X-ray diffraction in polydomain crystals modulated by transverse waves of atomic displacements. 2. Two-wave modulation of crystals

X-ray diffraction in an orthorhombic crystal modulated by two transverse-displacement waves propagating along one of the crystallographic directions has been numerically studied within the framework of the kinematic approximation. Crystal models are considered that allow the superposition of the displacement waves or the coexistence of domains modulated by the displacement waves with different parameters. It is shown that the formation of peaks additional to the satellite ones is possible not only due to the superposition of the displacement waves, but also due to a certain correlation of the displacement waves in each domain.     

X-ray diffraction by polydomain crystals modulated by transverse waves of atomic displacements. 1. Single-wave modulation in crystals

The intensity distributions of diffuse X-ray scattering caused by domains characterized by the transverse wave of atomic displacements polarized in the (010) plane and propagating along the [001] direction are calculated by numerical methods analyzed in the kinematical approximation. The regular changes in the intensity and half-width of the satellite peaks are revealed as functions of the wave amplitude and the average domain size. The characteristic features of diffraction are considered in the case where the defect-density wave in the crystal affects the parameters of the displacement wave.     

X-ray determination of the polarity of zincblende-structure crystals

An X-ray diffraction procedure for the determination of the polarity of noncentrosymmetric crystals by measuring the integrated reflections of opposite polarity on one surface of the crystal is described. The observed intensities must be corrected for the different asymmetries of the two reflections. To estimate the influence of crystal perfection on the correction factor, the ratios of the integrated reflections were calculated numerically for dynamic diffraction. The method has been applied for determining the polarity of CdTe.     

Brittleness of protein crystals

A simple technique for studying the brittleness of small crystals is reported. The limits of fracture toughness of tetragonal hen‐egg white lysozyme crystals, oriented with their c‐axis normally to the substrate, were measured. The strong mechanics anisotropy of those crystals was confirmed. The role of the water present in the protein crystal lattice was re‐considered in seek for a more holistic understanding of the process, the idea being that the intra‐crystalline solution sustains the globular protein molecules in their native configuration. Also it is argued that this water may contribute for holding together the huge bio‐molecules in the crystal lattice (that is to act as additional “glue” in the crystal). The hypothesis is that dynamic chains of H‐bonds in the intra‐crystalline water are likely to be prolonged to connect protein‐to‐water‐to‐protein.     

Nucleation of protein crystals

Protein crystal nucleation is a central problem in biological crystallography and other areas of science, technology, and medicine. Recent studies have demonstrated that protein crystal nuclei form within crucial precursors. Data for several proteins provided by these methods have demonstrated that the nucleation precursors are clusters consisting of protein dense liquid, which are metastable with respect to the host protein solution. The clusters are several hundred nanometers in size, they occupy from 10⁻⁷ to 10⁻³ of the solution volume, and their properties in solutions supersaturated with respect to crystals are similar to those in homogeneous, i.e., undersaturated, solutions. The clusters exist due to the conformation flexibility of the protein molecules, leading to the exposure of hydrophobic surfaces and enhanced intermolecular binding. These results indicate that protein conformational flexibility might be the mechanism behind the metastable mesoscopic clusters and crystal nucleation. The investigations of the cluster properties are still in their infancy. Results on direct imaging of cluster behaviors and characterization of cluster mechanisms with a variety of proteins will soon lead to major breakthroughs in protein biophysics.     

Separate determination of the amplitude of thermal vibrations and static atomic displacements in titanium carbide by neutron diffraction

The amplitude of thermal (dynamic) atomic vibrations and meansquare static atomic displacements in titanium carbide TiC _x (x = 0.97, 0.88, 0.70) have been separately determined by measuring neutron diffraction patterns at two temperatures (T ₁ = 300 K and T ₂ = 80 K). The static lattice distortions in stoichiometric titanium carbide are experimentally found to be negligible. In the TiC _x homogeneity range, the amplitude \(\sqrt {\overline {u_{dyn}^2 } } \) of thermal atomic vibrations significantly increases with a decrease in the carbon concentration. The Debye temperature has been determined for the first time in the TiC _x homogeneity range at both room and liquid-nitrogen temperatures.     

Orientation of protein crystals grown in a magnetic field

Three crystal forms of hen egg-white lysozyme, and ribonuclease A and met-myoglobin crystals exhibited orientation in a magnetic field of <1 T. Magnetic field application is thus shown to be a possible means to orient protein crystals. The conditions for the orientation to occur and some of its applications are discussed.     

Adhesion of protein crystals: Measurement of the detachment force

The degree of adhesion of protein crystals, heterogeneously nucleated and grown on different supports (e.g. glass plates and plates coated with poly‐L‐lysine, hexamethyl‐disilazane and silicon) is measured directly with a purposely‐developed technique. The sticking force crystal/support is determined by means of a flexible glass fibre, which bending is calibrated by means of series of weights. In this way an elastic constant, specific for each glass fiber is determined individually. Appropriate glass fibres with relative bending less than 10% (Hook's law) are used. The force which is necessary to be exerted, by means of a micro‐manipulator, in order to detach the crystal from the support is taken as a quantitative measure for the adhesion strength. Forces between 10 N cm^‐2 and 1 N cm^‐2 for differently oriented tetragonal hen‐egg‐white lysozyme and cubic ferritin crystals, and 0.1 N cm^‐2 for rhombohedral (porcine) insulin and orthorhombic trypsin crystals are measured. The tetragonal HEWL and rhombohedral insulin crystals show anisotropy of the adhesion strength. In contrast, the cubic ferritin crystals are isotropic also in this respect. For comparison purposes adhesion measurements are performed with NaCl and sugar crystals. An attempt is made to evaluate also the adhesion energy of the protein crystals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polarity determination of rough and smooth surface grains in AlN crystals

The polarity of rough and smooth grains in textured aluminum nitride boules were analyzed by transmission electron microscopy. Specifically, convergent beam electron diffraction method was applied to determine polarity. The grains corresponding to smooth and rough surfaces were identified as having Al and N polarities, respectively. Aluminum oxide (Al₂O₃) was observed to form at the grain boundaries. The oxide may precipitate due to the low mutual solubility between Al₂O₃ and AlN at the high crystal growth temperature (∼2000°C). Oxygen may be the cause of polarity inversion that leads to the formation of Al and N polar grains.     

