Effect of seeded surface area on crystal size distribution in glycine batch cooling crystallization: a seeding methodology

In batch cooling crystallization, if the seeding process is not carefully carried out, the crystal size distribution (CSD) is dispersed. The aim of this work is to determine the optimal conditions for seeding operations. Results show that the CSD is controlled if the seed surface area reaches a specific value called critical surface S_c. Nevertheless, S_c is not the only parameter to be considered. The mean crystal size of the product obtained actually depends on the size of the seeds used because of the growth rate distribution. In fact, seeds behave differently according to their crystal sizes, which accounts for the difference in crystal growth rates. Rules are proposed for seeding with the view to obtain a uni-modal CSD and a final product size predefined by the seed crystals.     

Resistivity distribution of silicon single crystals using codoping

Numerous studies including continuous Czochralski method and double crucible technique have been reported on the control of macroscopic axial resistivity distribution in bulk crystal growth. The simple codoping method for improving the productivity of silicon single-crystal growth by controlling axial specific resistivity distribution was proposed by Wang [Jpn. J. Appl. Phys. 43 (2004) 4079]. Wang [J. Crystal Growth 275 (2005) e73] demonstrated using numerical analysis and by experimental results that the axial specific resistivity distribution can be modified in melt growth of silicon crystals and relatively uniform profile is possible by B–P codoping method. In this work, the basic characteristic of 8 in silicon single crystal grown using codoping method is studied and whether proposed method has advantage for the silicon crystal growth is discussed.     

Solute trapping and the effects of anti-trapping currents on phase-field models of coupled thermo-solutal solidification

We explore how the inclusion of an anti-trapping current within a phase-field model of coupled thermo-solutal growth formulated in the thin interface limit actually affects the observed levels of solute trapping during dendritic growth. The problem is made computationally tractable by the use of advanced numerical techniques including local mesh adaptivity, implicit temporal discretization and a multigrid solver. Contrary to published results for pure solutal models we find that the inclusion of such an anti-trapping current does not lead to the recovery of the equilibrium partition coefficient, except in the limit of vanishing growth velocity. At higher growth velocities non-vanishing amounts of solute trapping are observed.     

Compositional variation in Si-rich SiGe single crystals grown by multi-component zone melting method using Si seed and source crystals

The effect of the supply of depleted Si solute elements on the compositional variation in the Si-rich SiGe bulk crystals was studied using the method which was used to grow Ge-rich SiGe single crystals with a uniform composition. By selecting the proper pulling rate, we can obtain Si-rich Si_1−xGe_x bulk crystals with uniform composition of x=0.1 without using the supply mechanism of depleted Si solute elements. When the supply mechanism of Si solute elements was used, the initial composition in Si-rich SiGe crystals can be much more easily determined by controlling the growth temperature than that in Ge-rich crystals because the Si seed crystal is not melted down. The supply of Si solute elements is very effective to change the compositional variation even for Si-rich SiGe crystals.     

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.     

The effect of calcium cations on the precipitation of barium sulfate 2: calcium ions in the presence of organic additives

Calcium ions have been implicated in changing the precipitation of barium sulfate when organic additives are present, although whether it inhibits or promotes nucleation and/or growth has been disputed in the literature. We conducted a thorough investigation into the effect of calcium when additives are present and show that calcium cations do indeed promote nucleation of barium sulfate particles when compared to the appropriate control. This result is independent of the analytical method (conductivity or turbidity) used to assess precipitation. The nucleation promotion produces no change in the crystal morphology, thus morphology is not always a good indicator of nucleation or growth behavior. The extent of nucleation promotion depends on the functional group of the additive.     

