Activity of a Growth Hill,Generated by Two Crossed Screw Dislocations with Equal Burgers' Vectors at Constant Supersaturation and Temperature

The activity of a growth centre, consisting of two transversal screw dislocations with equal Burgers' vectors at constant supersaturation and temperature, is theoretically discussed. A non-linear squared differential equation of the type describing oscillations in autonomous systems is obtained and solved approximately and numerically. The correlation theory - experiment is analysed and the applicability of the results is assessed.     

Metastability and crystal growth kinetics on L‐arginine phosphate

Stability of saturated L‐Arginine Phosphate (LAP) solution studied as a function of supercooling rate and crystal growth kinetics investigated as a function of supersaturation are reported in this communication. Solution stability was studied by observing the metastable zone width at different cooling rates employing a polythermal method. Analysis of the experimental data yielded the kinetic constant of nucleation and the order of nucleation. Crystal growth rates studied on small seed crystals with regular morphology, under normal growth conditions and at different supersaturation levels were found to satisfy BCF surface diffusion model. Crystal growth rates were investigated normal to the (100), (010) and (00 ) faces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Growth rate of single acetaminophen crystals in supersaturated aqueous solution under different operating conditions

Single crystal growth experiments were conducted to investigate the growth rate of acetaminophen (paracetamol) crystals under carefully controlled conditions of temperature, supersaturation and pH value. The relative growth rate of the different faces was studied. Growth Rate Dispersion (GRD) was observed by studying the effect of supersaturation and temperature on the growth rate. The growth rate in all directions was found to be temperature dependant. Elongation of the crystals was measured due to the faster growth in the Y‐ direction and Xa direction compared to in the Xb direction. Dissolution of the crystals was observed at pH values greater than 8.5, and a growth rate retardation was observed when increasing the pH from 5.6, which is the normal value without additions, to higher values in both acidic and basic mediums up to 8.5. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

LPE growth of DH laser structures with the double source method

For the reproducible processing of double heterojunction injection laser structures to stripe geometry laser diodes, e.g. by proton bombardment, the thickness of the p-Ga_0.7Al_0.3As confining layer and of the p-GaAs top layer are of great importance. It is shown that the thickness control of these layers grown by liquid phase epitaxy can be improved considerably by introducing two source crystals into the growth system. Both source crystals are brought into contact with the solutions consecutively and prior to the seed. If this method is combined with the use of relatively thin melts (about 2 mm), a growth scheme may be chosen such that the growth rates of the p-GaAlAs and of the p-GaAs layers have reached a practically constant value on the seed crystal, independent of the initial degree of supersaturation. This behaviour is found to be in accordance with the diffusion-limited growth model applied for thin solutions, including a temperature dependence for both the diffusion constant and the slope of the liquidus curve. The results indicate that a second solid phase may appear in the p-GaAlAs solutions at a supersaturation as small as 4°C, which reduces the growth rate on the substrates by a factor of about 2. This situation is different from that of GaAs solutions, where a second phase appears only at a much higher degree of supersaturation. For the p-GaAlAs and the p-GaAs layers a thickness control of ⁺_-0.2 μm is thus achieved with this growth method, without the necessity of very precise temperature control and weighing so as to keep the total supersaturation less than 0.2°C.     

Study on the Growth of Triglycinsulphate Single Crystals

Crystallization of TGS at 52.0°C - above the transition point - has been studied in a wide range of supersaturation of the solution (σ = 0 to 10⁻²). The rates of growth of {110} and {001} faces were measured as a function of supersaturation at constant hydrodynamical conditions (Re = 3.4 · 10⁻³). Further, the influence of hydrodynamical conditions on the growth of {110} faces at constant supersaturation (σ = 4.2 · 10⁻³) was established. The parameters of the experimentally found dependences are determined on the basis of the surface-diffusion model of BURTON . CABRERA and FRANK . From these dependences follows that the growth rate of the {110} faces is already almost limited by the volume diffusion of TGS molecules towards the crystal surface, while in the case of {001} faces the surface diffusion mechanism of crystallization is clearly manifested. Dislocation densities in the crystals have been determined by means of etching technique. The number of dislocations increases with increasing supersaturation; hence, supersaturation of the solution together with the processes taking place in the regeneration zone surrounding the seed determine the number of dislocations in the crystal volume and thus the resulting structural perfection of single crystals. Investigation of the spontaneous redistribution of domains showed that the growth rate of TGS crystals influences the dielectric properties to much smaller extent than does chemical purity.     

Activity of nonparallel center of growth of (001) face of TGS single crystal under inconstant conditions of crystallization

Morphologic and kinetic behaviour of the hill of the (001) face of TGS crystal, generated by unparallel dislocation center of growth under inconstant supersaturation and temperature has been experimentally examined. Some irreversible changes in the shape of the hill top, as a hysteresis in its normal rate of growth is registered. A model, on the base of which a qualitative anylsis of the phenomenon is proposed.     

