Diffraction electron electron handbook in microscope microscopy transmission

The main principles of electron microscopy can be understood by use of optical ray diagrams [ 2 , 3 ], as shown in Fig. Diffracted waves scattered by the atomic potential form diffraction spots on the back focal plane after being focused with the objective lens. The diffracted waves are recombined to form an image on the image plane.

The use of electromagnetic lenses allows diffracted electrons to be focused into a regular arrangement of diffraction spots that are projected and recorded as the electron diffraction pattern. If the transmitted and the diffracted beams interfere on the image plane, a magnified image of the sample can be observed. The space where the diffraction pattern forms is called reciprocal space, while the space at the image plane or at a specimen is called real space.

The transformation from the real space to the reciprocal space is mathematically given by the Fourier transform. Optical ray diagram with an optical objective lens showing the principle of the imaging process in a transmission electron microscope. A great advantage of the transmission electron microscope is in the capability to observe, by adjusting the electron lenses, both electron microscope images information in real space and diffraction patterns information in reciprocal space for the same region.

By inserting a selected area aperture and using the parallel incident beam illumination, we get a diffraction pattern from a specific area as small as nm in diameter. The recently developed microdiffraction methods, where incident electrons are converged on a specimen, can now be used to get a diffraction pattern from an area only a few nm in diameter.

Therefore single crystal structural information can be obtained for many materials for which single crystals of the sizes suitable for x-ray or neutron diffraction are unavailable. Such materials include metastable or unstable phases, products of low temperature phase transitions, fine precipitates, nanosize particles etc. In order to investigate an electron microscope image, first the electron diffraction pattern is obtained. Then by passing the transmitted beam or one of the diffracted beams through a small objective aperture positioned in the back focal plane and changing lenses to the imaging mode, we can observe the image with enhanced contrast.

When only the transmitted beam is used, the observation mode is called the bright-field method accordingly a bright-field image , Fig. When one diffracted beam is selected Fig. The contrast in these images is attributed to the change of the amplitude of either the transmitted beam or diffracted beam due to absorption and dynamic scattering in the specimens. Thus the image contrast is called the absorption-diffraction, or the amplitude contrast. Amplitude-contrast images are suitable to study mesoscopic microstructures, e.

Both kinematic and dynamic scattering theories are developed to identify crystallographic details of these heterogeneities [ 2 , 3 ]. Three observation modes in electron microscope using an objective aperture. The center of the objective aperture is on the optical axis.

It is also possible to form electron microscope images by selecting more than two beams on the back focal plane using a large objective aperture, as shown in Fig. This observation mode is called high-resolution electron microscopy HREM.

The image results from the multiple beam interference because of the differences of phase of the transmitted and diffracted beams and is called the phase contrast image. For a very thin specimen and aberration-compensating condition of a microscope, the phase contrast corresponds closely to the projected potential of a structure. For a thicker specimen and less favorable conditions the phase contrast has to be compared with calculated images. Theory of dynamic scattering and phase contrast formation is now well developed for multislice and Bloch waves methods [ 5 ].

HREM can be used to determine an approximate structural model, with further refinement of the model using much higher resolution powder x-ray or neutron diffraction.

However, the most powerful use of HREM is in determining disordered or defect structures. Many of the disordered structures are impossible either to detect or determine by other methods. These characteristics mean that much smaller objects can be studied as single crystals with electrons than with other radiation sources.

It also means a great sensitivity to small deviations from an average structure caused by ordering, structural distortions, short-range ordering, or presence of defects.

Such changes often contribute either very weak superstructure reflections, or diffuse intensity, both of which are very difficult to detect by x-ray or neutron diffraction. In addition, modern transmission electron microscopes provide a number of complementary capabilities known as analytical electron microscopy [ 6 ].

Different detectors analyze inelasticly scattered electrons Electron Energy-Loss Spectroscopy, or EELS , excited electromagnetic waves Energy Dispersion Spectroscopy, or EDS and Z-contrast that provide information on chemical compositions and local atomic environments. Such information, when combined with elastic electron diffraction, is important in determining structural models, especially when a material consists of multiple phases.

The emphasis is on crystallographic aspects of the research. The presented contributions come mainly from the Materials Science and Engineering Laboratory. Starting in the early s the Metallurgy Division of NBS was actively involved in studying the fundamentals of rapid solidification of a melt. Such extreme conditions very often result in the formation of either new metastable or non-equilibrium crystalline or glassy structures.

The rapid cooling also causes the formation of small-grain polycrystalline microstructures, the consequence of a high nucleation rate within the liquid.

The combination of metastable and therefore most probably unknown structures with very small grain sizes makes such materials extremely difficult to study by x-ray diffraction, but very suitable for TEM. A study of rapidly solidified Al-Mn alloys by Dan Shechtman resulted in one of the most important discoveries of modern crystallography—a quasiperiodic structure with icosahedral symmetry, thus including 5-fold, 3-fold, and 2-fold rotation axes of symmetry [ 7 ].

Such symmetry was inconsistent with the entire science of crystallography at that time. The icosahedral symmetry of the phase was demonstrated by carefully constructing a reciprocal lattice using a series of selected area electron diffraction.

For the first time the existence of a well-ordered homogeneous not twinned! Cahn and D. Shechtman discuss the history of this remarkable discovery and its crystallographic aspects in a separate article in this issue. The discovery of the icosahedral phase triggered a period of very active research in the new field of quasicrystals. Shortly after the Shechtman et al. The importance of the discovery was not only discovery of a novel structure, but also demonstration of the general principles of quasiperiodicity.

Since the discovery of the first quasiperiodic structures in Al-Mn alloys in , enormous progress, both experimental and theoretical, has been made. Quasicrystalline phases have been found in more than hundred different metallic systems, and several quasicrystalline phases have been shown to be thermodynamically more stable than periodic crystals [ 9 ].

A series of SAD electron diffraction patterns obtained from the Al 78 Mn 22 rapidly solidified alloy by tilting a single grain. Based on these patterns, a unique non-crystallographic fold axis and a one-dimensional periodicity of the decagonal phase were established.

Here the methods of convergent beam electron diffraction CBED were applied for the first time to a quasiperiodic structure. The lines indicate the mirror planes m. The motifs are parallel throughout the entire polycrystalline aggregate, and the crystal axes change across grain boundaries.

Based on this finding, the entire concept of twinning and special grain boundaries was re-examined. A new definition of special orientations, including hypertwins, based on reduction of the number of arithmetically independent lattice vectors was proposed.

This new classification of special orientations within crystalline structures includes both old and new special orientations and can be easily interpreted in terms of quasilattices. Abir Roy. Doni Kurniawan.

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