Spinodal Limit Research Articles

Dynamics of nucleation in binary alloys

ABSTRACT Nucleation in binary alloys is studied in the capillary approximation of classical theory. By allowing both the size of the cluster and its composition to vary, the phase transition is investigated in a two-dimensional space. This parametrisation allows to derive diffusivities of the Fokker-Planck equation for the distribution function of clusters from the Cahn–Hilliard equation. It is shown how kinetics, together with thermodynamics, determine the direction of the nucleation current as well as the magnitude of the nucleation rate. The properties of the critical clusters and the direction of the nucleation current at the saddle point are derived for a generic model, from the binodal line to the spinodal limit. The critical clusters are found to exhibit properties that are very similar to that of non-classical theories. Once moderate supersaturation is reached, the interplay between kinetics and thermodynamics is found to invalidate the classical picture by modifying the direction of the nucleation current. The consequences on the magnitude of the rate of nucleation are discussed. The model is then applied to decomposition of FeCr solid solutions and is shown to constitute a reasonable sharp-interface approximation of the diffuse-interface theory of nucleation for the determination of both the cluster properties and the nucleation rate.

Atomic contributions to ZnO mechanical properties at negative and positive pressures

The energy-volume curve of a crystalline solid is critically examined in terms of the mechanical contributions of its constituent atoms. In addition to the usual analysis in the positive compression regime, our computational approach covers the tensile behavior in the negative pressure region up to the spinodal stability limit. Using the rich polymorphism of ZnO as a test-bed example, we propose two atomic decomposition schemes that are able to recover the bulk moduli and the critical strengths of four ZnO phases providing an intriguing interpretation of the chemical bonding network as a parallel circuit of mechanical resistors. Our scheme also allows the identification of the role played by the cation and anion in the densification of the high-pressure polymorphs and up to the material rupture points. This approach may help in the quest for tailored materials with outstanding mechanical performance.

Dislocation assisted phase separation: A phase field study

In this paper, we show the influence of dislocations on phase separation in alloys with a miscibility gap. Specifically, solute segregation to dislocations leads to spinodal phase separation even in systems with nominal compositions outside the spinodal limit. Further, when spinodal decomposition occurs along the dislocation cores, geometrically, the evolution is like that of a perturbed cylinder. Thus, unless the faster atomic mobility along the dislocation overcomes the bulk diffusion flux, the spinodal is transient and the fluctuations die down as time proceeds due to the bulk flux. We have summarised this interaction between the chemical instability and the cylindrical geometry of the instability in the form of mechanism maps. Our simulations also show the surprising phenomena of phase separation through both (i) nucleation and growth, and, (ii) spinodal decomposition, at the same time – for the case of intersecting dislocations. Finally, the prominent role played by dislocation and solute strain fields in influencing the morphology of precipitates is explored. We show that the range of parameter values chosen by us are of relevance to real alloys, and, some of the microstrucural features and morphologies agree qualitatively with recent Atom Probe Tomography (APT) results in iron based systems.

Insights into propagating surface plasmons in Ag–Cu alloy thin films: Enhancement of spin angular momentum of light

Surface plasmon polaritons (SPPs) can be supported by metal–dielectric interfaces and have been exploited for various applications. Typically, most studies deal with plasmons excited in pure metallic films or homogenous alloy thin films and the understanding of plasmon behavior in films with complex microstructures is limited. In this work, we numerically study the surface plasmons that are supported at the interface of an Ag–Cu alloy film that undergoes spinodal decomposition to produce a two-phase microstructure, when an initially compositionally homogenous alloy film (with composition within spinodal limits) is processed within the miscibility gap. We use phase-field simulated spinodally decomposed microstructures for our optical simulations to study the effect of microstructure on propagating surface plasmons in Ag–Cu alloy films. We demonstrate that the far-field response is governed principally by the composition of the alloy film and is not affected by the microstructural feature size. On the contrary, near-fields are strongly dependent on the microstructure and composition of the films. The origin of inhomogenous fields is demonstrated to be the result of constructive and destructive interference of SPPs. Finally, we demonstrate the enhancement of both transverse and longitudinal components of spin angular momentum in these phase-separated alloy films. The longitudinal components can be enhanced by more than a hundred times in the alloy films as compared to the pure metal films. This study paves the way for exploiting multi-phase alloy thin films for applications in sensing, nanomanipulation, and light modulation.

