Observation of concentration boundary layers around growing or dissolving KH2PO4 crystals in stagnant solutions

The solute concentration profiles around KH₂PO₄ crystals growing or dissoloving in stagnant aqueous solutions were studied by the schlieren method after Toepler. By this technique the thicknesses of concentration boundary layers around the crystals, formed by free convection of solution, were measured in dependence of crystal size and super (under) saturation. In the case of dissolution, theoretical estimation of the boundary layer thickness yielded a fair agreement with the observed value. For growth, the process is dominantly limited by surface kinetics, whereas volume diffusion plays a minor role.     

Effect of surface tension‐driven flow on BaB2O4 crystal growth from high temperature melt‐solution

The surface tension driven‐flow in BaB₂O₄ (BBO) melt‐solution is visualized by differential interference microscope coupled with Schlieren technique, and the streamline of the steady thermocapillary convection is found to be in form of an axially symmetric pattern. Based on the observation of BBO crystal rotation caused by the convective vortex, the widths of interfacial concentration, heat and momentum boundary layer are calculated. The effect of thermocapillary convection on boundary layer thickness is also investigated. Results show that the width of boundary layer decreases linearly with the increasing of dimensionless Marangoni number. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coarse crystal layer growth and liquid entrapment study with gradient freeze technology

The coarse crystal layer growth and liquid entrapment processes were investigated with gradient freeze technology in this paper. The research system was hemihydrate phosphoric acid (H₃PO₄·0.5H₂O) crystal‐phosphoric acid aqueous solution. The distribution coefficients of ions (Ca²⁺, Fe³⁺ and Na⁺) in this system were measured. The effect of supercooling degree gradient on layer growth and the effect layer growth rate on ions redistribution were studied. The result indicated that the layer growth rate increased with supercooling degree gradient as an exponential curve. The distribution coefficient tended to increase as an approximate ‘S’ curve when coarse crystal layer growth rate increased. The ‘three region’ theory was applied to explain this phenomenon. Each ion's diffusion parameter was obtained, which contributed to explain the separation differences between different ions. The work in this paper also indicated that layer crystallization was an effective separation technology for electronic grade phosphoric acid preparation.     

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)     

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.     

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.     

Results of crystal growth of bismuth-antimony alloys (Bi100–xSbx) in a microgravity environment

Results of two experiments are presented for growth of crystals from (Bi_100–xSb_x) alloys in a microgravity environment. In the growth experiments different variants of the Bridgman technique were used. It was shown that in crystal growth from the melt in closed ampoules under microgravity conditions convection can be prevented completely. Therefore it is possible to grow crystals from melts of some components under diffusion controlled conditions of mass transfer. In microgravity a reduced interaction between the melt and the confining walls was observed even if they have large contact with each other. The investigation of surface morphology corroborated the importance of surface effects for crystal growth from the melt under microgravity conditions. Measurements of electronic properties of crystals grown in microgravity showed a good quality in comparison to earth grown crystals. Because under microgravity conditions in closed ampoules the diffusion controlled mass transfer can be realized and the interaction between the melt and confining wall is reduced, homogeneous crystals with high perfection can be grown melts of some components.     

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.     

Solutal convection around growing protein crystals and diffusional purification in Space

Convective and diffusional mass transport to an isolated crystal growing from solution, with slow linear interface kinetics, is considered analytically as a generic scaling model. We focus on the interface kinetics which is slow as compared to the diffusion mass transport which is typical of protein crystal growth. Independently, full-scale numerical solutions of transport equations around a cylindrical crystal, at the center of the bottom of a cylindrical cell filled with the solution, are found. The two approaches give results that agree over a wide range of parameters, providing dimensionless relationships that allow predictions of the contribution of convection and diffusion to mass transport. Requirements for microgravity level in Space experiments to achieve diffusional mass transport are estimated on the basis of these relationships. Coefficients of impurity distribution between a growing crystal and its solution, under the influences of convection and diffusion around the crystal, were numerically evaluated as functions of time. The results provide further support for the hypothesis concerning the role of the impurity depletion zone in the purification of a growing crystal. They also reveal that in general, the impurity distribution within the crystal is not homogeneous due to convection. The effects of various factors on growth kinetics and crystal purity are considered.     

