On the Mechanism of Crystal Growth from Undercooled Melts

The mechanism of crystal growth from undercooled melts is studied experimentally by means of a simple capillary technique. Thymol and Na₂S₂O₃ · 5 H₂O are used as model substances. Dislocation-free crystal faces of these compounds are obtained by continuous growth in the capillary or by prolonged annealing under appropriate conditions. Two-dimensional mechanism of growth was experimentally verified on such perfect crystal planes. The conditions under which the surface nuclation mechanism operates are described accounting for the supersaturation, the influence of impurities etc. Transition from two-dimensional into spiral growth of purposedly defected crystal faces is demonstrated and investigated. The mechanism of formation of perfect crystals is discussed and further experimental evidence on the possibility of two-dimensional growth from melts is given.     

Floating zone growth and characterization of ruby single crystals

Large, high optical quality single crystals of ruby have been grown successfully by the floating zone method under air atmosphere. The size of the grown crystal is typically 60‐70 mm in length and 7‐8 mm in diameter. The obtained crystals were red and did not have any macroscopic defects such as cracks and inclusions. Grown crystals were characterized by powder X‐ray diffraction (XRD) methods, polarized optical microscopy, scanning electron microscopy (SEM). The absorption and fluorescence spectra were measured at room temperature and the dielectric constant measurements of ruby crystals were also presented. Defects occurring in single crystals of ruby during crystal growth by floating zone method are described, and their correlation with the growth parameters is discussed. The origin and control of these defects in grown crystals were studied and the optimum method was proposed. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zur quantentheoretischen Berechnung von Aktivierungsenergien für den Stoffübergang an Phasengrenzflächen von Ionenkristallen (IV). Zur radiochemischen Bestimmung und quantentheoretischen Berechnung von Aktivierungsenergien für den Stoffübergang an den Kristallflächen des NaCl

It is shown that a direct proportionality exists between the activation energy for the mass transfer at the respective crystal faces of ionic crystals and the frequency of the phonones (longitudinal-optical), Planck's constant being found once more as a proportionality constant. Thus it could be demonstrated that the different activation energies measured at different time intervals for the mass transfer processes at phase boundaries of ionic crystals can be attributed to the specific growth of the crystal faces. Thus, NaCl crystal fractions which were mechanically stressed (pulverized and sifted) and consequently contained a great amount of {111}- and {110}-faces, respectively, experimentally yielded an activation energy wich agrees with the values determined by quantum theory when the frequency of propagation of the phonons is inserted into a derived equation. This relation was also confirmed by NaCl crystal fractions predominantly containing cubic faces. This was indicates that in mass transfer processes on phase boundaries of ionic crystals quantum mechanical laws are of importance.     

Morphotypes of the quartz basic rhombohedra and crystallization conditions

An analysis of the combinatorial–morphological types of faceting for a quartz crystal head has provided 23 types of combinations of faces of basic positive and negative quartz rhombohedra, among which three full-face morphotypes are generally observed under natural conditions. The theoretical occurrence rates are obtained for these morphotypes under isotropic growth conditions, and a morphological analysis is performed over seven samples of natural quartz crystals. A method is proposed for estimating some most important parameters of the crystal formation system: the ratio of variation in the central distances to the faces of crystal rhombohedra, which is related to its growth rates; the ratios of the intermediate growth rates of the rhombohedra and prism, the index of infection with Dauphiné twins, and the feed dissymmetry factor.     

Electrocrystallization of silver: Growth kinetics of screw-dislocation-free (100) crystal faces

At given conditions, especially at higher supersaturation, the growth rate of a close packed, perfect crystal face depends on the formation rate of two-dimensional nuclei and on the propagation rate of the monoatomic layers. This multinuclear multilayer growth as well as the advancement rate of growth steps have been studied experimentally on electrocrystallization of silver. The advancement rate of mono- and polyatomic growth steps has been measured on screw dislocation-free (100) crystal faces. For low overvoltages a linear dependence of the rate on overvoltage has been found. A strong influence of the surface condition of the crystal face — “fresh” or “aged” on the step advancement rate has been established. It was also found that on a “fresh” surface mono- and polyatomic steps advance with the same rate. The average monoatomic step spacing of the polyatomic step has been determined. The kinetic constants of the step growth rate are established and a conclusion regarding the mechanism of electrolytic deposition of silver is drawn. The initial current—time curves were recorded on applying potentiostatic pulses on a perfect crystal face. The shape of these curves coincides very well with those theoretically calculated for the cases of multinuclear growth. On the basis of the theoretical dependences, one can determine from these curves the formation rate J of two-dimensional nuclei at a given overvoltage η since the rate of step advancement is known. A linear dependence of log J on 1/η has been established. The values of the pre-exponential term in Volmer's equation and the specific edge energy of the two-dimensional nucleus have been determined. The surface condition of the crystal face influences strongly also the process of two-dimensional nucleation.     