Optical cavitation in non-absorbent solutions using a continuous-wave laser via optical fiber

Optical cavitation can be induced by short pulse lasers focused into a solution with a low absorption coefficient or using a continuous-wave laser focused into highly absorbent solutions. In this work, we report the generation of cavitation bubbles in ethanol using a continuous-wave fiber optic laser with emission at 450 nm wavelength. Silver and copper nitrate nanoparticles were immobilized on the flat end-face of a multimode optical fiber tip using the photodeposition technique and then immersed into the solution. Laser light transmitted through the optical fiber is strongly absorbed by both nanoparticles causing an abrupt increase in temperature around the tip of the optical fiber, reaching the spinodal limit of ethanol (∼187 °C). At this temperature, an explosive phase transition (liquid–gas) occurs causing the generation of a microbubble, which grows until reaches its maximum radius (∼1072 μm in 132 µs) and subsequently collapses, emitting a shock wave. The dynamic behavior of the gas bubble was studied as a function of the laser power using a high-speed video camera, and the shock wave emitted immediately after the bubblés collapse was detected by a microphone. The pressure of the shock wave was analyzed photodepositing different thin films of silver nanoparticles at the tip of the optical fiber, causing optical attenuations of 1, 3, 5, and 7 dB. The experimental results obtained showed that when a thin film of copper nitrate nanoparticles was photodeposited on a film of silver nanoparticles (5 dB), the pressure of the shock wave increases up to ∼ 13-fold, in comparison, if we use only one film of silver nanoparticles. Energetic shock waves have potential applications in a variety of areas such as medicine, biological sciences, material processing, liquid microjets generation, among others.

Spinodal limits of supercooled liquid Al deduced from configuration heredity of crystal clusters

Whether one-component supercooled liquid encounters a spinodal limit at a sufficiently low temperature has been a controversial issue. To explore the homogeneous nucleation limit (HNL) in liquid Al, a series of molecular dynamics simulations have been performed, and a unique technique able to distinguish the critical nucleus from various embryos has been adopted to measure the crystal nucleation time τN of supercooled liquids and evaluate the nucleation energy barrier ΔEcri∗ in isothermal crystallization. The estimated kinetic spinodal (i.e., HNL) temperature Tks and thermodynamic spinodal temperature Tts are 0.51 Tm and 0.45 Tm, respectively. At the HNL, the nucleation energy barrier ΔEcri∗ is discovered to be very small, and a critical slowdown behavior is also observed near Tks. A careful analysis for the Stokes-Einstein (SE) relation reveals the temperature TSE of SE relation breakdown is only 0.02 Tm higher than Tks, and the occurrence of HNL is not affected by whether the SE relation breaks down or not. These results are consistent with previous reports. To some extent, the small gap between TSE and Tks can be attributed to a weak glass formation ability of liquid Al.

Spinodal and thermodynamic limit of superheat of gold

A four-parameter generalized Berthelot equation of state has been employed to determine the spinodal and the thermodynamic limit of superheat of liquid gold. It is established that gold obeys the two-parameter law of corresponding states. It is also established that the new parameters introduced in the attractive term of the equation of state are thermodynamic similarity parameters. It is shown that liquid gold can be superheated to a temperature 6719K. That is, liquid gold, under rapid heating, can be superheated to temperature 3476K above the boiling temperature without undergoing liquid-vapour phase transition. Above this temperature, liquid gold will undergo explosive boiling owing to homogeneous nucleation.

Dislocation Assisted Phase Separation: A Phase Field Study

Defects play a key role in deciding the mechanisms and kinetics of phase transformations. In this paper, we show how dislocations influence phase separation in alloys with miscibility gap. Specifically, depending on the ratio of pipe mobility to bulk mobility, it is seen that even in a system with nominal compositions outside the spinodal limit, spinodal phase separation is possible. Surprisingly, phase separation through both nucleation and growth, and spinodal decomposition, is seen concurrently (for the case of intersecting dislocations). Finally, the prominent role played by dislocations in influencing the morphology of precipitates is explored. We show that these results agree qualitatively with recent experimental results in iron based systems obtained using Atom Probe Tomography (APT).

