anomalous absorption

When an incident electron beam travels a crystalline specimen, two kinds of electron waves are produced due to the dynamical diffraction effect. That is, one electron wave runs on atomic columns and the other electron wave runs between atomic columns. The former electron wave undergoes a larger absorption than the average absorption, whereas the latter electron wave undergoes a smaller absorption than the average absorption. This phenomenon is termed "anomalous absorption." The main cause of the anomalous absorption is thermal diffuse scattering of incident electrons.

Fig. 1 (a) Bright-field image，(b) Diffraction pattern，(c) dark-field image, (d) dark-field image. Specimen: Al single-crystal thin film.
When a uniformly bent and wedge-shaped single-crystal thin film is observed under an electron incidence condition where only different order reflections (systematic reflections) are preferentially excited, equal-thickness and equal-inclination fringes are created in the bright-field and dark-field images. Here, those unique shaped interference fringes are named “bamboo-shoot shape fringes”. Intensity variations, which are seen along the excitation error “s = 0” (shown in the dark-field images Fig. 1(c), (d)), correspond to equal thickness fringes. On the other hand intensity variations, which are seen in orthogonal direction to “s = 0” (Fig. 1(c), (d)), correspond to equal inclination fringes (bend contours). In the positions satisfying “s = 0”, each Bragg condition of  is exactly excited.
Based on the dynamical theory of Electron Diffraction, when one diffracted wave is strongly excited, two type standing waves are produced. One standing wave runs on the atomic columns and another wave runs between the atomic columns. The former wave collides strongly with the atomic columns, suffering a strong absorption. The latter wave collides less with the atomic columns, thus experiencing a small absorption.
In the bright-field image (Fig.1(a)), the area between the two bamboo-shoot shape fringes indicated with the description appear dark because the standing wave running on the atomic columns is strongly excited and experiences a larger absorption than the average absorption. This phenomenon is called anomalous absorption. On the other hand, the areas outside the two bamboo-shoot shape fringes appear light because the standing wave running between the atomic columns is strongly excited and experiences a smaller absorption than the average absorption. This phenomenon is called anomalous transmission. At the center of bamboo-shoot shape fringes, that is, at “s = 0”, the two standing waves running on and between the atomic columns are equally excited, and thus interference effects become maximum, creating strong beats (equal thickness fringes).
In the dark-field images (Fig.1(c), (d)), the two standing waves running on and between the atomic columns are equally excited with respect to the position “s = 0”, and thus, the intensities of the bamboo-shoot shape fringes become symmetric about the position “s = 0”.

Fig. 2 Schematic of the bamboo-shoot fringes created from a uniformly bent and wedge-shaped single-crystal thin film (left figure), and a simulation set of interference fringes appearing in the bright-field image (000) and the dark-field images (111,). When a crystalline specimen is not bent, equal thickness fringes run parallel to the specimen edge, but in this specimen with a uniform bend, thickness fringes appear as bamboo-shoot shape fringes.
Specimen: Al crystal, Accelerating voltage: 100 kV, Specimen thickness: 10 to 500 nm.

(Simulation: Courtesy of Professor Kenji Tsuda, Tohoku University)

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