A phase-field/Monte-Carlo model describing organic crystal growth from solution

In this paper work we present a phase-field/Monte-Carlo hybrid algorithm for the simulation of solutal growth of organic crystals. The algorithm is subsequently used for an investigation of diffusion effects on the growth mechanisms. This method combines a two-scale phase-field model of the liquid phase epitaxial growth and a Monte-Carlo algorithm of the 2D nucleation and thus is faster than previous purely Monte Carlo simulations of crystal growth. The inclusion of supersaturation and diffusion in the method allows the study of crystal growth under various growth conditions. Parameters used in the hybrid algorithm are bound to the energetic parameters of crystal faces, which can be estimated from a detailed study of the actual crystal structure based on a connected nets analysis, which allows the prediction of the shape and morphology of real crystals. The study of the diffusion effect is carried out based on an example of a hydroquinone crystal, which grows from the water solution at various supersaturations. The dependencies of the growth rate and the nucleation rate on the supersaturation indicate the change of the growth mechanism from spiral growth to 2D nucleation. The difference in the growth rate for various faces is in agreement with the crystal morphologies derived from the attachment energy method and observed experimentally. The main result of the simulation is the evaluation of engineering limits for choosing appropriate external process conditions.     

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.     

Kinetics of a rough crystal face: Temperature dependence of the growth rate

We present measurements of the linear growth rate of the (110)-face of naphthalene growing from toluene solution at various equilibrium temperatures. Above a critical supersaturation the growth rate depends linear on the supersaturation and the (110)-face becomes round, which both indicates kinetic roughening. Within a temperature interval of 50° C the growth rate changes by nearly two orders of magnitude. The slope of the linear part of the growth curve can be described by an activated process, the activation energy turns out to be of the order of the evaporation enthalpy of naphthalene.     

Mathematical model of biocrystal growth under a thermal control field

A mathematical model for protein lysozyme crystallization from an aqueous solution, caused by the spatial distribution of a precipitant (NaCl) and the point control action of temperature, was constructed, and numerical studies were performed. The mathematical model describes the formation of crystal nuclei and their growth as a function of the local supersaturation, as well as heat-and-mass transfer in the entire solution region, including protein crystals. The heat-and-mass transfer is described by Navier-Stokes equations in the Boussinesq approximation, taking into account thermogravitational and concentration convection.     

非晶一次晶化过程微观组织演化和生长动力学的相场法研究

在晶化物理模型中添加扩散系数对晶化过程的影响, 采用相场方法研究初始形核率和初始形核半径对一次晶化过程中微观组织和生长动力学的影响。结果表明: 随着初始形核率的增加, 相同时间内非晶一次晶化的晶粒数量逐渐增加, 晶粒尺寸逐渐减小。晶化分数随着演化时间和初始形核率的增加逐渐增大, 初始形核率越大, 相同演化时间内的晶化分数越高。不同初始形核半径情况下, 非晶一次晶化过程中的晶粒数量和尺寸随着演化时间的增加基本保持不变。晶化分数随着演化时间的增加而增大。不同初始形核率和初始形核半径情况下所对应的生长指数均小于1, 表明初始形核率和初始形核半径对晶化方式无影响, 均为一次晶化。改变初始形核率和初始形核半径可调控一次晶化微观组织结构, 而晶粒尺寸及晶化分数直接关系到合金性能。     

The fluid phenomena in the crystallization of the protein crystal

This paper reports that an optical diagnostic system consisting of Mach-Zehnder interferometer with a phase shift device and image processor has been used for study of the kinetics of protein crystal growing process. The crystallization process of protein crystal by vapour diffusion is investigated. The interference fringes are observed in real time. The present experiment demonstrates that the diffusion and the sedimentation influence the crystallization of protein crystal which grows in solution, and the concentration capillary convection associated with surface tension occurs at the vicinity of free surface of the protein mother liquor, and directly affects on the outcome of protein crystallization. So far the detailed analysis and the important role of the fluid phenomena in protein crystallization have been discussed a little in both space- and ground-based crystal growth experiments. It is also found that these fluid phenomena affect the outcome of protein crystallization, regular growth, and crystal quality. This may explain the fact that many results of space-based investigation do not show overall improvement.     

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.     

