Growth kinetics of CaF2 in a pH-stat fluidized-bed crystallizer

In this study, experiments were first conducted in a stirred vessel to establish the metastable region of calcium fluoride, using a pH-stat apparatus for controlling the pH value of solution. The effects of pH value on the solubility and metastable region were observed. Then, operating variables, including supersaturation, superficial velocity, pH value, seed size, and types of seed and solution, that influenced the crystal growth of the same system were investigated in a fluidized-bed crystallizer. The crystal growth rates were determined from the consumption rates of fluoride ions. The growth kinetics was explored by using the two-step growth model. The effectiveness factor was used to judge whether a controlling step was existing. The kinetics of crystal growth in a lean bed and a dense bed was also discussed.     

KDP晶体生长的溶液流动和物质输运计算

本文采用有限容积法,对KDP晶体生长过程中溶液的流动和物质输运进行了数值模拟.结果表明:随着入口溶液流动速度的增大,籽晶的上表面因自然对流而引起的抽吸作用减小,表面过饱和度的最小值沿x正向发生右移,其上表面的剪切力先减小后增大.随着入口溶液过饱和度的增大,籽晶上表面剪切力增大.不同尺寸的籽晶表面过饱和度的分布差异较大.籽晶的生长边界层厚度与溶液流动密切相关,入口溶液流动速度越大,厚度越小,但其受入口溶液过饱和度的影响较小.     

Effect of mixing on the crystal size distribution of borax decahydrate in a batch cooling crystallizer

The effect of the impeller speed upon the metastable zone width, supersaturation level, crystal growth and the crystal size distribution of borax decahydrate have been investigated to find operating conditions of a batch cooling crystallizer. The importance of impeller speed was studied in baffled stirred crystallizer with a volume of about 2 dm³, equipped with four straight blade turbine (4-SBT) cooling at a constant cooling rate. The metastable zone width was determined by visual method, while concentration changes during the process were monitored in line using ion-selective electrode. The crystal size distribution was determined by optical microscope and sieve analysis respectively. The power consumption measurements were performed for all impeller speeds examined as well. On the basis of the experimental results and observations it is evident that in an agitated batch crystallizer the above mentioned parameters are significantly influenced by hydrodynamic regime in the system determined by impeller used and its revolution speed.     

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.     

Crystallization of zinc lactate in presence of malic acid

The influence of malic acid, which acts as an impurity on the cooling crystallization of zinc lactate is investigated in this paper by monitoring the relative supersaturation and the number of crystals during crystallization. The presence of malic acid increases the solution solubility and makes the metastable zone wider; it also changes the habit of the crystal. The purity of the final products is shown to be influenced by the amount and size of seed crystals, cooling rate, seeding temperature and final temperature, but appears to depend mainly on the particle size and level of supersaturation. Residual supersaturation thresholds are observed that depend on the final temperature. A model is proposed to predict the steady-state supersaturation value from the final temperature at a given impurity concentration. This model is based on Kubota and Gibbs equations.     

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.     

The influences of supersaturation on LPE growth of GaN single crystals using the Na flux method

The dependency of LPE growth rate and dislocation density on supersaturation in the growth of GaN single crystals in the Na flux was investigated. When the growth rate was low during the growth of GaN at a small value of supersaturation, the dislocation density was much lower compared with that of a substrate grown by the Metal Organic Chemical Vapor Deposition method (MOCVD). In contrast, when the growth rate of GaN was high at a large value of supersaturation, the crystal was hopper including a large number of dislocations. The relationship between the growth conditions and the crystal color in GaN single crystals grown in Na flux was also investigated. When at 800 °C the nitrogen concentration in Na–Ga melt was low, the grown crystals were always tinted black. When the nitrogen concentration at 850 °C was high, transparent crystals could be grown.     

