Electron, diffraction

Electrons are charged particles and interact very strongly with matter. This has two consequences for 

Electrons, however, do have one advantage. Because they are charged they can be focused by magnetic lenses to form an image. The mechanism of diffraction as an electron beam passes through a thin flake of solid allows defects such as dislocations to be imaged with a resolution close to atomic dimensions. Similarly, diffraction (reflection) of electrons from surfaces of thick solids allows surface details to be recorded, also with a resolution close to atomic scales. Thus although electron diffraction is not widely used in structure determination it is used as an important tool in the exploration of the microstructures and nanostructures of solids. 

Electron diffraction is generally done with commercial electron microscopes using three techniques (i) transmission with a diffraction camera accessory, (ii) selected-area diffraction, and (hi) reflection diffraction. I n determining unit cell dimensions, the precision decreases in the order given above. Claims have been made of lattice parameter determinations accurate to 0.1 % by electron diffraction, but this is unrealistic, and a figure of about 1 % is more typical. 

With good samples, the transmission camera is capable of 0.3 % using an internal standard. Selected-area diffraction gives about 0.5 %, and reflection diffraction about 1 %. Electron diffraction patterns are sensitive to surface defects, particle size, sample position and orientation, and refraction effects, so that most materials are unsuited to precision measurements. Normally, electron diffraction is a poor second to X-ray diffraction as far as accuracy is concerned. 

Electron diffraction should be used for routine identification only when the results cannot be obtained with X rays. Electron microscopy 

For polycrystalline materials, electron methods can be used to supplement and clarify X-ray results. For example, with X-ray powder patterns, it is often difficult or even impossible to index lines in a diffraction pattern if mixtures are present, whereas, using electron diffraction, the problem can be solved by obtaining unit cell data for each phase from selected-area diffraction patterns. Likewise, with complex powders of new materials, the indexing of X-ray patterns is especially difficult if the unit cell is large and of low symmetry. Electron diffraction patterns from small crystals reveal the reciprocal lattice, giving information on the principal axes and crystallographic symmetry. Many new materials are prepared as small samples of tiny crystals suitable only for electrons microscopy, so that electron diffraction is often the best way to obtain crystallographic data on the material. 

It is generally faster and more accurate to do structure analysis by single-crystal X-ray methods than by electron diffraction. While 

Results of electton diffraction data for BCI3 give bonded B-Cl distances of 174 pm (all bonds of equal length) and non-bonded Q...C1 distances of 301 pm (three equal distances). Show that these data are consistent with BCI3 being trigonal planar rather than trigonal pyramidal. 

In selected area electron diffraction (SAED) in the TEM, an aperture (the intermediate or selected area aperture) is used to select a region of the specimen for diffraction (for an example, see Fig. 5.146). A near-parallel beam of electrons illuminates the specimen. Generally, the region contributing to the pattern is several micrometers in diameter. This is a large area compared to that in STEM microdiffraction but very much smaller than that needed for normal x-ray diffraction. 

Convergent beam microdiffraction uses a convergent rather than a near-parallel beam, and this makes it possible to limit the beam to extremely small regions. The diffracting area is limited spatially by the beam diameter, but few polymers can withstand the focused beam. 

The technique of Low Energy Electron Diffraction (leed) is well suited to the observation of surface monolayers and the structure of clean surfaces. Farnsworth et 31,60.69,70 gre3.t deal of work in this field, obtaining measure- 

More recently Germer and co-workers have developed a different type of apparatus which allows the entire diffraction pattern to be displayed on a fluorescent screen. Both variations of the leed technique are rather difficult to apply to the measurement of adsorption kinetics, which in effect requires a measurement of the change in the intensity of the diffracted beam(s) with time. This intensity change is not necessarily proportional to the rate of adsorption however, detailed data on the adsorption of oxygen and carbon monoxide on nickeF have been obtained by a combination of leed and work function measurements. 

The study of X-ray diffraction in thin films is essentially a onedimensional problem and so we have been able to avoid any awkward geometry in that case. This is not true for the case of electron diffraction and it is thus worthwhile introducing the reciprocal lattice explicitly. We return once more to Equation (2.3) 

If it is possible to choose Q so that all the exponents are zero or 2ir/ti, where n is an integer, then the terms on the right hand side will sum so as to reinforce and represent a diffraction maximum. We thus seek values of Q which will bring this about. 

