Dynamical theory of electron diffraction for the electron microscopic image of crystal lattices II. Image of superposed crystals (moiré pattern)

1961 ◽  
Vol 253 (1033) ◽  
pp. 490-516 ◽  
Keyword(s):  
Electron Diffraction ◽  
Present Theory ◽  
Dynamical Theory ◽  
Bragg Angle ◽  
Electron Microscopic ◽  
Microscopic Images ◽  
Electron Microscopic Image ◽  
Moire Patterns ◽  
Lattice Images ◽  
Moiré Patterns

The dynamical theory of electron diffraction is applied to the interpretation of electron microscopic images of moire patterns. Two cases often observed are treated. One is the case where two plate-shaped crystals are superposed closely without a vacuum layer between them and another is the case where two crystals are superposed with a vacuum layer between them. Resolved lattice images of two superposed crystals are also interpreted. The intensity profiles of the images vary with the thicknesses of the crystals and vacuum layer and with the deviation from the Bragg angle. The shifts of the fringes and anomalies of the contrast which are expected from the present theory were observed in the electron microscopic images of moire patterns of cupric sulphide, palladiumgold and platinum-phthalocyanine. The relation between moiré patterns and crystal structure is also discussed.

Dynamical theory of electron diffraction for the electron microscopic image of crystal lattices I. Images of single crystals

1961 ◽  
Vol 253 (1033) ◽  
pp. 459-489 ◽  
Keyword(s):  
Electron Diffraction ◽  
Wave Length ◽  
Present Theory ◽  
Dynamical Theory ◽  
Bragg Angle ◽  
Electron Microscopic ◽  
Microscopic Images ◽  
Exit Surface ◽  
Extinction Contour ◽  
Electron Microscopic Image

The dynamical theory of electron diffraction is applied to the interpretation of electron micro­ scopic images of lattice planes of plate- and wedge-shaped crystals. The wave functions and corresponding intensities predicting interference fringes on the exit surface of a crystal are derived. It is shown in both cases that the fringes are composed of parallel lines and the spacing of the fringes at the exact Bragg angle coincides with that of the original lattice but the positions of the lines do not coincide with those of potential maxima in the crystal, i.e. intensity profiles of the fringes do not represent the variation of mass-thickness in the crystal. The intensity profiles and the spacings of the fringes vary with the thickness of crystal and the deviation from the Bragg angle. The fringes from a bent plate-shaped crystal, which are formed on the extinction contour bands, show the same spacing as that of the crystal lattice along the centre of the contour but they have an increased or decreased spacing near the edge of the contour. The fringes which are formed on the subsidiary extinction contour also show spacing anomaly; they are shifted by half the corresponding amount for the principal contour. The spacing of the fringes of a wedge-shaped crystal coincides with that of the original lattice at the exact Bragg angle, but the contrast of the lines reverses wherever the thickness of the crystal increases by an amount of XE/2V g (A, wave length; E , accelerating potential; V g , Fourier coefficient of inner potential of the crystal). For deviation from the Bragg angle, the spacing of the fringes, in general, does not coincide with that of the original lattice and, moreover, the contrast of the lines reverses wherever the thickness of the crystal increases by an amount of The anomalies of spacing and reversal of contrast which are expected from the present theory were observed in the electron microscopic images of metal-phthalocyanine and sodium faujasite crystals respectively. The effects of absorption by the crystal and divergence of illumination on the contrast of the image are discussed and the possibility of obtaining two-dimensional projections of the atomic arrangement in a crystal by using electron microscopic images is also discussed.

Systematic-Reflection Effects in Electron Diffraction

1968 ◽  
Vol 26 ◽  
pp. 400-401
Author(s):  
A. Fukuhara
Keyword(s):  
Electron Diffraction ◽  
Present Report ◽  
Decisive Role ◽  
Dynamical Theory ◽  
Bright Field Image ◽  
Line Printer ◽  
Electron Microscopic ◽  
Bright Field ◽  
First Order ◽  
Electron Microscopic Image

Many workers have recently noticed what is called many-beam effects In the electron diffraction by crystals. In particular it was found and studied by several people that some second-order reflections vanish even at the exact Bragg position when the acceleration energy coincides with a particular characteristic value EC. This phenomenon has been confirmed to be due to the effect of the first order reflection which is not exactly excited at this position. Systematic reflections sometimes have a decisive role as in this example depending upon the crystal and the reflection. Furthermore it must be noted that the effect is intensified with the rise of the acceleration energy owing to the relativistic change in the electron diffraction.In this study the effects of systematic reflections on extinction contours obserable in an electron-microscopic image of a crystal have been investigated on the basis of dynamical theory taking more than two beams into account. Suppose a wedge-shaped crystal which bends uniformly. As is well known extinction fringes are observed in a bright-field image of such a crystal. This intensity distribution due to diffraction contrast has been computed and printed as in half-tone process by a line-printer of an electronic computor Hitac 5020. Four groups of systematic reflections are studied in the present report: Al(nnn) at 100kv, Al(nnn) at 1000kv, Si(nnn) at 100kv and hexagonal CdS(noo) at 150kv.