Analysis of SiC crystal sublimation growth by fully coupled compressible multi-phase flow simulation

A fully coupled compressible multi-phase flow solver was developed to effectively design a large furnace for producing large-size SiC crystals. Compressible effect, convection and buoyancy effects, flow coupling between argon gas and species, and the Stefan effect are included. A small and experimental furnace is used to validate the solver. First, the essentiality of 2D flow calculation and the significance of incorporating buoyancy effect and gas convection, the Stefan effect, and flow interaction between argon gas and species were investigated by numerical results. Then the effects of argon gas on deposition rate, growth rate, graphitization on the powder source, and supersaturation and stoichiometry on the seed were analyzed. Finally, the advantages of an extra chamber design were explained, and improvement of growth rate was validated by the present solver.     

Segregation of Ga during growth of Si single crystal

Segregation phenomenon of Ga in Czochralski (CZ)–Si crystal growth has been investigated. The effective segregation coefficient, k_eff, of Ga was obtained for different growth rates by assuming the simple relationship between the concentration of Ga in Si crystal and the bulk Ga concentration in melt. Applying BPS theory to effective segregation coefficients which is valid for the melt-solidified fraction up to 0.38, an equilibrium segregation coefficient of Ga was obtained, k₀=0.0079.     

Solvent effects on the growth kinetics of subtilisin crystals

The effects of salts on subtilisin crystallization were investigated. Three salts—NaCl, NaNO₃ and NaSCN—were selected to study the effects of different anions on growth kinetics of three subtilisin mutants—Properase^®, Purafect^® and Purafect^®OX. The effectiveness of salts in decreasing the solubility of Properase^® and Purafect^® subtilisin followed the reverse order of the Hofmeister series: SCN⁻>NO₃⁻>Cl⁻. The average length and diameter of crystals were measured during crystallization. The nature of salt changed the length/diameter ratio of crystals, indicating the changes in the relative growth rate of different crystal faces. The required supersaturation, (c−s)/s, for a given growth rate increased in the order of NaCl, NaNO₃ and NaSCN. The observed trend in required supersaturation indicates a kinetic effect and was counter to the trend for the solubility data. A rationale is provided based on the influence of ion binding and kinetics on the energetics of crystal growth and growth rate is correlated to the molar Gibbs free energy of hydration of the anion.     

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.     

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.     

Growth of SiGe bulk crystals with uniform composition by utilizing feedback control system of the crystal–melt interface position for precise control of the growth temperature

We developed an automatic feedback control system of the crystal–melt interface position to keep the temperature at the interface constant during growth, and demonstrate its successful application to grow Ge-rich SiGe bulk crystals with uniform composition. In this system, the position of the crystal–melt interface was automatically detected by analyzing the images captured using in situ monitoring system based on charge-coupled-devices camera, and the pulling rate of the crucible was corrected at every 1 min. The system was found to be effective to keep the crystal–melt interface position during growth even when the variation of the growth rate is quite large. Especially, the interface position was kept for 470 h during growth of Ge-rich SiGe bulk crystal when we started with a long growth melt of 80 mm. As a result, a 23 mm-long Si_0.22Ge_0.78 bulk crystal with uniform composition was obtained thanks to the constancy of the growth temperature during growth through the control of the interface position. Our technique opens a possibility to put multicomponent bulk crystal in a practical use.     

Influence of growth conditions on microstructure and properties of GaSe crystals

GaSe crystals have been grown from melt. There are several reasons why it is difficult to meet ideal demands for nonlinear optic material, GaSe single crystal. First, these crystals have a tendency towards lamination because of great difference in a and c crystal lattice parameters and very weak Vander der Waals forces in c direction. Next, there is a great difference in saturation vapor pressure of the components, which can cause nonstoichiometry of a melt-grown crystal composition. Another obstacle in the growth of perfect GaSe crystals is dendrite formation caused by instability of the growth front. To overcome this obstacle we used Bridgman technique and have found the temperature and pressure conditions, and growth velocity which provide growth of perfect bulk single crystals of about 100 mm in length and 20 mm in diameter. Sharp Laue patterns and a rocking curve confirm perfect structure of the grown crystals. Electron-probe X-ray microanalysis shows stoichiometric composition of GaSe crystals and X-ray phase analysis reveals presence of single-phased hexagonal structure.     

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.     

