This means that only very small apertures could be used, and since microscope resolution is given by 0.61 λ/sin α, where λ is wavelength, the best resolution would be limited by diffraction to ∼50 λ. With electron lenses, C s is of the same order as the focal length. Spherical aberration is the dominant aberration, and leads to a ray deviation of C s α 3, where α is the semiangle of the objective lens. The major limitation was realized early in the history of the microscope to be the high inherent aberrations of a round magnetic lens. However, it is only very recently that atomic resolution imaging could be said to be at all trivial. It would therefore appear relatively trivial to form atomic resolution images of materials. For accelerating voltages of 100–1000 kV, the electron wavelength ranges from 0.004 to 0.001 nm, orders of magnitude lower than atomic spacings in materials. Electrons also interact much more strongly with matter and electron diffraction can be performed on materials of nanometer dimensions. The scattered beams can be collected by a lens, and refocused to form a true real space image in the manner of an optical microscope, where each point in the image corresponds to a specific point in the object. The unique role of the TEM arises because electrons are charged particles, and therefore, unlike X-rays or neutrons, are able to be accelerated and precisely focused by electromagnetic fields. As condensed matter physics moves toward the study of ever more complex materials, and at the same time interest in nanoscale physics and devices is increasing, TEM or its scanning counterpart STEM, is finding a rapidly increasing role in basic condensed matter physics research. These techniques can determine the average structure of complex materials very precisely, but not the structure of a local region or individual nanostructure. X-ray or neutron diffraction provide quite complementary information. TEM plays a critical role whenever macroscopic properties are controlled or influenced by defects or interfaces, for example, in the development of advanced structural materials with their complex microstructure of second phases or electronic materials which rely on the exquisite control of interfaces and multilayers. It provides a view of the microstructure, that is, the variations in structure from one region to another, and the interfaces between them. The distinguishing feature of transmission electron microscopy (TEM) is its ability to form images of atomic arrangements at localized regions within materials. Pennycook, in Encyclopedia of Condensed Matter Physics, 2005 Introduction
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