Theory of X-ray diffraction from a nonideal crystal with a trapezoidal cross section

The theory of X-ray diffraction from a nonideal lateral crystal with a trapezoidal cross section in the Born (kinematical) approximation has been developed. Distortions of the crystal structure are caused by continuous (nonrandom) lattice strains and randomly distributed defects. Continuous lattice strain is a combination of elastic bending of atomic planes and a linear variation in the interplanar spacing with increasing distance from the crystal surface. Within the method of triple-crystal X-ray diffraction, numerical simulation of the angular intensity distribution of coherent and diffuse scattering has been performed for different continuous and random lattice strains in the lateral and vertical directions.     

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.     

Study of X-ray diffraction from a surface acoustic wave in the grazing geometry with allowance for the curvature of the unperturbed crystal surface

Fresnel X-ray diffraction from a concave crystal surface in the presence of a surface acoustic wave (SAW) has been considered for grazing angles of incidence in noncoplanar symmetric Laue geometry. It is shown that the main peak and diffraction satellites are focused at different distances from a crystal. The effect of deviation from the Bragg angle, the spectral line width, and the SAW amplitude on the X-ray diffraction pattern has been analyzed. It is established that the contrast of an X-ray diffraction pattern of an SAW in Bragg-Laue grazing geometry is related to the character of irregularities of the crystal surface, and the pattern details depend on the measurement mode. The sensitivity of the method is about a nanometer. The focal image of the SAW serves as a scale landmark for determining the crystal surface characteristics.     

X-ray diffraction studies of protein crystal disorder

Protein crystals contain many kinds of disorder, but only a small fraction of these are likely to be important in limiting the diffraction properties of interest to crystallographers. X-ray topography, high-angular-resolution reciprocal space measurements, and standard crystallographic data collection have been used to probe three factors that may produce diffraction-limiting disorder: (1) solution variations during crystal growth, (2) macromolecular impurities, and (3) post-growth crystal treatments. Variations in solution conditions that occur in widely used growth methods may lead to variations in equilibrium protein conformation and crystal packing as a crystal grows, and these may introduce appreciable disorder for sensitive proteins. Tetragonal lysozyme crystals subjected to abrupt changes in temperature, pH, or salt concentration during growth show increased disorder, consistent with this mechanism. Macromolecular impurities can have profound effects on protein crystal quality. A combination of diffraction measurements provides insight into the mechanisms by which particular impurities create disorder, and this insight leads to a simple approach for reducing this disorder. Substantial degradation of diffraction properties due to conformation and lattice constant changes can occur during post-growth crystal treatments such as heavy-atom compound and drug binding. Measurements of the time evolution of crystal disorder during controlled crystal dehydration – a simple model for such treatments – suggest that structural metastability conferred by the constraints of the crystal lattice plays an important role in determining the extent to which the diffraction properties degrade.     

Determination of the parameters of a rough surface from the dynamical X-ray diffraction data

A new method is proposed for determining the roughness parameters from X-ray diffraction data. The method is based on a controllable displacement of reflecting planes under an external tangential pressure. It is shown that the displacement of atomic planes near the rough surface upon sample compression increases in proportion to the applied stress and strongly depends on the roughness parameters. Rough surfaces with determinate periodic and random reliefs are considered together with the corresponding features of X-ray rocking curves.     

A method for automated determination of the crystal structures from X-ray powder diffraction data

An algorithm is proposed for determining the crystal structure of compounds. In the framework of this algorithm, X-ray powder diffraction patterns are compared using a new similarity index. Unlike the indices traditionally employed in X-ray powder diffraction analysis, the new similarity index can be applied even in the case of overlapping peaks and large differences in unit cell parameters. The capabilities of the proposed procedure are demonstrated by solving the crystal structures of a number of organic pigments (PY111, PR181, Me-PR170).     

Synthesis and powder X-ray diffraction of new Schiff-base liquid crystal

Liquid crystals (LCs) are soft materials that combine the fluidity of disordered liquids and the long-range orientational or positional order of crystalline solids, along one or two directions of space. A search for better stationary phases, including highly selective ones, is an important trend in chromatography development. Among the stationary phases under investigation are LC stationary phases that have been recently generated much interest. A variety of isomeric molecules were separated with high accuracy. Successfully, X-ray scattering is widely used to investigate and characterise the microscopic structure of most LCs. In this paper, a new liquid crystalline material that can be used potentially as stationary phase in gas chromatography was synthesised and characterised by means of nuclear magnetic resonance (NMR), infrared (IR) spectra, elemental analysis and X-ray diffraction.     

