Effect of crystallization conditions on the shape of polymer single crystals: Experimental and theoretical approaches

A modified system of Mansfield equations with different step propagation rates to the right and left was applied to describe the shape of solution-grown single crystals of long-chain alkanes with asymmetrically curved faces ?ub;110?ub;. Solution of this system of equations and simulation of the shape of single crystals of polyethylene, α-polyvinylidene fluoride, and polyethylene oxide shows good agreement with the experimental data. Comparison of the simulated shapes and experimental micrographs makes it possible to determine the ratio of the intensity of secondary nucleation to the average propagation rate of the layer as well as the ratio of the rates of lateral steps to the right and left and to calculate the absolute values of the main crystallization parameters when the growth rates of single crystals in certain directions are known. It is shown that the asymmetry of the step propagation rate to the right and left is significant only for crystallization at very small supercoolings.     

In situ Observed Twin Formation on ZnSe Crystals Growing by Sublimation

ZnSe crystals were grown by sublimation in closed ampoules between 1335 K and 1365 K. The growth was observed in situ with a video camera after an abrupt change of the supersaturation. The crystals developed preferably {110} faces. Repeatedly a nucleus was formed in ortho-twin position on a small {111} face which truncated the corner of three adjacent {110} faces. The repeated twin formation led to a preferred growth into the relevant 〈111〉 direction. The twinning already occurred at a low supercooling of less than 1 K and accelerated the growth distinctly.     

氧化锌单晶的水热生长与结晶习性

本文应用水热生长法,采用双温区高压反应釜,黄金内衬(φ35mm ×2mm),碱性溶液矿化剂,生长出了毫米级的透明氧化锌单晶,最大单晶可达2mm ×3mm ×6mm.所生长氧化锌晶体为纤锌矿型的六方晶体,晶体呈上部锥形的六棱柱体,{10(1-)1}、{10(1-)0}和{000(1-)}面有较大的显露平面.本文中从温差和填充度方面研究了实验条件对ZnO晶体的生长及其形貌的影响,使用黄金内衬前后的结果表明,用贵金属内衬可以有效阻止釜内壁杂质的进入,使晶体完整透明.     

Atomic Force Microscopy Studies on Growth Mechanisms and Defect Formations on {110} Faces of Cadmium Mercury Thiocyanate Crystals

Growth mechanisms and defect formations on {110} faces of cadmium mercury thiocyanate crystals grown at 30°C (σ=0.24) were investigated by using atomic force microscopy (AFM). It was found that, under this condition, spiral dislocation controlled mechanism and 2D nucleation mechanism operates simultaneously and equally during growth, which is completely different from the traditional 2D nucleation and dislocation source controlled mechanisms. A number of 2D nucleus are formed at the large step terraces generated by dislocation sources, leading to the unequal growth rates of the elementary steps and thereby “step bunches” arecaused. Various defects are formed under this growth condition, which is assumed to result from the incongruence between the steps generated by different sources. A new kind of 2D defect, corresponding to one growth layer in height, was observed for the first time.     

Desymmetrization of the polyhedral crystal shape of tetragonal lysozyme due to face-growth rate fluctuations

We have studied the desymmetrization of the polyhedral crystalline shape of tetragonal lysozyme crystals due to the growth rate differences of the equivalent {1 0 1} planes. Using atomic force microscopy, we have observed the evolution of the multifaceted structures composed of four equivalent {1 0 1} faces during growth. In our growth condition, lateral step flow, where a large density of dislocations acts as a source of steps, is the dominant growth mechanism. The measured step flow velocities are almost independent of the separation between the neighboring steps, revealing that the local face normal growth rate is determined by the local step density. By tracing the motion of the vertex surrounded by the {1 0 1} faces, we have found that the desymmetrization of the crystalline shape is due to the large fluctuation of the local face normal growth rate, which is comparable in magnitude to the average growth rate.     

