An Assessment of the High-Energy Approximation in the Dynamical Theory of Electron Diffraction

1982 ◽  
Vol 109 (2) ◽  
pp. 807-816 ◽  
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Electron Diffraction ◽  
High Energy ◽  
Dynamical Theory ◽  
Energy Approximation

On the applicability of bloch’s theorem to the total wave function in the dynamical theory of electron diffraction

1992 ◽  
Vol 50 (2) ◽  
pp. 1448-1449
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Materials Science ◽  
High Energy ◽  
Dynamical Theory ◽  
Crystal Defects ◽  
Special Cases ◽  
Energy Approximation ◽  
Diffraction Patterns ◽  
Bloch’S Theorem

The dynamical theory of electron diffraction is widely used in materials science problems such as determining the contrast in electron microscope images of crystal defects, calculations of structure images and calculations of diffracted beam intensities in electron diffraction patterns. In carrying out these calculations, the high energy approximation is normally made and it is usually assumed that the crystal is in a symmetrical Laue orientation. In practice, however, a specimen in the electron microscope will generally be oriented so that the non-symmetrical Laue case is obtained. Even in those special cases where the symmetrical Laue case is obtained for the zero order Laue zone reflections, non-symmetrical Laue effects may occur if reflections in higher order zones are important. It has been shown in the literature that the Bloch functions are not orthogonal in more general forms of the dynamical theory in which the high energy approximation is not made and the nonsymmetrical Laue case is considered,.

Calculation of many-beam dynamic electron diffraction without high-energy approximation

1996 ◽  
Vol 54 ◽  
pp. 128-129
Author(s):  
B. R. Ahn ◽  
N. J. Kim
Keyword(s):  
Electron Diffraction ◽  
Flat Surface ◽  
Dynamic Theory ◽  
High Energy ◽  
Perfect Crystal ◽  
Zone Axis ◽  
Beam Dynamic ◽  
Diffraction Angle ◽  
Energy Approximation ◽  
The Many

High energy approximation in dynamic theory of electron diffraction involves some intrinsic problems. First, the loss of theoretical strictness makes it difficult to comprehend the phenomena of electron diffraction. Secondly, it is difficult to believe that the approximation is reasonable especially in the following cases: 1) when accelerating voltage is not sufficiently high, 2) when the specimen is thick, 3) when the angle between the surface normal of the specimen and zone axis is large, and 4) when diffracted beam with large diffraction angle is included in the calculation. However, until now the method to calculate the many beam dynamic electron diffraction without the high energy approximation has not been proposed. For this reason, the authors propose a method to eliminate the high energy approximation in the calculation of many beam dynamic electron diffraction. In this method, a perfect crystal with flat surface was assumed. The method was applied to the calculation of [111] zone axis CBED patterns of Si.

A general matrix representation of the dynamical theory of electron diffraction. I. General theory

1990 ◽  
Vol 431 (1881) ◽  
pp. 111-123 ◽  
Keyword(s):  
Electron Diffraction ◽  
General Theory ◽  
Plane Wave ◽  
Matrix Representation ◽  
High Energy ◽  
Dynamical Theory ◽  
High Energy Electron ◽  
Plane Wave Expansion ◽  
General Matrix ◽  
Original Approach

A general matrix representation of the dynamical theory of high-energy electron diffraction by crystals is developed. The formulation is based on the plane wave expansion of Bloch waves, following the original approach of Bethe, and is applicable to both the Laue and Bragg cases with the influence of surface potential and structure incorporated.

DETERMINATION OF LINEAR-CHAIN MULTIPLE BOUND STATE RESONANCES IN REFLECTION HIGH-ENERGY ELECTRON DIFFRACTION

1994 ◽  
Vol 01 (02n03) ◽  
pp. 261-271 ◽  
Author(s):  
T.C. ZHAO ◽  
S.Y. TONG ◽  
A. IGNATIEV
Keyword(s):  
Electron Diffraction ◽  
Bound States ◽  
Energy Levels ◽  
Linear Chain ◽  
Bound State ◽  
High Energy ◽  
Dynamical Theory ◽  
Energy Electron ◽  
High Energy Electron ◽  
Discrete Energy

Using the R-matrix dynamical theory of Reflection High-Energy Electron Diffraction (RHEED), we analyze the intensity anomalies commonly observed in RHEED rocking curves. Results for Ag(001) and Pt(111) show that the anomalies are associated with the trapping of particular components of the electron wave field inside the crystal by linear chain potential parallel to the surface. These pseudobound states correspond to minima in the total elastic flux of an ultrathin film (≤10 monolayer) and maxima in the inelastic flux. The discrete energy levels of the bound states in Ag(001) and Pt(111) are determined for the first time and the effect of such bound states on the rocking curves is discussed.

