Understanding supersaturation‐dependent crystal growth of L‐alanine in aqueous solution

The dependence of crystal growth rate of L‐alanine on solution supersaturation was investigated by combining experiments and molecular dynamics (MD) simulations. The experimental results show that lower supersaturated solution yields more elongated L‐alanine crystals along the c‐axis, i.e., the aspect ratio (c/b) of the crystal decreases with the increase of solution supersaturation, which is due to the higher supersaturation inducing a rise in the relative growth rate between the main side surface (the (120) surface) and the main end surface (the (011) surface). MD simulations on the two surfaces in contact with different supersaturated solutions revealed that the solute molecules tend to be more efficiently attached to the (011) surface than to the (120) surface at both supersaturations studied, as the interaction between the solute molecules and the L‐alanine molecules in the first layer of the (011) surface is stronger than that of the (120) surface. However, higher supersaturation leads to larger relative interaction energy between the (120) and (011) surfaces, suggesting an increase in the relative growth rate of the two surfaces (R₍₁₂₀₎/R₍₀₁₁₎) with supersaturation, which is in agreement with the experimental results.     

Measurement of three‐dimensional concentration gradients around a crystal growing from its aqueous solution using laser schlieren

Schlieren measurements of the gradients of the concentration field around a KDP crystal growing from its aqueous solution are reported. The measurement of the concentration gradient field is important for crystal growth because it controls the rate of solute transport from the bulk of the solution to the crystal surface. In the crystal vicinity, the concentration gradients have a three dimensional distribution. The concentration gradient field has been imaged using monochrome schlieren technique. Four view angles, namely 0, 45, 90 and 135° have been utilized. By interpreting the schlieren images as projection data of solute concentration gradient, the three‐dimensional concentration gradient field around the crystal has been determined using an algebraic reconstruction technique. At low supersaturation levels, the growth process is accompanied by weak fluid movement during which diffusion effects are significant. At higher levels of supersaturation and large crystal size, a well‐defined convective plume around the growing crystal is observed. Reconstruction of concentration gradients around the crystal explains the preferential growth rates of various faces of the crystal. The non‐circular shape of the crystal is seen to affect the symmetry of the distribution of concentration gradients in its vicinity. The effect of crystal morphology on the orientation of convection currents rising from the crystal surface has also been brought out on the basis of the reconstructed concentration gradients distribution in the growth chamber. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal was conducted. The results show that the surface shear stress is mainly affected by the inlet velocity, and the distribution of the surface supersaturation is determined by the bulk supersaturation and the inlet velocity. By adjusting the inlet velocity, the homogeneity of surface supersaturation can be improved, which is helpful for reducing the occurrence of inclusions and enhancing the crystal quality. The thickness of solute boundary layer is closely related to the flow intensity, but it is almost free from the impact of the bulk supersaturation.     

一水甲酸锂晶体生长界面过饱和度的测量

本文采用激光全息相衬干涉显微术研究了有机非线性光学晶体一水甲酸锂晶体的生长,计算了晶体生长的界面过饱和度.我们的研究结果表明,晶体生长的界面过饱和度随体过饱和度的增加而非线性增加;不同晶面的界面过饱和度不同;当体过饱和度增加到一定程度时,不同晶面的界面过饱和度趋于相同.     

Concentration distribution in crystallization from solution under microgravity

Concentration distribution in crystallization from solution under microgravity is numerically studied. A quasi-steady state growth and dissolution in a 2D rectangular enclosure filled with sodium chlorate (NaClO₃) aqueous solution, in which one wall is the growth surface of the crystal and the opposite one is the dissolution surface, is considered. The solute transport process at the growth surface is described by the diffusion-reaction theory with finite interface kinetics coefficient. The results show that the concentration at the growth surface is supersaturated and the supersaturation distribution is of non-uniformity, i.e. the supersaturation in a region facing an incoming flow is high. On the other hand, the non-uniformity of supersaturation at the growth surface is closely related to the gravity level even under microgravity, it exponentially increases as the thermal Rayleigh number on behalf of the gravity level rises.     

