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)     

一水甲酸锂晶体生长界面过饱和度的测量

本文采用激光全息相衬干涉显微术研究了有机非线性光学晶体一水甲酸锂晶体的生长,计算了晶体生长的界面过饱和度.我们的研究结果表明,晶体生长的界面过饱和度随体过饱和度的增加而非线性增加;不同晶面的界面过饱和度不同;当体过饱和度增加到一定程度时,不同晶面的界面过饱和度趋于相同.     

Study on rapid growth of highly‐deuterated DKDP crystals

Highly‐deuterated potassium dihydrogen phosphate (DKDP) crystals were grown rapidly from point seeds under high supersaturation in a temperature range of 40‐60 °C. The growth rate was about 1‐2 order of magnitude higher than that of the traditional temperature reduction method. It was found that highly pure raw materials, overheating at high temperature, ultrafine filtration and supersaturation stability were needed to keep the solution from spontaneous nucleation at high overcooling. The effect of growth conditions on pyramid faces was different from that of prismatic faces. The tetragonal to monoclinic phase solubility transition scarcely occurred in our experiments even though the overcooling of monoclinic phase was as high as 10 °C in some cases. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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.     

Fundamental aspects of VLS growth

The kinetics and the mechanism of the vapor-liquid-solid (VLS) growth are discussed. Emphasis is placed on the dependence of the growth rate on the whisker diameter. It is found that the rate decreases abruptly for submicron diameters and vanishes at some critical diameter d_c ? 0,1 μm according to the Gibbs-Thomson effect. A new method for simultaneous determination of kinetic coefficients and of supersaturations has been developed. The method can be used to measure the coefficients of some materials as well as the temperature dependence of the coefficient for silicon and the activation energy of the process. From the dependence of supersaturation on the diameter we conclude that whiskers grow by a poly-nuclear mechanism. The periodic instability of the diameter is discussed and the rate-determining step is analysed. We conclude that phenomena on the liquid-solid interface are the decisive ones. In determining the role of liquid phase in vapor growth we measured the “liquid phase effectivity coefficient” as a function of crystallization condition; the coefficient typically was about 10²?10³. It is stressed that the liquid phase reduces the activation energy both on vapor-liquid interfaces (for chemical reactions) and on liquid-solid interfaces (for nucleation). The liquid phase ensures growth rates as high as 1 cm/sec, provided there are no barriers between the interfaces. The growth mechanism of the side faces was studied, and it was observed that the faces grow mainly by a chain mechanism rather than by two-dimensional nucleation. In work on surface diffusion in the VLS whiskers growth by CVD, we found that the whiskers grow mainly by direct deposition rather than by diffusion on the side faces. It is concluded that the VLS mechanism is important also for the vapor growth of platelets, films, and bulk crystals.     

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)     

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.     

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: I. Growth habit and surface morphology

The effect of concentration of Mn(II) ions on the growth habit and the surface micromorphology of different as‐grown faces of ammonium oxalate monohydrate (AO) single crystals grown from aqueous solutions was studied at a constant temperature of 30 °C and predefined supersaturations up to 20%. It was observed that the growth habit and the surface morphology of the crystals strongly depend on the supersaturation used for growth and the impurity concentration in the solution. The experimental results were analysed in terms of connected nets determined from different projections of the structure of AO crystals. Analysis of the observations revealed that: (1) the directions of connected nets corresponding to basic growth units composed of single (NH₄)₂C₂O₄ · H₂O molecules are in excellent agreement with the low‐index crystallographic directions of the orientations of growth layers, (2) all faces appearing in the growth morphology of AO crystals are F faces, and (3) the {001} face growing from pure aqueous solutions is essentially a kinetically rough face but the presence of Mn(II) impurity leads to their appearance in the morphology due to increase in the strength of bonds of the connected nets composing the surface graph.     

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)     

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)     

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。     

一水甲酸锂单晶生长和(110)面边界层的全息研究

本文合成一水甲酸锂原料,选择适宜生长条件,用水溶液法培育出完美一水甲酸锂单晶(LFM).利用全息相衬干涉显微术对(110)面边界层特性进行实时观测和研究.实验表明,在自然对流情况下,边界层内折射率梯度分布函数Δn(x)和浓度分布函数Cx(x)为指数形式;另外,体过饱和度与晶面过饱和度之间呈指数关系.     