Optimization of control parameters of cadmium zinc telluride Bridgman single crystal growth

The temperature gradient within a furnace chamber and the crucible pull rate are the key control parameters for cadmium zinc telluride Bridgman single crystal growth. Their effects on the heat and mass transfer in front of the solid‐liquid interface and the solute segregation in the grown crystal were investigated with numerical modeling. With an increase of the temperature gradient, the convection intensity in the melt in front of the solid‐liquid interface increases almost proportionally to the temperature gradient. The interface concavity decreases rapidly at faster crucible pull rates, while it increases at slow pull rates. Moreover, the solute concentration gradient in the melt in front of the solid‐liquid interface decreases significantly, as does the radial solute segregation in the grown crystal. In general, a decrease of the pull rate leads to a strong decrease of the concavity of the solid‐liquid interface and of the radial solute segregation in the grown crystal, while the axial solute segregation in the grown crystal increases slightly. A combination of a low crucible pull rate with a medium temperature gradient within the furnace chamber will make the radial solute segregation of the grown crystal vanish. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetics of crystal growth of strontium tungstate from solutions in sodium tungstate melts by continuous cooling

The crystallisation kinetics of strontium tungstate from unstirred saturated solutions in sodium tungstate melts was studied by continuous cooling from initial crystallisation temperatures T₀ = 1000° to 800°C to room temperature at cooling rates R_T = 0.67° to 3.3°C min⁻¹. The main crystal growth was diffusion rate-controlled; the final crystal growth was rate-controlled by the development rate of excess solute concentration. The estimated diffusion rate constant (k_D) values increased with cooling rates and initial crystallisation temperatures. They are higher than the rate constants for diffusion-controlled growth of calcium tungstate from sodium tungstate melts, but very much smaller than those for strontium tungstate from lithium chloride melts.     

Crystal growth and transport rates of GeSe and GeTe in micro-gravity environment

Six vapor transport experiments on the systems GeSe-GeI₄ and GeTe-GeI₄ were performed on Skylab to determine the effects of micro-gravity on crystal growth and transport rates. Based on a direct comparison of crystals and transport data obtained on earth and in space, employing X-ray diffraction, microscopic and etching techniques, the results demonstrate a considerable improvement of the space grown crystals in terms of growth morphology and bulk perfection. The observation of greater mass transport rates than expected in micro-gravity for diffusion-controlled transport could indicate the existence of other transport modes in a reactive solid-gas phase system. The combined results show that the interference of gravity-driven convection with the transport process causes negative effects on crystal growth as observed on earth for otherwise identical conditions. This points to the unique environment of weightlessness for the observation of basic transport phenomena.     

CFD modelling of single crystal growth of potassium dihydrogen phosphate (KDP) from binary water solution at 30 °C

Crystal growth rate depends on both diffusion and surface reaction. In industrial crystallizers, there exist conditions for diffusion-controlled growth and surface reaction-controlled growth. Using mathematical modelling and experimental information obtained from growth studies of single crystals, it is possible to separate these phenomena and study how they are affected by concentration, slip velocities of particles, temperature and finally estimate the parameters for crystal growth models.In this study, a power-law growth model using activity-based driving force is created. Computational fluid dynamics (CFD) was used to evaluate the thickness of a diffusion layer around the crystal. Parameters of the crystal growth model were estimated using a non-linear optimization package KINFIT. Experimental data on growth rate of the (1 0 1) face of a potassium dihydrogen phosphate (KDP) single crystal and simulated data on the thickness of a diffusion layer at the same crystal face were used in parameter estimation. The new surface reaction model was implemented into the CFD code. The model was used to study the effect of flow direction on growth rate of the whole crystal with various slip velocities and solute concentrations.The developed method itself is valid in general but the parameters of crystal growth model are dependent on the system. In this study, the model parameters were estimated and verified for KDP crystal growth from binary water solution.     

Nonlinear dynamics of layer growth and consequences for protein crystal perfection

In situ high-resolution optical interferometry of lysozyme crystal growth reveals that under steady external conditions, the local growth rate R, vicinal slope p and step velocity are not steady but fluctuate by several times their average values. The variations in p, which is proportional to the local step density, indicate that these fluctuations occur through the dynamic formation of step bunches. Our previous work with unstirred solutions has shown that the fluctuation amplitude of R increases with supersaturation and crystal size (Vekilov et al., Phys. Rev. E 54 (1996) 6650). Based on scaling arguments and numerical simulations, we have argued that the fluctuations are the response of the coupled bulk transport and nonlinear interface kinetics to finite amplitude perturbations provided by the intrinsically unsteady step generation. In this paper, we emphasize the recently discovered spatio-temporal correlation between the sequence of moving step bunches and striations (compositional variations) in the crystal, visualized by polarized-light microscopy. Hence, these unsteady kinetics have detrimental effects on the perfection of the crystals, and means to reduce and eliminate them should be sought. To this end, based on the above conclusion as to the mechanism of the kinetic unsteadiness, we accelerated the bulk transport towards the interface by forced solution flow. We found that this results in lower fluctuation amplitudes. This observation confirms that the system-dependent kinetic Peclet number, Pe_k, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe_k can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities. Interestingly, on further increase of the solution flow velocities >500 μm/s, the fluctuation amplitudes in R increased again, while the average growth rate decreased. At low supersaturations, this leads to growth cessation. The growth instability, deceleration and cessation were immediately reversible upon reduction of the flow velocity. When solutions, intentionally contaminated with ∼1% of covalent lysozyme dimer were used, these undesirable phenomena occurred at about half the flow rates required in pure solutions. Thus, we conclude that enhanced convective supply of impurities to the interface causes an increase in step-bunching related defects, growth deceleration and, in some cases, cessation. Finally, we correlate the “slow protein crystal growth” to step bunch formation. We show that in the absence of significant step density variations, the kinetic coefficient for step propagation is as high as 4×10⁻³ cm/s, which is 1–2 orders of magnitude higher than the previously determined, apparent values for any protein.     