Effect of supersaturation on the crystallization of phenylbutazone polymorphs

The article describes the effect of degree of supersaturation, σ, on the crystallization of specific polymorphs of phenylbutazone from its methanolic solution at 20 °C. At low initial supersaturation, σ ≤ 2.0, the fraction of the metastable α polymorph in the crystallized product exceeds that of the δ polymorph, while at σ ≥ 5.0, the fraction of the stable δ polymorph increases in the crystallized product. The results are explained by the effect of supersaturation on the relative rates of nucleation and crystal growth of the polymorphs. Furthermore, the mechanism of nucleation and crystal growth also change with supersaturation. Supersaturated methanolic solutions of phenylbutazone exhibit a critical temperature at which the nucleation rates of the polymorphs decrease drastically. This effect is partly explained by the decreased mobility of phenylbutazone molecules at lower temperatures. Nucleation is most rapid when the crystallization temperature is close to the transition temperature, T_t(α ⟷ δ), between the polymorphs, α and δ. The nucleation rate decreases as the temperature difference between T_t(α ⟷ δ) and the crystallization temperature increases. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measurement and analysis of the dextran partition coefficient in sucrose crystallization

The effect of crystallization conditions on the dextran partition coefficient between impure syrup and sugar crystal has been investigated in a batch crystallizer. The crystallizer is operated isothermally at temperatures of 30, 40, and 50 °C, at constant relative supersaturations of 0.05, 0.07, and 0.09, and with mother liquor dextran concentrations of 1000 and 2000 ppm/Brix. The dextran content has been determined by the CSR method. A 1:1 mass ratio of high-fraction dextran (approximately 250,000 Da) and low-fraction dextran (60,000-90,000 Da) is used to represent a wide range of dextran contamination. It is seen that the dextran partition coefficient in sucrose crystallization increases with both increasing supersaturation and increasing crystallization temperature. However it appears that these are secondary effects, with the partition coefficient strongly correlating with crystal growth rate alone, despite the regressed data having large variations in temperature, mother liquor dextran content, and supersaturation. Dextran incorporation into the sugar crystal results from both dextran adsorption onto the crystal surface and mother liquor inclusions. The explanation for the variation in the dextran content in sugar crystal with respect to the growth rate is due to increased adsorption due to the higher surface roughness of crystals grown at high growth rates. Although the dextran concentration in the solution affects the dextran content in the crystal, it does not strongly affect the dextran partition coefficient.     

Concept of specific supersaturation (specific supercooling) and practical aspects of its application

It is demonstrated that the normal growth rate of crystals from solutions and melts depends on the area of the crystallization front. New growth parameters, namely, the specific supersaturation and the specific supercooling, are introduced, and the quantitative dependence of the normal growth rate on these parameters is determined. It is noted that the normal growth rate affects the formation of defects. The criteria and the range of the possible use of the specific supersaturation (specific supercooling) for optimizing the conditions of crystal growth from solutions and melts are revealed.     

Kinetics of protein crystal nucleation and growth in the batch method

We have applied the Johnson–Mehl–Avrami–Kolomogorov (JMAK) theory of crystal nucleation and growth to the problem of protein crystallization in the batch method. Without integrating the JMAK equation explicitly, we use dimensional analysis to derive a general formula for the half-life for decay of the protein supersaturation. This formula includes a dimensioned group and an arbitrary dimensionless function. We integrate the JMAK equation exactly for the special case where the growth rate is independent of the supersaturation and the nucleation rate is proportional to its square. This gives an equation for the time decay of the supersaturation and a formula for the half-life in which all arbitrary dimensionless functions are evaluated. The results are consistent not only with Von Weimarn's rule, which asserts that the average size of a crystal increases as the supersaturation decreases, but also with our experimental results for crystallization of lysozyme, in which the half-life at fixed pH decreases with increasing ionic strength and decreasing temperature.     

In situ measurement of growth kinetics of {100} KDP crystal faces in the presence of polyphosphate impurities

The face growth rate and critical supersaturation of {100} face were in situ measured using the laser‐polarization‐interference technique in the presence of potassium pyrophosphate, trimetric sodium phosphate and sodium hexametaphosphate impurities. The polyphosphate impurities inhibit the growth rate of prismatic faces. The face growth rate as a function of supersaturation at different impurity concentrations, as well as critical supersaturation as a function of impurity concentrations, was found in good agreement with a two‐dimensional nucleation model in the pure system and Kubota and Mullin's model in the presence of impurities. The average distance L between active sites available for impurity adsorption as well as the edge free energy was calculated. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of forced solution flow on lysozyme crystal growth

