Finite-size effects on nucleation in a first-order phase transition

We discuss finite-size effects on homogeneous nucleation in first-order phase transitions. We study their implications for cosmological phase transitions and to the hadronization of a quark–gluon plasma generated in high-energy heavy ion collisions. Very general arguments allow us to show that the finite size of the early universe has virtually no relevance in the process of nucleation and in the growth of cosmological bubbles during the primordial quark–hadron and the electroweak phase transitions. In the case of high-energy heavy ion collisions, finite-size effects play an important role in the late-stage growth of hadronic bubbles.     

Monte-Carlo study of scaling exponents of rough surfaces and correlated percolation

In spallation neutron sources, liquid mercury, upon adsorbing the proton beam, is exhibited to large thermal and pressure shocks. These local changes in the state of mercury can cause the formation of unstable bubbles in the liquid, which can damage at their collapse the enclosing the liquid solid material. While there are methods to deal with the pressure shock, the local temperature shock cannot be avoided. In our paper we calculated the work of the critical cluster formation (for mercury micro-bubbles) together with the rate of their formation (nucleation rate). It is shown that the homogeneous nucleation rates are very low at the considered process conditions even after adsorbing several proton pulses, therefore, the probability of temperature induced homogeneous bubble nucleation is negligible.     

金属熔体中气泡形核的理论分析

引入界面接触角，考虑表面张力对气泡形貌的影响，以熔体中均质形核、夹杂物的平表面上异质形核和圆锥形凹坑内异质形核三种典型模型对气泡形核机理进行理论研究.研究发现，三种形核模型下具有相等的微米量级的气泡临界形核半径，并随气压的增大而减小.结果表明，用以制备藕状规则多孔金属的Gasar工艺中能够形成的最小气孔的直径为微米量级(0.1—1.0 MPa气压).在圆锥形凹坑内异质形核时存在最佳圆锥顶角(对应最小气泡体积)，其值与气压无关，只随接触角的增大而增大.在接触角处于90°—180°范围内，最佳圆锥顶角下圆锥形 关键词： 气泡 形核 多孔金属 Gasar     

Analytical calculation of the nucleation rate for first order phase transitions beyond the thin wall approximation

First order phase transitions in general proceed via nucleation of bubbles. A theoretical basis for the calculation of the nucleation rate is given by the homogeneous nucleation theory of Langer and its field theoretical version of Callan and Coleman. We have calculated the nucleation rate beyond the thin wall approximation by expanding the bubble solution and the fluctuation determinant in powers of the asymmetry parameter. The result is expressed in terms of physical model parameters. Received: 18 August 1999 / Published online: 14 October 1999     

Quantum meaning of classical (field) theory for fermi systems

We investigate the cosmological consequences of a phase transition which is driven primarily by slow nucleation of bubbles of the new phase via the effectively zero temperature quantum tunneling process of Coleman and Callan. These bubbles will asymptotically fill an arbitrarily large fraction of the space, yet they never percolate. Instead they form finite clusters, with each cluster dominated by a single largest bubble. The large scale thermalization required by the original “inflationary universe” scenario does not take place. The Coleman-De Luccia formalism for bubble formation in curved space is reviewed, with minor extensions. We argue that a single uncollided bubble would contain much less total entropy than the observed universe, unless the Higgs field potential involves widely disparate mass scales, as in the new inflationary universe scenario. We also argue that finite clusters are unlikely to yield a homogeneous and isotropic region containing sufficient entropy. Thus, unless the Higgs potential has the special form required by the new inflationary scenario, it appears quite implausible that there was such a phase transition in our past.     

