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.

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.

scholarly journals Electron and Positron Density Distribution of Bloch Waves

1973 ◽  
Vol 28 (1) ◽  
pp. 1-8
Author(s):  
G. Lehmpfuhl
Keyword(s):  
Density Distribution ◽  
Charge Density ◽  
Incident Beam ◽  
Bloch Wave ◽  
Zone Axis ◽  
Charge Density Distribution ◽  
Bloch Waves ◽  
Electrons And Positrons ◽  
Beam Diffraction ◽  
Small Charge

The charge density distribution in the strongest Bloch waves for a dynamical many-beam diffraction situation was calculated for electrons and positrons. Near the [110] zone axis of MgO there exist three strong Bloch waves for electrons. One Bloch wave is concentrated at the rows of Mg-atoms, a second at the rows of O-atoms and a third one between the atoms. The positron Bloch waves are mainly concentrated between the atom rows and have only small charge density at the positions of the atoms. For an incident beam parallel to the [110] axis there exists only one strong positron Bloch wave while for electrons more than three Bloch waves are strong, explaining the channeling behaviour of positrons and electrons. Strong partial waves of different electron Bloch waves can be identified in the diffraction pattern from a MgO crystal wedge.

Electron and Positron Density Distribution of Bloch Waves

1973 ◽  
Vol 28 (5) ◽  
pp. 661
Author(s):  
G. Lehmpfuhl
Keyword(s):  
Density Distribution ◽  
Charge Density ◽  
Incident Beam ◽  
Bloch Wave ◽  
Zone Axis ◽  
Charge Density Distribution ◽  
Bloch Waves ◽  
Electrons And Positrons ◽  
Beam Diffraction ◽  
Small Charge

The charge density distribution in the strongest Bloch waves for a dynamical many-beam diffraction situation was calculated for electrons and positrons. Near the [110] zone axis of MgO there exist three strong Bloch waves for electrons. One Bloch wave is concentrated at the rows of Mg-atoms, a second at the rows of O-atoms and a third one between the atoms. The positron Bloch waves are mainly concentrated between the atom rows and have only small charge density at the positions of the atoms. For an incident beam parallel to the [110] axis there exists only one strong positron Bloch wave while for electrons more than three Bloch waves are strong, explaining the channeling behaviour of positrons and electrons. Strong partial waves of different electron Bloch waves can be identified in the diffraction pattern from a MgO crystal wedge.

Interpretation of low-voltage field-emission projection interferograms

1992 ◽  
Vol 50 (2) ◽  
pp. 938-939
Author(s):  
J.C.H. Spence ◽  
W. Qian
Keyword(s):  
Field Emission ◽  
Low Voltage ◽  
Single Scattering ◽  
Bloch Wave ◽  
Crystal Sample ◽  
Transmission Electron ◽  
Transparent Crystal ◽  
Scattering Approximation ◽  
Ewald Sphere ◽  
Lattice Images

Remarkable transmission electron interference patterns have been reported from very thin crystals at energies Eo < 400 volts using a field emission tip, distance z1 ≈ 200 nm from a semi-transparent crystal sample, which acts as the grounded anode. As predicted, “atomic resolution” Fourier images ar observed on a screen distance z2 from the sample, with magnification z2/z1 ≈ 106 at interior sample regions, confused by Fresnel fringes at edges. The same geometry is used to observe lattice images without scanning in coherent CBED patterns with overlapping orders. The interpretation of these patterns must be based on the theory of transmission LEED (TLEED), including multiple scattering. Figure 1 shows the Ewald sphere construction for 250 volt electrons along [110] gold. Image resolutio is limited to the inner reflections by the small sphere (large wavelength). TLEED computations using the Bloch-wave method of Collela are compared with the single scattering approximation in figure 2 Convergence tests show that 58 forward and backscattered beams are sufficient (Backscattered beams hop along the surface under the repulsive influence of the tip field).

Imaging of the helical arrangement of cellulose fibrils in wood by synchrotron X-ray microdiffraction

1999 ◽  
Vol 32 (6) ◽  
pp. 1127-1133 ◽  
Author(s):  
H. Lichtenegger ◽  
M. Müller ◽  
O. Paris ◽  
Ch. Riekel ◽  
P. Fratzl
Keyword(s):  
Incident Beam ◽  
Special Choice ◽  
Local Orientation ◽  
Cell Axis ◽  
Beam Position ◽  
X Ray ◽  
Diffraction Geometry ◽  
Ewald Sphere ◽  
Cellulose Fibrils ◽  
Diffraction Patterns

A complete image of the helical arrangement of cellulose fibrils in the S2 layer of adjacent wood cells ofPicea abies(Norwegian spruce) was obtained by applying position-resolved synchrotron X-ray microdiffraction on cells in cross section. In contrast to conventional fiber diffraction studies, the incident beam was parallel to the longitudinal cell axis, resulting in a glancing angle μ far from 90° with respect to the cellulose fibrils. This special choice of diffraction geometry allowed us to take advantage of an asymmetry effect in the two-dimensional diffraction patterns arising from the curvature of the Ewald sphere to obtain information on the local orientation of the cellulose fibrils. The small size of the beam, smaller than the thickness of a single cell wall, allowed mesh scans over intact transverse sections of adjacent wood cells with a microscopic position resolution. The scan yielded a map of diffraction patterns that could readily serve as a microscopic image. Each of the diffraction patterns was then used to evaluate the local orientation of the cellulose fibrils at the actual beam position. The combination of these results gave an image of cellulose fibrils forming (Z) helices in several adjacent wood cells.

