Determination of linear growth rates of crystals (II). The shape factors method

A method using dimensionless shape factors for the determination of linear growth rates of crystals is described. The relevant shape coefficients are assessed on the basis of properly selected linear parameters of the crystal.     

A method for determination of size-dependent crystal growth kinetics from batch experiments (I). One-experiment estimation

The method developed for determining size-dependent crystal growth kinetics makes use of the assumption that the linear growth rate is a product of a size-dependent factor and a supersaturation-dependent one. The transformed form of the population balance equation, obtained by means of this assumption, is the basis of the evaluation utilizing measurement data from one seeded batch crystallization experiment, namely the size distributions of the seed and product crystals as well as the supersaturation course. The application of the method is illustrated by evaluating an experiment with potash alum crystals.     

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.     

Role of microcrystals in the growth and development of prism faces of cultured quartz (I). Attached microcrystals

Microcrystals attached in random orientations to growing host prism faces of cultured quartz grown by the hydrothermal crystallization technique are described. The microcrystals are established to be quartz. Growth layers and pyramids initiated by the attached guest microcrystals of quartz on the growing host prism faces of bulk quartz crystals are illustrated. Also described are striations, parallel, perpendicular and inclined to the c-axis, and polygonal growth pyramids on the prism surfaces of attached guest microcrystals. Formation of the microcrystals of quartz is linked to the possibilities of creation of quartz micronuclei in the autoclaves which further establishes and solidly supports the explanation put forward by KOTRU . Effect of unoriented attached tiny crystals of quartz and impurities on the progress of growth layers on the host prism faces is dealt with. Role of attached guest microcrystals in the growth and development of the host prism faces in particular and the cultured quartz in general is discussed. Possibilities of the incorporation of quartz micronuclei inclusions and impurity inclusions in the quartz structure and its effect on the crystalline quality of cultured quartz is briefly dealth with.     

Polyhedral stability ‐ on the growth of flat crystal faces on small molecule and protein crystals

The old standing problem of face morphology is discussed. A special emphasis is put on the macroscopically flat faces, appearing on small molecule crystals mostly during calm growth, under low supersaturations. As distinct, protein crystals are growing with macroscopically flat faces even under surprisingly high supersaturations. Explanations of these facts are suggested by considering the surface micro‐profile of crystal faces which growth is driven by screw dislocations. It is shown that, due to kinetic reasons, the tips of the growth hillocks and the valley between them have to be levelled to some extent (at least on a quasi‐atomic scale) under low enough supersaturations. The amplitude of the surface roughness has to be suppressed also due to the surface energy gain, especially under quasi‐equilibrium. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Temperature distribution in growing semi-transparent crystals (I). Theory

Simplified analytical and computational solutions of the temperature distribution in crystals grown by Czochralski method including the temperature difference on the liquid/solid interface are given. The model used is based on experiments with oxide crystals with melting points above 2000 K. Computational solution was more extended because it enables to calculate actual temperature distribution with a relatively small error.     

Three-dimensional simulation of floating-zone crystal growth of oxide crystals

The floating-zone (FZ) method is a popular technique for the growth of high-temperature oxide crystals. However, the growth usually requires skillful control of the zone stability, which is strongly coupled with heat flow, interfaces, and the grown crystal morphology. In this report, we present a three-dimensional self-consistent simulation of floating-zone oxide growth in a mirror furnace by taking these factors into account simultaneously. This model is based on an efficient finite volume method with multigrid acceleration and interface tracking. The steady growth of a YAG crystal in a double-ellipsoid mirror furnace is taken as an example to illustrate the intricate coupling of convection, interfaces, meniscus, and the grown crystal shape.     

Studies on epitaxial growth of organic compounds on sucrose by the fourier transform method (I). On crystal growth of the participants

Epitaxial growth of organic compounds on sucrose crystals has been observed. In any case two-dimensional lattice analogies exist. The structural relations are, as a rule, unknown. In the present first part crystal growth of the participants was investigated. Equilibrium and growth forms of host (sucrose) and guest crystals (β-succinic acid, hexachlorobenzene, anthraquinone, isatin) have been determined by the Fourier transform method. The growth polyhedra fully correspond to the experimental observations.     

