Modeling of the shape of polyethylene oxide single crystals and determination of the kinetic crystallization parameters: Theoretical and experimental approaches

The curvature of faces of polymer single crystals is described by the system of Mansfield equations, which is based on the Frank-Seto growth model. This model assumes the velocity of nucleus steps to be the same for their propagation to the right and left and is valid only for symmetric crystallographic planes. To describe the shape of polyethylene oxide single crystals grown from melt and limited by the {100} and {120} folding planes, it is assumed that the layer velocities to the right and left are different on {120} faces. This approach allows modeling, with a high accuracy, of the observed shapes of polymer single crystals grown at different temperatures, which makes it possible to determine unambiguously the fundamental crystallization parameters: the dimensionless ratio of the secondary homogeneous nucleation rate to the average velocities of nuclei along the crystallization planes and the ratio of nucleus velocities to the right and left. In addition, it was found that a known macroscopic single-crystal growth rate can be used to determine the absolute values of the secondary homogeneous nucleation rate and the velocities of nuclei along the growth plane.     

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。     

Preparation and characterization of superfine ammonium perchlorate (AP) crystals through ceramic membrane anti-solvent crystallization

In this paper, a novel ceramic membrane anti-solvent crystallization (CMASC) method was proposed for the safe and rapid preparation ammonium perchlorate (AP) crystals, in which the acetone and ethyl acetate were chosen as solvent and anti-solvent, respectively. Comparing with the conventional liquid anti-solvent crystallization (LASC), CMASC which successfully introduces ceramic membrane with regular pore structure to the LASC as feeding medium, is favorable to control the rate of feeding rate and, therefore, to obtain size and morphology controllable AP. Several kinds of micro-sized AP particles with different morphology were obtained including polyhedral-like, quadrate-like to rod-like. The effect of processing parameters on the crystal size and shape of AP crystals such as volume ratio of anti-solvent to solvent, feeding pressure and crystallization temperature were investigated. It is found that higher volume ratio of anti-solvent to solvent, higher feeding pressure and higher temperature result in smaller particle size. Scaning electron microscopy (SEM) and X-ray diffraction (XRD) were used to characterize the resulting AP crystals. The nucleation and growth kinetic of the resulting AP crystals were also discussed.     

The growth of controlled profile crystals by Stepanov's method

Single crystals in the shapes of plates, tubes and rods of various cross sections are widely used in many areas of science and technology. Of great importance is the production of such single crystal specimens directly from the melt. By Stepanov's method, the desired shape of the crystal is obtained by the proper selection of a device which shapes the melt column which rises due to the capillary effect. The capillary parameters determine the shape of the profile curve. The thermal parameters, taking into account the equilibrium crystal shape, define the position and shape of the crystallization front. The use of the shaper makes the process self-stabilizing. A negative feedback which damps out perturbations appears in the crystal-melt system and thus permits the production of controlled profile crystals with constant cross-section along their length. Thermoelastic stresses created in ribbons and rods as a result of temperature-induced misfit deformations are considered. The generation of dislocations in crystals occurs mainly due to stresses arising near the crystallization front. Various versions of the method and their applications to some materials are discussed.     

Kinetics and morphology of nonequilibrium growth of ice in supercooled water

The kinetics of free growth of ice in a distilled-water film supercooled to ?30°C was studied by the video recording technique in the polarized light. In the supercooling range 12 < ΔT < 16 K, a first-order kinetic morphological transition was observed between the structure formed by needlelike crystals of ice and the quasiadiabatic “structure” of single grains having the shape of planar platelets with the thickness proportional to the thickness of the water film and relative supercooling. It was found that this transition is accompanied by jumplike changes in the main crystallization parameters such as the growth rate of grains, their size and number, their kinetic behavior, and the fractal dimension of the structure.     

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)     

Phosphoric acid purification by suspension melt crystallization: Parametric study of the crystallization and sweating steps

In order to purify phosphoric acid, the suspension melt crystallization process was studied. The suspension crystallization experiments were carried out with 80, 84 and 88 wt% phosphoric acid melt at the cooling rates of 0.05, 0.1 and 0.2 K/min, respectively. Sweating experiments were executed for various crystals obtained in suspension crystallization step. The purification effects of the sweating parameters including sweating time, initial inclusion amount and initial impurity content were studied. The inclusion fraction increases with the increase in cooling rate. The inclusion fraction of the crystals which were formed with feed concentration of 84 wt% phosphoric acid melt is lowest among the three feed concentrations. Different impurities have different purification performances during sweating. High inclusion amount and low impurity concentration favor the purification of H₃PO₄·0.5H₂O crystals during sweating.     

Modeling the distribution of Ga and Sb impurities in Ge‒Si single crystals grown by double feeding of the melt: Growth conditions for homogeneous single crystals

Mathematical modeling of the distribution of Ga and Sb impurities in homogeneous (with respect to the content of the main components) single crystals of Ge–Si alloys, grown by double feeding of the melt, has been performed in the Pfann approximation. It is shown that the axial gradient of impurity concentration in Ge–Si crystals can be controlled in wide limits by changing the ratio of crystallization rate and the rates of feeding of the melt by silicon and germanium rods. The conditions for growing alloy single crystals, homogeneous both with respect to the content of the main components and to the impurity concentration distribution, have been determined.     