Theoretical considerations in the construction of hard X-ray resonators at inclined incidence with ultra-high efficiency and resolution

2016 ◽  
Vol 49 (5) ◽  
pp. 1653-1658 ◽  
Author(s):  
Y.-H. Wu ◽  
Y.-Y. Chang ◽  
Y.-W. Tsai ◽  
S.-L. Chang
Keyword(s):  
High Efficiency ◽  
Incident Beam ◽  
Normal Incidence ◽  
Dynamical Theory ◽  
X Ray ◽  
Multiple Beam ◽  
Back Reflection ◽  
Diffraction Geometry ◽  
Fabry Perot ◽  
Beam Diffraction

Detailed considerations of how to construct inclined-incidence hard X-ray resonators are presented. Owing to the symmetry of the crystals used, the Bragg back reflection usually employed in normal-incidence two- and multi-plate resonators to reflect the X-ray beam is often accompanied by unavoidable multiple-beam diffraction, and thus the reflectivity and cavity finesse are quite low. In contrast, crystal-based Fabry–Perot (FP) resonators at inclined incidence utilize multiple-beam diffraction to excite the back reflection inside the resonator to generate FP resonance with high efficiency, while avoiding the incident beam suffering from crystal absorption. The useful characteristics of inclined-incidence resonators are derived from numerical calculations based on the inclined-incidence diffraction geometry and the dynamical theory. Experimental results with Laue inclined incidence are in accordance with the simulation. The sub-millielectronvolt energy resolution and ultra-high efficiency of the transmission spectrum of the proposed resonators are also described.

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.

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.

Bloch wave degeneracies in systematic high energy electron diffraction

1976 ◽  
Vol 282 (1308) ◽  
pp. 485-525 ◽  
Keyword(s):  
Band Structure ◽  
Incident Beam ◽  
High Energy ◽  
Real Space ◽  
Bloch Wave ◽  
Critical Voltage ◽  
Bloch Waves ◽  
One Dimensional ◽  
Symmetry Properties ◽  
Reflexion Coefficient

For the systematic diffraction of high energy electrons by a thin crystalline slab, we study the accidental degeneracies of the Bloch waves excited in the specimen by the incident beam. It is shown that these Bloch waves are the eigenstates of a one dimensional band structure problem, and this is solved by wave matching methods. For a symmetric potential, the symmetry properties of the Bloch waves are discussed, and it is shown how accidental degeneracies of these waves can occur when the reflexion coefficient for waves incident on one unit cell of the one dimensional periodic potential vanishes. The form of the band structure and the Bloch waves in the neighbourhood of a degeneracy are derived by expanding the Kramers function in a Taylor series. It is then shown analytically how the degeneracy affects the diffracted waves emerging from the crystalline specimen (in particular, the Kikuchi pattern). To understand these effects fully, W. K. B. approximations for the Bloch waves are used to derive the Bloch wave excitations and the absorption coefficients. However, to predict the degeneracies themselves, it is shown that a different formula for the reflexion coefficient, due to Landauer, must be used. This formula shows how the critical voltage at which the Bloch waves degenerate depends on the form of the potential, and allows quick, accurate, computations of the critical voltages to be made. Also, a new higher order degeneracy is predicted for some of the systematic potentials of cadmium, lead and gold. Finally, to infer the potential in real space from measurements of critical voltages and several other quantities, we suggest an inversion scheme based on the Landauer formula for the reflexion coefficient. To a close approximation this potential is proportional to V 2 of the crystal charge density.

Electron-Channelling Patterns: Principles and Techniques

1976 ◽  
Vol 34 ◽  
pp. 400-401
Author(s):  
David C. Joy
Keyword(s):  
Crystal Structure ◽  
Electron Flux ◽  
Lattice Structure ◽  
Incident Beam ◽  
Bloch Wave ◽  
Crystalline Solid ◽  
Angle Of Incidence ◽  
Electron Channelling ◽  
Regular Arrangement ◽  
Backscattered Signals

In a crystalline solid the regular arrangement of the lattice structure influences the interaction of the incident beam with the specimen, leading to changes in both the transmitted and backscattered signals when the angle of incidence of the beam to the specimen is changed. For the simplest case the electron flux inside the specimen can be visualized as the sum of two, standing wave distributions of electrons (Fig. 1). Bloch wave 1 is concentrated mainly between the atom rows and so only interacts weakly with them. It is therefore transmitted well and backscattered weakly. Bloch wave 2 is concentrated on the line of atom centers and is therefore transmitted poorly and backscattered strongly. The ratio of the excitation of wave 1 to wave 2 varies with the angle between the incident beam and the crystal structure.

Sign in / Sign up

Export Citation Format

Share Document