Electron Diffraction Analysis

a method of studying the structure of matter based on the scattering of accelerated electrons by the subject specimen. Electron diffraction analysis is used to study the atomic structure of crystals, amorphous bodies and liquids, and molecules in gases and vapors.

The physical basis of electron diffraction analysis is electron diffraction (seeDIFFRACTION OF PARTICLES). Upon passing through matter, electrons, which exhibit wave properties, interact with the atoms, as a result of which individual diffracted beams are formed. The intensities and spatial distribution of the beams are in strict correspondence with the atomic structure of the specimen, the dimensions and orientation of the individual crystallites, and other structural parameters. The scattering of electrons in matter is determined by the electrostatic potential of the atoms, whose maxima in the crystal correspond to the positions of the atomic nuclei.

Electron diffraction studies are performed in special devices—electron diffraction cameras and electron microscopes; under conditions of a vacuum, electrons in these devices are accelerated by an electric field and are focused into a narrow intense beam, and the beams formed after passage through the specimen are either photographed (electron diffraction patterns) or are registered by a photoelectric device. Depending on the value of the electric voltage accelerating the electrons, a distinction is made between high-energy electron diffraction (voltage of 30–50 to 1,000 kilovolts or higher) and low-energy electron diffraction (voltage ranging from a few volts to hundreds of volts).

Like X-ray diffraction analysis and neutron diffraction analysis, electron diffraction analysis is a structural diffraction technique, possessing a number of unique features. Owing to the incomparably stronger interaction of electrons with matter, as well as to the possibility of creating an intense beam in an electron diffraction camera, the exposure required to obtain a diffraction pattern is usually about 1 sec, which makes it possible to investigate such processes as structural transformations and crystallization. On the other hand, the strong interaction of electrons with matter restricts the permissible thickness of the illuminated specimens to tenths of a micron (at a voltage of 1,000–2,000 kilovolts, the maximum thickness is a few microns).

Electron diffraction analysis has made it possible to study the atomic structures of a large number of substances that exist only in the fine-crystal state. It also has an advantage over X-ray diffraction analysis in that it can be used to determine the position of light atoms in the presence of heavy atoms (neutron diffraction analysis techniques are also capable of such studies but only of crystals much larger than the crystals studied by electron diffraction analysis).

The type of electron diffraction pattern obtained depends on the nature of the object being studied. Diffraction patterns of films that are made up of crystallites with quite precise mutual orientation or of fine single-crystal sheets consist of points or spots (reflections) with regular mutual disposition. Arclike reflections are obtained when the crystallites in films are partially oriented according to a certain law (seeTEXTURES). Diffraction patterns of specimens made up of randomly arranged crystallites consist, like Debye powder diagrams, of uniformly traced circles or, when a moving photographic plate is used (kinematic photography), of parallel lines. These types of diffraction patterns are obtained as a result of elastic, chiefly single, scattering (without energy exchange with the crystal). In the case of multiple inelastic scattering, secondary diffraction patterns of the diffracted beams arise. Such patterns are called Kikuchi lines, after the Japanese physicist who first obtained them. The diffraction patterns of gas molecules contain a small number of diffuse halos.

The determination of the unit cell of the crystal structure and cell symmetry is based on the measurement of the positions of reflections on diffraction patterns. The interplanar spacing d in a crystal is determined from the relation

d = Lλ/r

where L is the distance from the scattering object to the photographic plate, λ is the length of the de Broglie wave of the electron, which is determined by the electron’s energy, and r is the distance from the reflection to the central spot produced by unscattered electrons. The methods of calculating the atomic structure of crystals in electron diffraction analysis are similar to the techniques used in X-ray diffraction analysis (only some coefficients change). The measurement of the intensities of reflections makes it possible to determine the structure amplitudes ǀΦ_hklǀ The distribution of the electrostatic potential φ(x, y, z) of a crystal is represented in the form of a Fourier series:

where h, k, and I are Miller indexes and Ω is the volume of the unit cell (seeMILLER INDEXES). The maximum values of φ(x, y, z) correspond to the positions of atoms within the unit cell of the crystal. Thus, the calculation of the values of φ(x, y, z), which is usually performed by computer, makes it possible to establish the coordinates x, y, z of the atoms, the distances between the atoms, and other information.

The methods of electron diffraction analysis have been used to determine many previously unknown atomic structures and to refine and supplement X-ray diffraction data for a large number of substances, including many acyclic and isocyclic hydrocarbons, in which hydrogen atoms were first localized, molecules of nitrides of the transition metals (Fe, Cr, Ni, W), and a broad class of oxides of niobium, vanadium, and tantalum with localization of N and O atoms, as well as two-and three-component semiconductor compounds, clay minerals, and laminar structures. Electron diffraction analysis can also be used to study lattice defects. Together with electron microscopy, it makes possible the study of the degree of perfection of the structure of thin crystalline films, which are used in various branches of modern technology. For epitaxial processes, it is essential to monitor the degree of perfection of the substrate surface before application of the films; this is carried out by means of Kikuchi lines: even slight disruptions in the structure lead to the blurring of the lines.

Electron diffraction patterns for gases exhibit no clear-cut reflections, since gases have no strictly periodic structure, and consequently they are interpreted by other methods.

The intensity of each point on electron diffraction patterns is determined by both the molecule as a whole and its constituent atoms. The molecular component is important for structural studies, whereas the atomic component is treated as the background, and the ratio of molecular intensity to total intensity at each point of the diffraction pattern is measured. These data make it possible to determine the structures of molecules with up to 10–20 atoms, as well as the nature of their thermal vibrations over a broad temperature range. The structures of many organic molecules and the molecules of halides, oxides, and other compounds have been studied in this way. A similar technique is used to analyze short-range order atomic structure in amorphous bodies, glasses, and liquids (seeLONG-RANGE AND SHORT-RANGE ORDER).

When slow electrons are used, their diffraction is accompanied by the Auger effect and other phenomena arising as a result of the strong interaction of slow electrons with atoms. The inadequate development of theory and the complexity of carrying out the experiments make it difficult to interpret unambiguously the diffraction patterns. It is advisable to use electron diffraction analysis in conjunction with mass spectroscopy and Auger spectroscopy to investigate the atomic structure of adsorbed layers, such as gases, and the surfaces of crystals to a depth of a few atomic layers (10–30 angstroms). These techniques make it possible to study adsorption phenomena, the earliest stages of crystallization, and other phenomena.