We develop a stochastic approach for describing 3D-phase transformations ruled by time-dependent correlated nucleation at solid surfaces. The kinetics is expressed as a series of correlation functions and, at odds with modeling based on Poisson statistics, it is formulated in terms of actual nucleation rate. It is shown that truncation of the series up to second order terms in correlation functions provides a very good approximation of the kinetics. The time evolution of both total amount of growing phase and surface coverage by the new phase have been determined. The theory is applied to describe progressive nucleation with parabolic growth under time dependent hard-disk correlation. This approach is particularly suitable for describing electrochemical deposition by nucleation and growth where correlation effects are significant. In this ambit the effect of correlated nucleation on the behavior of kinetic quantities used to study electrodeposition has also been investigated.
The first part of the theory for the multicomponent nonisothermal nucleation is presented. On the base of analysis of the elementary acts of interation between an embryo and environment the kinetic equation is derived. This equation will be solved later and gives the nucleation rate for nonisothermal nucleation in the system with many condensating components. The orders of operators in this equation are estimated.
Several simple approximations for the evolution during the nucleation period have been presented. All of them have been compared with precise numerical solution and the errors have been estimated. All relative errors are enough small.
The profile of vapor around the droplet growing in the diffusion regime with known moving boundary have been calculated and expressed in terms of special functions.
In the standard treatment of heterogeneous nucleation on a surface, the energy of the surface is assumed to be homogeneous. Often its value is obtained from some macroscopic measurement. We ask the question what happens if we consider the surface energy to be heterogeneous. This is a straightforward generalization and may realistically be important in a number of scenarios, e.g. when the phase forming the surface is a binary alloy, solid solution, in presence of self-organized or artifically created patterns on the surface. We examine the effects of surface heterogeneity in a few scenarios in …
We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe homogeneous as well as heterogeneous nucleation starting from several general hypotheses. Thus we can investigate the influence of grain boundaries, localized impurities, or any general kind of imperfections in a systematic way. We also put forward the applicability of our model to study other physical situations such as island formation, amorphous crystallization…
Vapor condensation on nanoparticle with radius smaller than the Kelvin radius is considered as fluctuation or as the heterogeneous nucleation. The expression for steady-state heterogeneous nucleation rate is obtained. Nucleation on negatively charged nanoparticles is discussed. The report was made at 17th International Nucleation and Atmospheric Conferences, Galway, Ireland, 2007.
An effect of overlapping of exhausted regions around droplets of a new phase is analyzed. Several approximation to take overlapping into account are suggested. The small parameter responsible for convergence is extracted. The multi particle effects of overlapping are described.
In simulations of the 2D Ising model, we examine heterogeneous nucleation induced by a small impurity consisting of a line of $l$ fixed spins. As $l$ increases, we identify a limit of stability beyond which the metastable phase is not defined. We evaluate the free energy barrier for nucleation of the stable phase, and show that contrary to expectation, the barrier does not vanish on approach to the limit of stability. We also demonstrate that our values for the height of the barrier yield predictions for the nucleation time (from transition state theory) and the size of the critical cluster (f…
The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point nature of the droplets is verified using an intervention technique. The structure and symmetry of the nucleating droplets is found for a range of temperatures. We find that for deep quenches the nucleating droplets become more anisotropic and diffuse with no well defined core or surface. The environment of the nucleating droplets form randomly stacked …
Flat walls facilitate the condensation of a supersaturated vapor: Classical theory of heterogeneous nucleation predicts that the free energy barrier $ΔF_{\rm het}^*$ which needs to be overcome for the formation of sphere-cap shaped nucleation seeds is smaller than the barrier $ΔF^*_{\rm hom}$ for spherical droplets in the bulk by a factor $0<f(θ)<1$, which only depends on the contact angle $θ$. In this letter we compute both $ΔF^*_{\rm hom}$ and $ΔF^*_{\rm het}$ from Monte Carlo simulations and test the theory for the lattice gas model (for which $θ$ can be readily controlled). Even though the…
Kinetics of the first order phase transition has been investigated. The case when the droplets sizes have a limit value is considered. An analytical theory for such process has been constructed and all main characteristics of the process have been determined by rather simple approximate analytical formulas. The limit for a droplets size violates the avalanche consumption of the mother phase which is the basic feature of the first order phase transition and have been actively used in previous publications. Now one can not state that the main quantity of the already condensated substance is cont…
In principle, the answer to the posed titular question is undoubtedly 'yes.' But in practice, requisite reference data for homogeneous systems have been obtained with a treatment of intermolecular interactions that is different from that typically employed for heterogeneous systems. In this article, we assess the impact of the choice of truncation scheme when comparing water in homogeneous and inhomogeneous environments. Specifically, we use explicit free energy calculations and a simple mean field analysis to demonstrate that using the 'cut-and-shift' version of the Lennard-Jones potential (c…
Phase transformations such as freezing typically start with heterogeneous nucleation. Heterogeneous nucleation near a wetting transition, of a crystalline phase is studied. The wetting transition occurs at or near a vapour-liquid transition which occurs in a metastable fluid. The fluid is metastable with respect to crystallisation, and it is the crystallisation of this fluid phase that we are interested in. At a wetting transition a thick layer of a liquid phase forms at a surface in contact with the vapour phase. The crystalline nucleus is then immersed in this liquid layer, which reduces the…
The theoretical description of the heterogeneous nucleation kinetics is presented. This description takes into account the perturbation of the vapor phase initiated by the growing droplets. The form of the density profile around the growing droplet is analyzed which leads to some special approximations. Then the process of nucleation in the whole system is described. As the result all main characteristics of the process are determined analytically.
