Breakdown of classical nucleation theory near isostructural phase transitions

We report simulations of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1:10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model. We argue that the observed behavior is due to the surface stress of the crystal nuclei. The observed effect highlights a general deficiency of the most frequently used thermodynamic theories for crystal nucleation. Surface stress should lead to an experimentally observable expansion of crystal nuclei of colloids with short-ranged attraction and of globular proteins.     

Crystallization and characterization of crystallites in charge stabilized suspensions

For three different types of polymer latex particles with widely different particle charges the structure of suspensions before and after crystallization is investigated. A liquid-like ordered state was achieved by shear melting crystal-like ordered samples. The structure factors S(Q) of the liquid-like suspensions are analyzed in terms of the resealed mean spherical approximation (RMSA) of Hansen and Hayter. The Bragg diffraction pattern of the crystallized samples shows that the structure is b.c.c. It is found that the particle number concentration n and the distance of nearest neighbours in corresponding liquid- and crystal-like states differ by less than 4 %.

In the second part of the paper, Bragg diffraction was used to determine the crystallite size distribution in samples of different particle concentration.     

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.     

Computer simulation of water vapor nucleation on charged nanoparticles

The Monte Carlo method is applied to the study of the formation of condensed-phase nuclei from water vapor on electrically charged silver iodide nanocrystals. This study is a continuation of the investigations carried out earlier in [1] with electrically neutral nucleation centers. Nanoparticles with a size of up to 4 nm and flat nanoparticles with a size of up to 10 nm are investigated. The free energy, entropy, and the work of formation of nuclei with a size of up to 6729 molecules are calculated at the atomic level by the bicanonical statistical ensemble (BSE) method at a temperature of 260 K. Thermodynamic stability of nuclei is investigated depending on the size, shape, and charge of nanocrystal nucleation centers, as well as depending on the presence of crystal defects and the degree of spatial localization of charge on the surface of nanoparticles. The excess charge has a crucial effect on the work of formation of a nucleus only in the case of strong spatial localization of the latter near a point crystal defect; however, this effect is restricted to a relatively small size of the nuclei and therefore cannot substantially enhance the ice-forming activity of nanoparticles. A nucleus that grows on the surface of a nanoparticle evolves through three stages that differ in molecule retention mechanism and thermodynamic stability. The charge of a nanoparticle has a small effect on these factors. The leading factor that determines the ice-forming activity of ion nanocrystals is their intrinsic electric field due to the nonuniform distribution of charge within a unit cell of the crystal lattice.     

Crystal forms of hillocks and voids formed by electromigration on ultrapure gold and silver wires

Hillocks and voids (vacancy crystals) which were formed by electromigration on ultrapure gold and silver wires, showed only the combined crystal forms {111} and {100}. These planes are identical with the equilibrium planes G_I, calculated by Stranski and Kaishew for nonpolar substances under the assumption of only nearest neighbor interaction. Hillock and void nucleation occurred on crystal imperfections (heterogeneous nucleation). Hillocks and vacancy crystals (voids) on gold showed twin formation obeying the spinel law. Dedicated to Professor I. N. Stranski on the occasion of his 80th birthday.     

Evidence for out-of-equilibrium crystal nucleation in suspensions of oppositely charged colloids

We report a numerical study of the rate of crystal nucleation in a binary suspension of oppositely charged colloids. Two different crystal structures compete in the thermodynamic conditions under study. We find that the crystal phase that nucleates is metastable and, more surprisingly, its nucleation free-energy barrier is not the lowest one. This implies that, during nucleation, there is insufficient time for subcritical nuclei to relax to their lowest free-energy structure. Such behavior is in direct contradiction with the common assumption that the phase that crystallizes most readily is the one with the lowest free-energy barrier for nucleation. The phenomenon that we describe should be relevant for crystallization experiments where competing solid structures are not connected by an easy transformation.     

The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

The dynamical correlations of a model consisting of particles constrained on the line and interacting with a nearest-neighbour Lennard-Jones potential are computed by molecular-dynamics simulations. A drastic qualitative change of the spectral shape, from a phonon-like to a diffusive form, is observed upon reducing the particle density even ad moderate temperatures. The latter scenario is due to the spontaneous fragmentation of the crystal-like structure into an ensemble of “clusters" colliding among themselves. In both cases, the spectral linewidths do not follow the usual q² behaviour for small wavenumbers q, thus signalling a breakdown of linearized hydrodynamics. This anomaly is traced back by the presence of correlations due to the reduced dimensionality.     