LGAS晶体的微结构及声表面波特性研究

本文采用第一性原理计算了La3Ga5-xSiAlxO14 (LGAS)压电晶体几何结构、能带和态密度.并研究了其在X、Y和Z切型的声表面波速度、机电耦合系数及能流角.当x=0.5时,构建了La3Ga4.5SiAl0.5O14晶体的1×1×2超晶胞结构,发现A1原子替代2d四面体位置的Ga原子时体系总能量最低,体积最小,因此是最稳定的状态.与石英相比,LGAS具有声表面波速度较低、机电耦合系数较大且存在能流角为零的切型等优点.掺Al元素降低了成本但对结构和声表面波特性影响不大.Y切0是较好的切型,可用于制备声表面波器件.     

Hydrothermal Liquid Phase Epitaxy of Gallium Orthophosphate on Quartz Crystal Substrates

Gallium orthophosphate (GaPO₄) layers for surface acoustic wave (SAW) and sensor applications have been grown on quartz crystal substrates with sizes of about 30 x 30 mm² by hydrothermal liquid phase epitaxy (HLPE). The growth of epitaxial GaPO₄ layers is difficult because of a strong tendency for twinning. Besides, a retrograde solubility and an intense chemical aggressiveness of the solution has to be considered. Nevertheless, we found an effective crystal growth technique to deal with these problems using large and qualitatively good substrate crystals of quartz. The most important step of the epitaxy is the formation of an interlayer between the quartz substrate and the GaPO₄ deposit. Epitaxial layers with thickness up to 500 μm were obtained and characterised by means of X‐ray techniques.     

Growth and characterization of CdSe single crystals by modified vertical vapor phase method

Good quality, large single crystals of CdSe were grown by the modified growth method (i.e., vertical unseeded vapor phase growth with multi-step purification of the starting material in the same quartz ampoule without any manual transfer between the steps). Lower temperature gradients (8–9°C/cm) at the growth interface were used for the crystal growth. As-grown CdSe crystals was characterized by X-ray diffraction, scanning electron microscopy, energy dispersive analyzer of X-rays, high-resistance instrument measurement, and etch-pit observation. It is found that there are two cleavage faces of (1 0 0) and (1 1 0) orientations on the crystal, the resistivity is about 10⁸ Ω cm, and the density of etch pits is about 10^3–4/cm². The crystal was cut into wafers and was fabricated into detectors. The detectors were tested using an ²⁴¹Am radiation source. γ-ray spectra at 59.5 keV were obtained. The results demonstrated that the quality of the as-grown crystals was good. The crystals were useful for fabrication of room-temperature-operating nuclear radiation detectors. Therefore, the modified growth technique is a promising, convenient, new method for the growth of high-quality CdSe single crystals.     

Synthesis of nanoflakes‐based self‐assembling crossed structure of stannous oxide and photocatalysis property

Self‐assembling nanoflakes‐based crossed architectures of stannous oxide (SnO) were successfully synthesized via template‐free hydrothermal growth method by using SnCl₂·2H₂O and KOH as precursors. Crystal structures, morphology, chemical composition and optical properties were examined by X‐ray diffraction (XRD), field‐emission scanning electron microscopy (FESEM), energy dispersive X‐ray analysis, and Raman spectroscopy, respectively. The results indicate that the as‐synthesized product belongs to tetragonal phase SnO with crossed morphology self‐assembled by nanoflakes. Furthermore, UV‐vis spectrophotometry was used to determine optical band gap of the SnO nanostructures and the direct band gap of 2.90 eV was obtained. The photocatalysis of the product has been evaluated with methyl orange and the high degradation ratio of 87% is obtained in 240 minutes under the measuring condition which is attributed to the wide band gap and large specific surface area of the nanoflakes‐based crossed SnO architectures. A possible growth mechanism is proposed in the end.     

