical redistribution initiated from a supersaturated state was identified after aging for half an hour before the discontinuous precipitation (DP) process. Such redistribution was accompanied by a fine two-phase structure and non-lamellar morphology. Among the decomposition products at this early stage, a lath-shaped Nb-rich phase was confirmed to be the bcc (γ) phase, with Nb content in the range of 35∼45 at.%. Meanwhile, discrete regions of much smaller size were detected to bare an Nb content approaching the equilibrium of the α phase. It is envisaged that the γ precipitation was a preceding event of the α. Thermodynamic estimation was carried out to reveal the decomposition mechanism responsible for this unexpected behavior. The results were in favor of a nucleation and growth mechanism over the spinodal decomposition. These results provide a deeper understanding and a new sight into the aging phenomenon of U-13Nb alloys, which are also worth consideration in other binary systems slightly outside the coherent spinodal regions such as Fe-20Cr.

Unraveling the two-stage precipitation mechanism in a hierarchical-structured fcc/L21 high-entropy alloy: Experiments and analytical modeling

Understanding the phase stability and precipitation mechanisms is crucial for engineering multiphase nanostructured alloys with optimal mechanical properties. In this work, we studied the formation and temporal evolution of nanoprecipitates and their effect on mechanical properties of an fcc/L21 eutectic high-entropy alloy through a combination of experiments and analytical modeling. Aging the alloy at 1023 K results in the precipitation of coherent L12 nanoparticles in the fcc phase and coherent bcc nanoparticles in the L21 phase, leading to the formation of an fcc/L12 + L21/bcc hierarchical structure. Notably, the scanning transmission electron microscopy (STEM) results reveal that the precipitation in both the fcc and L21 phases is not through a one-step nucleation, but a two-stage transformation consisting of an initial chemical separation via spinodal decomposition and subsequent structural ordering/disordering. The Gibbs free energy diagrams of the fcc and L21 phases were modeled through numerical techniques, and the spinodal decomposition regions of the two systems at different temperatures were calculated. Based on the modeling results, we discussed the phase stability and thermodynamics of spinodal decomposition of the two phases. In addition, the formation of hierarchical structure substantially enhances the strength of the alloy. Modeling of the strengthening mechanisms reveals that the order strengthening of L12 nanoparticles plays a major role in enhancing the yield strength of the alloy, whereas the contribution from the bcc nanoparticles can be negligible. Our findings provide insights into the phase stability, precipitation and strengthening mechanisms of hierarchical-structured alloys.

Superferromagnetic Sensors

The strong ferromagnetic nanoparticles are analyzed within the band structure-based shell model, accounting for discrete quantum levels of conducting electrons. As is demonstrated, such an approach allows for the description of the observed superparamagnetic features of these nanocrystals. Assemblies of such superparamagnets incorporated into nonmagnetic insulators, semiconductors, or metallic substrates are shown to display ferromagnetic coupling, resulting in a superferromagnetic ordering at sufficiently dense packing. Properties of such metamaterials are investigated by making use of the randomly jumping interacting moments model, accounting for quantum fluctuations induced by the discrete electronic levels and disorder. Employing the mean-field treatment for such superparamagnetic assemblies, we obtain the magnetic state equation, indicating conditions for an unstable behavior. Respectively, magnetic spinodal regions and critical points occur on the magnetic phase diagram of such ensembles. The respective magnetodynamics exhibit jerky behavior expressed as erratic stochastic jumps in magnetic induction curves. At critical points, magnetodynamics displays the features of self-organized criticality. Analyses of magnetic noise correlations are proposed as model-independent analytical tools employed in order to specify, quantify, and analyze the magnetic structure and origin of superferromagnetism. We discuss some results for a sensor-mode application of superferromagnetic reactivity associated with spatially local external fields, e.g., the detection of magnetic particles. The transport of electric charge carriers between superparamagnetic particles is considered tunneling and Landau-level state dynamics. The tunneling magnetoresistance is predicted to grow noticeably with decreasing nanomagnet size. The giant magnetoresistance is determined by the ratio of the respective times of flight and relaxation and can be significant at room temperature. Favorable designs for superferromagnetic systems with sensor implications are revealed.

