A morphological study of vicinal surface growth based on a hybrid algorithm

A hybrid algorithm that combines a phase-field model and a lattice gas model evolving according to a kinetic Monte-Carlo (KMC) simulation scheme is used to investigate the dynamics of vicinal surface growth during vapor phase epitaxy. The algorithm is computationally far more efficient than pure KMC schemes, and this gain in efficiency does not correspond to a loss in information on the kinetics of individual atoms. We present numerical studies on the temperature dependence of macroscopic properties of the growing surface, evaluating the relevant stochastic processes (attachment, detachment, diffusion and island dynamics) as a function of their rates. We show that the temperature at which step flow is replaced by island nucleation depends on incoming flux, diffusion parameters and interstep distance. Moreover, we validate these finding by comparison to experiments and by analytical investigations.     

Two-scale modeling of adsorption processes at structured surfaces

We present an algorithm for the simulation of vicinal surface growth. It combines a lattice gas anisotropic Ising model with a phase-field model. The molecular behavior of individual adatoms is described by the lattice gas model. The microstructure dynamics on the vicinal surface are calculated using the phase-field method. In this way, adsorption processes on two different length scales can be described: nucleation processes on the terraces (lattice gas model) and step-flow growth (phase field model). The hybrid algorithm that is proposed here, is therefore able to describe an epitaxial layer-by-layer growth controlled by temperature and by deposition rate. This method is faster than kinetic Monte Carlo simulations and can take into account the stochastic processes in a comparable way.     

Microtopographical studies of prism faces of potassium dihydrogen phosphate crystals

Surface structures on prism faces of potassium dihydrogen phosphate crystals grown from aqueous solutions and also by gel method are described and illustrated. Density of growth centres increases as the supersaturation of the mother liquor is increased. Gel grown crystals predominantly show rectangular growth hillocks on their prism faces. In the needle shaped crystals further nucleation extends predominantly along theC axis than at right angles to it. Influence of misoriented guest microcrystals on the growth of the prism faces is described.     

The mass transfer process and the growth rate of NaCl crystal growth by evaporation based on temporal phase evaluation

The mass transfer process and the crystal growth rate have been proved to be very important in the study of crystal growth kinetics, which influence the crystal quality and morphological stability. In this paper, a new method based on temporal phase evaluation was presented to characterize the mass transfer process in situ and determine the crystal growth rate. The crystallization process of NaCl crystal growth by evaporation was monitored in situ by a Mach-Zehnder interferometer, and the absolute concentration evolution, the evaporation rate and the real-time supersaturation of solution were obtained using temporal phase analysis, which acted as a novel technique to extract phase variation along time axis recently. Based on the evaporation rate and the absolution concentration, a new method to calculate mass transfer flux during the crystal growth without the knowledge of the mass transfer coefficient was proposed, and then the crystal growth rate could also be retrieved under the hypothesis of cubic crystals. The results show that the crystal growth rate increases with the supersaturation linearly. It is in agreement with the diffusion theories, which presume that matter is deposited continuously on a crystal face at a rate proportional to the difference in concentration between the points of deposition and the bulk of solution. The method is applicable to the research of crystallization process based on evaporation or vapor diffusion of which the precise conditions of nucleation and supersaturation are usually unknown because of the complexity of the evaporation rate and crystal growth rate.     

The basic growth parameters of ZnS single crystals grown by sublimation

The application of the crystal growth dislocation theory [11] to ZnS single-crystal growth is discussed. The experimental material, above all for determining the actual supersaturation in the growth region and the mechanism of ZnS transport (diffusion, transport gas, chemical transport) was found to be insufficient. An expression for the growth rate of the ZnS crystal plane (the dependence on the supersaturation is not linear) is derived and two different stages in growing ZnS crystals are described.     

Nucleation studies and characterization of potassium thiocyanate added KDP crystals grown by seed rotation technique

The effect of the addition of potassium thiocyanate on potassium dihydrogen phosphate (KDP) crystals, grown from aqueous solution by the temperature lowering method using a microcontroller based seed rotation technique has been studied. As part of nucleation studies, metastable zone width, induction period and crystal growth rate of additive added KDP are determined and analyzed with the pure system. Dielectric measurements were carried out on pure and doped crystals at various temperatures ranging from 313 to 423 K and compared. The crystalline perfection of the grown crystal was studied by the high resolution X-ray diffraction analysis. The crystal grown from additive added solution was subjected to structural, optical transmission, second harmonic generation and hardness studies and the effect of additive on pure system is investigated.     

