Axial Channeling in Electron Diffraction

1978 ◽  
Vol 33 (3) ◽  
pp. 269-281 ◽  
Author(s):  
A. Ichimiya ◽  
G. Lehmpfuhl
Keyword(s):  
Electron Beam ◽  
Electron Diffraction ◽  
Intensity Distribution ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Zone Axis ◽  
Intensity Maximum ◽  
Bloch Waves ◽  
Axial Channeling

AbstractKossel patterns from Silicon and Niobium were obtained with a convergent electron beam. An intensity maximum in the direction of the zone axes [001] and [111] of Nb was interpreted as axial channeling. The intensity distribution in Kossel patterns was calculated by means of the Bloch wave picture of the dynamical theory of electron diffraction. Particularly zone axis patterns were calculated for different substance-energy combinations and they were compared with experimental observations. The intensity distribution in the calculated Kossel patterns was very sensitive to the model of absorption and it was found that a treatment of the absorption close to the model of Humphreys and Hirsch [Phil. Mag. 18, 115 (1968)] gave the best agreement with the experimental observations. Furthermore it is shown which Bloch waves are important for the intensity distribution in the Kossel patterns, how they are absorbed and how they change with energy.

Theory of bulk resonance diffraction in THEED

1993 ◽  
Vol 440 (1908) ◽  
pp. 95-115 ◽  
Keyword(s):  
Elastic Scattering ◽  
Incident Beam ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Zone Axis ◽  
Bloch Waves ◽  
Diffraction Geometry ◽  
Ewald Sphere ◽  
Lattice Images ◽  
New Type

A full dynamical theory has been developed for an off-axis diffraction geometry. A new type of resonance elastic scattering is found and discussed. This occurs when the Ewald sphere is almost tangential to one of the minus high order Laue zones, and is termed bulk resonance diffraction. It is shown that under certain diffraction conditions, i. e. bulk resonance diffraction conditions, effectively only a single distinct tightly bound Bloch wave localized around atom strings is excited within the crystal, and selection can be made of the particular bound Bloch waves by appropriately tilting the incident beam or the crystal. A new scheme for imaging individual tightly bound Bloch waves is proposed. Full dynamical calculations have been made for 1T–V Se 2 single crystals. It is demonstrated that chemical lattice images of V and Se atom strings can be obtained along the [0001] zone axis of a 1T–V Se 2 crystal for angles of incidence of 109.54 and 109.90 mrad respectively.

Interpretation of Electron Channeling by the Dynamical Theory of Electron Diffraction

1974 ◽  
Vol 29 (7) ◽  
pp. 1034-1044 ◽  
Author(s):  
K. Kambe ◽  
G. Lehmpfuhl ◽  
F. Fujimoto
Keyword(s):  
Electron Diffraction ◽  
Tight Binding ◽  
Diffraction Theory ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Two Dimensions ◽  
Band Theory ◽  
Bloch Waves ◽  
Electron Channeling ◽  
The Many

The connection between electron channeling and electron diffraction is discussed on the basis of the dynamical theory. Results of the many-beam calculations for 50 keV to 2 MeV electrons incident almost parallel to a [110] axis of a MgO crystal are used as examples. Bloch waves with a marked concentration of electron density at rows of atoms are obtained, and interpreted as states of electrons bound to the rows of atoms, corresponding to the classical picture of channeling. This can be shown properly by applying the tight-binding method of band theory in the two dimensions perpendicular to the axis. In this picture the "rosette motions"' in the classical theory are interpreted as p-tvpe, d-type, etc. Bloch waves, and the "weavons" as loosely-bound s-type Bloch waves. They are connected to the pictures of the Borrmann effect and the Bloch-wave channeling in the diffraction theory.

Electron diffraction from crystal defects: Fraunhofer effects from plane faults

1966 ◽  
Vol 293 (1433) ◽  
pp. 169-180 ◽  
Keyword(s):  
Electron Diffraction ◽  
Intensity Distribution ◽  
Stacking Faults ◽  
Dynamical Theory ◽  
Crystal Defects ◽  
Similar Calculation ◽  
Selected Area Electron Diffraction ◽  
Periodic Intensity ◽  
Diffraction Patterns ◽  
Calculated Intensity

The selected area electron diffraction patterns from a crystal containing a stacking fault have been observed to exhibit a number of unusual features. In some cases a periodic intensity distribution about the Bragg spot, in other cases streaking. By applying Kirchhoff’s theory of diffraction and using the dynamical theory of electron diffraction this intensity distribution around the Bragg spots in the electron diffraction patterns from stacking faults has been calculated. The calculated intensity distributions compare favourably with experiment. A similar calculation has also been carried out to predict the intensity distribution around Bragg spots in the selected area electron diffraction patterns from a crystal containing a grain boundary.