Unlike fluids at thermal equilibrium, biomolecular mixtures in living systems can sustain nonequilibrium steady states, in which active processes modify the conformational states of the constituent molecules. Despite qualitative similarities between liquid--liquid phase separation in these systems, the extent to which the phase-separation kinetics differ remains unclear. Here we show that inhomogeneous chemical reactions can alter the nucleation kinetics of liquid--liquid phase separation in a manner that is consistent with classical nucleation theory, but can only be rationalized by introduci…
The Kolmogorov-Johnson-Mehl-Avrami model, which is a nucleation and growth poissonian process in space, has been implemented by taking into account spatial correlation among nuclei. This is achieved through a detailed study of a system of distinguishable and correlated dots (nuclei). The probability that no dots be in a region of the space has been evaluated in terms of correlation functions. The theory has been applied to describe nucleation and growth in two dimensions under constant nucleation rate, where correlation among nuclei depends upon the size of the nucleus. We propose a simple for…
We introduce a new scheme to analyze the kinetics of homogeneous nucleation in terms of a global order parameter. Our approach is based on the application of the internal degrees of freedom formalism to derive a kinetic equation of the Kramers type formulated for a global reaction coordinate. We provide explicit expressions for the quantities and coefficients involved in the process, suitable for simulation. In addition, our picture recovers in the quasi-stationary case the transition rate obtained from the method of reactive flux. The equation we present may provide a link between theoretical…
Heterogeneous nucleation is studied by Monte Carlo simulations and phenomenological theory, using the two-dimensional lattice gas model with suitable boundary fields. A chemical inhomogeneity of length b at one boundary favors the liquid phase, while elsewhere the vapor is favored. Switching on the bulk field favoring the liquid, nucleation and growth of the liquid phase starting from the region of the chemical inhomogeneity is analyzed. Three regimes occur: for small fields, the critical droplet radius is so large that a critical droplet having the contact angle required by Young's equation i…
Inspired by recent experiments on DNA replication, we apply a one-dimensional nucleation-and-growth model to DNA-replication kinetics, focusing on how to extract the time-dependent nucleation rate I(t) and growth speed v from data. We discuss generic experimental problems, namely spatial inhomogeneity, measurement noise, and finite-size effects. After evaluating how each of these affects the measurements of I(t) and v, we give guidelines for the design of experiments. These ideas are then discussed in the context of the DNA-replication experiments.