Shear viscosity of nuclear matter in the spinodal region

Based on IBUU simulations calibrated by previous efforts of the transport model evaluation project, we have studied the specific shear viscosity $\eta/s$ of nuclear matter in the spinodal region using the Green-Kubo method. With the momentum-independent mean-field potential which reproduces reasonably well empirical nuclear matter properties and nuclear phase diagram, we have generated dynamically stable and thermalized nuclear cluster systems in a box with the periodic boundary condition. Extensive results of the $\eta/s$ at different average densities and temperatures in uniform and non-uniform systems are compared, and we found that the shear viscosity is smaller with nuclear clusters due to the enhanced correlation of the energy-momentum tensor and the stronger collision effect. The temperature dependence of the $\eta/s$ has a minimum only at low average densities of $\rho<0.3\rho_0$. The present study serves as a rigorous baseline calculation of the $\eta/s$ in nuclear systems with clusters, and helps to understand the relation between the shear viscosity and the nuclear phase diagram.

Elastic-stripe formation at electronic transitions

We investigate the possibility of a striped inhomoegenous phase occurring as an electronic system with an order parameter linearly coupled to the elastic degrees of freedom is tuned through the electronic phase transition. We find that in finite systems where boundary conditions create an eleastic incompatibility, a stripe pattern may emerge in the vicinity of the electronic transition. Stripes are stabilized when the gained elastic energy overcomes the typical electronic and domain wall energy costs. In thin film geometries, the stripes are found to extend across the entire depth of the system. We also study the behavior of the phase fraction across the spinodal region of a first order phase transition. The orientation of stripes and the possibility of more complicated patterns is also discussed.

Self-organized vertical multilayer structures in spinodally decomposed TiO2-VO2 films on glass substrates

In this study, we investigated the formation of vertical multilayer structures via phase separation in TiO2-VO2 films on glass substrates. A key point for the formation is to utilize the anisotropy in the spinodal decomposition of the system. Solid-solution films of Ti0.3V0.7O2 were grown on quartz glass substrates using pulsed laser deposition and annealed inside the spinodal region. X-ray diffraction, scanning transmission electron microscopy (STEM) measurements showed that spinodal decomposition occurs along the c-axis, and multilayer structures composed of alternating stacking of Ti- and V-rich phases were formed in the annealed film. In addition, STEM observations revealed that the multilayer structures were aligned vertically on the surface to the glass substrates. In resistivity measurements the annealed film showed a metal-insulator transition with the transition temperature lower than TixV1-xO2 bulk due to the strain effect induced by the coherent interface between Ti- and V-rich phases. The overall results clearly show that vertical multilayer structures were formed via spinodal decomposition along the c-axis direction in the Ti0.3V0.7O2 film on the glass substrates. Our study indicates that anisotropy in the spinodal decomposition is an effective approach for the formation of self-organized vertical multilayer structures in Ti0.3V0.7O2 films on glass substrates, and provides useful guidelines for generating self-organized novel nanostructures on amorphous substrates in oxide films.

A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains

The Navier-Stokes-Korteweg (NSK) system is a classical diffuse interface model which is based on van der Waals' theory of capillarity. Diffuse interface methods have gained much interest to model two-phase flow in porous media. However, for the numerical solution of the NSK equations two major challenges have to be faced. First, an extended numerical stencil is required due to a third-order term in the linear momentum and the total energy equations. In addition, the dispersive contribution in the linear momentum equations prevents the straightforward use of contact angle boundary conditions. Secondly, any real gas equation of state is based on a non-convex Helmholtz free energy potential which may cause the eigenvalues of the Jacobian of the first-order fluxes to become imaginary numbers inside the spinodal region.In this work, a thermodynamically consistent relaxation model is presented which is used to approximate the NSK equations. The model is complimented by thermodynamically consistent non-equilibrium boundary conditions which take contact angle effects into account. Due to the relaxation approach, the contribution of the Korteweg tensor in the linear momentum and total energy equations can be reduced to first-order terms which enables a straightforward implementation of contact angle boundary conditions in a numerical scheme. Moreover, the definition of a modified pressure function enables to formulate first-order fluxes which remain strictly hyperbolic in the entire spinodal region. The present work is a generalization of a previously presented parabolic relaxation model for the isothermal NSK equations.A high-order discontinuous Galerkin spectral element method which supports curved elements and hanging nodes is employed to discretize the system. The relaxation model and its corresponding boundary conditions are validated using solutions of the original NSK model and analytical results for one-, two- and three-dimensional test cases. The simulation of a spinodal decomposition in a three-dimensional porous structure underlines the capability of the presented approach.