Numerical study to investigate the effect of partition block and ambient air temperature on interfacial heat transfer in liquid bridges of high Prandtl number fluid

Surface heat transfer at the liquid–air interface in liquid bridges of high Prandtl number fluid is known to affect the transitional characteristics appreciably. The heat transfer characteristics under microgravity conditions become much different from those of normal gravity mainly due to the absence of natural convection. The present study deals with numerical computations of flow and heat transfer characteristics in the liquid and surrounding air and also at the liquid–air interface of thermocapillary flow in liquid bridges of high Prandtl number fluid. The governing equations are solved in the coupled domain of the liquid bridge and the surrounding air with the help of available commercial CFD software. The results obtained for a range of Marangoni numbers indicate that by placing a partition block in the air region under normal gravity conditions, the surface heat transfer characteristics of microgravity conditions could be effectively mimicked. The effect of ambient temperature on the surface heat transfer has also been investigated and it has been found that the behavior of heat transfer at the interface changes from heat loss to heat gain when the ambient temperature is increased. Moreover, the presence of partition block under normal gravity suppresses surface heat loss as well as surface heat gain similar to microgravity conditions. Streamlines and temperature contours have been presented for various conditions in order to clarify the underlying physics more meaningfully. The computed profiles for velocity and temperature at the liquid–air interface have been validated against established experimental results.     

Determination of kinetic parameters of crystal growth rate of borax in aqueous solution by using the rotating disc technique

Growth rate of polycrystalline disc of borax compressed at different pressure and rotated at various speed has been measured in a rotating disc crystallizer under well-defined conditions of supersaturation. It was found that the mass transfer coefficient, K, increased while overall growth rate constant, K_g, and surface reaction constant, k_r, decreased with increasing smoothness of the disc. It was also determined that kinetic parameters (k_r,r,K,g) of crystal growth rate of borax decreased with increasing rotating speed of the polycrystalline disc. The effectiveness factor was calculated from the growth rate data to evaluate the relative magnitude of the steps in series bulk diffusion through the mass transfer boundary layer and the surface integration. At low rotating speed of disc, the crystal growth rate of borax is mainly controlled by integration. However, both diffusion and integration steps affect the growth rate of borax at higher rotating speed of polycrystalline disc.     

Improvement of crystal quality in ammonothermal growth of bulk GaN

Several key improvements in crystal quality of bulk GaN grown by the ammonothermal method are presented. Full width at half maximum of (0 0 2) X-ray rocking curve was reduced to 53 and 62 arcsec for Ga-side and N-side, respectively. Transparent bulk GaN crystal was also demonstrated. Oxygen and sodium concentrations were reduced to mid-10¹⁸ and mid-10¹⁵ cm⁻³, respectively. We are currently searching for a growth condition that produces transparent bulk GaN with high structural quality and low impurities. Small-sized, semi-transparent GaN wafers were fabricated by slicing the grown bulk GaN crystals, which demonstrate the high feasibility of ammonothermal growth for production of GaN wafers.     

Solid mechanics and material strength studies on the melt growth of bulk single crystals

Microdefects such as dislocations and macrocracking should be controlled during the crystal growth process to obtain high-quality bulk single crystals. Solid mechanics and material strength studies on the single crystals are of importance to solve the problems related to the generation and multiplication of dislocations and the cracking of single crystals. The present paper reviews such research activities that comprise the thermal stress analysis during crystal growth process, the dislocation density estimation during crystal growth process, and the cracking of single crystal due to thermal stress.     

Study of the metastable region in the growth of GaN using the Na flux method

It was revealed that the metastable region, in which liquid phase epitaxy (LPE) of GaN single crystals proceeds without the generation of polycrystals, expands with growth temperature in the Na flux method. The metastable region appears when LPE growth proceeds at temperatures above 1073 K, although generation of polycrystals inevitably occurs on a crucible at temperatures less than 1073 K. The highest growth rate of 14 μm/h in a small experimental setup was achieved at a temperature of 1163 K with a nitrogen pressure of 5.5 MPa due to complete suppression of the growth of polycrystals on a crucible, even though the supersaturation at this condition reached a fairly high level.Also, an LPE crystal with a flat surface could easily be obtained under high-temperature conditions.