We study the heterogeneous nucleation of Ising model on complex networks under a non-equilibrium situation where the impurities perform degree-biased motion controlled by a parameter α. Through the forward flux sampling and detailed analysis on the nucleating clusters, we find that the nucleation rate shows a nonmonotonic dependence on αfor small number of impurities, in which a maximal nucleation rate occurs at α=0 corresponding to the degree-uncorrelated random motion. Furthermore, we demonstrate the distinct features of the nucleating clusters along the pathway for different preference of i…
Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab-initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy …
By focusing a high intensity acoustic wave in liquid helium, we have observed the nucleation of solid helium inside the wave above a certain threshold in amplitude. The nucleation is a stochastic phenomenon. Its probability increases continuously from 0 to 1 in a narrow pressure interval around Pm + 4.7 bars (Pm is the melting pressure where liquid and solid helium are in equilibrium). This overpressure is larger by two to three orders of magnitude than what had been previously observed. Our result strongly supports a recent suggestion by Balibar, Mizusaki and Sasaki that, in all previous expe…
A phase eld approach is developed to model wetting and heterogeneous crystal nucleation of an undercooled pure liquid in contact with a sharp wall. We discuss various choices for the boundary condition at the wall and determine the properties of critical nuclei, including their free energy of formation and the contact angle as a function of undercooling. We nd for particular choices of boundary conditions, we may realize either an analog of the classical spherical cap model or decidedly non-classical behavior, where the contact angle decreases from its value taken at the melting point towards …
Glass-like arrest of kinetics has been observed across many magnetic first-order transitions. By traversing the two control variable H-T space, tunable coexisting fractions of arrested and equilibrium phases have been observed. We report here a fortuitous situation in a half-doped manganite sample, where these features occur by varying only temperature (T) along the H=0 line. The resistivity at 5 K rises by more than a factor of three provided second cool-down is effected from a specified intermediate T. This significant enhancement results from heterogeneous nucleation during second cool-down…
We investigate heterogeneous and homogeneous nucleation in nearest-neighbor and long-range Ising models for various quench depths. We find that the system has a true crossover from heterogeneous to homogeneous nucleation for increasing quench depth only if the interaction is sufficiently long-range. The survival curves, defined as the fraction of systems that remain in the metastable state after a given time, have qualitatively different shapes as a function of quench depth for heterogeneous and homogeneous nucleation when the interaction is short-range, but have identical shapes within the ac…
Suspensions of purely repulsive but self-propelled Brownian particles might undergo phase separation, a phenomenon that strongly resembles the phase separation of passive particles with attractions. Here we employ computer simulations to study the nucleation kinetics and the microscopic pathway active Brownian disks take in two dimensions when quenched from the homogeneous suspension to propulsion speeds beyond the binodal. We find the same qualitative behavior for the nucleation rate as a function of density as for a passive suspension undergoing liquid-vapor separation, suggesting that the s…
We study low-temperature nucleation in kinetic Ising models by analytical and simulational methods, confirming the general result for the average metastable lifetime, <tau> = A*exp(beta*Gamma) (beta = 1/kT) [E. Jordao Neves and R.H. Schonmann, Commun. Math. Phys. 137, 209 (1991)]. Contrary to common belief, we find that both A and Gamma depend significantly on the stochastic dynamic. In particular, for a ``soft'' dynamic, in which the effects of the interactions and the applied field factorize in the transition rates, Gamma does NOT simply equal the energy barrier against nucleation, as it doe…
Despite its importance in atmospheric science, much remains unknown about the microscopic mechanism of heterogeneous ice nucleation. In this work, we perform hybrid Monte Carlo simulations of the heterogeneous nucleation of ice on a range of generic surfaces, both flat and structured, in order to probe the underlying factors affecting the nucleation process. The structured surfaces we study comprise one basal plane bilayer of ice with varying lattice parameters and interaction strengths. We show that what determines the propensity for nucleation is not just the surface attraction, but also the…
One of most intriguing problems of heterogeneous crystal nucleation in droplets is its strong enhancement in the contact mode (when the foreign particle is presumably in some kind of contact with the droplet surface) compared to the immersion mode (particle immersed in the droplet). Many heterogeneous centers have different nucleation thresholds when they act in contact or immersion modes, indicating that the mechanisms may be actually different for the different modes. Underlying physical reasons for this enhancement have remained largely unclear. In this paper we present a model for the ther…