A study on the primary and secondary nucleation of ice by power ultrasound

Several different investigations have been carried out to study the primary and secondary nucleation of ice by sonocrystallisation. Firstly, the primary nucleation of discrete ice crystals in a supercooled sucrose solution has been observed. For increasing concentrations of sucrose solutions from 0 to 45 wt%, the nucleation temperature consistently occurs at a higher nucleation temperature in the presence of ultrasound. The nucleation temperature also increases as the power output and duty cycle of a commercial ultrasonic horn are increased. Snap shot images of the bubble clouds obtained from the ultrasonic horn also show that the number of bubbles appears to increase as the ultrasonic output is increased. This suggests that the nucleation of ice is related to the power output and number of cavitation bubbles. The effect of a single bubble on the sonocrystallisation of ice is discussed. High-speed movies (1120 fps) have shown that the crystallisation appears to occur in the immediate vicinity of the single bubble. In most cases, many crystals are observed and it is not known whether a single ice crystal is being fragmented by the bubble or whether many crystals are being initiated. The bubble appears to undergo a dancing regime, frequently splitting and rejoining and also emitting some small microbubbles. A study on the secondary nucleation of ice in sucrose solutions has been carried out using a unique ultrasonic cold stage device. Images taken using a microscope system show that the pre-existing ice dendrite crystals can be broken up into smaller fragments by an ultrasonic field. Cavitation bubbles appear to be important during the fragmentation process, possibly melting any ice crystals in their path. Flow patterns around cavitation bubbles have also been observed, and these may be responsible for the fragmentation of ice crystals.     

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.     

Cavitation in superfluid helium-4 at low temperature

We have studied the nucleation of bubbles in pure superfluid helium-4 at temperatures down to 65 mK. We have found that the nucleation is a stochastic process, and that at temperatures below 600 mK the nucleation rate is independent of temperature. These results are consistent with the assumption that the nucleation takes place via quantum tunneling. Received: 15 November 1997 / Received in final form: 19 December 1997 / Accepted: 22 January 1998     

Vortex nucleation by collapsing bubbles in Bose-Einstein condensates

Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be 28+/-1 healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.     

Boiling-up of liquid argon at high superheatings under the impact of weak ultrasonic fields

The technique of lifetime measurement for metastable liquid and continuous depressurization technique were applied for study of kinetics of spontaneous cavitation in superheated liquid argon under impact of weak ultrasonic fields. It was demonstrated that acoustic cavitation may occur through the mechanism of homogeneous generation of vapor phase or through “swinging” of vapor bubbles generated by high-energy particles and/or other kinds of initiative factors. The thresholds of acoustic cavitation are described by the theory of homogeneous nucleation.     

Direct visualisation of homogeneous and heterogeneous crystallisation in an ensemble of confined domains of poly(ethylene oxide)

We present a study of homogeneous and heterogeneous nucleation in polymer crystallisation. In bulk samples the crystallization is typically dominated by nucleation from defects (heterogeneous nucleation), and consequently studies must rely on sample preparation to minimize this effect. We present a study of nucleation within discrete droplets of poly(ethylene oxide) that are formed by the dewetting of a thin film on an unfavourable substrate. The samples provide an ensemble of impurity-free droplets, with length scales that can easily be measured. We show that the data for heterogeneous and homogeneous nucleation is qualitatively different, and that the data mirrors the fundamental differences in the underlying mechanisms for the two nucleation processes. The experiments presented here provide a simple method that can be used to study heterogeneous and homogeneous nucleation in great detail.Received: 1 January 2003, Published online: 30 October 2003PACS: 61.41. + e Polymers, elastomers, and plastics - 68.55.-a Thin film structure and morphology - 81.10.-h Methods of crystal growth; physics of crystal growth     

快速降压下Tween20 液滴真空闪蒸特性

为探究闪蒸喷雾冷却的微观机理, 设计并搭建了液滴悬挂式真空闪蒸实验装置, 利用可视化窗口探究Tween20 液滴闪蒸过程中的闪蒸特性及气泡生长机理. 液滴在快速降压过程中形态会经历气泡成核、气泡生长、伴随气泡生长、爆裂这四个阶段的变化, 并反复循环这一过程直至液滴稳定蒸发. 对于液滴温度的变化, 闪蒸室的终态压力起到了决定性的作用, 并且其终态温度随压力的升高明显上升. 同时通过液滴闪蒸过程形态图分析发现, 液滴在剧烈爆炸阶段其温度也发生明显下降; 在稳定蒸发阶段, 其温度也将开始稳定不变. 因此可知液滴的剧烈爆炸会带走其自身的大量热量. 而 Tween20 浓度对液滴温度的影响微乎其微, 但其会使液滴内气泡的初始成核时间发生明显滞后, 并抑制液滴内的气泡发生破裂.     