Preferred growth of bismuth single crystals at slow growth rates by Bridgman technique

Bismuth single crystals having low mosaic spread are used as filters for obtaining clean beam of thermal and cold neutrons. The present study is of the role of growth rate (1 to 6.5 cm/h) and temperature gradient (11.4, 18.5 and 22.2/dgC/cm) on the preferred orientation of the (111) cleavage plane of bismuth single crystals grown by the unseeded Bridgman technique. The results are interpreted to give understanding of the preferred orientation so that previously reported random orientation at growth rates below 2 cm/h and parallel translation of orientation versus growth rate plots at growth rates over 8 cm/h can be correlated.     

A new method of site occupancy analysis in substitutional mixed crystals by means of X-ray crystal structure analysis (I). Pseudo lattice and superposition structure of a substitutional mixed crystal

In Part I the nature of disorder in mixed crystal structures will be discussed on the basis of a pseudo lattice concept. A mixed crystal pseudo lattice applicable to all atomic positions of these mixed crystal structures will be defined, and the concept of a statistically globaldisordered ideal structure will be introduced. The structure factor for mixed crystal structures will be derived in consideration of the statistic disorder of position and sort of the atoms. The interpretation of the mixed crystal structure as a superposition structure requires the replacement of Vegard's rule by a new one having a wider range of validity.     

On the modeling of crystal structures and the growth of crystals

It is demonstrated that the universal laws of system organization govern the growth of crystals and the construction of models of crystal structures. It is established that there is an interrelation between the growth of crystals of chemical compounds and the modeling of their crystal structures.     

Kinetic investigations within the transition region from polyhedral to skeletal growth mode (I). Growth kinetics of the basal face of zinc single crystals under diffusion conditions

The effect of diffusion in the vapour phase on the kinetics of growth of zinc single crystals in the presence of argon has been studied. The shift of the basal face in normal direction as a function of the time has been measured at constant temperature and supersaturation and argon pressures varying within the range 5–250 Torr as well as in vacuum 1 × 10⁻⁶ Torr. It has been established that the crystal size R changes with the time t following a linear and a parabolic law in the kinetic and the diffusion regimes, respectively. The kinetic critical size R_k for the transition from a kinetic to a diffusion regime has been experimentally obtained. A relatively good agreement is found between the experimentally established and theoretically calculated values of the critical size. The problems related to the transition of the basal faces of zinc single crystals from a kinetic to a diffusion growth mode is discussed.     

Nonstoichiometry in steps on AB crystals (I). General aspects,including bulk imperfections

Starting with a quasichemical treatment, simple model calculations are given for the equilibrium composition in surface steps containing A and B kinks, the amount and ratio of which is varied by changing the adjacent gas composition. In connection with deviations from step stoichiometry, the total amount of kinks increases strongly. A nearest neighbour approximation has been applied to the attachment of A or B atoms at kinks from the gas phase, and also from the bulk by formation of vacancies V_A or V_B. These processes can be formulated separately for the two elements, taking into account the effective formation of bulk atoms of the other kind (B_B or B_A).     

Growth of bis-dimethylglyoximate Co (III). Single crystals

Single crystals of bis-dimethylglyoximate Co(III) up to 8 × 6 × 2 mm. in size have been grown by the first time, using diffusion method at room temperature. Optimum size and quality were obtained at pH = 6. These crystals are orange in colour and an X-ray study shows it to be monoclinic, space group P 2₁/n, with a = 8.432(4), b = 14.147(3), c = 13.746 (6) and β = 103.78(3)°. The effects of different experimental devices on the growth features are discussed.     

Growth kinetics of (001) type faces of rochelle-salt crystals in solutions

Growth kinetic data of Rochelle-Salt crystals are presented and discussed in terms of the BCF theory. The characteristic constants for crystals grown in pure solution as well as in the impurified ones are determined. Experimental data obtained for the (001) and (210) type faces in other experimental conditions (Levina, Beliustin) are also discussed.     

A study of the relation between crystal growth kinetics and particle size distribution of crystals produced from solution

A new relation between crystal growth kinetics and particle size distribution based on statements in the literature is derived. It can be equally used for the determination of the characteristics of crystallization caused by cooling, evaporation or precipitation. Different kinetic constants (rate constants of nuclei formation k₁, k₂, k₃, and growth K₀, K₁, K₂) can be determined, and therefrom the particle size density curve. – The effect of kinetics characteristics on particle size distribution is summarized.     

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.     

Effect of magnetic field on melt flow and crystal growth of oxide crystals

The flow in an oxide melt such as LiNbO, and TiO₂ in a high magnetic field was observed by using magnetic-field-applied Czochralski equipment for oxide crystals. It was found that the flows in oxides melts were very much different from these in a semiconductor melt. The single crystals of TiO₂ were grown in a magnetic field by using this equipment.