Minimal heating rate for isobaric nucleation at the spinodal in liquids

A thermodynamic model is developed that resolves the minimal heating rate required for rapid isobaric nucleation at the spinodal limit for both homogenous and heterogenous nucleaiton. For heterogeneous nucleation, a semi-empirical correlation for the heterogeneity factor is developed.The question of how fast should isobaric heating be in order for Onset of Nucleate Boiling (ONB) to occur at spinodal conditions can be answered currently for 1 atmosphere. For water at 1 atmosphere, it was found that the minimal heating rate for heterogeneous nucleation is about 109 K/s, which is consistent with the available experimental results. The proposed model, however, allows to answer this question for a wide rage of pressure values.The effects of pressure, initial temperature, transition time into the metastable zone and heterogeneity factor are explored.It was found that the minimal heating rate decreases with the decrease of the degree of superheating and the increase in the degree of subcooling. It follows that the minimal heating rate required for reaching the spinodal decreases with the increase of pressure. For heterogeneous nucleation as a result of wall heating, it decreases with the decrease in the initial temperature.An explicit, analytical function is offered to correlate the minimal heating rate for water to the degree of subcooling at various pressure values, up to Pr∼0.5.

Liquid Metastable Precursors of Ibuprofen as Aqueous Nucleation Intermediates.

The nucleation mechanism of crystals of small organic molecules, postulated based on computer simulations, still lacks experimental evidence. In this study we designed an experimental approach to monitor the early stages of the crystallization of ibuprofen as a model system for small organic molecules. Ibuprofen undergoes liquid–liquid phase separation prior to nucleation. The binodal and spinodal limits of the corresponding liquid–liquid miscibility gap were analyzed and confirmed. An increase in viscosity sustains the kinetic stability of the dense liquid intermediate. Since the distances between ibuprofen molecules within the dense liquid phase are similar to those in the crystal forms, this dense liquid phase is identified as a precursor phase in the nucleation of ibuprofen, in which densification is followed by generation of structural order. This discovery may make it possible to enrich poorly soluble pharmaceuticals beyond classical solubility limitations in aqueous environments.

Role of induction time on carbon dioxide and methane gas hydrate kinetics

This study showed a significant variability in gas consumption rate values during gas hydrate growth at a same experimental condition for a specific experimental setup. This is important since many studies report a singular gas consumption rate or no associated statistics. Carbon dioxide hydrate gas consumption rates had of coefficient of variation of 2.7% for 204 kPa, 9.7% for 317 kPa and 9.6% for 435 kPa driving forces. The gas consumption rates decreased with increasing induction time following a first-order response. A high induction time resulted in a higher bulk liquid temperature increase meaning a greater amount of initial carbon dioxide hydrates formed. Methane hydrates did not exhibit the same behaviour of gas consumption rate with induction time. Variations in methane gas consumption rates were 4.8% for 698 kPa and 2.4% for 1564 kPa driving forces. A regression of metastable dissolution during these kinetic experiments demonstrated that the liquid mole fraction limit increased with increasing driving force. The dissolution time constant decreased with increasing mixing rate. Finally, the maximum experimental liquid mole fraction supersaturation achieved during all experiments was 75 times smaller than the thermodynamically predicted spinodal limit.

Phase Diagram of Rod–Coil Diblock Copolymer Melts

A unified phase diagram is presented for rod–coil diblock copolymer melts in the isotropic phase regime as a function of the asymmetric parameter. The study is based on free energy calculation, which incorporates three-dimensional spatial variations of the volume fraction with angular dependence. The wormlike-chain model is used in a self-consistent field treatment. Body-centered cubic, A15, hexagonal, gyroid, and lamellar structures where the rod segments are packed inside the convex rod–coil interface are found stable. As the conformational asymmetric parameter increases, the A15 phase region expands and the gyroid phase region reduces. The stability of the structures is analyzed by concepts such as packing frustration, spinodal limit, and interfacial curvature.