Homogeneous SiGe crystals grown by using the traveling liquidus-zone method

It is indispensable to estimate a diffusion coefficient in a solution zone in order to grow a homogeneous crystal by using the traveling liquidus-zone (TLZ) method. To estimate the diffusion coefficient of Ge in the SiGe solution zone, result of a two-dimensional numerical simulation is compared with an experimental result. From the comparison, the diffusion coefficient is estimated to be 9.5×10⁻⁵ cm²/s. By using this coefficient, a sample translation rate for obtaining a homogeneous SiGe crystal is determined. By translating samples with appropriate rates, homogeneous Si_0.5Ge_0.5 crystals are successfully grown. The typical Ge composition is 0.496±0.006 for more than 13 mm long. The experimental result shows the homogeneity of ±1.2% in the mole fraction. This deviation corresponds to the variation of less than ±0.03% in the lattice constant. Since this variation is negligibly small, the homogeneity is excellent. Thus it is found that the TLZ method is the universal growth technique, which is applicable to the crystal growth of not only the III–V compounds but also the IV–IV compounds.     

Model development for deactivation of bisphenol-A adduct particles during crystallization under the influence of impurity

A deactivation mechanism was developed to present the influence of 4-tert-butylphenol as a sample impurity on the bisphenol-A (BPA) adduct particles during the crystallization process. 4-tert-butylphenol is an organic sample impurity generally present in the reaction mixture of the industrial production of BPA. Kinetic parameters of growth, nucleation, agglomeration, and deactivation were estimated using the technique of model fitting to experimental data. The population and mass balances were used to model the adductive crystallization of BPA.     

Surface growth mechanisms and structural faulting in the growth of large single and spherulitic titanosilicate ETS-4 crystals

Morphological, surface and crystallographic analyses of titanosilicate ETS-4 products, with diverse habits ranging from spherulitic particles composed of submicron crystallites to large single crystals, are presented. Pole figures revealed that crystal surfaces with a-, b- and c- axes corresponded to 110, 010 and 001 directions, respectively. Thus, technologically important 8-membered ring pores and titania chains in ETS-4 run along the b-axis of single crystals and terminate at the smallest crystal face. Height of the spiral growth steps observed on 1 0 0 and 0 0 1 surfaces corresponded to the interplanar spacings associated with their crystallographic orientation, and is equivalent to the thickness of building units that form the ETS-4 framework. Data suggest that the more viscous synthesis mixtures, with a large driving force for growth, increased the two- and three-dimensional nucleation, while limiting the transport of nutrients to the growth surface. These conditions increase the tendency for stacking fault formation on 1 0 0 surfaces and small angle branching, which eventually results in spherulitic growth. The growth of high quality ETS-4 single crystals (from less viscous synthesis mixtures) occurred at lower surface nucleation rates. Data suggest that these high quality, large crystals grew due to one-dimensional nucleation at spiral hillocks, and indicate that under these conditions un-faulted growth is preferred.     

Crystal growth rate limited by step length — the case of oxygen-deficient TiO2 exposed to oxygen

We study how an oxygen-deficient crystal of TiO₂ crystal grows when exposed to O₂. While the O flux is external to the crystal, the Ti flux necessary for growth comes from internal (bulk) interstitials (Phys. Rev. Lett. 76 (1996) 791). We address where the reaction between O and Ti to form new crystal takes place in the regime of pure step flow (i.e., surface steps advancing without new-layers nucleating). The detailed partitioning of the growth flux among individual surface steps is studied using low-energy electron microscopy for two geometries on the (110) surface—an array of islands on a terrace and an island stack generated from a dislocation source. For both geometries, the areas of islands larger than the critical size grow at rates strictly proportional to their perimeter length, independent of the local step configuration. In addition, we find that the growth rate is proportional to the O₂ pressure. The step flow represents a simple limiting case of crystal growth (Phil. Trans. R. Soc. A. 243 (1951) 299)—only the growth species near a step edge becomes incorporated into the crystal. That is, only Ti and O reactions near the step edge lead to crystal growth. This case is in marked contrast to crystal growth controlled by species attaching to terraces and diffusing to steps, for which the growth rates depend upon the local step environment. Indeed, simulating the island array as if the growth flux was partitioned among the individual islands by concentration gradients (i.e., diffusion-controlled growth) totally failed to reproduce the experimental rates.     