On the understanding of a cryogenic two-phase LOX/GH2 flame: Parametric sensitivity, characteristic scaling and phase instability

This study concerns the cryogenic hydrogen combustion in subcritical pressure conditions, with practical relevance to rocket engine applications. A cryogenic two-phase flame in the counterflow configuration is calculated and analyzed with the consideration of real-fluid effects and heat/mass transfer across the liquid-gas interface. The effects of pressure, strain rate, fuel inlet temperature, and heat loss on the flame characteristic behaviors are examined. It is found that the vaporization rate of liquid oxidizer scales with the square-root of pressure (p) times strain rate (ast), and is not a limiting factor for combustion. The total heat release scales with past at lower strain rates while with p4/5ast1/3 at higher strain rates. The significant results on the phase-stability of cryogenic flame are also established. It is found that the unstable phase, in terms of vapor-liquid equilibrium, arises in the vicinity of the liquid-gas interface; however, all unstable-phase states still stay in the metastable region of the phase diagram. For all the flame solutions considered in this study, no thermochemical state enters the spinodal region.

Phase-field simulation for the formation of porous microstructures due to phase separation in polymer solutions on substrates with different wettabilities

The porous microstructure has been widely observed in a variety of polymer solutions that have been broadly applied in many industry fields. Phase separation is one of the common mechanisms for the formation of the porous microstructure in binary polymeric mixtures. Previous studies for the formation of porous microstructures mostly focus on the separation of the bulk phase. However, there is a paucity of investigation for the phase separation of polymer mixtures contacting the solid substrate. When the polymeric liquid mixtures interact with the solid substrate, the wetting boundary condition has to be taken into account. In this work, we present a phase-field model which is coupled with the wetting boundary condition to study the phase separation in binary polymer solutions. Our consideration is based on the polymerization-induced phase separation, and thermally induced phase separation by using the Flory–Huggins model. By taking the wetting effect into account, we find that polymer droplets spontaneously occur in the microstructure, even though the bulk composition is outside the spinodal region. This phenomenon is caused by the surface composition resulting from the wetting effect that was often overlooked in literature. For the phase separation in the binary polymer mixture, we also study the impact of the temperature gradient on the microstructural evolution. The porosity, the number of droplets, and the mean radius of the droplets are rationalized with the temperature gradient.

Linear Stability Analysis of the Cahn–Hilliard Equation in Spinodal Region

We study a linear stability analysis for the Cahn–Hilliard (CH) equation at critical and off-critical compositions. The CH equation is solved by the linearly stabilized splitting scheme and the Fourier-spectral method. We define the analytic and numerical growth rates and compare these growth rates with respect to the different average levels. In this study, the linear stability analysis is conducted by classifying three average levels such as zero average, spinodal average, and near critical point levels of free energy function, in the one-dimensional (1D) space. The numerical results provide insight for the dynamics of CH equation at critical and off-critical compositions.

Au composition dependent order-disorder transitions of Fe−Pt intermetallic compounds: Experiments and thermodynamic analysis

The Fe−Pt intermetallic nanocrystals exhibit good chemical stability, unique magnetic and catalytic properties, but suffer from the ordering difficulty. It has been found that the addition of Au can promote the disorder-order transitions, but the mechanism is far from being well understood. In this work, the phase equilibria and phase transformations of the Fe−Pt−Au alloys have been experimentally investigated and thermodynamically analyzed. The results show that the driving forces for both the L10_FePt and L12_FePt3 ordering are so weak that the homogeneous nucleation in the disordered fcc matrix is difficult, while a heterogeneous nucleation mechanism on the pre-existed phase boundary is preferred. On the other hand, there exists a metastable ternary miscibility gap between αAu and fcc-FePt or fcc-FePt3, and accordingly, when Au content is properly designed in the spinodal region, the enrichment of Au can take place spontaneously throughout a fcc Fe−Pt−Au structure during annealing. The segregation of αAu in the Fe−Pt−Au alloys can further accelerate the diffusion of Pt and Fe atoms, facilitate the nucleation of the ordered L10_FePt and L12_FePt3 phases, and stimulate the ordering process. These results correlate the Au addition with the ordering of Fe−Pt intermetallics and further the magnetic and catalytic properties, and it is thus expected to provide guidance for a rational alloy design of Fe–Pt–Au materials.