Mass transport effect within the boundary layers in solution crystal growth: Holographic study of KTP and KDP crystal growth

Using holographic phase-contrast interferometric microphotography, we have carried out real-time investigations of the mass transport processes taking place during the high temperature solution growth of KTiOPO₄ (KTP) crystal and low-temperature solution growth of KH₂PO₄ (KDP) crystal. Our experiments demonstrate that a mere diffusion boundary layer is not existing. The mass transport process within the boundary layers is a result of the coupled effect of diffusion and convection actions, no matter whether it is high-temperature or low-temperature solution growth. Under free convection state, the influence of bulk supersaturation on the thickness of solute boundary layer exists in the two different regions. The solute concentration distribution within the layer is an exponential function of the position.     

Measurement of two‐dimensional distribution of surface supersaturation over a sodium chlorate crystal surface using multidirectional interferometry

The two‐dimensional (2D) distributions of surface supersaturation of sodium chlorate crystals with and without solutal convection have been measured by means of a multidirectional interferometry (MDI) technique coupled with the principles of three‐dimensional (3D) computer tomography. When solutal convection was present over a top face, the supersaturation at the center of the face was depleted by a factor of >0.9 with reference to the value at the edges of the crystal. When the convection was suppressed using an upside‐down geometry, the depletion of supersaturation at the center of the face was much smaller, <0.4. Therefore, the supersaturation difference between the edges and the face center, which is responsible for the morphological stability due to volume diffusion for the solute, becomes less important compared to the effect of convection due to hydrodynamic reasons. This result should give us a key to solve why the crystal quality is sometimes better in convection‐free microgravity conditions because of improved stability of a crystal face caused by more homogeneous distribution of supersaturation over the crystal surface.     

The influence of concentration and supersaturation ratio of CuI·HI on CuI crystal growth by decomplexation method

The fundamental role of solubility and supersaturation of solute for crystal growth from solution has been widely realized. In order to optimize the process of CuI crystal growth by CuI·HI decomplexation in HI acid, the solubility and supersaturation curves of CuI in HI‐H₂O mixed solvent were measured, and then a modified concentration programming scheme was designed, which could grow high quality CuI single crystals of 2.5 mm on edge successfully. In this scheme, the concentration distribution of CuI·HI complex and HI acid in silica gel along their diffused direction were measured with spectrophotometer, and the evolution of CuI·HI complex supersaturation ratio was analysed. It was found that the excess CuI·HI complex concentration would lead to the high supersaturation ratio and the formation CuI dendrites. The condition for regular CuI single crystal growth in silica gel was measured as follow: when the crystal nuclei appears, the CuI·HI complex concentration in HI‐H₂O solvent should be kept in the range of 0.033–0.050 mol/L and its corresponding supersaturation ratio is 1.24–1.45, and then they should be respectively declined to a range of 0.025–0.033 mol/L and 1.14–1.26 at the stage of crystal growth. The results may provide a useful clue for further improvement of the experimental scheme. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of various factors on the liquid/liquid diffusion crystallization of proteins

From a numerical simulation of pre-nucleation solute transport in the liquid/liquid diffusion crystallization of proteins, it is derived that there are various factors influencing the spatial and temporal distributions of supersaturation. They include the ratio of the length of the protein solution to that of the salt solution in a tube crystallizer, the initial concentrations of protein and salt, and the initial salt concentration in the protein solution. Their influences on the protein crystallization have been demonstrated by the corresponding experiments of gel crystal growth. It may be deduced that the experimental conditions for the liquid/liquid diffusion growth of protein crystals could be optimized under given conditions in order to develop the advantages of this method.     

Unsteady-state transfer of impurities during crystal growth of sucrose in sugarcane solutions

In this work, we present growth rate data of sucrose crystals in the presence of impurities that can be used by both sugar technologists and crystal growth scientists. Growth rate curves measured in a pilot-scale evaporative crystallizer suggest a period of slow growth that follows the seeding of crystals into supersaturated technical solutions. The observed trend was enhanced by adding typical sugarcane impurities such as starch, fructose or dextran to the industrial syrups. Maximum growth rates of sucrose resulted at intermediate rather than high supersaturation levels in the presence of the additives. The effects of the additives on the sucrose solubility and sucrose mass transfer in solution were taken into account to explain the observed crystal growth kinetics. A novel mechanism was identified of unsteady-state adsorption of impurities at the crystal surface and their gradual replacement by the crystallizing solute towards the equilibrium occupation of the active sites for growth. Specifically designed crystallization experiments at controlled supersaturation confirmed this mechanism by showing increasing crystal growth rates with time until reaching a steady-state value for a given supersaturation level and impurity content.     