Explosive boiling of a metallic glass superheated by nanosecond pulse laser ablation

We report an explosive boiling in a Zr-based (Vitreloy 1) bulk metallic glass irradiated by a nanosecond pulse laser with a single shot. This critical phenomenon is accompanied by the ejection of high-temperature matter from the target and the formation of a liquid-gas spinodal pattern on the irradiated area. An analytical model reveals that the glassy target experiences the normal heating (melting) and significant superheating, eventually culminating in explosive boiling near the spinodal limit. Furthermore, the time lag of nucleation and the critical radius of vapor bubbles are theoretically predicted, which are in agreement with the experimental observations. This study provides the investigation on the instability of a metallic glass liquid near the thermodynamic critical temperature.

Optic cavitation with CW lasers: A review

The most common method to generate optic cavitation involves the focusing of short-pulsed lasers in a transparent liquid media. In this work, we review a novel method of optic cavitation that uses low power CW lasers incident in highly absorbing liquids. This novel method of cavitation is called thermocavitation. Light absorbed heats up the liquid beyond its boiling temperature (spinodal limit) in a time span of microseconds to milliseconds (depending on the optical intensity). Once the liquid is heated up to its spinodal limit (∼300 °C for pure water), the superheated water becomes unstable to random density fluctuations and an explosive phase transition to vapor takes place producing a fast-expanding vapor bubble. Eventually, the bubble collapses emitting a strong shock-wave. The bubble is always attached to the surface taking a semi-spherical shape, in contrast to that produced by pulsed lasers in transparent liquids, where the bubble is produced at the focal point. Using high speed video (105 frames/s), we study the bubble’s dynamic behavior. Finally, we show that heat diffusion determines the water superheated volume and, therefore, the amplitude of the shock wave. A full experimental characterization of thermocavitation is described.

On quantum mean-field models and their quantum annealing

This paper deals with fully connected mean-field models of quantum spins withp-body ferromagnetic interactions and a transverse field. Forp = 2 this corresponds to the quantum Curie–Weiss model (a special case of theLipkin–Meshkov–Glick model) which exhibits a second-order phase transition, while forp > 2 the transition is first order. We provide a refined analytical description both of the staticand of the dynamic properties of these models. In particular we obtain analytically theexponential rate of decay of the gap at the first-order transition. We also study the slowannealing from the pure transverse field to the pure ferromagnet (and vice versa) anddiscuss the effect of the first-order transition and of the spinodal limit of metastabilityon the residual excitation energy, both for finite and exponentially divergentannealing times. In the quantum computation perspective this quantity wouldassess the efficiency of the quantum adiabatic procedure as an approximationalgorithm.

Simple concentration-dependent pair interaction model for large-scale simulations of Fe-Cr alloys

This work is motivated by the need for large-scale simulations to extract physical information on the iron-chromium system that is a binary model alloy for ferritic steels used or proposed in many nuclear applications. From first-principles calculations and the experimental critical temperature we build a new energetic rigid lattice model based on pair interactions with concentration and temperature dependence. Density functional theory calculations in both norm-conserving and projector augmented-wave approaches have been performed. A thorough comparison of these two different ab initio techniques leads to a robust parametrization of the Fe-Cr Hamiltonian. Mean-field approximations and Monte Carlo calculations are then used to account for temperature effects. The predictions of the model are in agreement with the most recent phase diagram at all temperatures and compositions. The solubility of Cr in Fe below 700 K remains in the range of about 6 to 12%. It reproduces the transition between the ordering and demixing tendency and the spinodal decomposition limits are also in agreement with the values given in the literature.

Thermophysics of the Interfacial Region and Its Impact on Instability and Rupture of Thin Free Liquid Films

