Electron diffraction by crystals

Peng, L.-M. (1997) Anisotropic thermal vibrations and dynamical electron diffraction by crystals, Acta Cryst. A, 53, 663-672. 

The detailed interpretation of electron microscope images produced using any of the operating modes discussed in this chapter requires as complete an understanding as possible of the diffraction process. The next two chapters develop and explain as simply as possible the current theories of electron diffraction by crystals in order to provide a basis for the interpretation of images of crystal defects (such as dislocations, stacking faults, and twins) and of lattice images. 

The wave-like properties of electrons were confirmed four years later by Davison and Germer s measurements of electron diffraction by crystals and P.G. Thompson s measurements of diffraction by gold foil. 

Electron diffraction by lamellar, single crystals leads to a two-dimensional, tetragonal unit-cell with a = b = 22.9 A (2.29 nm). From X-ray diffraction data obtained from a film of sedimented, lamellar crystals, it was found that the c axis spacing (7.8 A 780 pm) is equivalent to that in 6-fold and 7-fold amylose helices. The true helical diameters of the 1-butanol, isopropyl alcohol, and 1-naphthol complexes were calculated from experimental data. The ratios of 6 7 8 indicated that the 1-naphthol complex has eight D-glucose residues per turn. The diversity of helical orientations in V-amylose crystals was discussed. 

Structure refinement based on dynamical scattering was developed by Zandbergen and Jansen (Zandbergen et al, 1997 Jansen et al, 1998), known as the MSLS software. Electron diffraction from crystal regions with relatively homogenous thicknesses was used. Both the crystal orientation, crystal thickness and the atomic coordinates could be refined simultaneously. 

The synthesis of Fe N(SiMe3)2 2 completed the divalent M(ll) series M = Mn—Ni. It was shown to have a two-coordinate monomeric structure in the vapor phase by gas electron diffraction. Its crystal structure showed that it was a symmetrically bridged dimer like its manganese and cobalt counterparts. Variable temperature H NMR spectroscopy indicated an association energy of only 3 kcal mol. The divalent series was also expanded to Cr(II) with use of the — NPr and —NCy2 (Cy = cyclohexyl) groups to afford the bridged... 

The electrons, however, besides properties which suggest a conception of them as charged particles, have as much the character of a wave phenomenon. Their diffraction by crystal lattices is entirely analogous to that of X-rays (p. 106). 

This relation found a direct experimental confirmation in the experiments of Davisson and Germer and of Thomson already mentioned on the diffraction of electron beams by crystal lattices. In fact for electrons which have traversed a potential difference P, the energy eP = 1/2 mv2 the kinetic energy, or (mv)2 = 2 meP thus ... 

Several types of diffraction by crystals are now studied. Neutron diffraction can be used with great effectiveness to give information on molecular structure. These results complement those from X-ray diffraction studies, because there are different mechanisms for the scattering of X rays and of neutrons by the various atoms. X rays are scattered by electrons, while neutrons are scattered by atomic nuclei. Neutron diffraction is important for the determination of the locations of hydrogen atoms which, because of their low electron count, are poor X-ray scatterers. Electron diffraction, while requiring much smaller crystals and therefore being potentially useful for the study of macromolecules, produces diffraction patterns that are more complicated. Their interpretation is hampered by the fact that the diffracted electron beams are rediffracted within the crystal much more than are X-ray beams. This has limited the practical use of electron diffraction in the determination of atomic arrangements in crystals to studies of surface structure. 

Once it had been shown that crystals diffract X rays, the relationship between the observed effect and the experimental conditions was put on a sound mathematical basis by Max von Laue, Paul P. Ewald and many others.X-ray diffraction by crystals represents the interference between X rays scattered by the electrons in the various atoms at various locations within the unit cell. It must, however, be stressed again that any molecule or ion can diffract X rays or neutrons. It is only when this diffraction is reinforced by the repetition of the unit cell in the crystal that diffraction by atoms is a conveniently observable effect, for example as spots of differing intensity on photographic film. Of particular interest to chemists and biochemists is the work by W. L. Bragg,who demonstrated that measurement of the diffraction patterns gives information on the distribution of electron density in the unit cell, (i.e., the arrangement of atoms within this unit cell). 

Methods for the experimental measurement of the intensities of the diffracted beams will be described in Chapter 7, and methods for deriving relative phases of these beams for recombination will be discussed in Chapter 8. The result of these mathematical calculations, which simulate the action of a lens, will be all the information that is needed for the calculation of a three-dimensional electron-density map. This is a map in which peaks are situated at or near atomic positions. In this way, measurements of the diffraction pattern lead to an image of the molecules or ions and their arrangement in the crystal under study. Details of the calculation of the electron density maps that reveal the atomic arrangement will be described in Chapter 9. For more information on each aspect of diffraction by crystals, the reader is referred to the many texts on the subject listed in the Preface to this book. 

