Gyrotropic absorbing crystals of lower symmetries

The specific features of polarization of natural waves propagating in crystals near their optical axes have been studied successively in transparent gyrotropic, absorbing, and gyrotropic absorbing crystals of classes 222, 2, 1, m, and mm2. The dependences of the ellipticities of natural waves and the azimuth of polarization of light transmitted through a crystalline plate (the case of normal incidence) on the orientation of the optical-axis plane of the plate axes with respect to the normal to surface are calculated for these crystals. These characteristics are compared for crystals of axial and planal classes with two different orientations of the optical-axis plane with respect to the symmetry elements of crystal.     

Construction of fractal nanostructures based on Kepler-Shubnikov nets

A system of information codes for deterministic fractal lattices and sets of multifractal curves is proposed. An iterative modular design was used to obtain a series of deterministic fractal lattices with generators in the form of fragments of 2D structures and a series of multifractal curves (based on some Kepler-Shubnikov nets) having Cantor set properties. The main characteristics of fractal structures and their lacunar spectra are determined. A hierarchical principle is formulated for modules of regular fractal structures.     

Non-crystallographic symmetries in the superstructure of (NH4)2ZnCl4

The modulation vector turned out to be equal 1/4. The lattice constants of the orthorhombic superstructure are determined: a = 12.6197(16) Å, b = 7.2107(81) Å, c = 4 × 9.2746(15) Å. The two of the four absences rules are interpreted as corresponding to the non-crystallographic symmetries: The space group P 2₁cn is determined on the basis of the single crystal X-ray pictures taking into account the experimental evidence of pyroelectricity in (NH₄)₂ZnCl₄.     

Fundamental laws of fracture region of solids

The present paper reports that the deformation is statistically symmetric even in the fracture region of solids. The major factor in the fracture region of brittle solids is the creation of new surfaces. On the basis of the creation of new surfaces, four fundamental laws are derived for the fracture region of brittle solids. These laws are: (i) New surfaces are created only after a particular strain of the crystal. (ii) For the smaller values of compressive strain, the area of newly created surfaces is directly proportional to the square of the strain. (iii) The proportionality constant between the area of the newly created surfaces and the square of strain may be termed as fracture constant. Mathematically the fracture constant is the area of newly created surface for unit compressive strain of the crystal. (iv) For larger values of the compressive strain, the logarithm of newly created surfaces is directly proportional to the strain. The experimental verification of the laws of fracture region of solids are discussed. The value of fracture constant of certain solids are estimated and their significance is discussed.     

Twin laws explained by partitions of space

Twin laws of monoclinic potassium feldspars, potassium sulphate, cerussite and hexabromobenzene can be explained by partitions of space. The face indices of the crystals denote points of a lattice in the reciprocal space. A Fourier transform leads to the morphological lattice. The reciprocal crystal is the Dirichlet domain of the morphological lattice and the structural content consisting of groups of atoms or molecules is the morphological unit. The bond strength between neighbouring morphological units is proportional to the area of the common face of the reciprocal crystals. The reciprocal crystal represents the energetical structure of a crystal. Twins can be explained by continuation of the energetical structures across the twin boundaries. The symmetry operations result from pseudosymmetries of the reciprocal crystals. It is possible to predict planes favoured for the formation of twins or parallel grown individuals.     

General laws of X-ray reflection from rough surfaces: II. Conformal roughness

Is shown that, if the expansions of the Debye-Waller formulas for the reflection and total scattering coefficients in the roughness height ?? are limited to terms of order ??², these expressions are valid for any layered inhomogeneous medium with conformal (depth-periodic) roughness and for any distribution function of the roughness heights if the roughness correlation length along the surface is sufficiently large. The advantages of measuring the total reflection coefficient, which characterizes the total intensity of radiation (both specularly reflected and diffusively scattered) directed by a rough surface back into vacuum, for solving the inverse problem of X-ray reflectometry (i.e., the reconstruction of the permittivity profile from a measured reflection curve) are discussed.     