The Use of Moiré Patterns in TEM Images to Measure Precipitate Composition in Al-Si-Ge Alloys

2001 ◽  
Vol 7 (S2) ◽  
pp. 238-239
Author(s):  
V. Radmilovic ◽  
D. Mitlin ◽  
S. Hinderberger ◽  
U. Dahmen
Keyword(s):  
Elastic Interaction ◽  
Lattice Parameter ◽  
Multiphase System ◽  
Orientation Relationships ◽  
Precipitate Crystal ◽  
Large Matrix ◽  
Moiré Fringes ◽  
Moire Patterns ◽  
Lattice Images ◽  
Moiré Patterns

Moiré patterns are commonly formed in multiphase system when diffracting planes of similar spacing and orientation lead to interference effects. They can be used experimentally to evaluate the stress distribution in materials [1], to analyze orientation relationships and latttice strain in diffraction contrast microscopy, or, combined with the related geometrical phase technique, to analyze displacements in high resolution lattice images [2,3]. The interpretation of moiré fringes is often not straightforward due to the elastic interaction between the crystals at the interface and the dynamical nature of electron diffraction [4]. However, if the two lattices are fully relaxed, or if a small precipitate crystal is embedded in a large matrix, moiré patterns can give a simple and direct measure of orientation and lattice constants. in the present work, the moiré technique has been applied to the quantitative analysis of lath-shaped Ge or Ge-Si precipitates in Al with the aim to determine the composition (the Si:Ge ratio) from the lattice parameter indicated by the moiré fringes.

An Efficient Adaptive Algorithm for Electron Microscopic Image Enhancement and Feature Extraction

2019 ◽  
Vol 9 (1) ◽  
pp. 1-16
Author(s):  
Vivek Arya ◽  
Vipul Sharma ◽  
Garima Arya
Keyword(s):  
Feature Extraction ◽  
Contrast Enhancement ◽  
Block Size ◽  
Sigmoid Function ◽  
Microscopic Image ◽  
Electron Microscopic ◽  
Microscopic Images ◽  
Electron Microscopic Image ◽  
Block Based

In this article, a block-based adaptive contrast enhancement algorithm has been proposed, which uses a modified sigmoid function for the enhancement and features extraction of electron microscopic images. The algorithm is based on a modified sigmoid function that adapts according to the input microscopic image statistics. For feature extraction, the contrast of the image is very important and authentic property by which this article enhances the visual quality of the image. In this work, for better contrast enhancement of image, a block based on input value, combined with a modified sigmoid function that is used as contrast enhancer provides better EMF values for a smaller block size. It provides localized contrast enhancement effects adaptively which is not possible using other existing techniques. Simulation and experimental results demonstrate that the proposed technique gives better results compared to other existing techniques when applied to electron microscopic images. After the enhancement of microscopic images of actinomycetes, various important features are shown, like coil or spiral, long filament, spore and rod shape structures. The proposed algorithm works efficiently for different dark and bright microscopic images.

An electron microscope study of synthetic graphite

1959 ◽  
Vol 253 (1274) ◽  
pp. 390-402 ◽  
Keyword(s):  
Electron Diffraction ◽  
Electron Micrographs ◽  
Stacking Faults ◽  
Grain Structure ◽  
Thin Sections ◽  
Average Value ◽  
Moire Patterns ◽  
Synthetic Graphite ◽  
Diffraction Patterns ◽  
Moiré Patterns

The ultra-microtome has been used to obtain thin sections of synthetic graphite blocks. The thickness of the sections was measured by shadowcasting and measuring the shadow length at appropriate edges. An average value of 150 Å was obtained. Transmission electron micrographs of thin sections showed moire patterns and the interrelation of these moire patterns revealed a characteristic grain structure in graphite akin to that seen in metals but with component microcrystals of smaller dimensions. The area of the individual micro - crystals forming the grain structure was measured and was found to be 0·11 + 0·074μ 2 . The boundary between neighbouring microcrystals was narrow and of around 50 A in width. Pores were visible at the junction of three or more contiguous microcrystals and were of diameter 400 to 800 Å. The selected-area electron diffraction technique was used to determine the orientation of individual microcrystals in the graphite sections. It was found that the hexagonal layer net planes were lying parallel or at a very small angle to the plane of the section. The electron diffraction patterns were also used to correlate the layer stacking faults in individual microcrystals both by counts of individual reflexions on the (1120) diffraction ring and by counts of the extra reflexions due to the long spacings between successive displaced layers. The average value of 13 Å found for the distance between successive stacking faults is equivalent to the distance between four hexagonal layer net planes. The moire patterns in the electron micrographs could be related to the long spacings in the electron diffraction patterns. It was possible to calculate the angle of twist between successive stacking faults from the long spacing or from the moire pattern. Dislocations were seen in many of the thin sections and were observed as extra terminating half-lines in the moire patterns; these dislocations were present in the hexagonal layer net planes themselves and indicated that there was in this region a considerable deformation of the benzenoid structure of the hexagonal layer nets. The measured frequency for their occurrence was 3·3 x 10 7 /cm 2 . Slip planes were also detected in some specimens.

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