Observation of faint contrast at planar faults in alloys

1978 ◽  
Vol 36 (1) ◽  
pp. 340-341
Author(s):  
K. Kuroda ◽  
Y. Tomokiyo ◽  
T. Kumano ◽  
T. Eguchi
Keyword(s):  
Reciprocal Lattice ◽  
Beam Theory ◽  
Al Alloys ◽  
Small Displacement ◽  
Electron Microscopic ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Planar Fault ◽  
Lattice Displacement ◽  
The Many

The contrast in electron microscopic images of planar faults in a crystal is characterized by a phase factor , where is the reciprocal lattice vector of the operating reflection, and the lattice displacement due to the fault under consideration. Within the two-beam theory a planar fault with an integer value of is invisible, but a detectable contrast is expected when the many-beam dynamical effect is not negligibly small. A weak fringe contrast is also expected when differs slightly from an integer owing to an additional small displacement of the lattice across the fault. These faint contrasts are termed as many-beam contrasts in the former case, and as ε fringe contrasts in the latter. In the present work stacking faults in Cu-Al alloys and antiphase boundaries (APB) in CuZn, FeCo and Fe-Al alloys were observed under such conditions as mentioned above, and the results were compared with the image profiles of the faults calculated in the systematic ten-beam approximation.

The effect of diffuse scattering on the dark-field contrast from precipitates

1978 ◽  
Vol 11 (3) ◽  
pp. 190-192 ◽  
Author(s):  
J. Gjønnes ◽  
J. K. Solberg
Keyword(s):  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Dark Field ◽  
Reciprocal Lattice Vector ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Field Technique

Precipitate contrast due to Bragg interactions in the diffuse scattering has been studied. Both ordinary dark-field contrast and moiré contrast were found to be preserved at quite large distances from the Bragg spots, especially along the direction normal to the reciprocal lattice vector. The effects, which are similar to those seen in thickness fringe contrast from perfect crystals, may be disturbing in the search for faint precipitate reflections with the dark-field technique, especially in thicker parts of the crystal.

Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

1990 ◽  
Vol 48 (2) ◽  
pp. 540-541
Author(s):  
I.N. Yadhikov ◽  
S.K. Maksimov
Keyword(s):  
Reciprocal Lattice ◽  
Unit Cell ◽  
Reciprocal Lattice Vector ◽  
Unit Cell Parameters ◽  
Lattice Vector ◽  
Cell Parameters ◽  
Accuracy Of Measurements ◽  
The Difference ◽  
Image Position ◽  
Convergent Beam

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

Angle calculations for a three-circle goniostat

2006 ◽  
Vol 39 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Helge B. Larsen ◽  
Jon Are Beukes
Keyword(s):  
General Procedure ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Laboratory System ◽  
Lattice Vector ◽  
New Approach ◽  
Rotation Matrices ◽  
Rotation Axes ◽  
Vector Description

A general procedure for angle calculations for a three-circle goniostat has been developed. This new approach is based on a vector description of the transformation of a reciprocal-lattice vector under the action of a rotation shaft. It does not invoke the use of rotation matrices and applies equally well to cases where the directions of the rotation axes do not conform with coordinate axes of the laboratory system adopted for the analysis.

scholarly journals Quasicrystalline 30° twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling

2018 ◽  
Vol 115 (27) ◽  
pp. 6928-6933 ◽  
Author(s):  
Wei Yao ◽  
Eryin Wang ◽  
Changhua Bao ◽  
Yiou Zhang ◽  
Kenan Zhang ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Graphene Layer ◽  
Rotational Symmetry ◽  
Reciprocal Lattice ◽  
Double Resonance ◽  
Interlayer Coupling ◽  
Bilayer Graphene ◽  
Lattice Vector ◽  
Graphene Layers ◽  
Twisted Bilayer Graphene

The interlayer coupling can be used to engineer the electronic structure of van der Waals heterostructures (superlattices) to obtain properties that are not possible in a single material. So far research in heterostructures has been focused on commensurate superlattices with a long-ranged Moiré period. Incommensurate heterostructures with rotational symmetry but not translational symmetry (in analogy to quasicrystals) are not only rare in nature, but also the interlayer interaction has often been assumed to be negligible due to the lack of phase coherence. Here we report the successful growth of quasicrystalline 30° twisted bilayer graphene (30°-tBLG), which is stabilized by the Pt(111) substrate, and reveal its electronic structure. The 30°-tBLG is confirmed by low energy electron diffraction and the intervalley double-resonance Raman mode at 1383 cm−1. Moreover, the emergence of mirrored Dirac cones inside the Brillouin zone of each graphene layer and a gap opening at the zone boundary suggest that these two graphene layers are coupled via a generalized Umklapp scattering mechanism—that is, scattering of a Dirac cone in one graphene layer by the reciprocal lattice vector of the other graphene layer. Our work highlights the important role of interlayer coupling in incommensurate quasicrystalline superlattices, thereby extending band structure engineering to incommensurate superstructures.