Nd:YVO4 crystal growth by Czochralski technique with a submerged plate

This paper is to investigate the growth of Nd:YVO₄ (yttrium vanadate) crystal by the modified Czochralski technique with a submerged plate. Numerical studies are performed to examine melt convection and heat transfer during Nd:YVO₄ growth. The attention is paid to study the effects of initial elevation of the submerged plate, crystal diameter, and melt level on melt inclusions. It is found that the increase in crystal rotation rate and crystal diameter, and the decrease in melt level will increase the axial temperature gradient at the edge and in the center of the crystal, and change the interface shape from convex to flat. The experiments are also carried out to confirm the feasibility of the proposed new technique for controlling melt inclusions in Nd:YVO₄ crystal growth.     

ACRT forced convection and its effects on solute segregation and heat and mass transfer during single crystal growth

A numerical simulation study was carried out for CdZnTe vertical Bridgman method crystal growth with the accelerated crucible rotation technique (ACRT). The convection, heat and mass transfer in front of the solid‐liquid interface, and their effects on the solute segregation of the grown crystal can be characterized with the following. ACRT brings about a periodic forced convection in the melt, of which the intensity and the incidence are far above the ones of the natural convection without ACRT. This forced convection is of multiformity due to the changes of the ACRT parameters. It can result in the increases of both the solid‐liquid interface concavity and the temperature gradient of the melt in front of the solid‐liquid interface, of which magnitudes vary from a little to many times as the ACRT wave parameters change. It also enhances the mass transfer in the melt in a great deal, almost results in the complete uniformity of the solute distribution in the melt. With suitable wave parameters, ACRT forced convection decreases the radial solute segregation of the crystal in a great deal, even makes it disappear completely. However, it increases both the axial solute segregation and the radial one notably with bad wave parameters. An excellent single crystal could be gotten, of which the most part is with no segregation, by adjusting both the ACRT wave parameters and the crystal growth control parameters, e.g. the initial temperature of the melt, the temperature gradient, and the crucible withdrawal rate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Heat transfer and fluid flow in HEM crystal growth of silicon in cylindrical cavity is studied numerically. The walls of the crucible are heated to a fixed temperature. The exchanger that causes and induces natural convection is seated at the middle‐bottom of the crucible. The finite‐volume method is employed to solve the governing equations with proper boundary conditions. The effects of transport mechanism on the temperature distribution, melt flow, pressure and stream function are presented. We focus our work on the pressure field which has not yet been studied in HEM crucible. Also, we extend our work on a wide range Grashof number and for large numbers until 10¹² not yet studied in HEM furnace. It is found that the onset of flow fluctuations appears at Gr = 10¹⁰. Uniform temperature is observed in the entire melt at high Grashof number with development of a thermal boundary layer close to the exchanger. The thermal boundary layer thickness is calculated for strong buoyancy regime. Besides, for very high Gr number, buoyancy has less effect on temperature and then on melt‐crystal interface shape. During enlarging Gr, pressure evolution is related to temperature variation more than flow pattern.     

Determination of individual rate constants of reaction and diffusion steps from over-all crystal growth coefficient

A universal method, being a solution of the problem formulated independently by NÝVLT and GARSIDE in 1971 is proposed. The method makes it possible — having at one's disposal the experimental growth rate constant — to determine individual rate constants of the main steps of the process of crystal growth i.e., the diffusion step and the surface integration step and thus indicate the step controlling the whole process of crystal growth. Experimental data on crystal growth of MgSO₄ and ZnSO₄ were evaluated.     

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)     

Change of symmetry and rotation of thermal field as a new method of control of heat and mass transfer in crystal growth (by example of β-BaB<Subscript>2</Subscript>O<Subscript>4</Subscript>)

It is suggested to change the symmetry and rotation of thermal field as a method of contact-free control of the heat and mass transfer in crystal growth. By the example of growth of the low-temperature barium borate (β-BaB₂O₄) phase, a technically important crystal with nonlinear-optical properties, it is shown that the use of the suggested method allows one to grow larger crystals of a higher quality.