Study of potassium titanyl phosphate (KTP) flux growth by holographic phase-contrast interferometric microphotography

This paper describes a special set of equipment we designed, which is suitable to be used to study the high temperature solution growth process by optical method. The variation regularities of the solid-liquid interface boundary layer in the potassium titanyl phosphate (KTP) crystal growth and dissolution process have been investigated by holographic phase-contrast interferometric microphotography. It has been found that under the condition of free convection, the relation between the thickness of the boundary layer and supersaturation is linear. Moreover, the variation of refractive index caused by the change of solute concentration in the boundary layer will form an exponential function of the distance from the crystal face.     

Kinetic studies on the influence of temperature and growth rate history on crystal growth

Crystallization experiments of sucrose were performed in a batch crystallizer to study the effect of temperature and growth rate history on the crystal growth kinetics. In one of the growth methods adopted, the isothermal volumetric growth rate (R_V) is determined as a function of supersaturation (S) at 35, 40 and 45 ºC. In the other, crystals are allowed to grow at constant supersaturation by automatically controlling the solution temperature as the solute concentration decreased. Using the latter method R_V is calculated as the solution is cooled. The obtained results are interpreted using empirical, engineering and fundamental perspectives of crystal growth. Firstly, the overall activation energy (E_A) is determined from the empirical growth constants obtained in the isothermal method. The concept of falsified kinetics, widely used in chemical reaction engineering, is then extended to the crystal growth of sucrose in order to estimate the true activation energy (E_T) from the diffusion‐affected constant, E_A. The differences found in the isothermal and constant supersaturation methods are explained from the viewpoint of the spiral nucleation mechanism, taking into account different crystal surface properties caused by the growth rate history in each method. Finally, the crystal growth curve obtained in the batch crystallizer at 40 ºC is compared with the one obtained in a fluidized bed crystallizer at the same temperature. Apparently divergent results are explained by the effects of crystal size, hydrodynamic conditions and growth rate history on the crystallization kinetics of sucrose. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

籽晶台形状对PVT法同质外延生长氮化铝单晶初始生长的影响

借助专业晶体生长模拟软件FEMAG和自主开发的对流、传质、过饱和度及生长速率预测等有限元模块研究了物理气相传输法(PVT)同质外延生长氮化铝(AlN)单晶工艺时的初始传热及传质过程,并分析了不同形状籽晶台对生长室内的温度场、流场、过饱和度及生长速率的影响。温度场模拟结果表明籽晶台侧部角度改变可影响籽晶表面轴向及径向温度梯度,流场及传质模拟表明籽晶台侧部角度变化对籽晶台周边的传质有巨大影响。传质及过饱和度模拟结果表明,当籽晶台侧部角度为130°时,籽晶表面温度梯度较小且可以完全抑制籽晶台侧部多晶沉积,有利于通过同质外延工艺生长出无寄生、无裂纹的高质量氮化铝单晶锭。     

Understanding the effect of solvent polarity on the habit modification of monoclinic paracetamol in terms of molecular recognition at the solvent crystal/interface

The habit change of monoclinic paracetamol crystallized from solutions with different solvents such as water, ethanol, methanol, acetone, isopropyl alcohol, tetrahydrofuran, cyclohexanone, acetonitrile and 1, 4 ‐ dioxane was investigated. Change in solubility, pH and nucleation time of paracetamol in these solvents at ambient condition was studied. The polymorphic form of the nucleated paracetamol was observed under in‐situ optical microscopy. Solutions with different solvents having different chemical nature and polarity yielded paracetamol crystals with different habits: columnar morphology from polar protic water and prismatic morphology from other selected polar protic, aprotic and in non‐polar solvents. The significant differences on the growth rate of various crystal habit faces of the monoclinic paracetamol grown from different solvents are attributed in context with the solubility of the solute, solvent polarity, evaporation number of the solvent, rate of generation of supersaturation and the role of hydrogen bonding interaction between the solvent molecules and protruding solute molecules on the crystal surface. Among the solution with different solvents, bulk monoclinic paracetamol single crystal was grown from ethanolic solution using seed rotation technique by controlled cooling method.     

