Surface nucleation in the freezing of gold nanoparticles

We use molecular simulation to calculate the nucleation free energy barrier for the freezing of a 456 atom gold cluster over a range of temperatures. The results show that the embryo of the solid cluster grows at the vapor-surface interface for all temperatures studied and that the usual classical nucleation model, with the embryo growing in the core of the cluster, is unable to predict the shape of the free energy barrier. We use a simple partial wetting model that treats the crystal as a lens-shaped nucleus at the liquid-vapor interface and find that the line tension plays an important role in the freezing of gold nanoparticles.     

The thermodynamics of cluster formation in nucleation theory

We have derived a precise thermodynamic definition of the standard free energy to form a cluster which is used in nucleation theory. The results [Eq. (9)] have a form differing slightly from the form usually used in nucleation theory and show that the Lothe-Pound correction factor is based on a misconception concerning the standard states involved.     

Nucleation theorems applied to the Ising model

We use Monte Carlo simulations to study a single cluster of "up" spins in a sea of "down" spins in the three-dimensional Ising model. We evaluate the growth and decay rates for clusters of different sizes, identify the critical size for which these rates are equal, and obtain the internal energy of the critical size cluster. The results of the simulations at different temperatures and magnetic fields are used together with the first and second nucleation theorems to predict how the cluster nucleation rate changes when the external magnetic field and the temperature are changed. Our results are in agreement with literature values, but our method requires significantly less computational effort than the simulations reported earlier and avoids the difficult evaluation of free energies.     

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.     

Interfacial contribution to cluster free energy

The Monte Carlo technique of “overlapping distributions” is used for computing directly the free energy difference F_{N + 1} ?F_N between two clusters containing respectively N + 1 and N solute atoms, in the square and the simple cubic Ising model with nearest neighbour interactions. High accuracy results are obtained within reasonable computer times. The capillarity approximation gives a good fit to the data, provided the following is taken into account: (i) the specific bulk and surface energies are given their macroscopic equilibrium values; (ii) a curvature correction to the surface specific energy has to be introduced: it is positive for two dimensions and negative for three dimensions; (iii) a size independent term is to be added in three dimensions; it may be viewed as a corner contribution; (iv) the coefficient of the logarithmic term is given its more recent value. When introduced in the master equation which describes the kinetics of the cluster population, within the simplifying assumptions of the classical nucleation theory, good agreement is found, for the shapes of the cluster size distributions, with the numerical experiments on the kinetic Ising model in two dimensions. However, the time scales of both computations do not match linearly. Possible reasons for this discrepancy are discussed.     

生长于微结构内点状结构的成核热力学

研究了汽相沉积过程中的衬底表面凹结构的成核热力学,指出可以通过衬底表面微结构设计来控制成核过程以实现点状结构的生长．计算了凹结构内的临界核形成能,表明与平面相比成核优先在凹结构发生．考虑凹结构的“等效势阱”效应,发现凹结构内稳定原子团的生长速率远远大于平面处稳定原子团的生长速率． 关键词：     

A monte carlo method for approximating critical cluster size in the nucleation of model systems

A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n ^2/3] is used to predict critical cluster size and critical supersaturation ratio, S^*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS ^*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.This material is based upon work supported by the National Science Foundation under Grant No. ATM80 15790 and the National Aeronautics and Space Administration under Grant No. NAS8-31150.     

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.     

Dynamical models of hadrons based on the string model and the behavior of strongly interacting matter at high density

We propose dynamical models of hadrons, the nucleation model and the free-decay model, in which results of the string model are used to represent interactions. The string model is examined by comparing its predictions with experimental data and parameters are fitted. The equilibrium properties of hadrons at high density are investigated in terms of the nucleation model; we find a singular behavior at energy density 3–5 GeV/fm³, where hadrons coalesce and create highly excited states. We argue that this singular behavior corresponds to the phase transition to quark-gluon plasma. The possibility of observing the production of high-density strongly interacting matter in collider experiments is discussed using the free-decay model, which produces pion distributions as decay products of resonances. We show that our free-decay model recovers features of hadron distributions obtained in hadron collison experiments. Finally, perspectives and extensions of the models are discussed.     

Elucidating the mechanism of nucleation near the gas-liquid spinodal

We have constructed a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. Close to the spinodal, the free energy, as a function of the size of the largest cluster, develops surprisingly a minimum at a subcritical cluster size. It is this minimum at intermediate size that is found to be responsible for the barrier towards further growth of the nucleus at large supersaturation. An alternative free energy pathway involving the participation of many subcritical clusters is found near the spinodal where the growth of the nucleus is promoted by a coalescence mechanism. The growth of the stable phase becomes collective and spatially diffuse, and the significance of a "critical nucleus" is lost for deeper quenches.     

Nucleation of magnetisation reversal, from nanoparticles to bulk materials

We review models for the nucleation of magnetisation reversal, i.e. the formation of a region of reversed magnetisation in an initially magnetically saturated system. For small particles, models for collective reversal, either uniform (Stoner–Wohlfarth model) or non-uniform like curling, provide good agreement between theory and experiment. For microscopic objects and thin films, we consider two models, uniform (Stoner–Wohlfarth) reversal inside a nucleation volume and a droplet model, where the free energy of an inverse bubble is calculated, taking into account volume energy (Zeeman energy) and surface tension (domain wall energy). In macroscopic systems, inhomogeneities in magnetic properties cause a distribution of energy barriers for nucleation, which strongly influences effects of temperature and applied field on magnetisation reversal. For these systems, macroscopic material parameters like exchange interaction, spontaneous magnetisation and magnetic anisotropy can give an indication of the magnetic coercivity, but exact values for nucleation fields are, in general, hard to predict. To cite this article: J. Vogel et al., C. R. Physique 7 (2006).     