Advancements (and challenges) in the study of protein crystal nucleation and growth; thermodynamic and kinetic explanations and comparison with small-molecule crystallization

This paper reviews advancements and some novel ideas (not yet covered by reviews and monographs) concerning thermodynamics and kinetics of protein crystal nucleation and growth, as well as some outcomes resulting therefrom. By accounting the role of physical and biochemical factors, the paper aims to present a comprehensive (rather than complete) review of recent studies and efforts to elucidate the protein crystallization process. Thermodynamic rules that govern both protein and small-molecule crystallization are considered firstly. The thermodynamically substantiated EBDE method (meaning equilibration between the cohesive energy which maintains the integrity of a crystalline cluster and the destructive energies tending to tear-up it) determines the supersaturation dependent size of stable nuclei (i.e., nuclei that are doomed to grow). The size of the stable nucleus is worth-considering because it is exactly related to the size of the critical crystal nucleus, and permits calculation of the latter. Besides, merely stable nuclei grow to visible crystals, and are detected experimentally. EBDE is applied for considering protein crystal nucleation in pores and hydrophobicity assisted protein crystallization. The logistic functional kinetics of nucleation (expressed as nuclei number density vs. nucleation time) explains quantitatively important aspects of the crystallization process, such as supersaturation dependence of crystal nuclei number density at fixed nucleation time and crystal size distribution (CSD) resulting from batch crystallization. It is shown that the CSD is instigated by the crystal nucleation stage, which produces an ogee-curve shaped CSD vs. crystal birth moments. Experimental results confirm both the logistic functional nucleation kinetics and the calculated CSD. And even though Ostwald ripening modifies the latter (because the smallest crystals dissolve rendering material for the growth of larger crystals), CSD during this terminal crystallization stage retains some traces of the CSD shape inherited from the nucleation stage. Another objective of this paper is to point-out some biochemical aspects of the protein crystallization, such as bond selection mechanism (BSM) of protein crystal nucleation and growth and the effect of electric fields exerted on the process. Finally, an in-silico study on crystal polymorph selection is reviewed.     

Growth‐Sector Boundaries and Growth‐Rate Dispersion in Potassium Alum Crystals

Crystals of potassium alum, pure and slightly doped with Cr³⁺, were grown from aqueous solution by slow temperature lowering. In addition, short re‐dissolution periods were introduced in order to provoke growth defects and changes of growth rates. Crystal slices of about 1 mm thickness were studied by conventional LANG X‐ray diffraction topography using MoKα radiation. For Cr‐doped crystals, boundaries between {100}, {100} and {111} growth sectors appear by pronounced dynamical X‐ray topographic contrast similar to that of stacking faults. Re‐dissolution experiments provoke the formation of inclusions on {100} faces, followed by an increase of the {100} growth rate by the factor of about six, relative to the neighboured {111} faces. X‐ray topographs show that this increase is correlated with the formation of dislocations, which interestingly have pure‐edge character. During further growth these dislocations penetrate the {100}‐{111} growth sector boundary and vanish from the {100} face, which slows down and finally adopts its former growth rate before re‐dissolution.     

Kinetic Investigations within the Transition Region from Polyhedral to Skeletal Growth Mode (V). Growth Kinetics of the Pyramidal Face of Zinc Single Crystals under Diffusion Conditions

The growth kinetics of the pyramidal face of zinc single crystals is studied in the presence of argon. The curves size vs. time provide evidence that smaller crystals grow in a kinetic regime and after reaching a certain critical size their growth continues in a diffusion regime. The growth kinetics of faces {101 } and {0001} are compared. It is established that the growth of both faces simultaneously changes from a kinetic to a diffusion growth mode. During the transition between the two regimes, however, loss of the morphological stability only of the smooth {0001} face is observed, while the {101 } face with macro steps formed on the surface acquires a skeletal shape after prolonged growth. It is shown that the appearance of morphological instability depends on the surface structure of the crystal faces.     