General laws of X-ray reflection from rough surfaces: I. Optical theorem and energy conservation law

The optical theorem is generalized for the general case of X-ray wave reflection from an arbitrary layered rough medium. It is proven strictly that in the absence of absorption the energy conservation law is exactly satisfied within the distorted wave Born approximation if the angular scattering distribution is calculated taking into account only the single wave scattering from the inhomogeneities of the medium and if the specular reflectance and transmittance are calculated with allowance for both single and double scattering.     

Electron Backscattered Diffraction for the Study of Matrices for Immobilization of Actinides Composed of the Murataite-Type Phases

Crystallography Reports - Electron backscattered diffraction (EBSD) has been used to analyze structures of natural minerals and artificial compounds for almost three decades. In recent years, it is...     

Experimental Investigations of the Conditions for the Formation of the Liquid Crystalline State of Polymers

The diagrams of state for concentrated PBG solution in coordinates relating volume fraction-geometric asymmetry and volume fraction-temperature are investigated. The order parameter for macromolecules in the anisortropic phase is dettermined. The experimental data compare with the existing theoretical models for th formation of the liquid crystalline state in solutions of stiff polymer molecule. It is shown that experimental data are in good quantitative agreement with the Flory's lattice model.     

Development of the DIFFRACALC program for analyzing the phase composition of alloys

Crystallography Reports - The DiffraCalc software package is developed for automatic indexing of electron diffraction patterns. The program can operate with the existing base of X-ray diffraction...     

Methods for the preparation of bimetallic xerogel catalysts designed for chlorinated wastes processing

The aim of this work is to simplify and generalize the synthesis procedure of bimetallic supported catalysts by sol–gel process. For Pd–Ag/SiO₂ co-gelled xerogels catalysts a number of synthesis procedures were compared: use of one or two specific alkoxides able to form a chelate with palladium and/or silver cations, reagent mixing in one or two steps, use of industrial grade chemicals instead of laboratory grade chemicals. The catalysts obtained are quite similar: same metal dispersion, same tailored morphology, same localization and accessibility of Pd–Ag alloy nanoparticles inside microporous silica, same activity and selectivity for hydrodechlorination of 1,2-dichloroethane into ethylene. For catalyst production at large scale the synthesis can be achieved in one step with 3-(2-aminoethyl)aminopropyltrimethoxysilane of industrial grade as chelating alkoxide, tetraethylorthosilicate (TEOS) of industrial grade and ethanol denatured with diethyl phthalate.     

Numerical integration methods for the Takagi-Taupin equations for crystals of rectangular cross section

Two independent methods for calculation of the rocking curves for laterally bounded crystals are developed. Numerical simulation of diffraction for crystals of different sizes is performed. The results obtained using the dynamical theory of diffraction are compared to those obtained in the kinematic approximation.     

Computation of the axial temperature distribution for the travelling heater method

A theoretical model for the computation of the axial temperature distribution for the THM arrangement is described considering the heat flow in radial direction. The calculated temperature distribution is compared with the measured one. The correspondence is sufficient. By means of this model, it is possible to estimate the effect of a change of important growth parameters prior to the experiment. The model also permits a calculation of temperature distributions of other crystal growth methods (e.g. Bridgman, zone levelling, zone melting) by changing the boundary conditions only.     

A Technique for the Characterisation of Langmuir-Blodgett Films

A method has been developed which allows the characterisation of Langmuir-Blodgett films. The technique utilises the liquid crystal aligning properties of the films and may be applied to films composed of any number of layers. Two materials were studied, ω-tricosenoic acid and cadmium arachidate. Differences between one and three layer samples of these materials are discussed and observed defects down to a size of approximately 1–2 microns are illustrated. Tentative explanations for the occurrence of some of the defects are put forward. The results of a preliminary study of electron beam damage in ω-tricosenoic acid are presented.