X-ray diffraction pattern of a Gulyaev-Bleustein surface acoustic wave in grazing geometry

The X ray diffraction pattern of a Gulyaev-Bleustein surface acoustic wave (SAW) under grazing angles of incidence in noncoplanar symmetric Laue geometry has been considered. It is supposed that the propagation direction of an SAW makes a small angle with the diffraction vector. It is shown that small deviations from the Bragg angle (～0.01″ induced by the SAW and do not affect the reflection coefficient lead to the formation of diffraction satellites both in the cases of standing and traveling SAWs. It has been established that the recorded diffraction pattern, which is a time-averaged intensity distribution, has characteristic profiles for odd and even satellites.     

An X-ray diffraction refinement of the crystal structure of natural apophyllite

The crystal structure of apophyllite (Andersberg — GDR), with a = 8.966(2), c = = 15.767(1) Å, P4/mnc, z = 2, Q = 2.35 gm · cm⁻³, has been refined (R = 0.035) by least squares with 976 reflections collected with a diffractometer. Apophyllite is a sheet structure with the bringing Si O bond lengths 1.6236 Å, while the non-bridging bond length Si O(3) is 1.5843 Å. The two independent Si O Si angles are 140.09, 140.76 degrees. The mean Si O bond length is 1.6138 Å. As it was not possible to locate unequivocally the H-atoms with the X-ray data, the interpretation of the of water in the structure was based on the charge balance approach of DONNAY and ALLMAN . Assuming that the fluorine ion is bonded to calcium ion (Ca-F = = 2.416 Å) and to H3 atom (F-H3 = 0.9145(1) Å) and water molecule hydrogen bonded to silicate framework. The average bond distances O-H are 0.962(2) Å and angle 105.24(1)°.     

Structural study of thiosaccharin by single crystal X-ray diffraction and infrared spectroscopy

The structure of thiosaccharin (1,2-benzisothiazol-3(2H)-thione 1,1-dioxide) has been investigated by X-ray diffraction and infrared spectroscopic methods. The compound crystallizes in the orthorhombic space groupFdd2 witha=26.591(3),b=25.058(3),c=4.934(5) Å,Z=16. The structure consists of thiosaccharin molecules bonded to each other through N–H...O intermolecular hydrogen bonds. The infrared spectra of the thiosaccharin at room and liquid-nitrogen temperature were recorded. The spectral features in the N–H stretching region were correlated with the crystallographic data on the geometry of the N–H...O hydrogen bonding. In an attempt to assign the bands due to the SO₂ stretching modes, the spectrum of thiosaccharin was compared with that of saccharin (1,2-benzoisothiazole-3(2H)-one, 1,1-dioxide).     

Measurement of piezoelectric constants of lanthanum-gallium tantalate crystal by X-ray diffraction methods

A method for measuring piezoelectric constants of crystals of intermediate systems by X-ray quasi-multiple-wave diffraction is proposed and implemented. This technique makes it possible to determine the piezoelectric coefficient by measuring variations in the lattice parameter under an external electric field. This method has been approved, its potential is evaluated, and a comparison with high-resolution X-ray diffraction data is performed.     

Dynamic variation in the lattice parameter of a crystal under ultrasonic treatment in X-ray diffraction experiments

The X-ray diffraction in the Laue geometry is investigated in germanium and silicon single crystals upon excitation of long-wavelength ultrasonic elastic strain waves traveling along the sample surface. The X-ray diffraction beam is bounded by a slit 0.2 mm in size, which is considerably less than the wavelength of the ultrasonic wave. The use of this slit makes it possible to separate crystal regions with a nearly homogeneous strain. As a consequence, the rocking curves stroboscopically measured in a double-crystal dispersionless scheme at different instants of time almost coincide with those for a perfect crystal with a lattice parameter varying in time. The rocking curves measured in a time-integrated mode turn out to be broadened, but their integrated intensities remain unchanged. Possible applications of the developed method are discussed.     

