Second neighbours velocities and size of faces in crystal habit

Influence of growth velocities of first and second neighbours on the presence and size of the face in the crystal habit has been studied. It was established and confirmed that the consecutive neighbour affects the face size only after the disappearance of the previous neighbour. The formula for critical growth velocity governing disappearance of faces has been discussed.     

Velocities of Disappearance and Lifetime of Faces of Growing Crystals

The formulae for absolute R_disap and relative R velocities of disappearance and lifetime τ of faces of growing crystals have been derived for stationary growth. It was shown that the quantities are determined by the relative growth velocity R_A/R_critA of the vanishing face A with respect to the critical growth velocity R_critA and by the geometry of a crystal expressed by the trigonometric functions of interfacial angles β and γ formed between face A and the adjacent faces. R increases and τ decreases with the increase in R_A/R_critA to certain limiting values. The calculations have been verified and illustrated by the experimental results for triclinic potassium bichromate (KBC) crystals. Results enable ones to predict values of velocities of disappearance and lifetimes of undesirable, supplementary faces of any real crystal.     

On the Critical Growth Velocities for the Presence of Faces on Growing Crystals

Faces of three-dimensional crystals have been divided into edge and corner ones to describe the phenomenon of their disappearance and appearance during the crystal growth. The expression for the critical growth velocity governing the presence of corner faces has been derived and verified and the validity of the previous relationship (SZURGOT , PRYWER ) for the edge faces confirmed. Three nearest neighbours control the presence of corner faces and two neighbours decide on the edge faces.     

On the Presence of Faces in the Habit of Growing Crystals

Presence and size of a face in the habit are conditioned by the value of relative growth velocity R_A/R_{crit A} with respect to the critical growth velocity. It has been established that during the growth of crystals only certain values of relative growth velocities R_A/R_{crit A} occur. Faces of KBC crystals realize values of R_A/R_{crit A} between 0 and 2. Unity is the demarcation level below which appearance and above which disappearance of faces takes place. Edges and corners of crystals are places where new faces appear during changes in growth conditions.     

On the Formation of Thick Sector Boundaries by Appearance and Disappearance of Faces of Crystals

Wide sector boundaries revealed in KBC crystals by chemical etching have been observed and analysed. It was established that the boundaries represent sectors of small faces appearing and vanishing in the habit during crystal growth. This nature of thick boundaries has been confirmed by the analysis of values of relative growth velocities of faces with respect to the critical velocities governing the presence of faces on growing crystals.     

Modeling of the shape of polyethylene oxide single crystals and determination of the kinetic crystallization parameters: Theoretical and experimental approaches

The curvature of faces of polymer single crystals is described by the system of Mansfield equations, which is based on the Frank-Seto growth model. This model assumes the velocity of nucleus steps to be the same for their propagation to the right and left and is valid only for symmetric crystallographic planes. To describe the shape of polyethylene oxide single crystals grown from melt and limited by the {100} and {120} folding planes, it is assumed that the layer velocities to the right and left are different on {120} faces. This approach allows modeling, with a high accuracy, of the observed shapes of polymer single crystals grown at different temperatures, which makes it possible to determine unambiguously the fundamental crystallization parameters: the dimensionless ratio of the secondary homogeneous nucleation rate to the average velocities of nuclei along the crystallization planes and the ratio of nucleus velocities to the right and left. In addition, it was found that a known macroscopic single-crystal growth rate can be used to determine the absolute values of the secondary homogeneous nucleation rate and the velocities of nuclei along the growth plane.     

Influence of Second and Further Neighbours on the Presence of Faces in Crystal Habit

Influence of growth volocities of further neighbours on the presence of faces in crystal habit has been analysed. It was established that the consecutive neighbour affects the face size only after the disappearance of the previous neighbour. The formula for the critical growth velocity governing disappearance of a face which includes the closest and further neighbours has been derived and discussed.     

Effect of Buoyancy-driven Convection on Surface Morphology and Macromorphology of Potassium Bichromate Crystals

Surface topography and macromorphology of potassium bichromate crystals grown from unstirred aqueous solution depend on diffusion and convection. Micromorphology of as-grown surfaces is a source of quantitative data on the local values of the degree of supersaturation σ at various parts of crystals. Micromorphology and values of growth velocities of faces, differently located in space with respect to the gravitational force show that upper parts of the crystals grow at about 5–25% lower values of σ than the lower ones. The cause of convection changes of size and number of faces is the characteristic distribution of supersaturation around the crystal induced by movement of the solution.     