Investigation of the variations in the crystallization front shape during growth of gadolinium gallium and terbium gallium crystals by the Czochralski method

Numerical investigation of the variations in the crystallization front shape during growth of gadolinium gallium and terbium gallium garnet crystals in the same thermal zone and comparison of the obtained results with the experimental data have been performed. It is shown that the difference in the behavior of the crystallization front during growth of the crystals is related to their different transparency in the IR region. In gadolinium gallium garnet crystals, which are transparent to thermal radiation, a crystallization front, strongly convex toward the melt, is formed in the growth stage, which extremely rapidly melts under forced convection. Numerical analysis of this process has been performed within the quasistationary and nonstationary models. At the same time, in terbium gallium garnet crystals, which are characterized by strong absorption of thermal radiation, the phase boundary shape changes fairly smoothly and with a small amplitude. In this case, as the crystal is pulled, the crystallization front tends to become convex toward the crystal bulk.     

In situ monitoring and control of lysozyme concentration during crystallization in a hanging drop

Fiber optic Raman spectroscopy combined with a partial least-squares regression model was demonstrated as a monitor of lysozyme concentration during crystallization in a hanging drop experiment in real time. Raman spectral features of the buffer and protein were employed to build the regression model. The use of fiber optic technology coupled with Raman spectroscopy, which is ideal for use with aqueous solutions, results in a powerful noninvasive probe of the changing environment within the solution. Lysozyme concentrations were monitored in experiments at a constant reservoir ionic strength. Data from these uncontrolled experiments were used to determine rates of supersaturation, induction times, and the number and size of the resultant lysozyme crystals. Control experiments were performed by introducing step changes in the reservoir ionic strength. The step changes were initiated by comparing in situ rates of supersaturation with the rates of supersaturation calculated from the uncontrolled data. Monitoring the concentration changes of the lysozyme within the hanging drop permits a measurement of the level of supersaturation of the system and enhances the possibility of dynamic control of the crystallization process.     

Influence of the nucleation time-lag on the activation energy in non-isothermal crystallization

In the present work, the influence of the nucleation time-lag on the non-isothermal glass crystallization is discussed. Differential thermal analysis (DTA) results of an iron-rich glass nucleated by Cr₂O₃ were obtained at different heating rates. The activation energy of crystallization, E_c, and the Avrami parameter, m, estimated by Kissinger's and Ozawa's equations were shown to be dependent on the heating rate. The value of E_c, obtained at 2.5, 5 and 7.5 K/min heating rates was calculated as 299 kJ/mol, while the value of E_c, obtained at 10, 15 and 20 K/min was as 499 kJ/mol. The value of m for ‘low' and ‘high' heating rates were 2.57 and 1.45, respectively. The results were interpreted on the basis of the non-steady state nature of the nucleation process. It was assumed that at high heating rates no nucleation takes place and the crystals grow on a existing fixed number of nuclei; the activation energy of crystal growth, E_g, can be estimated by applying the Kissinger equations. At low heating rates nucleation occurs and the number of nuclei formed is influenced by the heating rate; E_g can be estimated by the Matusita and Sakka equation.     

The precipitation of calcium carbonate via a bubbling method in the presence of Mg2+ and glucose

Abstract

The effect of Mg²⁺ on the crystallization of precipitated calcium carbonate (PCC) via a bubbling carbonation method and the mechanism of eliminating its influence by glucose were investigated. The polymorph and morphology of crystals were characterized by field emission-scanning electron microscopy, X-ray diffraction, and Fourier transform infrared spectroscopy. These results demonstrated that Mg²⁺ and Mg/Ca molar ratio played significant roles on the morphology of PCC. When the Mg/Ca molar ratio was below 0.5, only spindle-like calcite formed. The rod-like aragonite started to form when the ratio was 0.6. As the ratio increased, the amount of aragonite increased and the length of rod-like aragonite became longer. Notably, the effect of Mg²⁺ could be eliminated efficiently when the 1.5?wt% glucose was added into the carbonation system, in which system, the PCC crystals were all spindle-like calcite. Furthermore, the mechanism of the glucose to eliminate the influence of Mg²⁺ on PCC crystallization was proposed.     

Crystallization of inorganic salts from aqueous solutions in a microwave field

The crystallization of some inorganic salts (KH₂PO₄, NaCl, Sr(NO₃)₂, KNO₂, Ca(OH)₂) by the thermal-gradient (with decreasing temperature) and solvent-evaporation methods using microwave heating of solutions is investigated. It is established that the growth rates of single crystals in a microwave field are an order of magnitude higher than obtained in other known techniques at comparable crystallization temperatures and supersaturations. For example, the growth rate of prismatic faces {100} of KH₂PO₄ crystals is as high as 11 mm/day at supersaturations of ～1.2%. The results obtained are discussed in the context of the effect of microwave radiation on the adsorption surface layers of crystals. Fine-grained phases of the salts under study are obtained by evaporation of the solvent.     

