Incident electron wave

Theoretically, the asymptotic fonn of die solution for the electron wave fiinction is the same for low-energy projectiles as it is at high energy however, one must account for the protracted period of interaction between projectile and target at the intennediate stages of the process. The usual procedure is to separate the incident-electron wave fiinction into partial waves... 

The partial wave decomposition of the incident-electron wave provides the basis of an especially appealing picture of strong, low-energy resonant scattering wherein the projectile electron spends a sufficient period of time in the vicinity... 

The im< e mode produces an image of the illuminated sample area, as in Figure 2. The imj e can contain contrast brought about by several mechanisms mass contrast, due to spatial separations between distinct atomic constituents thickness contrast, due to nonuniformity in sample thickness diffraction contrast, which in the case of crystalline materials results from scattering of the incident electron wave by structural defects and phase contrast (see discussion later in this article). Alternating between imj e and diffraction mode on a TEM involves nothing more than the flick of a switch. The reasons for this simplicity are buried in the intricate electron optics technology that makes the practice of TEM possible. 

In this section we consider the problem of scattering of a well-collimated beam of high-energy electrons of energy E0 by a crystal. The incident electron wave function then has the form of a plane wave... 

The micrograph or the image obtained on an EM screen, photographic film, or (more commonly today) a CCD is the result of two processes the interaction of the incident electron wave function with the crystal potential and the interaction of this resulting wave function with the EM parameters which incorporate lens aberrations. In the wave theory of electrons, during the propagation of electrons through the sample, the incident wave function is modulated by its interaction with the sample, and the structural information is transferred to the wave function, which is then further modified by the transfer function of the EM. 

The phase contrast is produced by the phase modulation of the incident electron wave when it is transmitted through the sample crystal potential V(x, y). The propagation of a plane electron wave traversing through a thin sample is thus treated as a weak (scattering) phase object. The wavefunction at the exit... 

For elastic scattering, the absolute value of the scattered and the incident electron wave vector are equal, given by the reciprocal value of the wavelength, k = ko = 1/A. The angle between scattered and incident wave vector is the scattering angle 9 and the vector q, given by... 

High-resolution transmission electron microscopy can be understood as a general information-transfer process. The incident electron wave, which for HRTEM is ideally a plane wave with its wave vector parallel to a zone axis of the crystal, is diffracted by the crystal and transferred to the exit plane of the specimen. The electron wave at the exit plane contains the structure information of the illuminated specimen area in both the phase and the amplitude.. This exit-plane wave is transferred, however affected by the objective lens, to the recording device. To describe this information transfer in the microscope, it is advantageous to work in Fourier space with the spatial frequency of the electron wave as the relevant variable. For a crystal, the frequency spectrum of the exit-plane wave is dominated by a few discrete values, which are given by the most strongly excited Bloch states, respectively, by the Bragg-diffracted beams. 

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