Yb∶YAl3(BO3)4晶体形貌与生长速度的关系

观察测量了不同生长速度(相应于不同降温速度)自发成核生长的Yb∶YAl3(BO3)4晶体形貌。粒度较大(>2mm)的晶体不管降温速度快慢形态都很简单,只发育六方柱｛1120｝和菱面体｛1011｝;粒度较小(<2mm)的晶体形态随降温速度增快而变复杂,发育一些罕见的高指数晶面。说明在生长速度较快的条件下,在晶体生长早期,一些高能面发育,在晶体生长后期已尖灭了,晶体生长的大部分时间是在低能面｛1120｝和｛1011｝上进行的。对比了不同生长条件下晶面的粗糙度,随着降温速度的增快,六方柱面｛1120｝和菱面体面｛1011｝由光滑变粗糙,顶面｛0001｝永远是粗糙的。从晶体结构上定性地探讨了3种晶面的杰克逊因子α及生长机理     

Nucleation kinetics,micro-crystallization and surface morphology studies of the nonlinear optical single-crystal l-lysinium trifluoroacetate

The organic nonlinear optical crystal of amino-carboxyl acid family, l-lysinium trifluoroacetate (abbreviated as LLTF) was successfully grown from its aqueous solution by the temperature-lowering technique. Its growth morphology was investigated based on the X-ray single-crystal diffraction data and the growth habits were studied using the micro-crystallization method. The metastable zonewidth and induction period were determined for the aqueous solution growth of LLTF. The surface free energy values were calculated from the experimental data. Nucleation kinetics and fundamental growth parameters such as critical radius, critical free energy and volume free energy change were also evaluated. Crystals of LLTF were obtained by the optimized nucleation parameters.     

硫镓银晶体的化学腐蚀研究

采用改进的垂直布里奇曼(Bridgman)法自发成核生长AgGaS2晶体,在生长初期对生长安瓿籽晶袋进行上提回熔,生长出外观完整、无裂纹的大尺寸AgCaS2单晶体.采用XRD对晶体进行分析,获得了(112)、(001)和(101)面的高强度尖锐衍射峰.采用不同配比的腐蚀剂对晶体(101)、(112)及(001)晶面进行化学腐蚀,然后采用金相显微镜和扫描电镜观察,结果显示,(101)晶面蚀坑为清晰的近似三角形的四边形蚀坑,(112)晶面蚀坑为清晰的近似三角锥形,(001)晶面则呈现互相垂直的腐蚀线.初步分析了不同蚀坑的形成原因,计算出(101)和(112)面蚀坑密度约为105/cm2数量级.结果表明,改进方法生长出的大尺寸AgGaS2单晶体结构完整、位错密度低,质量较好.     

Growth kinetics on the (100) and (001) faces of TGS crystals

The growth kinetics and mechanisms on the (001) and (100) faces of TGS crystals were investigated. A phase contrast microscope with a CCD camera was used to observe the growth of the crystal. We found the growth on the (001) and (100) faces at high supersaturation was mainly controlled by a BCF surface diffusion mechanism. The kinetic data for the (100) face were also fitted by the nucleation and layer growth model of two-dimension nucleation at high supersaturation. Some important growth parameters for TGS crystals, such as edge energy, activation energy, and so on, were estimated.     

Simulating vapour growth morphology of crystalline urea using modified attachment energy model

We report a computational model to simulate vapour growth morphology of urea crystal by considering molecular anisotropy and surface relaxation of different crystal faces. It has been argued that the faces' growth occurs through the adsorption of molecular layers rather than a slice of thickness d_hkl. The molecular layer is a 2-D periodic arrangement of molecules in which each molecule has same the orientation. The molecular orientations in a slice of thickness d_hkl may differ from each other and depend on crystallographic orientation of the slice. The discussed approach has been employed to simulate vapour growth shape of crystalline urea by calculating attachment energy of molecular layers using Hartee–Fock and density functional theories. The calculated growth morphology is in good agreement with the vapour grown shape of urea crystal. The role of thermal and growth kinetics affecting the vapour growth morphology has been discussed. The observed polar growth morphology of urea crystal has also been discussed particularly in the context of different atomic environments of (111) and (?1?1?1) faces.     

Effects of anions on rapid growth and growth habit of KDP crystals

The synthesis of KDP from its raw material has been found exist in the growth solution. In the crystal growth experiment, significant extension of specific faces was observed at low dopant concentration. At high doping concentration, the growth rate of the whole crystal decreased with no significant habit modification. The inhibiting effects of phosphite and other H-bonding anionic ions on the growth of pyramidal faces are discussed. Rapid growth rate experiments have been carried out with purified material and an averaged growth rate of 18.6mm/day was obtained.     

Diffusion Control during Vapour Crystal Growth

The crystal growth rate under diffusion control is considered. Together with nutrient diffusion, the physi-sorption of an inert gas, which impedes the surface kinetics during vapour growth, is taken into consideration. In this way the size of the diffusion field surrounding vapour grown crystals was estimated. The relations obtained are checked with data for the growth of zinc single crystals in argon atmosphere. The appearance of shallow cavities on their basal faces is used as a morphological mark for growth under diffusion control. Besides, the microstructure of the inner edge of the macroscopically flat periphery, surrounding the shallow cavities is investigated experimentally, by means of SEM.     