Growth of α-NiSO<Subscript>4</Subscript> · 6H<Subscript>2</Subscript>O crystals at high rates

The high-rate growth of nickel sulfate hexahydrate NiSO₄ · 6H₂O (α-NSH) crystals up to 120 × 120 × 65 mm³ in size is described for the first time. The data on the distribution of related impurities in the {011} and {001} growth sectors of α-NSH crystals grown at different rates are reported. The transmission spectra of both growth sectors of these crystals are obtained. The structural quality and the optical properties of rapidly and slowly grown α-NSH crystals are compared. It is established that the {011} growth sector of crystals grown at rates exceeding 5 mm/day shows the best characteristics for application in UV filters.     

Vapor phase epitaxy of CdTe on sapphire substrates in dependence on the vapor-flow orientation

The growth of cadmium telluride films on a structured (0001) sapphire surface oriented at an angle of 44° to the vapor-flow direction and normal to the steps formed along the \(11\overline 2 0\) direction is studied. It is found that this geometry of the vapor source and a substrate (heated to a temperature of 300°С) provides the growth of single-crystal CdTe films if a step height on the substrate surface is more than 1 nm. The results are explained by the occurrence of a longitudinal component of the diffusion flux of СdTe molecules and atoms toward the steps from the inner side and their high density at the step edge from the outer side due to the presence of the Ehrlich–Schwoebel barrier, which ensures the efficient supply of material and minimum supersaturation necessary for the nucleation at the step edge and growth of oriented CdTe islands. The cadmium telluride films that are grown have the \(\left( {110} \right)\left[ {1\overline 1 0} \right]CdTe\left\| {\left( {0001} \right)} \right.\left[ {11\overline 2 0} \right]A{l_2}{O_3}\) orientation and a composition similar to stoichiometric CdTe.     

Crystallization mechanisms of acicular crystals

In this contribution, we present an experimental investigation of the growth of four different organic molecules produced at industrial scale with a view to understand the crystallization mechanism of acicular or needle-like crystals. For all organic crystals studied in this article, layer-by-layer growth of the lateral faces is very slow and clear, as soon as the supersaturation is high enough, there is competition between growth and surface-activated secondary nucleation. This gives rise to pseudo-twinned crystals composed of several needle individuals aligned along a crystallographic axis; this is explained by regular over- and inter-growths as in the case of twinning. And when supersaturation is even higher, nucleation is fast and random.In an industrial continuous crystallization, the rapid growth of needle-like crystals is to be avoided as it leads to fragile crystals or needles, which can be partly broken or totally detached from the parent crystals especially along structural anisotropic axis corresponding to weaker chemical bonds, thus leading to slower growing faces. When an activated mechanism is involved such as a secondary surface nucleation, it is no longer possible to obtain a steady state. Therefore, the crystal number, size and habit vary significantly with time, leading to troubles in the downstream processing operations and to modifications of the final solid-specific properties.These results provide valuable information on the unique crystallization mechanisms of acicular crystals, and show that it is important to know these threshold and critical values when running a crystallizer in order to obtain easy-to-handle crystals.     

Growth and morphological study of copper oxide single crystals

Experiments on the growth of CuO single crystals by crystallization from flux in the CuO-Bi₂O₃-PbO-PbF₂, CuO-Bi₂O₃-Li₂O, CuO-Bi₂O₃-B₂O₃, CuO-BaO-Y₂O₃, and CuO-MO_x systems (M = P, V, or Mo) have been performed. The best results were obtained in crystallization in the CuO-Bi₂O₃-PbF₂ system: prismatic single crystals of platelet-and needlelike or isometric habit with dimensions up to 1 × 10 × 10, 1 × 1 × 20, or 6 × 6 × 8 mm, respectively, have been grown. The CuO crystals show polysynthetic twinning in the form of numerous alternating light and dark bands bound by systems of parallel straight lines on the {110} and {111} faces. A possible model of twinning associated with the Cu₂O → CuO transformation is considered.     