We develop a theory in order to describe the effect of relaxation in a condensed medium upon the quantum decay of a metastable liquid near the spinodal at low temperatures. We find that both the regime and the rate of quantum nucleation strongly depend on the relaxation time and its temperature behavior. The quantum nucleation rate slows down with the decrease of the relaxation time. We also discuss the low temperature experiments on cavitation in normal $^3$He and superfluid $^4$He at negative pressures. It is the sharp distinctions in the high frequency sound mode and in the temperature beha…
Kinetics of homogeneous nucleation and growth of copper precipitates under electron irradiation of Fe_{1-x}Cu_x alloys at concentrations x from 0.06 at.% to 0.4 at.% and temperatures T from 290 to 450C is studied using the kinetic Monte Carlo (KMC) simulations and the statistical theory of nucleation (STN). The conventional assumption about the similarity of mechanisms of precipitation under electron irradiation and during thermal aging is adopted. The earlier-developed ab initio model of interactions in Fe-Cu alloys is used for both the KMC simulations and the STN calculations. Values of the …
The consistent and computationally efficient stochastic statistical approach (SSA) is suggested to study kinetics of nucleation and evolution of nano-sized precipitates in alloys. An important parameter of the theory is the size of locally equilibrated regions at the nucleation stage which is estimated using the "maximum thermodynamic gain" principle suggested. For several realistic models of iron-copper alloys studied, the results of the SSA-based simulations of precipitation kinetics agree well with the kinetic Monte Carlo simulation results for all main characteristics of microstructure. Th…
The first-order reversal curve (FORC) method is applied to the two-dimensional kinetic Ising model. For the system size and magnetic field chosen, the system reverses by the homogeneous nucleation and growth of many droplets. This makes the dynamics of reversal nearly deterministic, in contrast to the strongly disordered systems previously studied by the FORC method. Consequently, the FORC diagrams appear different from those obtained in previous studies. The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of phase transformation by nucleation and growth is applied to the system. Reasonable agree…
The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The relief of the free energy with surface excesses was analyzed, the valleys and ridges were described, their mutual interaction was studied. The new possibility to change the valley of nucleation is shown. The possibility to have one common valley instead of several neighbor ones which leads to the radical change in the height of the effective activation barrier and to the new value for the nucleation rate.
We have investigated the temperature driven first order metal-insulator (M-I) transition in thin films of NdNiO$_3$ and have compared it with the bulk behavior. The M-I transition of thin films is sensitive to epitaxial strain and a partial relaxation of epitaxial strain creates an inhomogeneous strain field in the films which broadens the M-I transition. Both the thin film and the bulk samples exhibit non equilibrium features in the transition regime which are attributed to the presence of high temperature metallic phases in their supercooled state. The degree of supercooling in the thin film…
Identifying nucleation pathway is important for understanding the kinetics of first-order phase transitions in natural systems. In the present work, we study nucleation pathway of the Ising model in homogeneous and heterogeneous networks using the forward flux sampling method, and find that the nucleation processes represent distinct features along pathways for different network topologies. For homogeneous networks, there always exists a dominant nucleating cluster to which relatively small clusters are attached gradually to form the critical nucleus. For heterogeneous ones, many small isolate…
A kinetic theory of homogeneous crystal nucleation in unary droplets is presented taking into account that a crystal nucleus can form not only in the volume-based mode (with all its facets within the droplet) but also in the surface-stimulated one (with one of its facets at the droplet surface). The previously developed thermodynamics of surface-stimulated crystal nucleation rigorously showed that if at least one of the facets of the crystal is only partially wettable by its melt, then it is thermodynamically more favorable for the nucleus to form with that facet at the droplet surface rather …
Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the or…
It is surprisingly difficult to freeze water. Almost all ice that forms under "mild" conditions (temperatures > -40 degrees Celsius) requires the presence of a nucleating agent - a solid particle that facilitates the freezing process - such as clay mineral dust, soot or bacteria. In a computer simulation, the presence of such ice nucleating agents does not necessarily alleviate the difficulties associated with forming ice on accessible timescales. Nevertheless, in this work we present results from molecular dynamics simulations in which we systematically compare homogeneous and heterogeneous i…
Kinetic Turnover in the Early-Stage Nucleation of Multi-Shell Condensed Clusters
Department of Chemistry, The Hong Kong University of Science and Technology（香港科技大学化学系）；IAS Center for AI for Scientific Discoveries, The Hong Kong University of Science and Technology（香港科技大学人工智能科学发现国际高等研究院中心）
While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we d…
A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demo…