Merging of adjacent bubbles is a particularly important process in nucleate boiling heat transfer, bubbly two-phase flow in small tubes, and the mechanisms that dictate the Leidenfrost transition. The merging process is ultimately associated with the rupture of the liquid film separating two bubbles, and the stability of the liquid film dictates whether coalescence is likely to occur. This paper examines two methods of exploring how the molecular-level features of the thin film and its interfaces affect the stability of the film and its subsequent impact on bubble merging. One method is an extended molecular capillarity model that has been developed for a free liquid film bounded by two liquid–vapor interfacial regions. This model predicts that as film thickness diminishes, a point is reached at which the mean centerline density in the film is between the spinodal limits for the fluid, implying that the film core lacks intrinsic stability. This suggests that loss of intrinsic stability may be the mechanism for film rupture in some cases. The second method examined here is use of molecular dynamics simulations to examine film structure and stability. Simulations using a Lennard–Jones interaction potential for non-polar fluids and the SPC/E potential for water and salt water are examined. Results of these explorations indicate that for water–NaCl solution films, surface tension increases with increasing NaCl concentration. These predictions are shown to be consistent with measured surface-tension data for such solutions. The results also indicate that for pure water and NaCl solutions, below a threshold thickness, the surface tension decreases with film thickness. Wave interface stability theory implies that this tends to make the film less stable. The implications of the results of these investigations for bubble merging in two-phase flow and boiling processes are also examined.

The air pressure effect on the homogeneous nucleation of carbon dioxide by molecular simulation

Vapour–liquid equilibria (VLE) and the influence of an inert carrier gas on homogeneous vapour to liquid nucleation are investigated by molecular simulation for quaternary mixtures of carbon dioxide, nitrogen, oxygen, and argon. Canonical ensemble molecular dynamics simulation using the Yasuoka–Matsumoto method is applied to nucleation in supersaturated vapours that contain more carbon dioxide than in the saturated state at the dew line. Established molecular models are employed that are known to accurately reproduce the VLE of the pure fluids as well as their binary and ternary mixtures. On the basis of these models, also the quaternary VLE properties of the bulk fluid are determined with the Grand Equilibrium method. Simulation results for the carrier gas influence on the nucleation rate are compared with the classical nucleation theory (CNT) considering the ‘pressure effect’ [Phys. Rev. Lett. 101: 125703 (2008)]. It is found that the presence of air as a carrier gas decreases the nucleation rate only slightly and, in particular, to a significantly lower extent than predicted by CNT. The nucleation rate of carbon dioxide is generally underestimated by CNT, leading to a deviation between one and two orders of magnitude for pure carbon dioxide in the vicinity of the spinodal line and up to three orders of magnitude in the presence of air as a carrier gas. Furthermore, CNT predicts a temperature dependence of the nucleation rate in the spinodal limit, which cannot be confirmed by molecular simulation.

Multi-Vapor Embryos Nucleation Process and Spinodal Analyses of Expandable Superheated Water System

A homogeneous nucleation process in superheated water is studied with molecular dynamics simulation. System temperature and pressure are controlled with Langevin dynamics and the volume is variable. During the simulation, there can be seen many regions with no molecules, which are termed vapor embryos here. The vapor embryo nucleation and phase transition process of the system is studied phenomenologically. Vapor embryos violate some predictions of classical bubble dynamics theory, which indicate that it is different from bubble. Systems under different temperature are simulated to investigate the effects of superheated rate. The spinodal limit of superheated water at atmospheric pressure is determined at about 535 K.

Gas-liquid nucleation in a two dimensional system

We study the nucleation of liquid phase from a supersaturated vapor in two dimensions, where the particles interact through Lennard-Jones (LJ) pairwise potential. Using different Monte Carlo simulation methods, we calculate the free energy barrier for nucleation, the line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinodal limit). In two dimensions, a surprisingly large cutoff (r(c) > or = 7.0sigma, sigma is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff [typically 2.5sigma which is generally sufficient in three dimensional (3D) studies] leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. It is found that in two dimensions, the classical nucleation theory (CNT) fails to provide a reliable estimate of the free energy barrier. It underestimates the barrier by as much as 50% at the saturation ratio S = 1.1 (defined as S = P/P(C), where P(C) is the coexistence pressure) and at the reduced temperature T(*) = 0.427 (defined as T(*) = k(B)T/epsilon, where epsilon is the depth of the potential well). Interestingly, CNT has been found to overestimate the nucleation free energy barrier in 3D systems near the triple point. In fact, the agreement of the calculated nucleation rate with CNT is much worse in two dimensions than in three dimensions. The reason for the inadequacy of the CNT can be attributed to the noncircular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable noncircular nature remains even without any cutoff to make the simple CNT inaccurate.