Electron diffraction, coherence

In Section II, we survey the structural analyses of ylides, summarizing the reported X-ray crystal structures, electron diffraction studies and calculational determinations. In Section III, we present spectroscopic data (primarily UV, NMR, ESCA and EPR) that pertain to characterizing the bonding in the ylides. Finally, we attempt in Section IV to bring together all the summarized evidence to present a cogent and coherent picture of the bonding in the ylides. 

H. Coherence in Electron Diffraction Complex Molecular Structures... 

As a closing example of the powerful application of the concept of coherence in structures and dynamics, we point to its importance in obtaining molecular structural changes with time using ultrafast electron diffraction (UED) (Fig. 12). The UED technique has been developed, so far with -1-ps resolution (Fig. 12). We have reported recently that the introduction of rotational orientation (Section D above) to the diffraction in real time can provide a three-dimensional image of the structure, instead of the conventional two-... 

Ultrafast Electron Diffraction. IV. Molecular Structures and Coherent Dynamics, J. C. Williamson and A. H. Zewail, J. Phys. Chem. 98, 2766 (1994). 

Figure 4. The HREM image and the selected area electron diffraction patterns of a typical example42 of autoepitaxy, where one substoichiometric perovskite CaMn0275 grows in coherent contact with its less fully reduced parent, CaMnO,s.

Fig. 4. Electron diffraction patterns from polished surfaces of a silver single crystal, (a) As polished by indus-trail methods. Surface consists of randomly oriented coherent fragments, (b) As for Fig.4(a), but given a very light etch. Fragments now show mis orientations of only 8° about the base crystal orientations, (c)...

In the case of electron diffraction, we consider the coherent, elastically scattered electrons only, so that the time-independent, static correlation function G(r, o) is obtained in terms of the number density Q(r) of atoms on the surface of a sphere a certain distance r from an atom at the origin ... 

In an electron microscope, the electron beam is produced by an electron gun, in which the electrons are boiled off a heated filament and then accelerated by a highly stabilized electrical potential difference of some hundreds of kilovolts. An electron beam produced in this way is not coherent, but its degree of coherence can be understood in terms of the concepts of optical coherence theory. Later chapters will show that the nature of electron diffraction patterns from crystals that exhibit long-period superstructures (which are not uncommon in many important rockforming minerals) depends critically on the degree of spatial coherence of the incident electron beam. Therefore, it is important to conclude this chapter with a brief review of the basic ideas of optical coherence. A detailed account of the theory is given by Born and Wolf (1965). 

As already indicated, the degree of coherence of the electron beam can have an important influence on the nature of electron diffraction patterns. However, in Chapters 3 and 4, which deal with the theories of electron diffraction, we assume, as we did earlier in this chapter, that the diameter of the coherence area is large compared with the [Pg.36]

In diffraction mode, the projector lens system is adjusted in order to image the electron wave located at the back focal plane of the objective lens. What is seen on the screen is the intensity of this electron wave, which for coherent elastic scattering is called an electron diffraction pattern. 

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