Correlation between growth of high-index faces, relative growth rates and crystallographic structure of crystal

According to contemporary crystal growth theories, crystals are bound by low-index faces which are the most slowly growing. However, high-index faces are observed in crystal habits more and more often. In this paper the growth of high-index faces is analysed from a crystallographic perspective. It is shown that the crystallographic structure of a given crystal, expressed by the trigonometric function of appropriate interfacial angles, influences to great degree the crystallisation process and the morphology of crystals, in particular the behaviour of high-index faces. Additionally, it is concluded that at particular crystallographic structure of a crystal, a given high-index face may exist in the habit and develop its size, although it grows much faster than the neighbouring faces. Received 31 July 2001     

Solution-grown crystals of poly(vinyl alcohol)

The growth mechanism and crystalline texture of solution-grown crystals of poly(vinyl alcohol) have been studied by electron microscopy. From morphological data it is shown that single crystals of poly(vinyl alcohol) (PVA) have two growth faces, i.e., the (100) and (101) fold planes. It is suggested that the parallelogrammic single crystals grow from the center by molecular folds. The rate of addition on the (100) plane is about three times larger than that on the (101) plane. Twinning of the PVA crystals takes place at the (100), (001), (101), and (101) planes at the time of the nucleation or during the growth. The single crystal and twins of PVA are corrugated lamellae. Granulated structure is observed on the surface in a figure similar to the external form of the crystals. Dark-field micrographs show that the PVA single crystals possess a mosaic structure with the arrangement of the blocks deviating slightly from parallel alignment in the lamella. The reactivities of single crystals to various aldehydes indicate that the single crystals contain crystal lattice defects.     

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.     

Towards a Fundamental Understanding of the Mechanics of Crystal Agglomeration: A Microscopic and Molecular Approach

A novel experimental apparatus has been developed which enables the measurement of adhesion forces between two crystals suspended in a supersaturated solution and allowed to agglomerate over a fixed time period. The geometry of the crystal surfaces at the contact points and the dynamic development of the bond are captured on video and characterised using an image analysis technique. The experimental apparatus has been designed to allow control of supersaturation, orientation of crystal faces, distance between crystals, relative movement of crystals and contact time. The experimental results show that the agglomerate bond strength, expressed as the agglomerate adhesion force per unit contact area, increases with increasing supersaturation and is higher for faster growing faces than for slower growing faces. In addition, a qualitative comparison has been made between the measured force and a theoretical estimation of the interaction force between crystal faces, determined through molecular modelling. It is shown that the speed of approach of two opposing crystal faces is a key parameter in the nature of the subsequent bond, as is their atomic structure.     

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.     

力和扩散机理下外延形貌的演化分析

本文提出了一个新的基于扩散界面的相场模型来描述外延生长中岛的形核、生长及熟化过程. 该模型同时考虑了弹性场、表面能、沉积、扩散、解吸和能量势垒等热力学及动力学过程对表面纳米形貌的影响. 采用经典的BCF模型来描述生长中的扩散形核过程, 而采用一个新的包含弹性应变能的自由能函数, 通过变分得到一个描述多层岛生长的相场方程, 该方法可以有效地描述外延生长中复杂的外延形貌. 采用有限差分格式对非线性耦合方程组进行求解. 数值结果显示, 该模型可以真实地再现外延生长中多层岛结构(即山丘状形貌)的演化过程, 模拟结果与已有实验结果一致. 同时模拟了生长过程中随外延形貌演化而形成的复杂生长应力, 研究表明, 在生长过程中, 岛中存在着复杂的应力分布, 且在岛边界处应力达到局部最大, 这与实验结果定性一致. 此外, 本文的重要发现是, 外延生长中的应力演化明显地影响原子的扩散过程, 当应力存在时, 外延结构变化较无弹性场时变快. 该项研究对理解外延生长中各物理机理的协同作用有重要的指导意义.     

Highly oriented electrospun polycaprolactone micro/nanofibers prepared by a field-controllable electrode and rotating collector

Novel ZnO tetrapod-shaped nanostructures with pearl-necklace-shaped arms were successfully synthesized using mixture of Zn, ZnO, and carbon powder as source. The definite supersaturation ratio provided by Zn, ZnO, and carbon powder was considered as the crucial factor of determining the formation of this kind of structure, and a negative feedback growth model combined with octahedral nucleation mechanism was proposed. Two other comparative experiments were also conducted to study the growth behavior of reagent species under different supersaturation ratios. Our experiments provided a beneficial experimental exploration in controlled growth of nanostructures through modulating supersaturation ratio by source, and these obtained novel nanostructures were also expected to have potential application as functional blocks in nanodevices. Furthermore, the study of photoluminescence indicated that the physical properties were strongly dependent on the crystal structure.     