大尺寸电阻加热式碳化硅晶体生长热场设计与优化

大尺寸低缺陷碳化硅(SiC)单晶体是功率器件和射频(RF)器件的重要基础材料,物理气相传输(physical vapor transport, PVT)法是目前生长大尺寸SiC单晶体的主要方法。获得大尺寸高品质晶体的核心是通过调节组分、温度、压力实现气相组分在晶体生长界面均匀定向结晶,同时尽可能减小晶体的热应力。本文对电阻加热式8英寸(1英寸=2.54 cm)碳化硅大尺寸晶体生长系统展开热场设计研究。首先建立描述碳化硅原料受热分解热质输运及其多孔结构演变、系统热输运的物理和数学模型,进而使用数值模拟方法研究加热器位置、加热器功率和辐射孔径对温度分布的影响及其规律,并优化热场结构。数值模拟结果显示,通过优化散热孔形状、保温棉的结构等设计参数,电阻加热式大尺寸晶体生长系统在晶锭厚度变化、多孔介质原料消耗的情况下均能达到较低的晶体横向温度梯度和较高的纵向温度梯度。     

Precipitates originating from tungsten crucible parts in AlN bulk crystals grown by the PVT method

In order to evaluate the possible involvement of crucible materials in the growth of AlN bulk crystals grown by physical vapor transport, we applied growth conditions with a high vertical thermal gradient and hence high supersaturation of aluminum vapor. Under these conditions, precipitates formed causing diffuse grayish substructures at the initial growth interface and in the crystal body, decorating dislocations. Electron microscopy studies revealed that the precipitates are elongated, single‐phase particles with sizes of 50–500 nm of commensurate structure, oriented along the <110> direction. Chemical analysis of the precipitates showed tungsten as well as carbon and oxygen. The lattice parameters of the precipitates are in close agreement to hexagonal tungsten hemicarbide (W₂C). The possible transport from the tungsten parts and its conversion into tungsten hemicarbide precipitates is discussed. We thus conclude that the W₂C precipitates may contribute to the decoration of dislocations, even in growth with moderate thermal gradients.     

Habit modification and improvement in properties of potassium hydrogen phthalate (KAP) crystals doped with metal ions

Potassium hydrogen phthalate (KAP) single crystals were grown by slow evaporation and slow cooling techniques. The growth procedure like temperature cooling rate, evaporation rate, solution pH, concentration of the solute, supersaturation ratio etc., has been varied to have optically transparent crystals. Efforts were made to dope the KAP crystals with rubidium, sodium and lithium ions. The dopant concentration has been varied from 0.01 to 10 mole percent. Good quality single crystals were grown with different concentrations of dopants in the mother phase. Depending on the concentration of the dopants and the solution pH value, there is modification of habit. Rubidium ions very much improve the growth on the prismatic faces. The transparency of the crystals is improved with rubidium and sodium doping. The role of the dopants on the non‐linear optical performance of KAP indicates better efficiency for doped crystals. The grown crystals were characterized with XRD, FT‐IR, chemical etching, Vickers microhardness and SHG measurements. The influence of the dopants on the optical, chemical, structural, mechanical and other properties of the KAP crystals was analysed. © 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

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)     

Developments in crystal growth from high-temperature solutions

With the technological advances in the past 12 years, and with the high quality of flux-grown crystals and layers, this crystal-growth technique has become increasingly important. The technological parameters which have to be optimized to achieve large structurally perfect crystals, of high purity and free of striations, are: choice of solvent, growth temperature and its control, temperature gradient at and along the growth interface, supersaturation, and hydrodynamics. Top-seeded solution growth and the accelerated crucible rotation technique are the most widely applied techniques for growth of large high-quality crystals.     

The influence of crystallization conditions on the onset of dendritic growth of calcium carbonate

Understanding the crystallization of calcium carbonate is relevant in numerous fields like biomineralization, geology and industrial applications where calcium carbonate forms. In order to enhance the knowledge about the formation of calcium carbonate with focus on the vaterite polymorph, in this work calcium carbonate has been crystallized in aqueous solutions at temperatures from 5 °C to 90 °C. Special attention has been directed to higher temperatures for which the effect of the initial supersaturation on the resulting crystal morphologies and the onset of dendritic growth have been studied. In analogy to snow crystal formation, it has been found that in a certain temperature range hexagonal plate‐like crystals form at low supersaturation whereas dendritic patterns start to appear at higher supersaturation. The symmetrical branches characteristic for dendritic growth get less pronounced as the temperature is decreased. The results reported here related to the interdependence between supersaturation, crystal morphology and growth mechanisms, can be used in future works to predict particle formation and to design crystal architectures. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Supersaturation and Temperature on the Growth Morphology of Ammonium Oxalate Monohydrate Crystals Obtained from Aqueous Solutions

The experimental results of a study of the effect of supersaturation and temperature on the growth morphology of ammonium oxalate monohydrate [(NH₄)₂C₂O₄H₂O; AO] single crystals obtained from aqueous solutions at 30 and 40 °C and supersaturation up to 9% are presented. The observations are analysed in terms of theoretical morphology, growth models and attachment energy for growth units in steps of growing faces.