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.     

Time and space domain separation of pulsed X-ray beams diffracted from vibrating crystals

It is known that a set of additional reflections (satellites) may arise on rocking curves in the case of X-ray diffraction in the Bragg geometry from crystals where high-frequency ultrasonic vibrations are excited. It is shown that, under certain conditions, the pulse wave fields of the satellites and main reflection may be intersected in space (playing the role of pump and probe beams) and in time (forming interference superlattices).     

Diffraction reflection of a focused X-ray wave by a multilayer crystal

The Bragg diffraction of a narrow X-ray beam in a multilayer crystal is studied in the reflection geometry. It is shown by computer simulation of the experiment that strong integrated kinematic reflection occurs at any boundary of a multilayer crystal at the point of intersection of a narrow beam with the boundary. In contrast to the dynamic diffraction of a plane wave, attenuation of a narrow incident beam due to the reflection is small in comparison with the conventional absorption. As an example of a multilayer crystal, a Fabry-Perot interferometer is considered, which consists of two 70-μm-thick crystal Si layers separated by a 100-μm-thick air layer. The 12 4 0 reflection is studied at a photon energy of 15 keV. Three methods of formation of a narrow beam are considered: wavefront limitation by a slit, focusing with a parabolic lens, and focusing with a zone plate. It is shown that, for a local analysis of the thickness of layers and scattering parameters, the method of parabolic lens focusing has some advantages in comparison with the other methods.     

Investigation of shallow strain distributions in silicon single crystals with X-ray bragg reflection

The use of X-ray double crystal diffractometry in Bragg case reflection for the determination of shallow strain distributions is investigated. Based on the theory of Takagi-Taupin theoretical calculations of reflection curves of silicon crystals with diffusion induced strain profiles are carried out for different wave lengths and reflections. Possibilities for an optimal choise of reflections are discussed and the limits of detectibility are estimated. Experimental results of boron diffused silicon crystals confirm the theoretical results. Triple crystal diffractometry of (+n, –n, +n) setting is discussed as one possibility to increase the sensibility.     

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.     

Analysis of X‐ray extinction in crystals with inhomogeniously distributed dislocations

The secondary extinction theory of Zachariasen for mosaic crystals as well as the formalism of Becker&Coppens have been used for substructure analysis (lattice disorientations, block size, density of excess dislocations, etc.) in crystals with inhomogeniously distributed dislocations in the Bragg case of diffraction geometry. In the case of large crystals D_S ≫ Λ_hkl the mean total density ρ_D of randomly distributed dislocations was also estimated taking into account additionally the primary X‐ ray extinction treatment. In this connection two cases are considered: I) pure secondary extinction related to arrangement of dislocation walls and II) mixed extinction in crystals with large subgrains related to randomly distributed dislocations and arrangement of dislocation walls. In order to check the considerations, the experimental and calculated data were compared for Be (model I) and Cu (model II) single crystals. The weakly distorted single crystals of Be and Cu were experimentally investigated in the Bragg case of diffraction geometry using Cu Kα₁ radiation by means of double crystal diffractometer. A new experimental procedure was proposed. Using alternative technique for substructure analysis (for instance EBSD) the reliability of analysis based on extinction phenomenon in weakly distorted single crystals has been checked. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Intensity and width of bragg reflections from imperfect icosahedral quasicrystals obtained by simulating atomic growth

The Bragg reflections from icosahedral quasicrystals obtained in the course of a computer experiment on the simulation of crystal growth have been studied. The computer experiments based on the theory developed earlier allow one to “grow” in a computer the imperfect quasicrystals of nanometer dimensions. It is shown that the absolute value of the structure factor can be close to the maximum possible one for crystals, i.e., to the structure factor in the case where all the atoms scatter in phase. The spectral width of Bragg reflections is studied, and it is shown that the reflection width depends not only on the quasicrystal dimensions in the physical space but, also, on the perpendicular component of the reciprocal-lattice vectors. The data obtained are compared with the known experimental data.     

Observation of individual dislocations in 6H and 4H SiC by means of back‐reflection methods of X‐ray diffraction topography

SiC crystals of high structural perfection were investigated with several methods of X‐ray diffraction topography in Bragg‐case geometry. The methods included section and projection synchrotron white beam topography and monochromatic beam topography. The investigated 6H and 4H samples contained in large regions dislocations of density not exceeding 10³ cm^‐2. Most of them cannot be interpreted as hollow core dislocations (micro‐ or nano‐pipes). The concentration of the latter was lower than 10² cm^‐2. The present investigation confirmed the possibility of revealing dislocations with all used methods. The quality of presently obtained Bragg‐case multi‐crystal and section images of dislocation enabled analysis based on comparison with numerically simulated images. The analysis confirmed the domination of screw‐type dislocations in the investigated crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamical theory of the resonant X-ray diffraction in coplanar Bragg geometry

A dynamical theory of the resonant diffraction of X-ray synchrotron radiation within the two-wave approximation in coplanar Bragg geometry at large grazing angles in perfect crystals has been developed. The predictions of the kinematical and dynamical diffraction theories are compared by the example of Ge crystals.     

Diffraction on the 2D quasi-periodic Rauzy tiling

Diffraction on scattering centers forming a Rauzy tiling has been theoretically investigated. It is proven that a set of Rauzy points is a model set and it is shown that a Rauzy tiling has a diffraction pattern with narrow Bragg peaks, whose positions and the corresponding intensities are functions of three integer indices. It is also shown that, as a result of the presence of similarity symmetry in the Rauzy tiling, the set of diffraction peaks is divided into nonintersecting classes. Peaks of each class fall on a bilateral spiral, expanding from the origin of coordinates to infinity. The specific features of diffraction in the case of scattering from the quasi-lattice of tiling singularities (Rauzy points) and the geometric centers of tiles are considered separately.     

Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals

The nonstandard theory of X-ray scattering in a deformed crystal has been generalized. The vector of atomic-plane displacement is introduced into the crystal polarizability model like in the generalized Takagi dynamic theory. The solution to the wave equation is sought for using the procedure of expanding the field amplitude and vector operators in the Fourier components of polarizability χ _H in a series according to the multiscale method. It is shown that considering lattice strain generally calls for introducing various characteristic spatial regions for the diffraction equation, which is in complete agreement with the main concept of the multiscale method. A particular case of a strain field depending on one scale is considered. If a relative change in strain occurs at a length on the order of the extinction length, one can obtain equations generalizing the Takagi equations to the case of arbitrary diffraction geometries.     

Spectrum of natural electromagnetic waves in a periodic ferromagnet-dielectric structure

The specific features of propagation of natural TE waves in a periodic ferromagnet-dielectric structure are investigated in the following geometry: a bias magnetic field is parallel to the ferromagnet/dielectric interface and perpendicular to the wave propagation direction. The transformation matrix for the period of the structure, the dispersion relation, and the energy reflection coefficient are obtained for the case of normal incidence of a wave on a semi-infinite periodic medium by solving the boundary-value problem. It is shown that an external field can be used to control the spectrum and characteristics of reflected waves.     

The Geometric Origin of Asymmetric Small Angle Neutron Scattering from an Elastically Bent Double Crystal Diffractometer

We have investigated the Small Angle Neutron Scattering (SANS) from a Double Crystal Diffractometer (DCD) in the (1, —1) setting using a focusing Si monochromator crystal in the symmetric (111) case and a defocusing analyser Si crystal in a completely asymmetric (111) case. We have found that SANS data from porous glassy carbon and Silica spheres are asymmetric about the Bragg Peak centre. We attribute this observation to a combination of factors, particularly geometrical effects, related to the angle of acceptance χ into the analyser crystal when a SANS sample is positioned between the crystal pair. A simple procedure for SANS data correction is outlined and shown to be effective in this case.     

On the Contrast Zones and Strain-Induced Bands in the Hydrocarbon (n-C28H58) Crystals

Formation of contrast zones due to a phase change and occurrence of strain induced band patterns are discussed in the case of n-octacosane crystals. Slip systems are considered.     

Increasing the lasing efficiency in cholesteric liquid-crystal photonic structures

Two types of lasing in cholesteric liquid crystals (LCs) in the range of luminescence of laser dye molecules have been investigated. The first type belongs to the Bragg modes at the photonic band edge, which propagate along the normal to the LC layer. The second type of lasing is related to the modes leaking into the substrate and propagating at small angles to the LC layer. It is shown that the Bragg lasing efficiency can be significantly increased under wide-aperture optical pumping. The method proposed for increasing the lasing efficiency is based on suppressing the excitation of leaky laser modes using partially absorbing thin films as the coatings for LC-orienting substrates. Both experimental results and the theoretical model of the effect using the numerical simulation data are discussed.     

γ-Ray diffraction studies of the perfection of large silicon single crystals

The sensitivity of Bragg diffraction experiments to lattice distortions in single crystals increases with decreasing wavelength. The integrated reflecting power has been measured with 0.0392 Å γ-radiation in several float-zone and Czochralski 001 grown silicon crystals, approximately 1 cm thick and 10 cm in diameter. Comparison is made with the results calculated from dynamical diffraction theory for a perfect crystal. Standard float-zone crystals show internal radial strain which is very much reduced when applying the improved Wacker float-zone technique. Czochralski grown silicon crystals, especially the sample grown under the application of a magnetic field, show much weaker internal strain which, nevertheless, could be made visible by means of γ-ray Pendellösung intensity beat measurements.     

On the possibility of strain determination by section topography in the parallel Geometry

A new approach to the problem of strain determination in a crystal by means of X-ray radiation is presented. In the proposed experiment the border of the windows etched in silicon oxide layer which covers the surface of the silicon crystal, is image using a section topography and geometry in which the edge of the windows is placed parallel to the vertical X-ray beam axis. That geometry allows to obtain the images giving the possibility of more Precise and easier determination of strains, because the interference fringes (Pendellösung) are considerably narrow. Their position can be defined with better precision.     

The reduction of the misfit dislocation in non-doped AlAs/GaAs DBRs

The non-doped AlAs/GaAs distributed Bragg reflectors (DBRs) with density of misfit dislocation (MD) close to zero had been obtained. The reduction of MD density was achieved by increasing temperature distribution homogeneity on the growing crystal in consequence of higher rotation rate of the wafer. Two structures of DBR were crystallized using molecular beam epitaxy (MBE) under the same optimal growth condition. The growth runs differ only in the rotation rate of the wafers. X-ray topograph showed no residual MDs in case of faster rotation. The DBR structure with residual MD density is still highly strained. No additional relaxation process has occurred, what was confirmed by an angular position of DBR zeroth-order peak on high-resolution X-ray diffractometry (HRXRD) rocking curve.     

Zur Defokussierungsabhängigkeit der elektronenmikroskopischen Netzebenenabbildung

The defocusing dependence of the lattice plane image contrast in the region of interplanar spacings between 8 Å and 1.4 Å is investigated experimentally and interpreted theoretically using calculated phase contrast transfer characteristics. On the one hand, it is well-known that in the case of coaxial illumination optimum image contrast is obtained if using suitable underfocus, on the other hand, contradictory statements exist for the conditions of contrast formation if using tilted illumination. In the present paper it is shown that in this case optimum contrast is attained with an appropriate overfocus. A possible explanation is given which takes into account the influence of the deviation from the exact symmetrically tilted illumination.