Conditions for growth of columnar and filamentary crystals

The computer model of the initial stage of condensation processes is developed. The stochastic processes of adsorption, surface diffusion, and desorption occur on the 70×70 lattice of adsorption vacancies. The model was tested by an example close to water vapor sorption on a conventional crystal surface. Computed results demonstrate the processes of nucleation, growth of crystals, and developed condensation. Computations were carried out for various adsorption energies. Results showed that with decreasing energy of adsorption the character and rate of nucleation and subsequent condensation vary. With decreasing energy of adsorption the probability of nucleation of islets on substrate reduces, the filling of the next atomic layers on islets occurs earlier than the filling of the substrate, the growth rate of islets in height increases as compared to condensation of a continuous film, and the growth rate of area of islets decreases. There is a typical energy of adsorption at which the growth rate of islets in height reaches its maximum. At a further drop of adsorption energy, there is a growth of islets only in height, the growth rate, however, reduces. The phenomena revealed in computations illustrate the mechanism of origin of columnar and filamentary crystals.     

Scale-bridging phase-field simulations of microstructure responses on nucleation in metals and colloids

In the present studies we investigate the connection between atomistic simulation methods, i.e. molecular dynamics (MD) and phase-field crystal (PFC), to the mesoscopic phase-field methods (PFM). While the first describes the evolution of a system on the basis of motion equations of particles the second uses a Cahn–Hilliard type equation to described an atomic density field and the third grounds on the evolution of continuous local order parameter field. The first aim is to point out the ability of the mesoscopic phase-field method to make predictions of growth velocity at the nanoscopic length scale. Therefore the isothermal growth of a spherical crystalline cluster embedded in a melt is considered. We also show simulation techniques that enable to computationally bridge from the atomistic up to the mesoscopic scale. We use a PFM to simulate symmetric thermal dendrites started at an early stage of solidification related to nucleation. These techniques allow to simulate three dimensional dendrites from the state of nuclei (≈50?Å) converted from MD up to a size of some μm where ternary side-arms start to grow.     

Monte-Carlo analysis of tracer diffusion mechanisms in YBa2Cu3O6+c

A method for estimating, via the Monte-Carlo simulation, the most often realized diffusion mechanisms in 2D ordered structures is presented. Taking as an example the diffusion of oxygen ions in high temperature superconductor we propose several diffusion mechanisms and show to what extent they depend on the temperature and concentration of the diffusing particles. Our results are compared with the ones proposed earlier on the basis of energy arguments. We find also additional trajectories, different from those earlier reported in that system. Received 9 November 1998     

New developments on size-dependent growth applied to the crystallization of sucrose

The effect of crystal size on the growth rate of sucrose (C₁₂H₂₂O₁₁) at 40 °C is investigated from a theoretical and an experimental point of view. Based on new perspectives resulting from the recently introduced spiral nucleation model [P.M. Martins, F. Rocha, Surf. Sci. 601 (2007) 3400], crystal growth rates are expressed in terms of mass deposition per time and crystal volume units. This alternative definition is demonstrated to be size-independent over the considered supersaturation range. The conventional overall growth rate expressed per surface area units is found to be linearly dependent on crystal size. The advantages of the “volumetric” growth rate concept are discussed. Sucrose dissolution rates were measured under reciprocal conditions of the growth experiments in order to investigate the two-way effect of crystal size on mass transfer rates and on the integration kinetics. Both effects are adequately described by combining a well-established diffusion-integration model and the spiral nucleation mechanism.     

Theory of the nucleation of protein macromolecular ions

Protein molecules are amphoteric and exist in aqueous solution as macromolecular ions that carry a charge which depends upon temperature and pH. Despite the repulsive Coulomb forces acting between them, protein macromolecular ions can form crystals in pH buffered solutions of strong electrolytes. It is proposed that the first step in the mechanism of crystallization is the formation of crystal nuclei made from partially discharged macromolecular ions that have exchanged H⁺ with the buffer. We suggest that the strength of the bare Coulomb repulsive force is weakened by the Debye-Hückel plasma screening provided by the inert electrolyte. This screening causes the rate of nucleus formation to increase with increasing ionic strength. Extending classic nucleation theory to account for these various charge effects, the results are applied to the case of lysozyme and a calculation is made of the dependence of the steady state nucleation rate upon temperature, pH, ionic strength, and protein supersaturation. It is found that the nucleation rate increases with increasing temperature and increasing ionic strength. Under condition of fixed temperature, supersaturation, and inionic strength, the nucleation rate has local maxima at low pH, where individual lysozyme macro ions are highly charged, and at pH ? 11, where they have zero average net charge. At both pH values, the nucleus that determines the rate has minimum size. In contrast to standard nucleation theory, which ignores charge, it is found that the size of the nucleus that controls the rate is different from the size of the nucleus that has the lowest concentration. All other conditions being the same, it is predicted that lysozyme crystals should nucleate most rapidly near pH = 2 and near pH = 11.