Growth aspects of barium oxalate monohydrate single crystals in gel medium

Single crystals of barium oxalate monohydrate (BaC₂O₄.H₂O, BOM) were grown in pure form by controlled diffusion of Ba²⁺ using the gel technique at different temperatures. Starting from aqueous Ba²⁺ chloride (BaCl₂) and acetic acid (C₂H₂O₄) in gel, this method offers a low‐cost and an easiest alternative to other preparation methods for the production of barium oxalate bulky single crystals. The optimal conditions for the growth of BOM crystals in silica gel were found by investigating different growth parameters such as gel pH, gel aging and crystallization temperature. Irrespective of all such crystallization environments, growth rate of the crystals were initially less and then exhibited supersaturation effect leading to non‐linearity. Gel aging and temperature has profound effect on nucleation density that resulted less number of crystals of maximum size in the gel matrix. Perfect single crystals were grown on gels of higher pH. The macropore morphology and porosity was controlled by changing age of the gel. It has been found that temperature has a fabulous effect in controlling the nucleation density by altering the supersaturation conditions for the formation of critical nuclei. The entire growth kinetics informed that the grown crystals were derived by the one dimensional diffusion controlled process. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

DKDP晶体的柱面形貌与缺陷分析

采用原子力显微镜观测全方位生长的DKDP晶体的{100}面形貌,发现有螺旋位错,由此推断DKDP晶体{100}面以螺旋位错机制生长;利用同步辐射X射线白光形貌术观测了DKDP晶体缺陷,探讨了不同生长条件及生长阶段对晶体完整性的影响.     

F-及SiF2-6对α型半水硫酸钙结晶成核及形貌的影响

本文模拟了半水法湿法磷酸生产过程中α型半水硫酸钙(α-HH)的结晶过程。在30%P₂O₅,反应温度95 ℃,过饱和度S=1.64~2.10条件下,通过浊度仪监测溶液中浊度变化,测定了不同F^-及SiF^2-₆浓度下α-HH结晶诱导时间,采用经典成核理论公式计算了α-HH的临界晶核半径及成核速率,并通过扫描电子显微镜(SEM)、X射线衍射(XRD)、X射线光电子能谱(XPS)表征分析了F^-及SiF^2-₆对α-HH结晶过程的影响。结果表明:随着F^-、SiF^2-₆浓度的升高,α-HH晶体的结晶诱导时间延长,表面能和临界晶核半径都增大,然而成核速率减小。当过饱和度S=1.64时,加入0.06 mol·L^-1 F^-,α-HH结晶诱导时间延长了465 s,成核速率减小到0.403×10²⁹ 晶核数·cm^-3·s^-1,然而,加入0.06 mol·L^-1 SiF^2-₆,α-HH结晶诱导时间延长了710 s,成核速率减小到0.339×10²⁹晶核数·cm^-3·s^-1。SiF^2-₆对α-HH晶体抑制成核作用大于F^-。F^-、SiF^2-₆阻碍了α-HH晶体沿C轴方向生长,使得晶体长径比减小,晶体形貌向短柱状变化。F^-、SiF^2-₆影响了α-HH晶体(200)、(310)、(400)晶面衍射峰强度和结晶度。控制半水法湿法磷酸中F^-及SiF^2-₆浓度水平,可以得到短柱状的α-HH晶体,有利于过滤洗涤。     

Ferrous Tartrate recognition of sodium chloride {111} and its effect on crystal growth

The surface morphology and growth pattern of some molecules could be altered by the recognition of ferrous tartrate (FeC₄H₄O₆, FeTA). We have explored this phenomenon in the aspect of growth rate and morphology alteration of sodium chloride crystals where few researches have been done. In this paper, the crystallization behavior of NaCl with added FeTA was studied by supersaturation test, conductivity, scanning electron microscopy (SEM), and X‐ray diffraction (XRD). The results showed that the supersaturation of NaCl solution could be increased to about 5.5 % in presence of FeTA prior to the onset of crystallization. Furthermore, SEM images and XRD results indicated that the addition of FeTA could change the morphology of NaCl crystal from cubic to octahedron by impeding the growth of {111} and {110} faces. Besides, the interaction between NaCl {111} face and FeTA was discussed and the possible spatial structure of FeTA was speculated through the lattice parameters of NaCl.     