An example is provided by a comparison of the diffraction patterns of the isostructural chlorides of sodium and potassium (see Figure 6.20). It is noted that alternate rows of diffraction spots are very faint in the potassium chloride diffraction pattern, unlike the situation for sodium chloride. This alternating pattern of intensity is due to the fact that potassium and chloride ions are isoelectronic (with 18 electrons), and therefore have approximately identical powers to scatter X rays. On the other hand, the difference in scattering power between a sodium ion (10 electrons) and a chloride ion (18 electrons) is appreciable. Therefore those diffraction spots in which scattering from the metal ion interferes with scattering from the chloride ion will have a measurable intensity for diffraction by crystals of sodium chloride but almost no intensity for diffraction by crystals of potassium chloride. 

The descriptions above were made using optical techniques, especially optical microscopy. However, the absolute arrangement of the atoms in a crystal cannot be determined in this way. This limitation was overcome in the early years of the 20th century, when it was discovered that X-rays were scattered, or diffracted, by crystals in a way that could be interpreted to yield the absolute arrangement of the atoms in a crystal, the crystal structure. X-ray diffraction remains the most widespread technique used for structure determination, but diffraction of electrons and neutrons is also of great importance, as these reveal features that are complementary to those observed with X-rays. 

B. G. Hyde, D. J. M. Bevan, and L. Eyring, International Conference on Electron Diffraction and Crystal Defects, Melbourne, II, C-4 (1965), published and distributed for the Australian Academy of Science by Pergamon Press (1966). 

Davisson/Germer electron diffraction by metal crystal... 

The structures of dimethyl disulfide and bis(trifluoromethyl) disulfide have been determined by electron diffraction, by Stevenson and Beach (211) and by Bowen (35), respectively. Crystal structure determinations of the following disulfides have been carried out di-p-bromophenyl disulfide by Toussaint (216) A M -diglycyl-L-cystine dihydrate by Yakel and Hughes (232) hexagonal L-cystine by Oughton and Harrison (183) L-cystine hydrochloride by Steinrauf et al. (210) and formamidinium disulfide diiodide and dibromidc monohydrates (104). 

Polythiophene, as obtained from Grignard-coupling polymerization from dibromothiophene, was vacuum deposited on various substrates and studied by electron diffraction by Yamamoto el al. [51]. They report diffraction patterns obtained from a single crystalline region, showing 44 distinct reflections of hkO-type. The indexing is in accordance with the a and 6-axes values obtained by Mo el al. Curiously the crystal is oriented with its c-axis perpendicular to the substrate, and the c-axis parameter could not be determined. The crystal is reported to deteriorate under the electron beam. 

Diffraction is a characteristic wave property. It is useful to recall that the mass of the electron was determined accurately by Millikan in 1909. A precise mass is very much a particle-type property. Geiger counters monitor P-particles (electrons) one by one ( click-click-click ) another particle property. The de Broglie equation suggests that wavelengths (X) are associated with electrons and that these should be on the order of 10"" m. In principle, electrons should be diffracted by crystals, a prediction confirmed in 1927 by Clinton Joseph Davisson (1881-1958) and Lester Halbert Germer (1896-1971), at Bell Telephone Laboratories. De Broglie was awarded the 1929 Nobel Prize in physics and Davisson won a share of the 1937 Nobel Prize in physics. 

Published data on the properties and reactions of phosphinine is still somewhat limited. A few years earlier the first phosphinine derivative, 2,4,6 triphenylphosphinine was synthesised by Markl from pyrilium fluoroborate (6.861). Electron diffraction and crystal structure analyses have confirmed the presence of planar rings with equivalent P-C bond lengths in both these compounds (6.862). The intense UV spectra, ring-vibration frequencies and low-field NMR shifts of the ring protons are all consistent with 3pji-2pjr aromatic delocalisation in this class of compound. Addition readily occurs (6.863). 

In 1927, Davisson and Germer demonstrated that electrons are diffracted by crystals in a manner similar to the diffraction of X rays. These electron-diffraction experiments substantiated de Broglie s suggestion that an electron has wave properties such as wavelength, frequency, phase, and interference. In seemingly direct contradiction, however, certain other experiments, particularly those of J. J. Thomson, showed that an electron is a particle with mass, energy, and momentum. 

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