Unidirectional seeded single crystal growth from solution of benzophenone

A novel crystal growth method has been established for the growth of single crystal with selective orientation at room temperature. Using volatile solvent, the saturated solution containing the material to be crystallized was taken in an ampoule and allowed to crystallize by slow solvent evaporation assisted with a ring heater. The orientation of the growing crystal was imposed by means of a seed fixed at the bottom of the ampoule. By selecting a suitable ring heater voltage and by controlling the ring heater voltage, nucleation and the growth rate of the crystal were controlled more effectively. By employing this novel method, benzophenone single crystal ingots of diameters 10 and 20 mm and length more than 50 mm were successfully grown using xylene as solvent. The ease in scaling up of diameter from 10 to 20 mm shows the vital advantage of this technique. It was possible to achieve solute–crystal conversion efficiency of 100 percent. The grown benzophenone crystal was characterized by FTIR, TG and DTA, powder X-ray diffraction, X-ray rocking curve, optical transmission study and powder SHG measurement. The results show that the crystal quality is at least as good as the quality of the crystal grown by other known methods. Also, microbial growth was naturally avoided in this method, as the fresh solution is constantly made available for the growing crystal.     

Crystallization kinetics of the borax decahydrate

The growth and dissolution rates of borax decahydrate have been measured as a function of supersaturation for various particle sizes at different temperature ranges of 13 and 50 °C in a laboratory-scale fluidized bed crystallizer. The values of mass transfer coefficient, K, reaction rate constant, k_r and reaction rate order, r were determined. The relative importances of diffusion and integration resistance were described by new terms named integration and diffusion concentration fraction. It was found that the overall growth rate of borax decahydrate is mainly controlled by integration (reaction) steps. It was also estimated that the dissolution region of borax decahydrate, apart from other materials, is controlled by diffusion and surface reaction. Increasing the temperature and particle size cause an increase in the values of kinetic parameters (K_g, k_r and K). The activation energies of overall, reaction and mass transfer steps were determined as 18.07, 18.79 and 8.26 kJmol⁻¹, respectively.     

Investigation of the growth rate of β-cyclodextrin in water during both flow-cell and batch experiments

Growth rate measurements of β-cyclodextrin in water were performed both ways. Firstly, experiments were conducted with single monocrystals located in a supersaturation-controlled flow cell. Diffusional limitations and perturbations due to a competition between surface secondary nucleation and growth at high level of supersaturation have been put in evidence. The evolution of the growth rate with supersaturation has been modelled with a BCF law, assuming a screw dislocation mechanism. Secondly seeded cooling batch trials have been carried on in a well-mixed suspension crystallizer in order to assess the growth rate of the seeds. Refractometry was used as an in situ sensor for measuring the evolution of the concentration of the solute. Measurements of the crystals size distribution of the seeds and of the final crystals are performed off line with laser diffraction technique. A kinetic law with three parameters allows a consistent assessment of the growth of the seeds. The comparison of the two sets of data shows that overall growth rate of the seed is partially limited by diffusion. Nevertheless, the estimation of a surface integration growth kinetic coefficient from batch trials is rather difficult. The theoretical framework of nucleation models developed by Mersmann et al. (Crystallization Technology Handbook, second ed., Marcel Dekker, New York, 2001, pp. 45–80 and 81–144) coupled with the estimated growth kinetics can therefore be used to better monitor the seeding process during batch crystallization operations so as to favor the growth of the seed crystals.     

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.     

Total pressure‐controlled PVT SiC growth for polytype stability during using 2D nucleation theory

A total pressure‐controlled physical vapor transport growth method that stabilizes SiC polytype is proposed. The supersaturation of carbon during SiC growth changed as a function of the growth time due to changes in the temperature difference between the surfaces of the source and the grown crystal. Supersaturation also varied as a function of the pressure inside the furnace. Therefore, modification of the pressure as a function of growth time allowed for constant supersaturation during growth. The supersaturation was calculated based on classical thermodynamic nucleation theory using data for heat and species of Si₂C and SiC₂ transfer in a furnace obtained from a global model. Based on this analysis, a method for polytype‐stabilized SiC growth was proposed that involves decreasing the pressure as a function of growth time. The 4H‐SiC prepared using this pressure‐controlled method was more stable than that of 4H‐SiC formed using the conventional constant‐pressure method.     