HRTEM simulation in determination of thickness and grain misorientation for hydroxyapatite crystals

High-resolution transmission electron microscopy (HRTEM) and HRTEM simulation by the Bloch wave method (JEMS) are used to determine the structure and thickness of micro-and nanocrystals of biominerals and hydroxyapatite grown from aqueous solutions. It is established that thin (from one to several lattice parameters) crystals, including hydroxyapatite in mineralized biological tissues, are usually formed in low-temperature (up to 40°C) solutions. Relatively thick (up to several tens of lattice parameters) crystals grow only in high-temperature (~95°C) aqueous solutions. HRTEM simulation showed that crystals with a thickness exceeding one lattice parameter consist of nanograins misoriented with respect to one another along various directions within an angle of 0.7°.     

A method for the determination of the cyclic stress-strain curve of presistent slip bands in fatigued single crystals

Single crystals of pure nickel oriented for single slip were fatigued at constant total strain amplitude (ε_at) at room temperature. The dependence of the saturation resolved shear stress amplitudes (τ_as) on the saturation plastic resolved shear strain amplitudes (γ_aps) (cyclic stress-strain curve — CSSC) was determined. In the plateau range of the CSSC the volume fraction f of persistent slip bands (PSBs) was found to be linearly related to γ_aps. The reduction of the total strain amplitude after saturation in the plateau range of the CSSC leads to the so-called secondary CSSC with a slope n > 0 in the log-log plot. From the secondary CSSC the ”︁true”︁ cyclic stress-strain curve of the PSB-volume (PSB-CSSC) can be determined. The method is based on the two assumptions that firstly the PSB-groups (or ”︁macrobands”︁) penetrate the whole cross-section of the specimen and secondly the volume fraction of PSBs in the secondary range of the CSSC remains constant.     

Solutal convection around growing protein crystals and diffusional purification in Space

Convective and diffusional mass transport to an isolated crystal growing from solution, with slow linear interface kinetics, is considered analytically as a generic scaling model. We focus on the interface kinetics which is slow as compared to the diffusion mass transport which is typical of protein crystal growth. Independently, full-scale numerical solutions of transport equations around a cylindrical crystal, at the center of the bottom of a cylindrical cell filled with the solution, are found. The two approaches give results that agree over a wide range of parameters, providing dimensionless relationships that allow predictions of the contribution of convection and diffusion to mass transport. Requirements for microgravity level in Space experiments to achieve diffusional mass transport are estimated on the basis of these relationships. Coefficients of impurity distribution between a growing crystal and its solution, under the influences of convection and diffusion around the crystal, were numerically evaluated as functions of time. The results provide further support for the hypothesis concerning the role of the impurity depletion zone in the purification of a growing crystal. They also reveal that in general, the impurity distribution within the crystal is not homogeneous due to convection. The effects of various factors on growth kinetics and crystal purity are considered.     

Small-angle X-ray scattering study of conditions for the formation of growth units of protein crystals in lysozyme solutions

The structural composition of lysozyme solutions favorable for the formation of the tetragonal form of protein crystals was studied by synchrotron-based small-angle X-ray scattering depending on the protein concentration and the temperature. Along with lysozyme monomers, dimers and octamers are found in crystallization solutions; the octamer content increases with an increase in the protein concentration.     

New model of the bond diffractometer for precise determination of lattice parameters and thermal expansion of single crystals

A new model of diffractometer for very precise measurements (1 ppm accuracy) of lattice parameters and thermal expansion is presented. Special attention is paid to the temperature control and stability in a wide range from liquid nitrogen up to 800 K. Two examples of the application of the diffractometer in a study of solid state phase transitions are given.     

Growth of near‐stoichiometric LiNbO3 crystals and Li2O contents determination

Two kinds of near‐stoichiometric LiNbO₃ crystals (SLN11 and SLN19) were grown by a flux pulling method from stoichiometric melt with addition of 11mol%K₂O and 19mol%K₂O, respectively. Compared with the congruent melting LiNbO₃, the ultraviolet absorption edges of two crystals shift towards shorter wavelengths, and the locations of the OH^‐ infrared absorption band have obvious change and the bandwidths become greatly narrower. From these experimental results, the Li₂O contents are determined indirectly to be about 49.6mol% for SLN11 and 49.9mol% for SLN19, respectively. The Li₂O content in SLN19 is very close to the ideal value of 50mol%. The coercive fields of two crystals were measured by the poling method at room temperature. A linear relationship between the Li₂O content and the coercive field was fitted. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Transient regimes in the growth of large-diameter crystals

The behaviour of crystallization rate and interface position under the change of Czochralski growth system parameters is theoretically and experimentally investigated for the case of large diameter crystals growth. It is shown that the large value of crystal diameter leads to the inertia and nonmonotonic character of system relaxation after the perturbation. The possibility of hesitative nonstability is discussed. The transient regimes in the growth of 30 cm diameter KCl single crystals are investigated experimentally. The behaviour of crystallization rate differs from the case of small diameter crystals and corresponds to the results of theoretical analysis.