冷却速率对温敏聚N-异丙基丙烯酰胺胶体结晶过程的影响

冷却速率对结晶过程具有重要的影响. 本文采用温敏poly-N-isopropylacrylamide (PNIPAM) 胶体晶体体系实时观察了冷却速率对结晶晶粒尺寸的影响. 通过高倍透射明场观察和Bragg衍射观察研究连续冷却下的晶粒形核和生长实时演化过程, 发现随着冷却速率的增加, PNIPAM胶体晶体晶粒尺寸不断减少. 晶粒尺寸与冷却速率符合幂指数关系, 与金属体系具有相似的演化规律.     

Heterogeneous crystal nucleation: the effect of lattice mismatch

A simple dynamical density functional theory is used to investigate freezing of an undercooled liquid in the presence of a crystalline substrate. We find that the adsorption of the crystalline phase on the substrate, the contact angle, and the height of the nucleation barrier are nonmonotonic functions of the lattice constant of the substrate. We show that the free-growth-limited model of particle-induced freezing by Greer et al. [Acta Mater. 48, 2823 (2000)] is valid for larger nanoparticles and a small anisotropy of the interface free energy. Faceting due to the small size of the foreign particle or a high anisotropy decouples free growth from the critical size of homogeneous nuclei.     

Role of the prestructured surface cloud in crystal nucleation

For the homogeneous crystal nucleation process in a soft-core colloid model, we identify optimal reaction coordinates from a set of novel order parameters based on the local structure within the nucleus, by employing transition path sampling techniques combined with a likelihood maximization of the committor function. We find that nucleation is governed by solid clusters that consist of an hcp core embedded within a cloud of surface particles that are highly correlated with their nearest neighbors but not ordered in a high-symmetry crystal structure. The results shed new light on the interpretation of the surface and volume terms in classical nucleation theory.     

Characterization of crystal growth using a spiral nucleation model

Classical concepts of two-dimensional nucleation and spiral growth are used together with recent findings on the dynamics of dislocation spirals to derive a new crystal growth model. Initial growth nuclei result from the organization of adsorbed molecules in spirals around surface dislocations. The energetic barrier for the activation of the spiral nuclei is considerably lower than the admitted by classical two dimensional nucleation models. Stable nuclei evolve into bigger growth hillocks in supersaturated media through the incorporation of adsorbed units into their steps. The displacement velocity of steps during solution and vapour growth is calculated by different kinetic approaches, taking into consideration the distinct role of surface diffusion in each process, and avoiding known limitations of conventional theories. A generalized expression is obtained relating the crystal growth rate with main variables such as supersaturation, temperature, crystal size, surface topology and interfacial properties. At the end of the paper, the crystallization kinetics of sucrose measured at 40 °C is interpreted in the light of the new perspectives resulting from the proposed model. The application example illustrates how to estimate interfacial and topological properties from the experimental crystal growth results.     

The phase coexistence method to obtain surface free energies and nucleation barriers: a brief review

ABSTRACT

A recently developed method where one analyses the finite size effects associated with liquid–solid phase equilibria including vapour–crystal coexistence is briefly reviewed. It is shown that the estimation of the chemical potential of the vapour surrounding the crystal as function of the crystal volume yields information on the bulk coexistence conditions, when an extrapolation to the thermodynamic limit is performed. Estimating the pressure of the fluid surrounding the crystal nucleus in the finite simulation box and the volume of this nucleus that coexists with the fluid in thermal equilibrium, an estimate for the total surface excess free energy can be obtained, which to a very good approximation is independent of the size of the simulation box. The free energy barrier against homogeneous nucleation of crystals thus can be estimated as a function of the nucleus volume. Monte Carlo simulations for the soft effective Asakura–Oosawa model of colloid-polymer mixtures which form face-centered cubic colloidal crystals are used to exemplify this method, computing the surface excess free energy of these crystals over a wide range of crystal volumes, without the need to characterise the non-spherical crystal shape. A possible extension of these concepts to heterogeneous nucleation is also briefly discussed.     

不同衬底条件下石墨烯结构形核过程的晶体相场法研究

利用可描述气-固转变的三模晶体相场模型,在原子尺度上研究了不同衬底条件下石墨烯结构的形核过程.结果表明:无论衬底存在与否,气态原子均是先聚集为无定形过渡态团簇,随着气态原子的不断堆积和固相团簇中原子位置的不断调整,过渡态团簇逐渐转变为有序的石墨烯晶核,在此过程中,五元环结构具有重要的过渡作用;石墨烯在结构匹配较好的衬底(如面心立方(face-centered cubic,FCC)结构(111)和(110))上生长时,可形成几乎没有结构缺陷单晶石墨烯岛;在无衬底或结构匹配性较差的衬底(如FCC结构(100)面)上生长时,形成的石墨烯岛结构缺陷和晶界较多,不利于高质量石墨烯的制备.     