Statistical prefactor and nucleation rate near and out of the critical point

The nucleation rate derived in the classical theory contains at least one undetermined parameter, which may be expressed in terms of the Langer first-principles theory. But the uncertainties in the accounting for fluctuation modes, which are either absorbed into the free energy of a critical cluster or not, result in different evaluations of the statistical prefactor and nucleation rate. We get the scaling approximations of the nucleation rate for the vapour condensation both near and out of the critical range. The results obtained deserve the experimental verification to resolve the theoretical uncertainty.     

Probing free xenon clusters from within

Inner-shell and valence-shell photoionization of van-der-Waals Xe clusters have been measured using both angle-resolved photoelectron spectroscopy and velocity map ion imaging technique. Both techniques have been used to probe the electronic properties and the fragmentation dynamics of clusters as a function of photon energy and cluster size. In particular, the evolution of the photoelectron angular distributions and partial cross sections as a function of photon energy and cluster size has revealed cluster size effects similar to the ones found in solids. Our cluster angular distribution parameters have been compared to the free atoms. In addition, the measurement of the fragmentation dynamic of the clusters seems to be photon energy dependent.     

Grain size distributions for competitive growth with nucleation

The paper introduces and discusses an idealized competitive growth model with nucleation for the microstructure formation during dense branching phase separation in thin Al/Ge films. Grain size and grain length distributions for the new model are obtained analytically and by simulation. These distributions exhibit a characteristic scaling form similar to cluster size distributions in many other growth models. The cutoff functions in these scaling forms and their influence on the determination of effective exponents are studied in detail. It is found that nucleation introduces a new length scale into the other-wise selfsimilar competitive growth model. This length scale appears only inside the cutoff function and diverges algebraically as the nucleation rate vanishes. We find both analytically and by simulation that the cutoff functions can exhibit stretched exponential behaviour exp(–x ) for large arguments. Our analytical and simulation results for grain size and grain length distributions are in excellent quantitative agreement.     

Origin of the failure of classical nucleation theory: incorrect description of the smallest clusters

We carry out molecular Monte Carlo simulations of clusters in an imperfect vapor. We show that down to very small cluster sizes, classical nucleation theory built on the liquid drop model can be used very accurately to describe the work required to add a monomer to the cluster. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range. We calculate factors needed to correct the cluster formation work given by the liquid drop model. The corrected work of formation results in nucleation rates in good agreement with recent nucleation experiments on argon and water.     

Distributions of ions in a cluster plasma created by a laser pulse

Energy and charge distributions of ions are calculated for a cluster beam irradiated by a high-power ultrashort laser pulse. It is shown that the self-consistent field of a cluster ionized by the laser beam strongly affects the characteristics of the ion distributions obtained after the cluster explodes. The mean concentration of atoms bound into clusters in a beam, the cluster size distribution, and the focal-spot diameter are found to have a weak effect on both energy and charge distributions of the ions, whereas the energy spectrum of the produced ions is determined by the mean cluster size.     

Stimulation of vapor nucleation on perfect and imperfect hexagonal lattice surfaces

Monte Carlo simulations of water vapor nucleation on a perfect crystal surface and on a surface with defects are performed. Mass exchange with the vapor phase is modeled by using an open ensemble. Cluster-substrate interaction is described in terms of conventional atom-atom potentials. The Hamiltonian of the system includes expressions for electrostatic, polarization, exchange, and dispersion interactions. The Gibbs free energy and work of adsorption are calculated by Monte Carlo simulation in the bicano?nical ensemble. The microscopic structure of nuclei is analyzed in terms of pair correlation functions. Periodic boundary conditions are used to simulate an infinite substrate surface. Molecule-substrate and molecule-molecule long-range electrostatic interactions are calculated by summing the Fourier harmonics of the electrostatic potential. Dispersion interactions are calculated by direct summation over layers of unit cells. Nucleation on a surface with matching structure follows a layer-by-layer mechanism. The work of adsorption per molecule of a monolayer on the substrate surface has a maximum as a function of nucleus size. The steady rate of nucleation of islands of supercritical size is evaluated. The work of adsorption per molecule for layer-by-layer film growth is an oscillating function of cluster size. As a function of layer number, it has a minimum depending on the vapor pressure. The electric field generated by a microscopic surface protrusion destroys the layered structure of the condensate and eliminates free-energy nucleation barriers. However, point lattice defects do not stimulate explosive nucleation.     

Molecular dynamics simulation of homogeneous nucleation of KBr cluster

We perform molecular dynamics simulations to study the homogeneous nucleation in the freezing of molten potassium bromide clusters. The nucleation rates tend to decrease with increasing cluster size and temperature. The solid-liquid interfacial free energy σ_sl of 42.4-52.3 mJ/m² is close to the values predicted by Turnbull's relation and comparable to the experimental observation by Buckle and Ubbelohde. It is interesting to find that there is no cluster size effect on the critical nucleus size. Critical nucleus sizes inferred from classical nucleation theory are of 6.5-20.7 K⁺Br⁻ ionic pairs in the temperature range of 400-600 K. The critical nucleus size at bulk MD freezing temperature obtained by extrapolation is about 45 K⁺Br⁻ ionic pairs, which is comparable to the experimental value of NaCl.     

Study of cluster fluctuations in the two-dimensional q-state Potts model

The two-dimensional Potts model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.