Dynamical Theory of Electron Diffraction for the Electron Microscopic Image of a Crystal Containing Two Stacking Faults

1965 ◽  
Vol 20 (6) ◽  
pp. 1035-1047 ◽  
Author(s):  
Hatsujiro Hashimoto ◽  
Kenzaburo Marukawa

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.


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.


Author(s):  
A. Fukuhara

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.


Author(s):  
Vivek Arya ◽  
Vipul Sharma ◽  
Garima Arya

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.


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.


2004 ◽  
Vol 12 (1) ◽  
pp. 3-7
Author(s):  
Stephen W. Carmichael ◽  
Jon Charlesworth

The use of fluorescent probes is becoming more and more common in cell biology. It would be useful if we were able to correlate a fluorescent structure with an electron microscopic image. The ability to definitively identify a fluorescent organelle would be very valuable. Recently, Ying Ren, Michael Kruhlak, and David Bazett-Jones devised a clever technique to correlate a structure visualized in the light microscope, even a fluorescing cell, with transmission electron microscopy (TEM).Two keys to the technique of Ren et al are the use of grids (as used in the TEM) with widely spaced grid bars and the use of Quetol as the embedding resin. The grids allow for cells to be identified between the grid bars, and in turn the bars are used to keep the cell of interest in register throughout the processing for TEM. Quetol resin was used for embedding because of its low auto fluorescence and sectioning properties. The resin also becomes soft and can be cut and easily peeled from glass coverslips when heated to 70°C.


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