Asymmetry of isolated dislocation mobility in Silicon single crystals

The main quantitative characteristics of asymmetry of isolated dislocation mobility in Si single crystals manifested in an essential difference (up to an order of magnitude) of the velocities of broadening and narrowing dislocation half-loops have been investigated. Transition from broadening to narrowing of the dislocation half-loop is found to result in the nonmonotonic temperature dependence of the 60° segments velocities as well as in changing the stress dependence of the velocity. The high temperature annealing of the sample befor the reversal of the dislocation glide is found to cause the asymmetry disappearance. The analysis of the results obtained is performed. It is concluded that the phenomenon observed may be due to a rearrangement of the point defect structure during the course of the dislocation glide.     

Mechanical amorphization in the Ni---Zr system investigated by positron lifetime spectroscopy

The process of solid-state amorphization induced by high-energy ball milling of binary mixture of crystalline elemental powders is investigated by positron lifetime spectroscopy along with X-ray diffraction and differential scanning calorimetry. The experiments are performed on compacted samples of powders mechanically alloyed over a wide composition range (state range) at different milling times (state times) and intensities. The positron lifetime spectra is decomposed into two components. The short-lived component is composition and milling-time dependent. The second lifetime component, found during the initial stages of the milling process, appears to be due to annihilation from states trapped at crystalline interface joints. The results indicate that the solid-state reactions during ball milling involve the transformation and disappearance of the crystalline interface joints in the powder particles.     

Growth of faces of K2Co x Ni1 – x(SO4)2 · 6H2O mixed crystals

Data on the morphology and normal growth rate of the (110) and (001) faces, velocities of step motion, and slopes of dislocation hillocks on the (001) face of K₂Co _x Ni₁– _x (SO₄)₂ · 6H₂O crystals at different supersaturations of solutions with a Co/Ni ratio equal to 1: 1 or 1: 2 have been obtained using a Michelson interferometer. The morphology of the (110) faces is found to be the same for solutions of both compositions. Powerful dislocation sources with large Burgers vectors dominate on the (001) face. The morphology of the (001) surface is rougher than that of (110), especially in a 1: 2 solution at high supersaturation. The (110) faces grow more slowly as compared with (001). The kinetic coefficients of steps on the (001) face are identical in the 1: 1 and 1: 2 solutions. The influence of the kinetic and morphological characteristics of (001) faces on the single-crystal quality is analyzed.

     

Atomic force microscopy study of lysozyme crystallization

Crystallization of lysozyme from solutions has been studied by the atomic force microscopy method. The surface morphology and the growth kinetics of several faces of the orthorhombic and monoclinic modifications of lysozyme crystals are considered. The surface images are obtained at molecular resolution. For the (010) face of orthorhombic lysozyme, the phenomenon of the surface reconstruction is established—doubling of the unit-cell parameter along the a-axis. The main growth parameters of lysozyme are determined—the kink density at steps, probabilities of the attachment and detachment of building blocks, the kink and step velocities, and the dependence of the fluctuation in the step position on time.     

Desymmetrization of the polyhedral crystal shape of tetragonal lysozyme due to face-growth rate fluctuations

We have studied the desymmetrization of the polyhedral crystalline shape of tetragonal lysozyme crystals due to the growth rate differences of the equivalent {1 0 1} planes. Using atomic force microscopy, we have observed the evolution of the multifaceted structures composed of four equivalent {1 0 1} faces during growth. In our growth condition, lateral step flow, where a large density of dislocations acts as a source of steps, is the dominant growth mechanism. The measured step flow velocities are almost independent of the separation between the neighboring steps, revealing that the local face normal growth rate is determined by the local step density. By tracing the motion of the vertex surrounded by the {1 0 1} faces, we have found that the desymmetrization of the crystalline shape is due to the large fluctuation of the local face normal growth rate, which is comparable in magnitude to the average growth rate.     

Der Einfluß der Abkühlungsgeschwindigkeit auf die Keimauslese bei erschmolzenem Al2O3

Polycrystalline disc-like pellets of Al₂O₃ are moulded superficially and then cooled down at different velocities. In this way areas of single crystal character are created. The angle ϑ measuring the inclination of the crystallographic c-axis against the pellet's normal proves to be a statistical quantity. Nevertheless it will be shown that the probability distribution of this angle is differnt for slow and fast cooling rates. In both cases the anisotropy of the crystallization process uniquely represented by a suitable factor k(ϑ) exhibits a remarkable relationship to some stable faces of natural grown single crystals of corundum. Furthermore, the importance of the mean value ϑ and of the variance σ is discussed in detail.     