Effect of Crystallization Front Shape on the Dislocation Density in Germanium Single Crystals

Crystallography Reports - The effect of crystallization front shape on the dislocation density in Ge single crystals with a diameter of 100 mm, grown by the Czochralski method, has been studied....     

Continuous cooling approximation for the formation of a glass

Non-isothermal equations describing the liquid-crystal transformation are derived using the isothermal Avrami equations. A theoretical expression for the critical cooling rate for the formation of a glass is found. Calculations based on this expression are in better agreement with experimental values than those derived from TTT (time-temperature-transformation) curves. A study performed on typical glass forming materials enables the glass forming ability (GFA) to be determined by experimentally measuring crystallization temperatures at different cooling rates which are easily accessible with commonly available technology. The behaviour of the rate constant for crystallization is also obtained from the same data in the experimental range considered. In both cases no previous knowledge of the parameters involved is needed.With some assumptions the values of the viscosity in the crystallization temperature range can be estimated.Although the study was performed for an Avrami index of 4 an extension to other values of n is made under some restricted conditions and a more general treatment is outlined.     

Effect of CuCl2 on hydrothermal crystallization of calcium sulfate whiskers prepared from FGD gypsum

Using purified flue‐gas desulfurization (FGD) gypsum as raw material, effects of CuCl₂ on crystal morphology, phase structure, aspect ratio and crystallization of hydrothermal products prepared via hydrothermal crystallization in H₂SO₄‐H₂O solutions were investigated. The results show that dosage of CuCl₂ has a significant effect on the morphology, aspect ratio and crystallization of calcium sulfate whiskers (CSWs), but no effect on their phase transformation . At a dosage of 15 g CuCl₂/kg FGD gypsum, the produced calcium sulfate whiskers had diameters ranging from 1 to 3 μm with average aspect ratio greater than 200 . Transmission electron diffraction patterns and highly magnified surface morphology of CSWs were found different from those of self‐assembly crystals. Compared to self‐assembly crystals, the produced CSWs showed a single crystal structure and their surface was very smooth.     

Simplified version of calculation of the composition distribution along a single crystal of a binary solid solution obtained by pulling from a feeding melt

The possibility of obtaining single crystals of binary solid solutions exhibiting strong segregation upon crystallization by pulling from a feeding melt with the use of a crucible shaped as a truncated cone and a feeding ingot of complex shape is shown. The composition distribution along the crystal length is found by solving the continuity equation for the second component flux under certain initial and boundary conditions. It is shown that single crystals can be obtained in which the second-component concentration in the stationary mode exceeds the corresponding value in the feeding ingot. The method developed is applied to Ge-Si solid solutions.     

The growth of single crystals of Ni-W alloy under conditions of high temperature gradient

The structure of single crystals of the NV-4 nickel alloy containing 32–36 wt % W is investigated. The temperature gradient at the crystallization front and the velocity of the crystallization front are the variable parameters of directional crystallization. The degrees of structural perfection of the single crystals grown under different conditions are compared. The crystallization parameters providing growth of single crystals that have high structural perfection and can be successfully used as seeds for the growth of single-crystal blades are determined. Typical defects formed upon directional crystallization of single crystals of the Ni-W (35 wt %) alloy are examined. The studied defects are classified, and the factors responsible for the disturbance of the single-crystal structure are analyzed.     

Crystallization of proteins under an external electric field

An external electric field affects the crystallization of proteins when applied under some conditions of temperature, pH, and precipitating agent composition. As suggested in the theoretical part of this paper, it produces large protein concentration gradients inside the mother liquor leading to a local supersaturation area in the crystallization solution. Such an experiment has been used for the first time on the crystallization of a protein. The effects of an external electric field on the crystallization of hen egg-white lysozyme at 293 K, pH 4.5, and two NaCl concentrations (0.6–0.7 M) have been investigated using the vapor diffusion method. The application of electric field results in a smaller number of crystals with larger size. The crystals grew at the droplet surface, near the cathode. The nucleation rate is drastically reduced and this experimental method could be used to control the number of crystals in the droplet.     

Particle size influence on crystallization behavior of Ge2Sb2Se5 glass

Differential scanning calorimetry was used to study crystallization in the Ge₂Sb₂Se₅ glass under non-isothermal conditions. The crystallization kinetics was described in terms of autocatalytic ?esták–Berggren model. An extensive discussion of all aspects of a full-scale kinetic study for a crystallization process was performed. Number of suggestions regarding the experimental part and importance of the particle size influence study was introduced in order to maximize precision, reproducibility and predicative potential of the experimental data. Complexity of the crystallization process was identified to be represented by closely overlapping consecutive competing surface and bulk mechanisms. Mutual interactions of both mechanisms as well as all other observed effects were discussed in relation to the ability of nowadays theoretical models to accurately and correctly describe the experimental data. Advanced error analysis was performed for each step of the kinetic study.