Three-particle correlations in simple liquids

We use videomicroscopy to follow the phase-space trajectory of a two-dimensional colloidal model liquid and calculate three-point correlation functions from the measured particle configurations. Approaching the fluid-solid transition by increasing the strength of the pair-interaction potential, one observes the gradual formation of a crystal-like local order due to triplet correlations, while being still deep inside the fluid phase. Furthermore, we show that in a strongly interacting system the Born-Green equation can be satisfied only with the full triplet correlation function but not with three-body distribution functions obtained from superposing pair correlations (Kirkwood superposition approximation).     

Elektronen-Kern-Doppelresonanz-Untersuchung vonU 2-Zentren in Kaliumchlorid

U ₂-centers in alkali halides are neutral hydrogen atoms in interstitial lattice sites, as has been shown by EPR measurements. The hyperfine interactions with the proton and with the four nearest halogen nuclei are resolved in the EPR spectrum. In order to resolve hyperfine interactions with further nuclei of the surrounding lattice ENDOR measurements have been performed onU ₂-centers in KCl at 77 °K. The analysis of the ENDOR spectra gave precise values for the hyperfine and quadrupole interaction constants of the nearest neighbour chlorine and potassium nuclei. The isotropic hyperfine constant of the chlorine neighbours is 24 times larger than that of the potassium neighbours although both nuclei are on equivalent first shell lattice positions. The hyperfine interactions of second shell potassium nuclei [(1/2, 1/2, 3/2)-position] show an unexpectedly large isotropic hyperfine constant. One expects a pure magnetic dipole-dipole interaction for the outer shell nuclei because of the concentrated hydrogen wave function. Two further chlorine shells could be approximately analysed. A theoretical estimate of the hyperfine and quadrupole interaction constants was made by orthogonalizing the 1s hydrogen wave function to the cores of the surrounding ions. If one takes into account the mutual overlap of neighbouring potassium and chlorine ions, one gets the right order of magnitude of the measured constants and a value of 10.4∶1 for the ratio of the isotropic hyperfine constants of the first shell chlorine and potassium nuclei. The relatively large isotropic constant of the second shell potassium nuclei can also be explained on this basis.     

Easy collective polarization switching in ferroelectrics

The actual mechanism of polarization switching in ferroelectrics remains a puzzle for many decades, since the usually estimated barrier for nucleation and growth is insurmountable ("paradox of the coercive field"). To analyze the mechanisms of the nucleation we consider the exactly solvable case of a ferroelectric film with a "dead" layer at the interface with electrodes. The classical nucleation is easier in this case but still impossible, since the calculated barrier is huge. We have found that the interaction between the nuclei is, however, long range, hence one has to study an ensemble of the nuclei. We show that there are ensembles of small (embryonic) nuclei that grow without the barrier. We submit that the interaction between nuclei is the key point for solving the paradox.     

超声场强化溶液结晶研究进展

溶液结晶技术在很多领域有着广泛的应用，超声强化溶液结晶不仅可刺激结晶成核，而且也可提高结晶生长速率，控制晶体粒径的分布，提高产品的质量和结晶设备的生产能力，具有重要的理论和实际意义，本文论述了这方面的研究进展情况，并提出了存在的问题和展望。     

Formation of Calcium Carbonate Sub‐Micron Particles in a High Shear Stress Three‐Phase Reactor

The production of precipitated calcium carbonate (PCC) was investigated experimentally under industrially relevant conditions, i.e. at high solid concentrations and increasing amount of solid product in the slurry. Temperature is an important parameter since it determines the crystal structure, the particle shape and, as a consequence, the viscosity of the slurry. Of course, the mass concentration of the raw material also has an important influence on the viscosity. From the particle size distributions of primary particles and agglomerates, it can be concluded that the nucleation process is governed by primary nucleation. Also, heterogeneous nucleation occurs on solid calcium hydroxide particles that are present in the slurry. Especially if the raw material contains impurities heterogeneous nucleation occurs and large and unwanted particles are formed. If the slurry is not stabilized, strong agglomeration occurs that can be influenced by the shear stress introduced to the slurry: a high shear stress which is linked to the viscosity of the slurry limits the upper particle diameter and leads to a steep particle size distribution of the product.     

Homogeneous bulk, surface, and edge nucleation in crystalline nanodroplets

The birth of a crystal is initiated by a nucleus from which the crystal grows--a dust grain in a snowflake is a familiar example. These nuclei can be heterogeneous defects, like the dust grain, or homogeneous nuclei which are intrinsic to the material. Here we study homogeneous nucleation in nanoscale polymer droplets on a substrate which itself can be crystalline or amorphous. We observe a large difference in the nucleating ability of the substrate. Furthermore, the scaling dependence of nucleation on the size of the droplets proves that the birth of the crystalline state can be directed to originate predominantly within the bulk, at the substrate surface, or at the droplets' edge, depending on how we tune the substrate.