Massenspektrometrische untersuchungen der kondensation von dünnen schichten auf fremden unterlagen: II. Wachstums- und desorptionskinetik von Ag auf W

The growth and desorption kinetics of silver films on clean polycrystalline tungsten were investigated with a mass-spectrometric technique. The growth of the crystal phase started in the third monolayer by nucleation. This process occurred initially with increasing supersaturation until steady-state growth conditions were established. The evaporation coefficient β for the room-temperature films was unity. For the high-temperature films β was found to be lower than 1. The light and scanning micrographs showed that the silver films consist of isolated islands with strong epitaxial orientation to the substrate. The thermal desorption spectra confirmed qualitatively the island structure of the deposit. The kinetics data were explaned by the formation of diffusion zones around the growing cluster.     

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.     

相场晶体法模拟过冷熔体中的晶体生长

利用相场晶体(phase-field crystal)模型,采用有限差分法,模拟了过冷熔体中晶体生长过程,研究了不同相区、不同过冷度对晶体生长过程的影响.结果表明,在共存区中,随着演化的进行,晶体生长被抑制,液-晶边界层逐渐变厚;在单相区中,随着过冷度的增大,晶态区面积显著增加,液-晶边界层逐渐变薄.晶体生长速度和过冷度成近似线性的关系. 关键词： 相场晶体 自由能函数 过冷熔体 晶体生长     

Dispersity and growth kinetics of K<Subscript>2</Subscript>SO<Subscript>4</Subscript> crystals in drops of an evaporating solution

Growth of K₂SO₄ crystals is studied in solution drops that have different initial heights and evaporate in different times. The dependences of the crystal size on the crystal growth time are obtained. The following three crystal growth modes are detected: rapid crystal growth in a supersaturated solution, a stop in the growth as a result of complete removal of supersaturation, and slow growth at a quasi-equilibrium solution concentration. The dispersities of the crystals that are retained at the bottom of the drop after complete evaporation of the solvent are calculated. A linear relation between the crystal dispersity and the reciprocal crystal growth time is revealed. The dispersity of K₂SO₄ crystals and the dispersity of the solid-solution dendrites in aluminum alloys are found to exhibit the same character of their dependences on the reciprocal crystal growth time.     

A stochastic model for solidification

A 3-dimensional (2-space, 1-time) model relating the diffusion of heat and mass to the kinetic processes at the solid-liquid interface, using a stochastic approach is presented in this paper. This paper is divided in two parts. In the first part the basic set of equations describing solidification alongwith their analysis and solution are given. The process of solidification has a stochastic character and depends on the net probability of transfer of atoms from liquid to the solid phase. This has been modeled by a Markov process in which knowledge of the parameters at the initial time only is needed to evaluate the time evolution of the system. Solidification process is expressed in terms of four coupled equations, namely, the diffusion equations for heat and mass, the equations for concentration of the solid phase and for rate of growth of the solid-liquid interface. The position of the solid-liquid interface is represented with the help of a delta function and it is defined as the surface at which latent heat is evolved. A numerical method is used to solve the equations appearing in the model. In the second part the results i.e. the time evolution of the solid-liquid interface shape and its concentration, rate of growth and temperature are given.     

Calculations of the complete morphological phase diagram for nonequilibrium growth of a spherical crystal under arbitrary surface kinetics

Complete morphological diagrams (with stable, metastable, and absolutely unstable regions) were calculated for the problem of morphology selection under the conditions of nonequilibrium growth of a spherical crystal taking into account arbitrary kinetic process rates at the boundary and a linear dependence of the growth rate on supersaturation. The consideration was performed by jointly using linear stability analysis and the principle of maximum entropy production. The principal difference between kinetically and diffusion-controlled crystal growth is the possibility of the coexistence of three or more morphological phases under the same conditions in the former case. It was shown that, at the transition point, the rate of accretion of the growing crystal mass increased in a jump. The jump value was studied as a function of the parameters of the problem.     