Failure of the Conservation of Flux in the Dynamical Theory of the Electron Diffraction

1985 ◽  
Vol 43 ◽  
pp. 76-77
Author(s):  
H. S. Kim ◽  
S.S. Sheinin
Keyword(s):  
Electron Diffraction ◽  
Dynamical Theory ◽  
Dynamical Matrix ◽  
Laue Diffraction ◽  
Bloch Waves ◽  
Reflected Waves

It is widely believed that flux is conserved in the dynamical theory of electron diffraction. Conservation of flux requires thatwhere ϕg is the amplitude of a diffraction beam and the sum is over all diffracted beams. (1) is valid if the crystal is assumed to be non-absorbing and if reflected waves are neglected. It can also be shown that (1) only holds if the eigenvectors of the dynamical matrix are orthogonal. Orthogonality of these eigenvectors is, however, only obtained when certain approximations and assumptions are made including, for example, the column approximation and the assumption of symmetrical Laue diffraction conditions.In order to see the possible effects of relaxing these assumptions and approximations on conservation of flux, consider the expression for diffracted beam amplitude in non-symmetrical Laue casewhere the summation is over all Bloch waves excited in the crystal.

Bloch-wave solution in the Bragg case

1989 ◽  
Vol 45 (2) ◽  
pp. 174-182 ◽  
Author(s):  
Y. Ma ◽  
L. D. Marks
Keyword(s):  
Electron Diffraction ◽  
Current Flow ◽  
High Energy ◽  
Bloch Wave ◽  
Zone Axis ◽  
Wave Method ◽  
High Energy Electron ◽  
Stepped Surfaces ◽  
Reflection Electron Microscopy ◽  
Wave Phenomena

The Bloch-wave method for reflection diffraction problems, primarily electron diffraction as in reflection high-energy electron diffraction (RHEED) and reflection electron microscopy (REM), is developed. The basic Bloch-wave approach for surfaces is reviewed, introducing the current flow concept which plays a major role both in understanding reflection diffraction and determining the allowed Bloch waves. This is followed by a brief description of the numerical methods for obtaining the results including specific results for GaAs near to the [010] zone axis. A number of other Bloch-wave phenomena are also discussed, namely resonance diffraction and its relationship to internal and external reflection and variations in the boundary conditions and Bloch-wave character, splitting of diffraction spots due to stepped surfaces, which can be completely explained, and the reflection equivalent of thickness fringes.

Energy Loss Analysis in Bloch Waves

1974 ◽  
Vol 29 (6) ◽  
pp. 955-956
Author(s):  
F. Fujimoto ◽  
G. Lehmpfuhl
Keyword(s):  
Electron Diffraction ◽  
Energy Loss ◽  
Single Crystal ◽  
Bloch Wave ◽  
Diffraction Spot ◽  
Loss Peak ◽  
Bloch Waves ◽  
Loss Analysis ◽  
Partial Waves

In electron diffraction experiments with a single-crystal wedge Bloch waves can be analyzed directly because of their separation into partial waves when leaving the crystal. In a two-beam case the diffraction spot is split into a double representing two partial waves of the two Bloch waves. The energy-loss spectrum in the 220 doublet of MgO was investigated with a Möllenstedt velocity-analyzer. Two loss peaks at about 14 and 22 eV were found in each Bloch wave. Thermal losses were identified as a background in the no-loss peak.

Bloch-wave interpretations of Gjønnes–Moodie lines in convergent-beam electron diffraction for non-symmorphic space-group crystals

2021 ◽  
Vol 77 (3) ◽  
pp. 222-231
Author(s):  
Hirofumi Matsuhata
Keyword(s):  
Electron Diffraction ◽  
Dimensional Space ◽  
High Energy ◽  
Bloch Wave ◽  
Convergent Beam Electron Diffraction ◽  
Bloch Waves ◽  
Beam Electron ◽  
Space Group ◽  
Space Groups ◽  
Convergent Beam

The contrast of Gjønnes–Moodie (GM) lines which appear in convergent-beam electron diffraction patterns for non-symmorphic space-group crystals is explained using Bloch waves. In the two-dimensional space groups p2mg and pg the Bloch waves for electron diffraction are described. In both space groups along the Δ line, Bloch waves are arranged as two different types, and it is shown that the two types of Bloch waves do not contribute to the intensity of forbidden reflections. Along the position where the forbidden reflection satisfies the Bragg condition, degeneracies of two Bloch waves are found and it is shown that the degenerated pair of Bloch waves do not contribute to the intensity. These Bloch-wave results provide a new perspective in the understanding of the contrast mechanism of GM lines previously described using scattering polynomials. They also advance the understanding of Bloch-wave behaviour in high-energy electron diffraction.

Effects of Non-Systematic Reflections on Bloch Wave Absorption Coefficients

1972 ◽  
Vol 30 ◽  
pp. 640-641
Author(s):  
C.D. Cann ◽  
A.E.B. Monk ◽  
S.S. Sheinin
Keyword(s):  
Electron Microscope ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Contrast Effects ◽  
Bragg Condition ◽  
Absorption Coefficients ◽  
Bloch Waves ◽  
Crystalline Materials ◽  
Good Image ◽  
Microscope Images

In the dynamical theory, absorption of Bloch waves plays an important role in explaining contrast effects observed in electron microscope images of crystalline materials. Although the effects of systematic reflections on the absorption coefficients of Bloch waves have been studied, little is known about the effects of non-systematic reflections. It was with a view to investigating these effects that this work was undertaken.The orientation chosen for this investigation is one commonly employed for obtaining good image contrast at low accelerating voltages, namely, a low order systematic reflection g, set close to its Bragg condition. Under these circumstances two Bloch waves with widely differing absorption coefficients are strongly excited. In this paper the effect of non-systematic reflections on these absorption coefficients has been studied. This has been done by determining the effect of the reflection on the (220) systematic set in Si at 150 kV.

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