Let the primitive translations in the real lattice be the vectors a, b, c, then these quantities multiplied by the integers u, v, w, respectively define the lattice points. Thus 

In a similar manner let the primitive translations in the reciprocal lattice be the vectors a, b c corresponding to the integers h, k, /. (The asterisk here denotes the reciprocal lattice, not a complex conjugate.) The reciprocal lattice vectors are defined implicitly by the equations 

if Q corresponds to the vector joining the origin to any other point in the reciprocal lattice multiplied by 2-w, then a diffraction 

Photoelectron spectral data have been collected for MeSCl, MeSBr, MeSCN, and MeSeCN. The trigonal-bipyramidal structure has been established for methylenesulphur tetrafluoride through p.e. spectroscopy, electron diffraction, and Z-ray analysis.  

Electron Diffraction.—Among completed electron-diffraction studies are ethyl methyl sulphide, chloromethyl methyl sulphide, methyl phenyl sulphide, di-(2-pyridyl) sulphide, sulphones, sulphoxides and sulphones, and trifluoro-methanesulphonyl chloride. A number of precise analyses of gas-phase conformational equilibria have emerged. Methyl ethyl sulphide shows a preference for the gauche conformation rather than for the trans form.  

Proper interpretation of the intensities of spots in a diffraction pattern gives the positions of the atoms in the crystal. Intensities are difficult to measure because of background from inelastic scattering of electrons. Electrons interact so strongly with matter that an electron can be scattered into one diffracted beam and then from that to another, even in a very thin crystal. This multiple scattering makes full theoretical treatment of electron diffraction complex [25]. It is not usual to determine atomic positions in a polymer crystal from an electron diffraction pattern, but it has been done by several groups [26-29]. 

Polymer crystals are frequently small and imperfect, so that the diffraction spots are fuzzy, or they are arcs from an oriented polycrystalline texture. The degree of perfection of crystals of known structure can be determined from measurement of diffraction linewidths and intensities. The analysis used for x-ray diffraction [30-32] can be transferred directly to electron diffraction. One can distinguish between crystal size effects and the effects of disorder within the crystals, but in many cases a simple estimate of the mean crystal size, 0.9A/(angular breadth), is 

There are numerous physical methods that can be used to determine partial molecular structures. But here we will limit our discussion to the four methods that are in wide current use and that may be utilized to accurately determine a total molecular structure. These are three diffraction methods, namely electron diffraction, neutfon diffraction, and X-ray diffraction, and one spectfoscopic method, microwave spectfoscopy. (There are, of course, many other methods for studying molecular stfucture, some of which are extremely powerful, although usually in limited areas. But, not all of chemistfy can be discussed here, so we will limit the topics to those mentioned.) Each of these methods measures something that is a little different, sometimes quite a bit different, from what the other methods measure. The calculational methods, described in the next chapter, generally calculate something that is still different from any of the above. The structures of the same molecule determined by these different methods are not, in general, identical. Hence, we need to understand how the structures obtained from each of these methods are interrelated. 

The procedure for determining a structure by electron diffraction consists of allowing the molecules that are to be studied in the gas phase to flow into an evacuated chamber 

Molecular Structure Understanding Steric and Electronic Effects from Molecular Mechanics, 

If the atoms in a molecule were rigidly held at certain distances, then the radial distribution function would consist of a series of lines, corresponding to those distances, with intensities that would depend on the atomic numbers of the pair of atoms and the distance between them. But, of course, the atoms vibrate. Thus, instead of a line, one obtains a Gaussian function where the area under the curve depends upon the variables mentioned. 

This experimental technique of electron diffraction is quite difficult to apply in practice, and the equipment for making the measurements is not commercially available. Accordingly, there are only a few gronps worldwide that do this kind of work. The molecules studied have to be rather small or alternatively highly symmetrical, because otherwise the radial distribution function shows so many overlapping bands that it cannot be unambiguously interpreted with much accuracy. However, for small molecules, the method can be quite accurate, and bond lengths to an accuracy of the order of 0.002 A can be obtained under favorable circumstances. 