Interface motion and nucleation of solid helium-4 induced by acoustic waves

Crystallization and melting of helium-4 was experimentally observed to be induced by acoustic radiation pressure where the liquid-solid interface is highly mobile at low temperatures. We discuss the observed anomalous reversal of this effect as a function of temperature and the nucleation by acoustic wave pulses of crystals in the liquid phase or liquid bubbles in the solid phase. A high-speed camera was used for the in situ observation of large interface velocities as high as 1 m/sec.     

Thermodynamic and kinetic considerations of nucleation and stabilization of acoustic cavitation bubbles in water

Qualitative explanation for a homogeneous nucleation of acoustic cavitation bubbles in the incompressible liquid water with simple phenomenological approach has been provided via the concept of the desorbtion of the dissolved gas and the vaporization of local liquid molecules. The liquid medium has been viewed as an ensemble of lattice structures. Validity of the lattice structure approach against the Brownian motion of molecules in the liquid state has been discussed. Criterion based on probability for nucleus formation has been defined for the vaporization of local liquid molecules. Energy need for the enthalpy of vaporization has been considered as an energy criterion for the formation of a vaporous nucleus. Sound energy, thermal energy of the liquid bulk (Joule-Thomson effect) and free energy of activation, which is associated with water molecules in the liquid state (Brownian motion) as per the modified Eyring's kinetic theory of liquid are considered as possible sources for the enthalpy of vaporization of water molecules forming a single unit lattice. The classical nucleation theory has then been considered for expressing further growth of the vaporous nucleus against the surface energy barrier. Effect of liquid property (temperature), and effect of an acoustic parameter (frequency) on an acoustic cavitation threshold pressure have been discussed. Kinetics of nucleation has been considered.     

过热液氦均匀核化速率的确定

预测不同压力下过热液氦的均匀核化速率是十分重要的,它与液氦的极限过热度密切相关。文中通过回顾动力学理论、分子聚集理论、涨落理论等研究液体均匀核化的方法,对过热液氦的均匀核化速率进行了计算,并且对各种方法进行了比较与分析。结果表明,用能量涨落理论来计算过热液氦的均匀核化速率是一种比较合理的方法。     

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     

Field-theoretical treatment of the liquid-vapor phase transition in nuclear systems

The liquid-vapor phase transition in hot nuclear matter is investigated in a field-theoretical approach employing euclidean-space (imaginary time) path-integral techniques. This approach allows us to study the nucleation due to both quantum and thermodynamic fluctuations. The bubbles of the new phase appear as instanton solutions of the euclidean-space field equations. The critical bubble sizes and associated transition probabilities are calculated. We examine the temperature and density values for which a phase transition may develop in hot nuclear matter produced in the course of a heavy-ion reaction.     

Ultrasonic-induced nucleation of ice in water containing air bubbles

Cavitation induced by ultrasonic vibrations can cause nucleation of ice in supercooled water. In this study, the time required for ultrasonic-induced nucleation of ice was measured for water containing two different size distributions of air bubbles. When the water was supersaturated with air bubbles, there was a time lag of about 0.5 s between the onset of ultrasonic irradiation and the onset of ice nucleation, and the probability of ice nucleation was unusually high within 0.5-1.1 s after the onset of ultrasonic irradiation. These results cannot be explained by conventional models alone, in which the collapse of a cavitation bubble triggers the nucleation of ice. Secondary effects appear to also influence ice nucleation.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.