On the nature of growth hillocks on sodium chlorate crystals

Optical examination of as-grown {100} surfaces of sodium chlorate crystals grown from aqueous solution revealed the presence of elliptical growth hillocks. The hillocks were present on both enantiomorphous forms and originated from dislocations, inclusions, and microcrystals attached to the growing surface. The value of the surface entropy factor equal to 4.55 at 313 K suggests that crystals grow via/or with the participation of dislocation mechanism, and the hillocks are dislocation growth centers. Compound mechanism controlled growth of some crystals because edge nucleation and dislocation centers operated simultaneously on the same surfaces.     

Nucleation kinetics in deionized charged colloidal suspension

A systematic experimental study on the nucleation, crystallization and crystal-growth of one-component charged colloidal particles (122 nm diluted in pure water with densities between 0.5 μm⁻³ < n_p < 5 μm⁻³) is present by means of time resolved static light scattering spectroscopy revealing the heterogeneous and homogenous nature of the crystallization. The interactions between the charged colloidal particles are sufficiently strong to cause crystallization which described in terms of Debye-Hückel approximation. Crystallization starts always with the formation of compressed structurally heterogeneous precursor domains. The results show that the heterogeneous nucleation at the cell walls starts simultaneously with the homogeneous bulk nucleation and the rate density of the heterogeneous nucleation appears slightly higher. It has been also found that the overall crystallization consists of at least a two-step nucleation process involving formation of early stage nuclei or crystal precursor then followed by the main crystallization. The induction time, the number density of nuclei and the growth rate of crystals, is strongly dependent on particle concentration and on whether the nucleation are homogeneous in cell center or heterogeneous on cell walls.     

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: I. Growth habit and surface morphology

The effect of concentration of Mn(II) ions on the growth habit and the surface micromorphology of different as‐grown faces of ammonium oxalate monohydrate (AO) single crystals grown from aqueous solutions was studied at a constant temperature of 30 °C and predefined supersaturations up to 20%. It was observed that the growth habit and the surface morphology of the crystals strongly depend on the supersaturation used for growth and the impurity concentration in the solution. The experimental results were analysed in terms of connected nets determined from different projections of the structure of AO crystals. Analysis of the observations revealed that: (1) the directions of connected nets corresponding to basic growth units composed of single (NH₄)₂C₂O₄ · H₂O molecules are in excellent agreement with the low‐index crystallographic directions of the orientations of growth layers, (2) all faces appearing in the growth morphology of AO crystals are F faces, and (3) the {001} face growing from pure aqueous solutions is essentially a kinetically rough face but the presence of Mn(II) impurity leads to their appearance in the morphology due to increase in the strength of bonds of the connected nets composing the surface graph.     

Initial stages of SiC crystal growth by PVT method

Initial stages of SiC crystal growth by Physical Vapor Transport method were investigated. The following features were observed: (a) many nucleation crystallization centres appeared on the seed surface during the initial stage of the growth, (b) at the same places many separate flat faces generated on the crystallization front, (c) the number of facets was dependent on the shape of the crystallization front and decreased during growth, (d) appearance of many facets lead to decrease of structural quality of crystals due to degradation of regions where crystallization steps from independent centres met. The results revealed that the optimal crystallization front should be slightly convex, which permits the growth of crystals with single nucleation centre and evolution of single facet on the crystallization front. The subjects of study were the shape and the morphology of growth interface. Defects in the crystallization fronts and wafers cut from the crystals were studied by optical microscopy, atomic force microscopy (AFM) combined with KOH etching and X‐ray diffraction. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)