Finally, low-angle neutron scattering can provide information about the shape of these molecules within the ribosome, which may not be the same as their shape when free in solution. 

For an example of neutron diffraction applied to a crystallographic problem, see D. Pignol, J. Hermoso, B. Kerfelec, I. Crenon, C. Chapus, and J. C. Fontecilla-Camps, The lipase/colipase complex is activated by a micelle Neutron crystallographic evidence, Chem. Phys. Lipids 93, 123-129, 1998. 

The electrons produced by transmission electron microscopes, whose design is analogous to light microscopes, have de Broglie wavelengths of less 

Among the main difficulties with electron crystallography are (1) sample damage from the electron beam (a 0.1-A wave carries a lot of energy), (2) low contrast between the solvent and the object under study, and (3) weak diffraction from the necessarily very thin arrays that can be studied by this method. Despite these obstacles, cryoscopic methods (Chapter 3, Section V) and image processing techniques have made electron crystallography a powerful probe of macromolecular structure, especially for membrane proteins, many of which resist crystallization. 

Transmission electron microscopy is analogous to light microscopy, with visible light replaced by a beam of electrons produced by a heated metal filament, and glass lenses replaced by electromagnetic coils to focus the beam. An image of the sample is projected onto a fluorescent screen or, for a permanent record, onto film or a CCD detector (Chapter 4, Section ni.C). Alternatively, an image of the sample s diffraction pattern can be projected onto the detectors. 

To calculate the principal moments of inertia and the rotational characteristic temperature of PF3. 

The radial distribution cur e from the electron diffraction by gaseous PFg has two pronounced maxima corresponding to the interatomic distances P—F = 1.47 A and F—F = 2.41 A (Pauling and Brockway, J. Amer. Chem. Soc. 1935, 57, 2684). 

In the diagrams A, B, C represent the three F atoms and N is their centre of mass. The P atom is marked P and the centre of mass of the molecule is G. 

By geometry we calculate the lengths AN, PN and GN. We then calculate the moments of inertia about the axis PN and about an axis through G parallel to AN. 

The rotational characteristic temperature r is related to the principal moments of inertia 7i, Jj, I3 by 

It is the off-axis reflections (those on neither line) that prove that there is crystalline order in a fiber (Fig 3.5D). 

A large and perfect crystal scatters electrons into a diffraction pattern of sharp spots. General interpretation of this pattern requires a knowledge of crystallography. There are many texts in this field [18-20], with some specifically aimed at microscopists [21, 22]. Books on crystal optics (Section 2.3) contain basic summaries [23, 24]. There are also many texts on diffraction from materials 125-27], some concentrating on electron diffraction [28, 29]. The most common use of a crystal diffraction pattern is to find the orientation of a crystal of known structure. Wunderhch [30] contains a listing of many polymer crystal structures. 

In simple terms we can regard the crystal as a set of lattice planes, reflecting radiation according to Bragg s law. The diffraction angle is then 26 where 2d sin 6 = 1. For electrons A C d so 0 is very small. This means that lattice planes will diffract only if they are almost parallel to the 

Objective lens a (rad) resolution (fim) System magnification Depth of field (pm) Depth of focus 

---

Electron diffraction studies are usually limited to transferred films (see Chapter XV), One study on Langmuir films of fatty acids has used cryoelectron microscopy to fix the structures on vitrified water [179], Electron diffraction from these layers showed highly twinned structures in the form of faceted crystals. 

Transmission electron microscopy (TEM) can resolve features down to about 1 nm and allows the use of electron diffraction to characterize the structure. Since electrons must pass through the sample however, the technique is limited to thin films. One cryoelectron microscopic study of fatty-acid Langmuir films on vitrified water [13] showed faceted crystals. The application of TEM to Langmuir-Blodgett films is discussed in Chapter XV. 

HEED High-energy electron diffraction [104] Diffraction of elastically back-scattered electrons (-20 keV, grazing incidence) Surface structure... 

