Suppression of ice nucleation in supercooled water under temperature gradients

Understanding the behaviours of ice nucleation in non-isothermal conditions is of great importance for the preparation and retention of supercooled water. Here ice nucleation in supercooled water under temperature gradients is analyzed thermodynamically based on classical nucleation theory (CNT). Given that the free energy barrier for nucleation is dependent on temperature, different from a uniform temperature usually used in CNT, an assumption of linear temperature distribution in the ice nucleus was made and taken into consideration in analysis. The critical radius of the ice nucleus for nucleation and the corresponding nucleation model in the presence of a temperature gradient were obtained. It is observed that the critical radius is determined not only by the degree of supercooling, the only dependence in CNT, but also by the temperature gradient and even the Young's contact angle. Effects of temperature gradient on the change in free energy, critical radius, nucleation barrier and nucleation rate with different contact angles and degrees of supercooling are illustrated successively. The results show that a temperature gradient will increase the nucleation barrier and decrease the nucleation rate, particularly in the cases of large contact angle and low degree of supercooling. In addition, there is a critical temperature gradient for a given degree of supercooling and contact angle, at the higher of which the nucleation can be suppressed completely.     

Scaling regimes for second layer nucleation

Nucleation on top of two-dimensional islands with step edge barriers is investigated using scaling arguments. The nucleation rate is expressed in terms of three basic time scales: the time interval between deposition events, the residence time of atoms on the island, and the encounter time required for atoms forming a stable nucleus to meet. Application to the problem of second layer nucleation on growing first layer islands yields a sequence of scaling regimes with different scaling exponents relating the critical island size, at which nucleation takes place, to the diffusion and deposition rates. Second layer nucleation is fluctuation-dominated, in the sense that the typical number of atoms on the island is small compared to , when the first layer island density exponent satisfies . The upper critical nucleus size, above which the conventional mean field theory of second layer nucleation is valid, increases with decreasing dimensionality. In the related case of nucleation on top of multilayer mounds fluctuation-dominated and mean field like regimes coexist for arbitrary values of the critical nucleus size . Received 4 September 2000     

大块非晶临界冷却速率的非等温转变计算模型

在非等温转变理论以及非稳态形核理论基础上提出了计算大块非晶合金连续冷却转变曲线和 临界冷却速率的新模型,以用于评估合金的非晶形成能力. 依据此模型对Zr基和Pd基8种合金 进行了计算，计算结果与实验值符合较好. 计算结果表明，影响临界冷却速率的主要因素为 黏度、临界形核功和临界结晶分数. 随着黏度增大，临界冷却速率降低；随临界形核功增大 ，临界冷却速率急剧降低；随临界结晶分数增大，临界冷却速率起初降低较快，达到一定程 度后下降速率趋于缓慢. 关键词： 临界冷却速率 非晶形成能力 大块非晶 连续冷却转变曲线     

Homogeneous nucleation and growth of droplets in vapours

The theory of homogeneous nucleation of liquid drops in supersaturated vapours is reviewed. A new kinetic treatment which accounts for the heating of the growing clusters due to the latent heat of condensation is presented, and the irreversible thermodynamics of non-isothermal nucleation discussed. It is found that growing clusters are generally colder than the surrounding vapour during their sub-critical growth period.

Time dependent nucleation is discussed and a simple estimate for the time-lag in establishing the steady state is given. The nucleation in cloud chambers expanding with constant speed is discussed in detail, and the number of droplets formed and their final mean size is calculated as a function of the terminal expansion ratio. Re-evaporation of nucleated clusters is discussed. Numerical results are given for a number of typical situations in experiments on water-vapour. These results for the nucleation rate as corrected by Lothe and Pound predict much lower ‘critical’ expansion ratios than indicated by the limited experimental data available, even when the non-isothermal theory is used.