In order to study quantitatively the effects of forced solution on crystal growth, we designed a new set of experimental equipment, in particular, a microchannel mixer was used as crystallization container so that the consumption of protein samples was much reduced and thus an exact syringe pump could be used for precise control of the flow rates. Since the mixer's section was designed to be rectangular, the solution velocity in its center was steady and constant, and thus repeatable experiments were facilitated. Experimental results showed that the effects of forced solution on protein crystal growth were different under different levels of supersaturation, and new results were obtained for cases of high supersaturation. When the supersaturation is σ = 2.3, with increasing flow rates the growth rates of the lysozyme crystal's (110) face hardly change when the flow rates are lower than 1300 μm/s, and decrease quickly afterwards. When the flow rate reaches 2000 μm/s, the crystal nearly ceases to grow. When the supersaturation is σ = 2.7, with increasing flow rates the (110) face growth rates increase at the beginning then reach the maximum values at 1700 μm/s – 1900 μm/s and decrease afterwards, approaching zero or so when the flow rate reaches 12000 μm/s. The higher the supersaturation, the larger the flow rate at which the crystal ceases to grow. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the flow velocity,supersaturation and temperature on the crystal growth from solutions

This paper is a review of our experimental research on the influence of the supersaturation, flow velocity and temperature on the linear crystallization rate of different faces of model crystal systems. The obtained experimental results are discussed in the light of the new theoretical treatments on crystal growth from low temperature solutions.     

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: II. Growth kinetics

The experimental results of the effect of concentration of Mn(II) ions on the growth kinetics of different faces of ammonium oxalate monohydrate single crystals from aqueous solutions at a constant temperature and different predefined supersaturations are described and discussed. It was observed that: (1) at a given supersaturation σ, Mn(II) ions lead to a decrease in the growth rates of different faces of AO crystals, (2) the growth of a particular face of the crystals occurs above a critical supersaturation σ_d but there is also another supersaturation barrier σ* when the rate abruptly increases with σ, (3) the values of σ_d and σ* increase with increasing concentration of the impurity, and (4) the values of σ_d depend on the growth kinetics of a face but those of σ* are independent of face growth kinetics. The experimental R(σ) data for different Mn(II) concentrations c_i were analysed according to the model involving complex source of cooperating screw dislocations and concepts of instantaneous and time‐dependent impurity adsorption. It was found that: (1) for a given face the differential heat of adsorption Q_diff is higher during instantaneous impurity adsorption than that during time‐dependent adsorption, and (2) the values of Q_diff involved during instantaneous adsorption are related with face growth kinetics but those during time‐dependent adsorption are independent of face growth kinetics.     

籽晶台形状对PVT法同质外延生长氮化铝单晶初始生长的影响

借助专业晶体生长模拟软件FEMAG和自主开发的对流、传质、过饱和度及生长速率预测等有限元模块研究了物理气相传输法(PVT)同质外延生长氮化铝(AlN)单晶工艺时的初始传热及传质过程,并分析了不同形状籽晶台对生长室内的温度场、流场、过饱和度及生长速率的影响。温度场模拟结果表明籽晶台侧部角度改变可影响籽晶表面轴向及径向温度梯度,流场及传质模拟表明籽晶台侧部角度变化对籽晶台周边的传质有巨大影响。传质及过饱和度模拟结果表明,当籽晶台侧部角度为130°时,籽晶表面温度梯度较小且可以完全抑制籽晶台侧部多晶沉积,有利于通过同质外延工艺生长出无寄生、无裂纹的高质量氮化铝单晶锭。     

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.     

Growth kinetics of ammonium oxalate monohydrate single crystals from aqueous solutions containing Co(II) and Ni(II) impurities

The growth kinetics of different faces of ammonium oxalate monohydrate (AO) single crystals from aqueous solutions containing different concentrations of Co(II) and Ni(II) ions at a constant temperature are described and discussed. It was found that: (1) at a given supersaturation σ, both Co(II) and Ni(II) ions lead to a decrease in the growth rates R of different faces of AO crystals, (2) the growth of a particular face of the crystals occurs above a critical supersaturation σ_d, but there is also another supersaturation barrier σ* when the rate abruptly increases with σ, and (3) the values of σ_d and σ* increase with increasing concentration c_i of the impurity. The experimental R(σ) data for different concentrations c_i of the impurities were analysed according to the model involving complex source of cooperating screw dislocations and concepts of instantaneous and time‐dependent impurity adsorption. Analysis of the data showed that: (1) adsorption of Co(II) and Ni(II) impurities occurs on the surface terrace of AO crystals, (2) there is a simple relationship between Langmuir constant K and the impurity concentration c_i* corresponding to maximum surface coverage, and (3) the ratio σ_d/σ* of the supersaturation barriers observed in the presence of both impurities increases with an increase in impurity concentration c_i, and may be explained from the standpoint of the mechanism of adsorption of impurity particles at kinks and ledges. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Growth kinetics of zinc(tris)thiourea sulphate (ZTS) crystals

Growth kinetics of zinc (tris) thiourea sulphate (ZTS) crystals investigated as a function of supersaturation is reported in this communication. Crystal growth rates were investigated normal to the (100), (010) and (001) faces under growth conditions employed for bulk crystal growth. The growth rates normal to (010) and (100) were found to follow the continuous growth model (R_G = Cσ) with respect to the supersaturation whereas the growth rates normal to (001) was found to satisfy birth and spread (B+S) model (R_G = Aσ^5/6 exp(‐B/σ)). The growth rates observed normal to the studied face are in agreement with the growth mechanism predicted from the estimated α (Jackson) factor. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)