scholarly journals Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping

2017 ◽  
Vol 50 (5) ◽  
pp. 1256-1266 ◽  
Author(s):  
Vasily I. Punegov ◽  
Konstantin M. Pavlov ◽  
Andrey V. Karpov ◽  
Nikolai N. Faleev
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Two Dimensional ◽  
Instrumental Function ◽  
X Ray Diffraction ◽  
Reciprocal Space Mapping ◽  
Lattice Vector ◽  
Reflected Waves ◽  
X Ray ◽  
Special Case

The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.

scholarly journals Spatial aliasing and distortion of energy distribution in the wave vector domain under multi-spacecraft measurements

2009 ◽  
Vol 27 (8) ◽  
pp. 3031-3042 ◽  
Author(s):  
Y. Narita ◽  
K.-H. Glassmeier
Keyword(s):  
Energy Distribution ◽  
Brillouin Zone ◽  
Wave Vector ◽  
Flow Direction ◽  
Reciprocal Lattice ◽  
Periodic Pattern ◽  
Lattice Vector ◽  
Model Calculations ◽  
Spatial Aliasing ◽  
Spacecraft Data

Abstract. Aliasing is a general problem in the analysis of any measurements that make sampling at discrete points. Sampling in the spatial domain results in a periodic pattern of spectra in the wave vector domain. This effect is called spatial aliasing, and it is of particular importance for multi-spacecraft measurements in space. We first present the theoretical background of aliasing problems in the frequency domain and generalize it to the wave vector domain, and then present model calculations of spatial aliasing. The model calculations are performed for various configurations of the reciprocal vectors and energy spectra or distribution that are placed at different positions in the wave vector domain, and exhibit two effects on aliasing. One is weak aliasing, in which the true spectrum is distorted because of non-uniform aliasing contributions in the Brillouin zone. It is demonstrated that the energy distribution becomes elongated in the shortest reciprocal lattice vector direction in the wave vector domain. The other effect is strong aliasing, in which aliases have a significant contribution in the Brillouin zone and the energy distribution shows a false peak. These results give a caveat in multi-spacecraft data analysis in that spectral anisotropy obtained by a measurement has in general two origins: (1) natural and physical origins like anisotropy imposed by a mean magnetic field or a flow direction; and (2) aliasing effects that are imposed by the configuration of the measurement array (or the set of reciprocal vectors). This manuscript also discusses a possible method to estimate aliasing contributions in the Brillouin zone based on the measured spectrum and to correct the spectra for aliasing.

scholarly journals Pattern-matching indexing of Laue and monochromatic serial crystallography data for applications in materials science

2020 ◽  
Vol 53 (3) ◽  
pp. 824-836
Author(s):  
Catherine Dejoie ◽  
Nobumichi Tamura
Keyword(s):  
Pattern Matching ◽  
Materials Science ◽  
Reciprocal Lattice ◽  
Unit Cell ◽  
Crystallographic Structure ◽  
Experimental Conditions ◽  
Lattice Vector ◽  
Small Unit ◽  
Orientation Matrix ◽  
Serial Crystallography

Serial crystallography data can be challenging to index, as each frame is processed individually, rather than being processed as a whole like in conventional X-ray single-crystal crystallography. An algorithm has been developed to index still diffraction patterns arising from small-unit-cell samples. The algorithm is based on the matching of reciprocal-lattice vector pairs, as developed for Laue microdiffraction data indexing, combined with three-dimensional pattern matching using a nearest-neighbors approach. As a result, large-bandpass data (e.g. 5–24 keV energy range) and monochromatic data can be processed, the main requirement being prior knowledge of the unit cell. Angles calculated in the vicinity of a few theoretical and experimental reciprocal-lattice vectors are compared, and only vectors with the highest number of common angles are selected as candidates to obtain the orientation matrix. Global matching on the entire pattern is then checked. Four indexing options are available, two for the ranking of the theoretical reciprocal-lattice vectors and two for reducing the number of possible candidates. The algorithm has been used to index several data sets collected under different experimental conditions on a series of model samples. Knowing the crystallographic structure of the sample and using this information to rank the theoretical reflections based on the structure factors helps the indexing of large-bandpass data for the largest-unit-cell samples. For small-bandpass data, shortening the candidate list to determine the orientation matrix should be based on matching pairs of reciprocal-lattice vectors instead of triplet matching.

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