Plasmon excitation (< 50 eV, ~100 nm TEM specimen) Cerenkov effect Effects of interactions of electrons in solids.Įlectron Compton effect electron excitation (from 50 eV to a few keV: EDS and EELS) The angle between incident and reflected waves is equal to 2θ B as shown in Figure 3882. Very strong intensities known as Bragg peaks are obtained in the diffraction pattern when scattered waves satisfy the Bragg condition. widely used to explain electron and X-ray diffraction phenomena. The Bragg angle θ B is a very important concept in diffraction theory, e.g. Λ - The wavelength of the charged particle or electromagnetic radiation waves Īngle between the incident wave vector and the Therefore, we can obtain the well-known Bragg’s diffraction condition, given by, Assuming the hkl planes are spaced a distance d hkl apart and the wave is incident and reflected at angles θ B, both AB and BC are equal to dsin(θ B) and the total path difference should be equal to 2dsin(θ B).
Therefore, the path difference between electron waves reflected from the upper and lower planes in Figure 3882 is equal to the total length (AO+BO). The scattered waves interfere constructively if they remain in phase. The waves reflected off adjacent scattering centers must have a path difference equal to an integral number of wavelengths. In the classic diffraction theory, Bragg diffraction occurs when charged particle or electromagnetic radiation waves with a wavelength comparable to atomic spacing are incident to a crystalline sample. It should be noted that the gradient of the phase-shift against specimen thickness depends on the sign of the excitation error as discussed in the simulation part, i.e., when s 220 0, the gradient of the phase-shift is low.This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers. 3(h)–(n) s 220 is positive (the reciprocal lattice point of 220 is located inside the Ewald sphere). 3(a)–(g), the excitation error of the 220 reflection s 220 is negative (which means that the reciprocal lattice point of 220 is located outside the Ewald sphere) and for Fig. The tilting was changed in constant steps (0.39 mrad), such that for the tilting condition of Fig. 3(a) to 3(n) is estimated to be 5.04 mrad. 3(o), (p), the total tilting angle from Fig. From a movement of a cross point of Kikuchi lines indicated by black arrows in Figs. Figures 3(o) and 3(p) are diffraction patterns obtained in the diffraction condition of Figs. The bright field images, the reconstructed phase images and the phase shift profiles for each tilt conditions are shown in Fig. Next, we systematically tilted the direction of the incident electron beam around the 220 Bragg diffraction condition using a beam tilt function of the illumination system. The thicknesses of the positions are about 50 nm and 150 nm which were estimated by our calculations. The red arrows indicate the positions of dark thickness fringes. (b) Bragg diffraction condition with 220 reflection is exactly satisfied. (a) Strong Bragg reflections are not excited. 1(c).īright-field images, reconstructed phase images, and phase shift profiles of a wedge shaped Si crystal. But they can be explained by dynamical theory of electron diffraction as shown in Fig. Under the exact 220 Bragg diffraction condition, thickness fringes appear in the bright-field image, and the phase shift jumps by π (indicated by red arrows in the reconstructed phase image and the phase-shift profile) where the dark thickness fringes appear in the corresponding bright-field image. Under the non-Bragg condition, there are no thickness fringes in the bright field image, and the phase shift increases in proportion to the specimen thickness. 2(b) is under an exact 220 Bragg diffraction condition. 2(a) is under a non-Bragg condition and that shown in Fig. (1).įigure 2 shows bright-field images and reconstructed phase images of a wedge shape Si specimen, and the phase shift profiles in the region of the specimen indicated by the red rectangles in the bright-field and reconstructed phase images. (4) explains the characteristic phase shift around the Bragg condition that is not explained by eq. 1(d-i)), the small loop does not include the origin of the complex plane, which means the increase of the phase shift is less than 2π. This means the increase of the phase shift is larger than 2π. 1(b-i)), the small loop includes the origin of the complex plane. When the sign of s 220 is negative ( Fig. \sigma = \frac)$, shown as red bold lines for thicknesses from 20 nm to 80 nm, forms a shape of a small loop.
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