To restore agreement between theory and experiments the surface tension for small droplets (?100 molecules) could be increased some 15% above that of the bulk liquid, or the pre-exponential in the nucleation rate could be decreased by some 10^?15. This latter expedient roughly corresponds to use of the ‘classical’ instead of the Lothe-Pound nucleation rate. These two alterations would, however, affect the theoretical curves in different manners and careful experiments could possibly distinguish between them.     

Crystal nucleation of colloidal suspensions under shear

We use Brownian dynamics simulations in combination with the umbrella sampling technique to study the effect of shear flow on homogeneous crystal nucleation. We find that a homogeneous shear rate leads to a significant suppression of the crystal nucleation rate and to an increase of the size of the critical nucleus. A simple, phenomenological extension of classical nucleation theory accounts for these observations. The orientation of the crystal nucleus is tilted with respect to the shear direction.     

Decline of nucleation in the heating process with a high heating rate

The effect of the heating rate on the nucleation of metallic glass in a rapid heating process starting from the glass transition temperature is investigated. The critical nucleus radius increases with the increase of the temperature of the undercooling liquid. If the increment rate of the critical nucleus radius, owing to the heating process, is higher than the growth rate of the nuclei, the nuclei generated at the low temperature will become the embryos at the high temperature. This means that the high heating rate can make no nucleation happen in the heating process. In consideration of the interfacial energy, the growth rate of the nuclei increases with the increase of their size and the growth rate of the critical nucleus is zero. Thus, the lower heating rate can also make the nuclei decline partially. Finally, this theory is used to analyze the nucleation process during laser remelting metallic glass.     

Nucleation and creep of vortices in superfluids and clean superconductors

The paper is devoted to vortex nucleation in uniform and nonuniform superflows in superfluids, and to creep of vortices trapped by twin boundaries and columnar defects in isotropic and anisotropic superconductors. The shape of a nuclated loop which yields the maximal nucleation rate is defined from the balance of the Lorentz and the line-tension forces. If the trapping energy is small, the contact angle at which the vortex line meets the plane of the twin-boundary or the axis of the columnar defect is also small. This may strongly enhance the rate of thermal nucleation and especially of quantum nucleation. In the analysis of quantum tunnelling it was assumed that the vortex has no mass and its motion is governed by the Magnus force, as expected for superfluids and very pure superconductors. Quantum nucleation rate from the traditional quasiclassical theory of macroscopic tunnelling is compared with the nucleation rate derived from the Gross-Pitaevskii theory of a weakly nonideal Bose-gas.     

A new theory of the solid-state growth of embryos during nucleation: the fundamental role of interfacial mobility

One of the major challenges in nucleation theory is to explain the kinetic pathway allowing multicomponent precipitates to grow until they reach stability. This problem is particularly challenging when the supersaturation is low, so that the critical size of nucleation is large and requires the condensation of thousands of atoms. A new theory is proposed to explain the growth of embryos before they reach the critical size of nucleation. This theory is not a substitute of the classical nucleation theory, but a complement aiming to understand the kinetic pathway allowing unstable embryos to grow at the expense of their neighbours. The theory stands on the strong interactions between embryos. The latter may exchange atoms via impingement and coarsening, which are possible when there are no concentration gradients between the embryos. This condition is supposed to be met during the unstable growth regime of nucleation considering that the growth is limited by the interface during that period. Assuming that the embryos behave in a collective manner when they are grouped in a cloud, we show that the growth velocity of the most active embryos will be limited only by their interfacial mobility and the available driving force.     

Liquid nucleation at superheated grain boundaries

Grain boundaries with relatively low energies can be superheated above the melting temperature and eventually melt by heterogeneous nucleation of liquid droplets. We propose a thermodynamic model of this process based on the sharp-interface approximation with a disjoining potential. The distinct feature of the model is its ability to predict the shape and size of the critical nucleus by using a variational approach. The model reduces to the classical nucleation theory in the limit of large nuclei but is more general and remains valid for small nuclei. Contrary to the classical nucleation theory, the model predicts the existence of a critical temperature of superheating and offers a simple formula for its calculation. The model is tested against molecular dynamic simulations in which liquid nuclei at a superheated boundary were obtained by an adiabatic trapping procedure. The simulation results demonstrate a reassuring consistency with the model.     