Twinning in hydrothermally grown synthetic quartz as revealed by etch structures

Etch structures obtained by HF etching on habit and cleaved rhombohedral surfaces of synthetic quartz grown by hydrothermal crystallization technique, indicative of twinning in them are described, illustrated and discussed. The twin traces appear in the form of lines of dis-continuity in [1121] and [1211] directions. Etch pits within the parallelogram-shaped bound areas are oppositely oriented with respect to those on the rhombohedral surface of the main crystal. The form of twinning observed is found to be of parallel lattice type and the surface within and outside the bound areas are coplanar in most of the cases. The rhombohedral faces of the twinned crystals are found to be geometrically related to each other as if one part is derived from the other by a rotation of 180° about [1210] direction. Discontinuation in the crystal lattice along the twin trace is evidenced by obstructions in the normal development of an etch pit. Deep penetration of twin traces and parallelogram-shaped regions, enclosing etch pits of opposite orientation (twinned areas), well within the crystal structure is demonstrated by comparison of etch patterns on matched rhombohedral cleavages and the results on their successive etching. The type of twinning displayed by the crystals is discussed in the light of models suggested. Causes for the generation of twinning in synthetic quartz are explained to lie in the availability of twinned nuclei in the seed plates used for hydrothermal crystallization of quartz.     

Effect of impurity adsorption on the growth of Rochelle salt crystals

The influence of impurities of copper compounds on the growth of Rochelle salt crystals of the composition KNaC₄H₄O₄ · 4H₂O is studied. The growth rates of the faces of various simple forms experimentally measured as functions of the CuCO₃ concentration in solution at a constant supersaturation and temperature are compared with the theoretical models of impurity adsorption on the faces of a growing crystal. Deceleration of the growth of various faces of a Rochelle salt crystal is satisfactorily described by the Bliznakov equation with the use of the Langmuir, Frumkin-Fowler, and de Boor adsorption isotherms for all the faces except for {010}. However, such a comparison does not allow one to reveal the cause of adsorption or its type on different faces. Photometric scanning of Rochelle salt solutions with copper-compound impurity showed that a small addition of alkali (0.06–0.4 g/l) to the solution results in the appearance in the absorption spectra of both the solution nd the crystal grown from it of a maximum at the wavelength 660–670 nm. The intensity of this maximum increases with an increase in the copper concentration. The EPR data, the absorption spectra of the solution and the crystal, and the modified crystal shape showed that the addition of alkali to the solution results in the formation of new copper complexes that more actively decelerate the growth of Rochelle salt faces.     

Geometric modeling of homoepitaxial CVD diamond growth: I. The {1 0 0}{1 1 1}{1 1 0}{1 1 3} system

Plasma-assisted CVD homoepitaxial diamond growth is a process that must satisfy many stringent requirements to meet industrial applications, particularly in high-power electronics. Purity control and crystalline quality of the obtained samples are of paramount importance and their optimization is a subject of active research. In the process of such studies, we have obtained high purity CVD diamond monocrystals with unusual morphologies, namely with apparent {1 1 3} stable faces. This phenomenon has led us to examine the process of CVD diamond growth and build up a 3D geometrical model, presented here, describing the film growth as a function of time. The model has been able to successfully describe the morphology of our obtained crystals and can be used as a predictive tool to predetermine the shape and size of a diamond crystal grown in a given process configuration. This renders accessible control of desirable properties such as largest usable diamond surface area and/or film thickness, before the cutting and polishing manufacture steps take place. The two latter steps are more sensitive to the geometry of the growth sectors, which will be addressed in a companion paper.Our model, applicable to the growth of any cubic lattice material, establishes a complete mapping of the final morphology state of growing diamond, as a function of the growth rates of the crystalline planes considered, namely {1 0 0}, {1 1 1}, {1 1 0}, and {1 1 3} planes, all of which have been observed experimentally in diamond films. The model makes no claim as to the stability of the obtained faces, such as the occurrence of non-epitaxial crystallites or twinning. It is also possible to deduce transient behavior of the crystal morphology as growth time is increased. The model conclusions are presented in the form of a series of diagrams, which trace the existence (and dominance) boundaries of each face type, in presence of the others, and where each boundary crossing represent a topology change in terms of number of faces, edges and vertices. We validate the model by matching it against crystals published in the literature and illustrate its predictive value by suggesting ways to increase usable surface area of the diamond film.     

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.