In recent decades, computer simulations have found increasingly widespread use as powerful tools of studying phase transitions in wide variety of systems. In the particular and very important case of aqueous systems, the commonly used force-fields tend to offer quite different predictions with respect to a wide range of thermodynamic and kinetic properties, including the ease of ice nucleation, the propensity to freeze at a vapor-liquid interface, and the existence of a liquid-liquid phase transition. It is thus of fundamental and practical interest to understand how different features of a gi…
Computational studies of crystal nucleation can be impacted by finite size effects, primarily due to unphysical interactions between crystalline nuclei and their periodic images. It is, however, not always feasible to systematically investigate the sensitivity of nucleation kinetics and mechanism to system size due to large computational costs of nucleation studies. Here, we use jumpy forward flux sampling to accurately compute the rates of heterogeneous ice nucleation in the vicinity of square-shaped model structureless ice nucleating particles (INPs) of different sizes, and identify three di…
Studies of nucleation generally focus on the properties of the critical cluster, but the presence of defects within the crystal lattice means that the population of nuclei necessarily evolve through a distribution of pre-critical clusters with varying degrees of structural disorder on their way to forming a growing stable crystal. To investigate the role pre-critical clusters play in nucleation, we develop a simple thermodynamic model for crystal nucleation in terms of cluster size and the degree of cluster order that allows us to alter the work of forming the pre-critical clusters without eff…
We probe through magnetization and resistivity measurements a kinetically arrested glass-like but long-range ordered magnetic state. The transformation kinetics of the magnetic field-temperature induced broad first-order transition from ferromagnetic-metallic (FMM) to antiferromagnetic-insulating (AFI) state gets hindered at low temperature in a La(0.5)Ca(0.5)MnO3 sample. A fraction of high-temperature FMM phase persists to the lowest temperature, albeit as a non-ergodic state. We present a phenomenology for this glass-like but long-range order FMM phase which devitrifies on heating and conver…
Low temperature dynamics of Ising ferromagnets under finite magnetic fields are studied in terms of quantum spin representations of stochastic evolution operators. These are constructed for the Glauber dynamic as well as for a modification of this latter, introduced by K. Park {\it et al.} in Phys. Rev. Lett. {\bf 92}, 015701 (2004). In both cases the relaxation time after a field quench is evaluated both numerically and analytically using the spectrum gap of the corresponding operators. The numerical work employs standard recursive techniques following a symmetrization of the evolution operat…
When a system undergoes a transition from a liquid to a solid phase, it passes through multiple intermediate structures before reaching the final state. However, our knowledge on the exact pathways of this process is limited, mainly due to the difficulty of realizing direct observations. Here, we experimentally study the evolution of symmetry and density for various colloidal systems during liquid-to-solid phase transitions, and visualize kinetic pathways with single-particle resolution. We observe the formation of relatively-ordered precursor structures with different symmetries, which then c…
The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov…
Nucleation is a key step in the synthesis of new material from solution. Well-established lattice-gas models can be used to gain insight into the basic physics of nucleation pathways involving a single nucleus type. In many situations a solution is supersaturated with respect to more than one precipitating phase. This can generate a population both stable and metastable nuclei on similar timescales and hence complex nucleation pathways involving competition between the two. In this study we introduce a lattice-gas model based on two types of interacting dimer representing particles in solution…
We present a computer simulation study on crystal nucleation and growth in supersaturated suspensions of mono-disperse hard spheres induced by a triangular lattice substrate. The main result is that compressed substrates are wet by the crystalline phase (the crystalline phase directly appears without any induction time), while for stretched substrates we observe heterogeneous nucleation. The shapes of the nucleated crystallites fluctuate strongly. In the case of homogeneous nucleation amorphous precursors have been observed (Phys. Rev. Lett. {\bf 105}(2):025701 (2010)). For heterogeneous nucle…
Contact freezing is a mode of atmospheric ice nucleation in which a collision between a dry ice nucleating particle (INP) and a water droplet results in considerably faster heterogeneous nucleation. The molecular mechanism of such enhancement is, however, still a mystery. While earlier studies had attributed it to collision-induced transient perturbations, recent experiments point to the pivotal role of nanoscale proximity of the INP and the free interface. By simulating heterogeneous nucleation of ice within INP-supported nanofilms of two model water-like tetrahedral liquids, we demonstrate t…
The heterogeneous condensation of a Lennard-Jones vapor onto a nanoscale seed particle is studied using molecular dynamics simulations. Measuring the nucleation rate and the height of the free energy barrier using the mean first passage time method shows that the presence of a weakly interacting seed has little effect on the work of forming very small cluster embryos but accelerates the rate by lowering the barrier for larger clusters. We suggest that this results from a competition between the energetic and entropic features of cluster formation in the bulk and at the heterogeneity. As the in…