Fluctuations in growth rate of gypsum crystals

Growth of needlelike gypsum crystals from highly supersaturated aqueous solutions has been studied by the methods of the optical and electron microscopies. The average growth rates of the end faces and their fluctuations are determined. It is shown that the fluctuations in the growth rates of end faces are described by the Fokker-Planck equation and that the end faces of gypsum crystals grow by the layer mechanism with the layer nucleation in the vicinity of one of the crystal vertices.     

Determination of linear growth rates of crystals (I). Calculation of linear growth rates of individual crystal faces from overall rates

The presented paper (Part I and II) is devoted to the fundamental principles of the kinetics of crystal growth. The number of studies in this field has been increasing and some authors have introduced different terms and definitions. To avoid possible mistakes and confusions, the individual definitions of the rate of crystal growth are specified and their interrelations are discussed in detail. Basic methods for measuring the kinetics of crystal growth are described. The rate of growth of individual crystal faces or the average rate of crystal growth can be determined using the selected experimental method. The presented study demonstrates that the results obtained by either of the two measuring methods (linear rate of growth of crystal faces and average rate of crystal growth) can be interrelated. The established method of calculating linear growth rates of individual crystal faces is based on an analysis of the time dependence of the volume of a growing crystal. The relationship between the linear growth rates of individual crystal faces and the over-all crystal growth rate is presented and a method for assessing the linear growth rates of individual crystal faces from over-all growth rate data, which can be measured readily, is suggested.     

On the theory of two-dimensional nucleation on a structureless substrate. Effect of supersaturation

The work of formation of two-dimensional nuclei of the (100), (110), and (111) faces of crystal with simple cubic lattice on a structureless substrate was calculated. The simplification of the equilibrium form with increasing supersaturation was taken into consideration. At low supersaturations the formation of nuclei of the (100) face alone is possible. With increasing supersaturation the appearance of two-dimensional nuclei of the other two faces becomes possible. The probability of their formation increases but never exceeds the probability of the formation of two-dimensional nuclei of the (100) face. There exists a limiting supersaturation above which the work of formation of two-dimensional nuclei of the three kinds of faces becomes equal to zero.     

BGO熔体急冷自发结晶形貌

本文研究了BGO熔体在急冷的条件下自发结晶的显露形貌.在急冷的条件下,组成BGO的各个面族自由发育.{321}面族、{211}面族和{111}面族都是按[GeO4]4-四面体以顶角相连的化学键链生长发育的,生长速度快,优先显露,在熔体急冷时保留下来.表面形貌显露不完整的{100}面族是[GeO4]4-四面体以棱相连所对应的面族,生长速度较慢,尚未显露完全熔体就已冷却.从生长速度考虑,在实际生长晶体时以[321]、[211]、[111]方向生长可以获得较快的速度.     

Kinetic Investigations within the Transition Region from Polyhedral to Skeletal Growth Mode (V). Growth Kinetics of the Pyramidal Face of Zinc Single Crystals under Diffusion Conditions

The growth kinetics of the pyramidal face of zinc single crystals is studied in the presence of argon. The curves size vs. time provide evidence that smaller crystals grow in a kinetic regime and after reaching a certain critical size their growth continues in a diffusion regime. The growth kinetics of faces {101 } and {0001} are compared. It is established that the growth of both faces simultaneously changes from a kinetic to a diffusion growth mode. During the transition between the two regimes, however, loss of the morphological stability only of the smooth {0001} face is observed, while the {101 } face with macro steps formed on the surface acquires a skeletal shape after prolonged growth. It is shown that the appearance of morphological instability depends on the surface structure of the crystal faces.     

Measurement of specific surface free energy of ruby and quartz single crystals using contact angle of liquids

The specific surface free energy of ruby and quartz single crystal was experimentally obtained using contact angle of water and formamide droplets on the crystal surfaces, and compared with the morphology of each crystal. The ruby crystals satisfied Wulff's relationship even though their shape were not equilibrium form. The specific surface free energies of the growing faces of synthetic quartz crystal, ‐X, +X, Z, and S faces were obtained as 51.9, 55.6, 57.4, and 58.9 mN/m, respectively. The growth rates of these faces were 0.09, 0.23, 0.28, and 0.33 mm/day, respectively. The growth rate of each face of the quartz crystal can be regarded as a function of the experimentally obtained specific surface free energy. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)