LEED Low-energy electron diffraction [62, 75, 105] Elastic backscattering of electrons (10-200 eV) Surface structure... 

RHEED Reflection high-energy electron diffraction [78, 106] Similar to HEED Surface structure, composition... 

SHEED Scanning high-energy electron diffraction [106] Scanning version of HEED Surface heterogeneity... 

Bartell and co-workers have made significant progress by combining electron diffraction studies from beams of molecular clusters with molecular dynamics simulations [14, 51, 52]. Due to their small volumes, deep supercoolings can be attained in cluster beams however, the temperature is not easily controlled. The rapid nucleation that ensues can produce new phases not observed in the bulk [14]. Despite the concern about the appropriateness of the classic model for small clusters, its application appears to be valid in several cases [51]. 

The technique of low-energy electron diffraction, LEED (Section VIII-2D), has provided a considerable amount of information about the manner in which a chemisorbed layer rearranges itself. Somotjai [13] has summarized LEED results for a number of systems. Some examples are collected in Fig. XVlII-1. Figure XVIII-la shows how N atoms are arranged on a Fe(KX)) surface [14] (relevant to ammonia synthesis) even H atoms may be located, as in Fig. XVIII-Ih [15]. Figure XVIII-Ic illustrates how the structure of the adsorbed layer, or adlayer, can vary wiA exposure [16].f There may be a series of structures, as with NO on Ru(lOTO) [17] and HCl on Cu(llO) [18]. Surface structures of... 

Takayanagi K, Tanishiro Y, Takahashi M and Takahashi S 1985 Structural analysis of Si(111)-7 7 by UFIV-transmission electron diffraction and microscopy J. Vac. Sot Technol. A 3 1502... 

Another mode of electron diffraction, low energy electron diffraction or FEED [13], uses incident beams of electrons with energies below about 100 eV, with corresponding wavelengths of the order of 1 A. Because of the very strong interactions between the incident electrons and tlie atoms in tlie crystal, there is very little penetration of the electron waves into the crystal, so that the diffraction pattern is detemiined entirely by the... 

The otiier type of noncrystalline solid was discovered in the 1980s in certain rapidly cooled alloy systems. D Shechtman and coworkers [15] observed electron diffraction patterns with sharp spots with fivefold rotational synnnetry, a syimnetry that had been, until that time, assumed to be impossible. It is easy to show that it is impossible to fill two- or tliree-dimensional space with identical objects that have rotational symmetries of orders other than two, tliree, four or six, and it had been assumed that the long-range periodicity necessary to produce a diffraction pattern with sharp spots could only exist in materials made by the stacking of identical unit cells. The materials that produced these diffraction patterns, but clearly could not be crystals, became known as quasicrystals. 

As noted earlier, most electron diffraction studies are perfonned in a mode of operation of a transmission electron microscope. The electrons are emitted themiionically from a hot cathode and accelerated by the electric field of a conventional electron gun. Because of the very strong interactions between electrons and matter, significant diffracted intensities can also be observed from the molecules of a gas. Again, the source of electrons is a conventional electron gun. 

Figure Bl.8.6. An electron diffraction pattern looking down the fivefold synnnetry axis of a quasicrystal. Because Friedel s law introduces a centre of synnnetry, the synnnetry of the pattern is tenfold. (Courtesy of L Bendersky.)...

For bulk structural detemiination (see chapter B 1.9). the main teclmique used has been x-ray diffraction (XRD). Several other teclmiques are also available for more specialized applications, including electron diffraction (ED) for thin film structures and gas-phase molecules neutron diffraction (ND) and nuclear magnetic resonance (NMR) for magnetic studies (see chapter B1.12 and chapter B1.13) x-ray absorption fine structure (XAFS) for local structures in small or unstable samples and other spectroscopies to examine local structures in molecules. Electron microscopy also plays an important role, primarily tlirough unaging (see chapter B1.17). 

We will, in the latter part of this discussion, focus only on those few methods that have been the most productive, with low-energy electron diffraction (FEED) receiving the most attention. Indeed, LEED has been the most successfiil surface stmctiiral method in two quite distinct ways. First, LEED has become an almost universal characterization... 

---