KABO晶体生长形态演化机理的分析

用高温晶体生长实时观察装置，发现了KABO晶体生长形态随着生长体系过饱和度的增大从六方形态逐渐向三角形态过渡，然后又从三角形态逐渐向六方枝蔓晶形态过渡的过程.通过KABO生长溶液高温拉曼谱的测试结果，证明了溶液中存在［BO₃］^3-三角形、［AlO₄］^5-四面体生长基元.运用负离子配位多面体生长基元理论模型，分析了KABO晶体上述生长形态演化的机理.发现KABO的生长形态是由其内部结构和生长基元共同决定的，在不同过饱和度溶液中，KABO生长基元的种类和维度将会发生变化，由此相应引起了KABO的生长形态从六方形态到三角形态，又从三角形态向六方枝蔓晶形态的演变过程. 关键词： KABO晶体 负离子配位多面体 生长形态 枝蔓晶     

Thermal and chemical diffusion in the rapid solidification of binary alloys

Solidification of binary alloys is characterized by the necessity to reject away from the advancing front two conserved quantities: the latent heat released at the solid-liquid interface and the solute atoms that cannot be accommodated in the solid phase. As thermal diffusion is much faster than chemical diffusion, the latter is generally assumed to be the rate limiting mechanism for the process, and the problem is addressed through the isothermal approximation. In the present paper we use the phase-field model to study the planar growth of a solid germ, nucleated in its undercooled melt. We focus on the effects of a noninstantaneous thermal relaxation. The steady growth predicted at large supersaturation in the isothermal limit is prevented. Depending on the value of the Lewis number the growth rate is limited by either mass or heat diffusion; in the latter case we observe a sharp transition between two different regimes, in which originates a nonmonotonic time dependence of the interface temperature. The effects of this transition reflect in the composition of the solidified alloy.     

3D problem of heat and mass transfer at the ignition of a combustible liquid by a heated metal particle

A nonlinear nonstationary 3D problem of heat and mass transfer at gas phase ignition of a combustible liquid spread on the surface of a solid body by a metal particle heated to a high temperature is solved. This is done within the framework of a model taking into account the heat conduction and evaporation of the liquid, the diffusion and convection of the combustible vapors in the oxidizer medium, the crystallization of the ignition source, the kinetics of the processes of evaporation and ignition of liquids, the dependence of the thermophysical characteristics of the interacting substances on the temperature, and the moisture content of the oxidizer—air. The dependences of the ignition delay time of the liquid on the temperature and sizes of the heating source are established. Limiting values of the temperature and particle sizes at which the ignition conditions take place are determined. The influence of the air humidity on the inertia of the process being investigated is analyzed. A comparison of numerical values of typical parameters of the process under investigation for 2D and 3D models is performed.     

Spirals on Si(1 1 1) at sublimation and growth: REM and LODREM observations

Using recently proposed improvements of reflection electron microsopy (REM) we study, in perfectly controlled thermodynamics conditions, spiral and spirals shapes on Si(1 1 1) surface. It is shown that the new method named low distortion reflection electron microscopy (LODREM) is a powerful instrument, resolving in much more details (compared with REM) growth or evaporation spirals at the crystal surface. More precisely, we examine the distance between two successive steps of a spiral at growth (or evaporation) with respect to the supersaturation (or undersaturation). It is found that this distance scales with an exponent close to −1/2. This result, which deviates from the BCF theory, originates from a non-local behavior with a slow kinetic of attachment of the adatoms at the steps.     

The activation energy of crystallization of amorphous Fe40Ni40P14B6

The isothermal crystallization of Fe₄₀Ni₄₀P₁₄B₆ (Metglas 2826) has been studied by transmission electron microscopy, using static observations of partially crystallized ribbons at room temperature and in situ dynamic registration of the crystallization process at elevated temperatures. At all temperatures crystallization takes place by the nucleation and growth of individual crystals. Analysis of the transformation kinetics allowed to determine the nucleation rates and the activation energy for crystal growth. The growth velocity of the crystal phase was found to be controlled by the diffusion coefficient of phosphorus in this alloy withD ₀=2.5×10^10±1cm{swu2}/s andQ=(3.4±0.15)eV.     

微重力条件下晶体生长过程的实时观察

从材料科学的微重力效应和晶体生长基本过程等两个方面出发，阐明了一种新的生长技术（晶体生长过程的光学实时观察法）的必要性，并介绍了空间高温实时观察装置的基本特性．在我国的科学技术探测卫星上，该装置进行了搭载实验，并首次清楚地观察到了空间溶质扩散效应和高温溶液的表面张力对流图像．