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.

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.

Intensity distribution of electron diffraction pattern from Ti-14Wt%Mo alloy containing ωphase plate crystal

1990 ◽  
Vol 48 (4) ◽  
pp. 986-987
Author(s):  
Mitsuhiro Awaji ◽  
Hatsujiro Hashimoto ◽  
Eiichi Sukedai ◽  
Fumio Akao
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Electron Diffraction ◽  
Electron Diffraction Pattern ◽  
Dynamical Theory ◽  
Β Phase ◽  
Ω Phase ◽  
Microscope Images ◽  
Phase Crystal ◽  
Diffraction Patterns

The study of ω-phase in various alloys such as Ti-Mo, Ti-Cr, Zr-Nb etc. have been carried out so far by electron diffraction and electron microscopy. However, the shape of ω-phase particles has not been fully clarified yet. This is due to the facts that ω-phase is formed in ω-phase crystal, and rather difficult to obtain isolated crystal particles and also that w-phase is produced only by the displacement of atoms in characteristic directions which makes no contrast in the electron microscope images projected along this directions and hence the crosssectional shape can not be studied. Since the intensity of electron diffraction patterns is very sensitive to the amount of ω-phase existing in β-phase, its thickness dependence has been studied in the present paper by using multi-slice dynamical theory of electron diffraction for the various thickness combination of the ω- and β-phases so that the thickness and location of ω-phase can be seen.

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 Elastic Scattering of Bloch Waves in Absorbing Crystals Containing Lattice Defects

1973 ◽  
Vol 28 (5) ◽  
pp. 681-690 ◽  
Author(s):  
M. Wilkens ◽  
K.-H. Katerbau ◽  
M. Rühle
Keyword(s):  
Electron Microscopy ◽  
Bloch Wave ◽  
Lattice Defects ◽  
Anomalous Absorption ◽  
Contrast Effects ◽  
Wave Type ◽  
Bloch Waves ◽  
Crystal Potential ◽  
Transmission Electron ◽  
Complex Crystal

The differential equations of Bloch wave type which are used in transmission electron microscopy for the calculation of the diffraction contrast from lattice defects are discussed with special reference to crystals with anomalous absorption (i. e. with a complex crystal potential). anomalous absorption is included, the eigenvalue equation by which the Bloch waves are defined in the perfect reference lattice, becomes non-Hermitian. It is shown that for some particular contrast effects not only the eigenvalues but also the eigenvectors must be corrected for the imaginary part of the crystal potential. As a consequence the orthogonality of the Bloch waves is violated. The correction of the eigenvectors may result in long-range contrast tails of the images of lattice defects (intraband scattering). If, however, only the peak positions of the contrast profiles are considered, it suffices in practical cases to correct only the eigenvalues as is usually assumed for the diffraction in perfect crystals.

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.

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