Kinematical Theory of Electron Diffraction

Author(s):  
Jian Min Zuo ◽  
John C. H. Spence
Author(s):  
D. L. Dorset ◽  
H. A. Hauptman

The significant impediment to the use of electron diffraction data for crystal structure analysis is, of course, the perturbation of n-beam dynamical effects. In more severe cases this dynamical perturbation gives an intensity distribution in the diffraction pattern which is not directly related to the underlying crystal structure, thus making the determination of complex structures nearly impossible by this technique.However, as was experimentally established in Vainshtein's laboratory and is theoretically predicted, the diffraction of electrons from thin mosaic crystals composed of light atoms is in accord with kinematical theory to a good first approximation and, furthermore, ab initiocrystal structure analyses are tractable viastandard crystallographic phase determination. To date the few electronographic determinations of unknown organic structures have used either trial and error or Patterson techniques.


The dynamical theory of electron diffraction is developed in a form suitable for the computation of images of crystal lattice defects such as dislocations observed by transmission electron microscopy. As shown in a previous kinematical theory, the contrast arises because the waves diffracted by atoms near the defect are changed in phase as a result of the displacements of these atoms from the perfect crystal positions. The two-beam dynamical theory of diffraction in the symmetrical Laue case is derived from simple kinematical principles by methods similar to those used by Darwin in the Bragg case. Simultaneous differential equations describing the changes of incident and diffracted wave amplitudes with depth in a crystal are obtained. In a perfect crystal these equations lead to the well-known Laue solutions of the dynamical equations of electron diffraction and in a deformed crystal they reduce to the kinematical theory when the deviation from the reflecting position is large. The effects of absorption can be included phenomenologically by use of a complex atomic scattering factor (complex lattice potential). Finally it is shown that an equivalent theory may be derived directly from wave mechanics in a way which allows the effects of absorption and several diffracted beams to be included. From the formal solution of this general theory some important symmetry relations for electron microscope images of defects can be deduced.


Author(s):  
S.W. Hui ◽  
D.F. Parsons

The development of the hydration stages for electron microscopes has opened up the application of electron diffraction in the study of biological membranes. Membrane specimen can now be observed without the artifacts introduced during drying, fixation and staining. The advantages of the electron diffraction technique, such as the abilities to observe small areas and thin specimens, to image and to screen impurities, to vary the camera length, and to reduce data collection time are fully utilized. Here we report our pioneering work in this area.


Author(s):  
J. B. Warren

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.


Author(s):  
P. Ling ◽  
R. Gronsky ◽  
J. Washburn

The defect microstructures of Si arising from ion implantation and subsequent regrowth for a (111) substrate have been found to be dominated by microtwins. Figure 1(a) is a typical diffraction pattern of annealed ion-implanted (111) Si showing two groups of extra diffraction spots; one at positions (m, n integers), the other at adjacent positions between <000> and <220>. The object of the present paper is to show that these extra reflections are a direct consequence of the microtwins in the material.


Author(s):  
R. E. Ferrell ◽  
G. G. Paulson ◽  
C. W. Walker

Selected area electron diffraction (SAD) has been used successfully to determine crystal structures, identify traces of minerals in rocks, and characterize the phases formed during thermal treatment of micron-sized particles. There is an increased interest in the method because it has the potential capability of identifying micron-sized pollutants in air and water samples. This paper is a short review of the theory behind SAD and a discussion of the sample preparation employed for the analysis of multiple component environmental samples.


Author(s):  
G. Lehmpfuhl

Introduction In electron microscopic investigations of crystalline specimens the direct observation of the electron diffraction pattern gives additional information about the specimen. The quality of this information depends on the quality of the crystals or the crystal area contributing to the diffraction pattern. By selected area diffraction in a conventional electron microscope, specimen areas as small as 1 µ in diameter can be investigated. It is well known that crystal areas of that size which must be thin enough (in the order of 1000 Å) for electron microscopic investigations are normally somewhat distorted by bending, or they are not homogeneous. Furthermore, the crystal surface is not well defined over such a large area. These are facts which cause reduction of information in the diffraction pattern. The intensity of a diffraction spot, for example, depends on the crystal thickness. If the thickness is not uniform over the investigated area, one observes an averaged intensity, so that the intensity distribution in the diffraction pattern cannot be used for an analysis unless additional information is available.


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