Structural studies of oxalohydroxamic acid by single crystal X-ray diffraction and spectroscopic methods

The structure of oxalohydroxamic acid has been investigated by X-ray and spectroscopic analyses. It has been shown that oxalohydroxamic acid exists in the oxamic form in the solid as well as in solution. The variable-temperature nuclear magnetic resonance (NMR) studies reveal an exchange of OH and NH protons, the exchange being faster at higher temperatures. The kinetic and the thermodynamic parameters such as the rate constant (K), the free energy of activation (G ^DG), and the energy of activation (E _a) for the exchange process have been obtained. The compound crystallizes in the monoclinic space groupP2₁/c witha=5.208,b=3.864,c=11.482 Å,=111.45°, andZ=2. The structure was solved withMultan 80. The refinement by block diagonal least squares and Fourier methods providedR=0.035. There is strong hydrogen bonding between the molecules which form dimer.     

Specular reflection of X-rays under the conditions of grazing diffraction in a crystal with an amorphous surface layer

Specific features of the anomalous angular dependence of the specular-reflection intensity under the condition of noncoplanar grazing X-ray diffraction in a crystal coated with an amorphous surface film were revealed and studied experimentally. The phenomenon was analyzed theoretically and its high sensitivity to the presence and the thickness of a several-nanometer-thick amorphous film was shown. The experimental data were used to determine the thickness and the density of a native oxide layer formed on the surface of a silicon single crystal.     

The study of bis-chloromethyl-phosphinic acid crystal by ATR and Raman spectroscopy and X-ray diffraction

Crystals of bis-chloromethyl-phosphinic acid ((CH₂Cl)₂POOH) are studied by attenuated total reflection (ATR) and Raman spectroscopy supported by X-Ray diffraction. The bands recorded in the ATR and in Raman spectra have the same wavenumbers within experimental uncertainty. It is in agreement with the X-Ray diffraction results which show that the molecules in crystals form infinite chains through hydrogen bonds and there is no center of inversion. The parameters of the unit cell, the bond lengths and angles, and the distance between two oxygen atoms in hydrogen bond bridges are determined. The spectral features and the intermolecular distance between oxygen atoms are characteristic for a strong hydrogen bonded system.     

X-ray diffraction study of an as-grown crystal of a two-phase sample of Lu0.65Ca0.35F2.65

The X-ray diffraction study of an “as-grown” crystal of Lu_0.65Ca_0.35F_2.65 revealed for the first time two phases with a regular mutual orientation. The c axis of the hexagonal phase (a = 3.88 Å, c = 6.89 Å) is oriented along the body diagonal to the cubic phase (a = 5.50 Å). The hexagonal phase has a tysonite-type structure with a “small” unit cell (P6₃/mmc, Z = 2). The cubic phase has a fluorite structure ( \(Fm\bar 3m\) , Z = 4).     

X-ray specular reflection under conditions of extremely asymmetric noncoplanar diffraction from a bicrystal

The angular dependence of the intensities of X-ray specular reflection has been rigorously analyzed under conditions of noncoplanar grazing Bragg diffraction in a crystal coated with a crystalline film (bicrystal). It is shown that the anomalous angular dependence of the specular-reflection intensity is extremely sensitive to the thickness (from fractions of a nanometer up to several nanometers), deformation, and the amorphization degree of the crystalline films. The optimum conditions for recording intensities are attained at grazing angles equal to 1.5–4.0 of the critical angle of the total external reflection.     

The crystal structure of Zr2Se reinvestigated by electron crystallography and X-ray powder diffraction

The metal-rich compound Zr₂Se is of particular interest for electron crystallography, since it was one of the first examples that proved that heavy-atom structures can be solved via quasi-automatic direct methods from selected area electron diffraction intensities [1]. For this reason, Zr₂Se has been chosen as a model to discuss the possibilities and the limits of the quasi-kinematical approach that has been successfully used to determine this and related structures from high-resolution electron microscopy (HREM) images and selected area electron diffraction. In order to quantify the achievable accuracy of the electron crystallography techniques used, the corresponding structures are compared with results from structural analysis with X-ray powder data and with a model received from first-principles calculations. The latter structure was chosen in this study as a reference, since the calculations do not depend on experimental parameters. Analysis of the obtained result from electron diffraction structural analysis (EDSA) shows that the structural model is, on average, only off by 0.08 Å, despite the investigated crystal having an effective thickness of 286 Å. The corresponding result from Rietveld refinement with X-ray powder data agrees to within 0.04 Å with the structure from calculation and within 0.03 Å with the result from an earlier single crystal X-ray study [2].