High-Resolution TEM Imaging
The Huygens principle of physical optics is developed qualitatively, and then quantitatively with Green’s functions. The relationship between phase and potential is developed. Phase shifts of materials and lenses are described, and combined with propagato
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High-Resolution TEM Imaging
Spatial resolution is important for any microscopy. This chapter presents the theory, technique, and examples of achieving the ultimate resolution of a transmission electron microscope with the method of “high-resolution transmission electron microscopy.” Recall (Sect. 2.3.5) that the HRTEM image is an interference pattern of the electron wavefunction with itself after it is diffracted from the specimen. Interference patterns require close attention to the phases of the waves. While the ray optics approach is useful for a few geometrical arguments, the most important issues in HRTEM are best understood in terms of the phase of the electron wavefront and how this phase is altered by the specimen and by the objective lens. The specimen itself is treated as an object that provides phase shifts to the electron wavefront, sometimes in proportion to its scattering potential. The method of HRTEM also demands close attention to the performance of the objective lens and other characteristics of the microscope. The physical optics theory presented in this chapter treats diffraction and microscopy in terms of phase shifts of wavefronts. Several elegant tools and models are B. Fultz, J. Howe, Transmission Electron Microscopy and Diffractometry of Materials, Graduate Texts in Physics, DOI 10.1007/978-3-642-29761-8_11, © Springer-Verlag Berlin Heidelberg 2013
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High-Resolution TEM Imaging
provided. Unfortunately, real images from real specimens can rarely be interpreted with simple and convenient models for the lens or for the specimen. For HRTEM to provide quantitative information about atom arrangements in a material, computer simulations of the image are generally required. Mature codes for the analysis of HRTEM images are available, and this chapter provides an overview of how they work and how they are used. Several examples are presented to show what types of research problems are possible with high-resolution imaging. These were chosen in part to show how much trust can be placed in simple interpretations of HRTEM images. The method of “high-angle annular dark-field imaging” (HAADF), or “Zcontrast imaging” is described in Chap. 12. Although HAADF imaging gives atomic resolution, it is fundamentally different from HRTEM. HAADF imaging uses coherent optics to form a sub-nanometer probe beam, but the scattering from the sample is incoherent.
11.1 Huygens Principle 11.1.1 Wavelets from Points in a Continuum This chapter uses the “physical optics” approach to electron diffraction. It is based on the Huygens principle of physical optics, which was developed to understand the diffraction of light. The physical optics approach is much older than the electron wave mechanics of electron wavelets scattered by individual atoms. The present approach to physical optics uses scattered wavelets, but assumes the scattering centers have a continuous distribution. The obvious way to do this is to set the potential U (r ) equal to a constant, U , in the Schrödinger equation itself: −2 ∂ 2 ∂
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