Kinetics of protein crystal nucleation and growth in the batch method

We have applied the Johnson–Mehl–Avrami–Kolomogorov (JMAK) theory of crystal nucleation and growth to the problem of protein crystallization in the batch method. Without integrating the JMAK equation explicitly, we use dimensional analysis to derive a general formula for the half-life for decay of the protein supersaturation. This formula includes a dimensioned group and an arbitrary dimensionless function. We integrate the JMAK equation exactly for the special case where the growth rate is independent of the supersaturation and the nucleation rate is proportional to its square. This gives an equation for the time decay of the supersaturation and a formula for the half-life in which all arbitrary dimensionless functions are evaluated. The results are consistent not only with Von Weimarn's rule, which asserts that the average size of a crystal increases as the supersaturation decreases, but also with our experimental results for crystallization of lysozyme, in which the half-life at fixed pH decreases with increasing ionic strength and decreasing temperature.     

Mass transport in the three-thermal-zone solute transport method

The mass transport process of the three-thermal-zone solute transport method is analyzed theoretically in this paper. The growth rate of a crystal is depending on the temperature gradient and the size of the curcible. Comparing with the normal temperature gradient solute transport method, this technique can be used to grow crystals in better quality.     

Growth mechanism of corundum crystals from cryolite (Na3AlF6) flux

Using the experimental data of the velocity versus supersaturation, υ(σ), relation and estimated values of liquid viscosity and density, flow velocity, and crystal density, the diameter of solute particles in solution in the growth of Al₂O₃ crystals from cryolite flux was estimated on the hard sphere model to be 11.8 Å. The step heights of single spiral layers on the (0001) face were measured by means of phase contrast microscopy and multiple-beam interferometry, which gave the values of 26 and 53 Å in two cases. Both values are in fair agreement in order of magnitude. It is suggested that the solute exists in the supersaturated solution in the form of culsters rather than ionic or molecular entities. Both from υ(σ) relation and diffusion coefficient values, the rate-controlling process in this case is considered to be volume diffusion through the unstirred boundary layer.     

Promotion of crystal growth rate in aqueous solution by direct contact with gas corona discharge

A new technique to promote crystal growth in aqueous solution using gas plasma is proposed. In this method, short‐lived radical species produced in solution which is contacted with gas corona discharge play a role to increase chemical potential of inorganic solute. In an experimental examination, single crystal of KDP was grown in a supersaturated solution which receives oxygen ions and radicals from adjacent corona discharge in air. KDP crystal has two unique growth faces (100) and (101), and the growth rates of both faces were increased considerably by generating the corona discharge. The both growth rates with and without corona discharge were well converged by one function based on chemical potential supersaturation. This result revealed that the solution in contact with gas corona discharge has a larger capacity of chemical potential than that without the discharge. Short‐lived species induced by gas corona discharge are considered to be anti‐solvents to cause this effect. The crystal growth process proposed here is considered to be an excellent method in terms of low impurity inclusion because such short‐lived species do not remain in the final crystal products and solution. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A parallel algorithm for multizone, multiphase systems with application to crystal growth

Materials processing systems, such as the Czochralski crystal growth system, are often characterized by the presence of a number of distinct materials and phases with significantly different thermophysical and transport properties. They may also contain irregular boundaries, moving interfaces and free surfaces. The understanding of the complex transport phenomena in these systems is of vital importance for the design and fabrication of equipment and the optimization and control of the manufacturing process. High-performance, high-resolution numerical simulation can prove to be an effective tool for the understanding of these transport mechanisms. Massively parallel computers promise to deliver the extensive computer resources required by these simulations. This paper presents a parallel implementation of a high-resolution numerical scheme which has been developed to simulate the Czochralski crystal growth processes. The scheme employs adaptive grid generation and curvilinear finite volume discretization to solve the transport equations in a domain with complex geometries. Selected results are presented to demonstrate the feasibility and potential of introducing parallel computations into crystal growth process modeling and simulation.     

Solute segregation in a lid driven cavity: Effect of the flow on the boundary layer thickness and solute segregation

Our objective in the present work is to study the effect of convective flows, ranging from laminar to fully turbulent, on solute segregation in directional solidification configurations. To do so, numerical simulations performed in a model 2D lid driven cavity; the problem parameters, apart from the species molecular diffusion coefficient, are the lid and growth velocities. Purely diffusive to fully convective mass transport conditions are modelled in our parametric study. In parallel, a scaling analysis aiming at the determination of the solute boundary layer thickness is proposed. The results show that a single non-dimensional number, based on the interface stress, is able to capture the physics of the solute transport phenomena.