Attainable superheating of solutions of cryogenic liquids

The kinetics of spontaneous boiling-up of superheated binary solutions of cryogenic liquids is studied. Within the framework of the Kramers-Zeldovich method, an expression is obtained for the steady state rate of homogeneous nucleation in a solution that takes into account free-molecular and diffusion regimes of the substance supply to a growing bubble. Viscous and inertial forces are also taken into account in the study of the nucleus growth dynamics. The work of critical nucleus formation is determined within the framework of the Gibbs and van der Waals capillarity theories. The dependence of the surface tension of critical bubbles in the solution on their size is investigated. The temperature of attainable superheating and nucleation rates in superheated solutions of cryogenic liquids with complete or partial solubility of the components are determined by a method of lifetime measurement. The experiments were conducted in a wide range of pressures and solution concentrations. The measurement results are compared with the theory of homogeneous nucleation taking or not taking into account the size effect in nucleation. It has been found that, by taking into account the size dependence of the surface tension of a nucleus, better agreement between the theory and experiment is obtained. The boundary of essential instability of the solution, that is, the diffusion spinodal, is computed.     

Adsorption and nucleation on smooth surfaces

The nucleation and growth of condensate nuclei on smooth surfaces, e.g., an immiscible liquid or a smooth solid, can occur both by the direct addition of molecules from the vapor and from those adsorbed on the substrate. We show how to generalize nucleation theory to allow for the simultaneous occurrence of both mechanisms. The vapor-condensate-substrate interfacial forces, the contact angle, the critical supersaturation, and the coefficient in the adsorption isotherm are different ways of expressing the affinity between vapor molecules and the substrate surface. The critical supersaturations for nucleation on the surface of an immiscible liquid and nucleation on the surface of a perfectly smooth solid are predicted in terms of these parameters and the relationships among them. For most values of these parameters we find that adsorbed molecules are usually far more important to the nucleation process than those in the vapor phase.     

Nucleation theory and the cloud-point

On the basis of a recent proposal for the droplet distribution in the lattice-gas model, we evaluate completion times and scaled supersaturations which are consistent with existing observations in cloud-point experiments near the critical temperature. Some general concepts in nucleation theory are also reviewed.     

Interplay between structure and size in a critical crystal nucleus

We study the kinetics of crystal nucleation of an undercooled Lennard-Jones liquid using various path-sampling methods. We obtain the rate constant and elucidate the pathways for crystal nucleation. Analysis of the path ensemble reveals that crystal nucleation occurs along many different pathways, in which critical solid nuclei can be small, compact, and face centered cubic, but also large, less ordered, and more body centered cubic. The reaction coordinate thus includes, besides the cluster size, also the quality of the crystal structure.     

Metastability and nucleation in capillary condensation

This paper is devoted to thermally activated dynamics of capillary condensation. On the basis of a simple model we identify the critical nucleus involved in the transition mechanism and calculate the nucleation barrier from which we obtain information on the nucleation time. Close to the condensation point, the theory predicts extremely large energy barriers leading to strong metastabilities, long time dependencies, and large hysteresis in agreement with experimental observations in mesoporous media. The validity of the model is assessed using a numerical simulation of a time-dependent Ginzburg-Landau model for the confined system.     

