scholarly journals Effect of n-beam Interaction

1988 ◽  
Vol 41 (3) ◽  
pp. 511
Author(s):  
A Okazaki ◽  
H Ohe ◽  
Y Soejima
Keyword(s):  
Reciprocal Lattice ◽  
Accurate Determination ◽  
Lattice Points ◽  
Careful Examination ◽  
Multiple Diffraction ◽  
Simulation Based ◽  
Beam Interaction

Weak spurious intensities arising from the n-beam interaction (the multiple diffraction) often obscure the existence of screw axes or glide planes. It is pointed out that the n-beam interaction may also introduce� significantly different intensities to a set of crystallographically equivalent reciprocal lattice points. These problems can be solved by making IJI scanning measurements and, more definitely, by a comparison with the simulation based on the Soejima-Okazaki-Matsumoto (1985) formalism; some examples are shown. Since the influence on the intensity reaches 10% for strong reftections and more for weaker ones, a careful examination is essential for the accurate determination of F values.

Fast calibration of CBED patterns for quantitative analysis

1993 ◽  
Vol 51 ◽  
pp. 674-675
Author(s):  
M.A. Gribelyuk ◽  
M. Rühle
Keyword(s):  
Reciprocal Lattice ◽  
Accurate Determination ◽  
Incident Beam ◽  
Crystal Thickness ◽  
Structure Model ◽  
Beam Direction ◽  
Transmitted Beam ◽  
Reciprocal Vector ◽  
On Line

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

Analyzing structure factor phases in pure and doped single crystals by synchrotron X-ray Renninger scanning

2013 ◽  
Vol 47 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Zohrab G. Amirkhanyan ◽  
Claúdio M. R. Remédios ◽  
Yvonne P. Mascarenhas ◽  
Sérgio L. Morelhão
Keyword(s):  
Small Difference ◽  
Accurate Determination ◽  
Nickel Sulfate ◽  
Lattice Parameter ◽  
Metallic Ions ◽  
Multiple Diffraction ◽  
Ionic Radii ◽  
X Ray ◽  
Model Structures

X-ray multiple diffraction has been applied to study the substitutional incorporation of Mg2+ions into NSH crystals (nickel sulfate hexahydrate, NiSO4·6H2O). Intensity profiles provide information on invariant phases, while angular positions of the multiple diffractions allow accurate determination of lattice parameters. By increasing the atomic disordering only of O2−sites in model structures of doped NSH, the sense and magnitude of induced phase shifts match those necessary to justify the observed changes in the intensity profiles. Causes of disordering and lattice parameter variation are discussed. Although the amount of extra oxygen disordering is relatively large with respect to the small difference in the ionic radii of the metallic ions, this disordering is beyond the resolution power achievable by analyzing diffracted intensities of isolated reflections, such as in standard crystallographic techniques.

scholarly journals Lattice row distance

2014 ◽  
Vol 70 (a1) ◽  
pp. C1454-C1454
Author(s):  
Hejing Wang ◽  
Ting Li ◽  
Ling Wang ◽  
Zhao Zhou ◽  
Lei Yuan
Keyword(s):  
Reciprocal Lattice ◽  
Early Time ◽  
Basic Feature ◽  
Lattice Points ◽  
Lattice Parameters ◽  
Parallel Lines ◽  
Basic Characteristics ◽  
Diffraction Patterns ◽  
Distance Formulae

Lattice and diffraction are two relating aspects of a crystal. The former reflects the nature of a crystal and the latter describes the basic feature of a crystal. A lattice possesses points and rows two basic characteristics. Great attention has been paid to the points and their distances and directions (angles) they form since the early time of crystallography. Starting from lattice points people have already revealed and found so many regulations in crystals and made great progresses in crystallography. What about the lattice rows? Starting from the geometric relations of reciprocal lattice, we propose six general formulae [1] to describe the relationships between the lattice row distance, the Miller indices h, k, l and the lattice parameters for all crystal systems along any direction. This, like the lattice points, establishes the foundation of the row-indexing, row-refinement of lattice parameters and row-determination of incidence direction theoretically. It is a new method from the lattice row distance to the Miller indices, to the lattice parameters or to the incidence direction. Five steps are optimized for the procedure of "Row-indexing" or "Row-refinement". For example, the procedure of row-indexing is described as 1) measurement of row distance; 2) calculation of row distance; 3) comparison of the measured with the calculated row distances; 4) indexing, and 5) check according to the crystallographic regulations. In respect to diffraction patterns, a series of diffraction spots (points) comprise row(s) and arrange into a series of parallel "lines". When diffraction is strong, diffraction spots are isolated and sharp. However, when diffraction is weak, those spots are obscure or gloomy and often distorted into elongation, asymmetry, deformation, etc. This leads to the outstanding of the rowing "lines" relatively and hence, the row-distance formulae are able to be utilized to structure analysis for those "linear diffraction patterns".