INTERPRETATION OF REFLECTION HIGH ENERGY ELECTRON DIFFRACTION FROM DISORDERED SURFACES: DYNAMICAL THEORY AND ITS APPLICATION TO THE EXPERIMENT

1999 ◽  
Vol 06 (03n04) ◽  
pp. 461-495 ◽  
Author(s):  
UWE KORTE
Keyword(s):  
Electron Diffraction ◽  
Multiple Scattering ◽  
Surface Science ◽  
Phonon Scattering ◽  
High Energy ◽  
Dynamical Theory ◽  
Energy Electron ◽  
Advanced Materials ◽  
Quantitative Interpretation ◽  
High Energy Electron

Reflection high energy electron diffraction (RHEED) is one of the few surface science techniques that are applied in a fabrication process, namely to monitor the epitaxial growth of ultrathin films and advanced materials. In spite of this technological relevance the multiple scattering nature of the involved scattering processes has hindered the quantitative interpretation of RHEED in the case of real, i.e. imperfect, surfaces for a long time. This article reviews recent progress in the understanding of RHEED from surfaces exhibiting various types of disorder. It concentrates on a multiple scattering formalism — based on perturbation theory with the nonperiodic part of the structure as perturbation — that allows the computation and interpretation of RHEED from real systems. The validity regime of the approach is discussed. We demonstrate the potential of the method by its application to the quantitative interpretation of experimental data. The range of treated problems comprises occupational disorder, intensity oscillations, structure of disordered metal/adsorbate systems, diffuse scattering from adatoms, Kikuchi scattering and phonon scattering.

Analysis of electron-diffraction intensity profiles using a photodiode-array detection system

1983 ◽  
Vol 41 ◽  
pp. 322-323
Author(s):  
J. B. Warren
Keyword(s):  
Electron Diffraction ◽  
Diffraction Pattern ◽  
Detection System ◽  
High Energy ◽  
Photographic Emulsion ◽  
Diffraction Intensity ◽  
Silicon Photodiode ◽  
Photodiode Array Detection ◽  
Analog To Digital ◽  
Photodiode Array

Electron diffraction intensity profiles have been used extensively in studies of polycrystalline and amorphous thin films. In previous work, diffraction intensity profiles were quantitized either by mechanically scanning the photographic emulsion with a densitometer or by using deflection coils to scan the diffraction pattern over a stationary detector. Such methods tend to be slow, and the intensities must still be converted from analog to digital form for quantitative analysis. The Instrumentation Division at Brookhaven has designed and constructed a electron diffractometer, based on a silicon photodiode array, that overcomes these disadvantages. The instrument is compact (Fig. 1), can be used with any unmodified electron microscope, and acquires the data in a form immediately accessible by microcomputer.Major components include a RETICON 1024 element photodiode array for the de tector, an Analog Devices MAS-1202 analog digital converter and a Digital Equipment LSI 11/2 microcomputer. The photodiode array cannot detect high energy electrons without damage so an f/1.4 lens is used to focus the phosphor screen image of the diffraction pattern on to the photodiode array.

Microdiffraction Patterns of Small Metallic Particles II; Theoretical Analysis

1982 ◽  
Vol 40 ◽  
pp. 668-669
Author(s):  
A. Gómez ◽  
P. Schabes-Retchkiman ◽  
M. José-Yacamán ◽  
T. Ocaña
Keyword(s):  
Experimental Data ◽  
Electron Diffraction ◽  
Theoretical Analysis ◽  
Size Range ◽  
Dynamical Theory ◽  
Metallic Particles ◽  
Splitting Effect

The splitting effect that is observed in microdiffraction pat-terns of small metallic particles in the size range 50-500 Å can be understood using the dynamical theory of electron diffraction for the case of a crystal containing a finite wedge. For the experimental data we refer to part I of this work in these proceedings.

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