The classical nucleation rate in two dimensions

In many systems in condensed matter physics and quantum field theory, first order phase transitions are initiated by the nucleation of bubbles of the stable phase. In homogeneous nucleation theory the nucleation rate can be written in the form of the Arrhenius law: . Here is the energy of the critical bubble, and the prefactor can be expressed in terms of the determinant of the operator of fluctuations near the critical bubble state. In general it is not possible to find explicit expressions for and . If the difference between the energies of the stable and metastable vacua is small, the constant can be determined within the leading approximation in , which is an extension of the ”thin wall approximation”. We have done this calculation for the case of a model with a real-valued order parameter in two dimensions. Received: 11 September 2002 / Revised version: 30 October 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: munsteg@uni-muenster.de RID="b" ID="b" e-mail: rut@ifttp.bas-net.by ^* Present address: Universit?t Essen, Fachbereich 7 - Physik, Universit?tsstr. 5, 45117 Essen, Germany     

Fusion of the extended modified liquid drop model for nucleation and dynamical nucleation theory

We present a new phenomenological approach to nucleation, based on the combination of the "extended modified liquid drop" model and dynamical nucleation theory. The new model proposes a new cluster definition, which properly includes the effect of fluctuations, and it is consistent both thermodynamically and kinetically. The model is able to predict successfully the free energy of formation of the critical nucleus, using only macroscopic thermodynamic properties. It also accounts for the spinodal and provides excellent agreement with the result of recent simulations.     

Initial nucleation stages and properties of CuCl nanoparticles in glasses

The time variation and temperature dependence of a CuCl phase nucleation in a glass was studied by exciton spectroscopy. The phase formation kinetics at three temperatures was measured. A time delay in attaining a stationary rate of the new phase growth was observed at all temperatures, in agreement with the Zeldovich theory. The kinetic parameters of the CuCl phase formation were determined in the initial stage, when the critical nuclei possessing a zero surface energy (and an effective radius below 1.3 nm) appear in the glass matrix. The first-order phase transition in the new phase is 200 K below the melting temperature of CuCl single crystals. The temperature dependence of the CuCl phase nucleation rate reveals the second and third stages of the new phase formation. The activation energies for diffusion of the CuCl phase components in the glass matrix are determined.     

Homogeneous two-dimensional nucleation of guest-free silicon clathrates

The difficulty in synthesizing guest-free semiconductor clathrates complicates the process of determining how these cage-like structures form. This work studies the microscopic mechanism of the nucleation of guest-free Si₁₃₆ clathrate using molecular dynamics simulations with the Stillinger–Weber potential. The homogeneous nucleation of Si₁₃₆, which is realized in a narrow negative pressure range before liquid cavitation, exhibits the characteristic feature of the two-dimensional (2D) mode. The critical nucleus is composed of one to two five-membered rings, and the nucleation barrier is close to 1 k_BT. According to a thermodynamic model based on atomistic nucleation theory, the effective binding energy associated with the formation of 2D critical nuclei is significantly low, which is responsible for the low nucleation barrier of Si₁₃₆ clathrate. In the post-nucleation period, the critical nucleus preferentially grows into a dodecahedron, and the latter continuously grows with sharing face along 〈1 1 0〉.     

Theory of anomalous critical-cluster content in high-pressure binary nucleation

Nucleation experiments in binary (a-b) mixtures, when component a is supersaturated and b (carrier gas) is undersaturated, reveal that for some mixtures at high pressures the a content of the critical cluster dramatically decreases with pressure contrary to expectations based on classical nucleation theory. We show that this phenomenon is a manifestation of the dominant role of the unlike interactions at high pressures resulting in the negative partial molar volume of component a in the vapor phase beyond the compensation pressure. The analysis is based on the pressure nucleation theorem for multicomponent systems which is invariant to a nucleation model.     

Second-phase nucleation on an edge dislocation

A model for nucleation of second phase at or around a dislocation in a crystalline solid is considered. The model employs the Ginzburg–Landau theory of phase transitions comprising the sextic term in the order parameter (η⁶) in the Landau free energy. The ground state solution of the linearised time-independent Ginzburg–Landau equation is derived, through which the spatial variation of the order parameter is delineated. Moreover, a generic phase diagram indicating tricritical behaviour near and away from the dislocation is depicted. The relation between classical nucleation theory and the Ginzburg–Landau approach is discussed, for which the critical formation energy of the nucleus is related to the maximum of the Landau potential energy. A numerical example illustrating the application of the model to the case of nucleation of hydrides in zirconium alloys is provided.