Determination of dispersion and polarization of thermal plane waves in crystals

1971 ◽  
Vol 134 (3-4) ◽  
Author(s):  
P. L. La Fleur
Keyword(s):  
Intensity Distribution ◽  
Phonon Scattering ◽  
Reciprocal Lattice ◽  
Plane Waves ◽  
Lattice Points ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
Reciprocal Lattice Point ◽  
X Ray

AbstractThe dispersion of the thermal plane waves (phonons) in crystals can be determined from the x-ray diffraction intensity distribution around a reciprocal lattice point. In the method presented here no higher-order phonon-scattering corrections are necessary. It is shown furthermore that polarizations and dispersion of the phonons can be determined from the intensity distributions around six properly chosen reciprocal lattice points.

scholarly journals Three-wave X-ray diffraction in distorted epitaxial structures

2013 ◽  
Vol 46 (4) ◽  
pp. 861-867 ◽  
Author(s):  
Reginald Kyutt ◽  
Mikhail Scheglov
Keyword(s):  
Reciprocal Lattice ◽  
Lattice Points ◽  
Angular Width ◽  
X Ray Diffraction ◽  
Structural Perfection ◽  
Multiple Diffraction ◽  
X Ray ◽  
Highly Sensitive ◽  
Integrated Intensities ◽  
Scanning Geometry

Three-wave diffraction has been measured for a set of GaN, AlN, AlGaN and ZnO epitaxial layers grown on c-sapphire. A Renninger scan for the primary forbidden 0001 reflection was used. For each of the three-wave combinations, θ-scan curves were measured. The intensity and angular width of both φ- and θ-scan three-wave peaks were analyzed. The experimental data were used to determine properties of the multiple diffraction pattern in highly distorted layers. It is shown that the FWHM of θ scans is highly sensitive to the structural perfection and strongly depends on the type of three-wave combination. The narrowest peaks are observed for multiple combinations with the largest l index of the secondary hkl reflection. An influence of the type of the dislocation structure on the θ-scan broadening was revealed. These experimental facts are interpreted by considering the scanning geometry in the reciprocal space and taking into account the disc-shaped reciprocal-lattice points. The total integrated intensities of all the three-wave combinations were determined and their ratios were found to be in only a qualitative agreement with the theory. For AlGaN layers, the presence of the nonzero 0001 reflection was revealed, in contrast to AlN and GaN films.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Symmetry breaking in convergent-beam diffraction

1989 ◽  
Vol 47 ◽  
pp. 480-481
Author(s):  
D.J. Eaglesham
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
Space Groups ◽  
Atomic Displacements ◽  
Small Probe ◽  
Phase Sensitive ◽  
Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

Computer-Assisted High-Re Solution TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 162-163
Author(s):  
F.A. Ponce ◽  
H. Hikashi
Keyword(s):  
Signal To Noise Ratio ◽  
Accurate Determination ◽  
Computer Software ◽  
Video Camera ◽  
Image Contrast ◽  
Objective Lens ◽  
Computer Assisted ◽  
Optical Parameters ◽  
Astigmatism Correction

The determination of the atomic positions from HRTEM micrographs is only possible if the optical parameters are known to a certain accuracy, and reliable through-focus series are available to match the experimental images with calculated images of possible atomic models. The main limitation in interpreting images at the atomic level is the knowledge of the optical parameters such as beam alignment, astigmatism correction and defocus value. Under ordinary conditions, the uncertainty in these values is sufficiently large to prevent the accurate determination of the atomic positions. Therefore, in order to achieve the resolution power of the microscope (under 0.2nm) it is necessary to take extraordinary measures. The use of on line computers has been proposed [e.g.: 2-5] and used with certain amount of success.We have built a system that can perform operations in the range of one frame stored and analyzed per second. A schematic diagram of the system is shown in figure 1. A JEOL 4000EX microscope equipped with an external computer interface is directly linked to a SUN-3 computer. All electrical parameters in the microscope can be changed via this interface by the use of a set of commands. The image is received from a video camera. A commercial image processor improves the signal-to-noise ratio by recursively averaging with a time constant, usually set at 0.25 sec. The computer software is based on a multi-window system and is entirely mouse-driven. All operations can be performed by clicking the mouse on the appropiate windows and buttons. This capability leads to extreme friendliness, ease of operation, and high operator speeds. Image analysis can be done in various ways. Here, we have measured the image contrast and used it to optimize certain parameters. The system is designed to have instant access to: (a) x- and y- alignment coils, (b) x- and y- astigmatism correction coils, and (c) objective lens current. The algorithm is shown in figure 2. Figure 3 shows an example taken from a thin CdTe crystal. The image contrast is displayed for changing objective lens current (defocus value). The display is calibrated in angstroms. Images are stored on the disk and are accessible by clicking the data points in the graph. Some of the frame-store images are displayed in Fig. 4.

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