Impurity segregation in directional solidified multi-crystalline silicon

In this paper numerical results on the impurity segregation in directional solidified multi-crystalline silicon are presented and compared with experimental results. A solute transport model has been established to predict the final segregation pattern of impurities in the ingot. The segregation is analyzed experimentally on the basis of Fourier transform infrared (FTIR) spectroscopy and glow-discharge mass spectrometry (GDMS). Precipitates were located by IR-transmission microscopy (IRM). Qualitative agreement between simulation and experiment is found. It is demonstrated how the flow pattern can influence the final solute distribution. The simulation also shows that the solubility limit of carbon and nitrogen is reached locally in the ingot and SiC and Si₃N₄ precipitates are likely to form.     

Fourier analysis based phase shift interferometric tomography for three-dimensional reconstruction of concentration field around a growing crystal

The present work is concerned with the three-dimensional reconstruction of concentration field around a crystal growing from its aqueous solution using Fourier analysis based phase shift interferometric tomography. Projection data of convective field around a growing NaClO₃ crystal have been recorded using a Mach–Zehnder interferometer. A new numerical method based on the concept of real time phase shift interferometry has been employed for the analysis of the interferograms. By interpreting the interferograms as projection data, the 3-D distribution of salt concentration has been determined using principles of tomography. Study shows that the Fourier analysis-based phase shift method is a novel approach for crystal growth studies as it requires only one interferometric image for the determination of full phase information as opposed to the conventional real time phase shift interferometry wherein at least three or more phase-shifted interferograms are needed. Results have been presented in the form of interferograms, path-integrated concentration contours and three-dimensional concentration profiles over select horizontal planes above the growing crystal. Based on the reconstruction results, distribution of salt concentration in the crystal vicinity is determined and an appropriate mechanism of buoyancy-induced fluid movement in the growth chamber is discussed.     

Growth and characterization of KY(WO4)2 crystals

Single-crystal growth of KY(WO₄)₂ (KYW) by top-seeded solution growth technique has been investigated. The effects of seed orientation, temperature gradient experienced by the growing crystal and rate of crystallization on crystal quality are reported. The best results are obtained when the growth is seeded along the 0 1 0 direction. Minute deviations from this growth direction are found to be detrimental to crystal perfection. The differential thermal analysis shows that the amount of super-cooling required for dissolution and crystallization of KYW in the flux is only 5° and this promotes an easy formation of tiny crystallites in the solution. Consequently, the crystal rotation and the solution cooling rates are found to have pronounced effects on the growth of KYW crystal.     

Explanation of some peculiarities of crystal morphology deduced from the BFDH law

The morphological variety of crystal habits is due to differences in relative growth rates of faces of which the crystal is composed. For equilibrium, the growth rates of faces are proportional to the distances from the centre of the crystal to the respective hkl faces. According to the BFDH law, such distances are inversely proportional to the interplanar distances, therefore the observed crystal faces are those with the largest interplanar distances. This paper tries to explain some peculiarities of the crystal morphology deduced from the BFDH law and shows that the crystal geometry influences morphological importance of faces and because of crystal geometry, the faces of the largest interplanar distances are not necessarily the largest faces in the BFDH morphology.     

ASL model for prediction of CSD in a continuous crystallizer

A Monte Carlo simulation scheme is proposed for crystal size distribution (CSD) in a continuous crystallizer for size dependent growth rate. Crystal growth rates are described by Abegg, Stevens, and Larson (ASL) model. The proposed model is used to predict CSD from potassium carbonate crystallizer. The agreement between theory and available data confirms the validity of the model.