By Jian Min Zuo, John C.H. Spence
This quantity expands and updates the assurance within the authors' renowned 1992 ebook, Electron Microdiffraction. because the identify implies, the focal point of the ebook has replaced from electron microdiffraction and convergent beam electron diffraction to all sorts of complicated transmission electron microscopy. targeted awareness is given to electron diffraction and imaging, together with high-resolution TEM and STEM imaging, and the applying of those the way to crystals, their defects, and nanostructures. The authoritative textual content summarizes and develops many of the valuable wisdom which has been received through the years from the examine of the a number of electron scattering challenge, the hot improvement of aberration correctors and their functions to fabrics constitution characterization, in addition to the authors' wide instructing event in those components. Advanced Transmission Electron Microscopy: Imaging and Diffraction in Nanoscience is perfect to be used as a sophisticated undergraduate or graduate point textual content in aid in fact fabrics in fabrics technology, Physics or Chemistry departments.
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Additional resources for Advanced Transmission Electron Microscopy: Imaging and Diffraction in Nanoscience
By replacing k with −k, another solution representing a converging spherical wave is obtained. For plane waves, changing the sign of wave vector reverses the wave propagation direction. By summing waves of different wave vectors together, three distinct important types of wave can be formed—the running waves treated above, the standing wave, and the pulse or wave packet. It is also possible to sum over a range of wave vectors and frequencies—in that case, the relationship between wave vector and frequency is called a dispersion relation, and this depends on the properties (the dielectric function in optics, or the electromagnetic potential for electron diffraction) of the medium in which the wave is traveling.
In this case, the arrival time to the detector point is same from each slit, and thus, s ¼ 0. According to Eq. 26), the intensity contribution from the source point at x is given by Â È ÉÃ hIðxÞidx ¼ 2IðxÞ 1 þ Re c012 ðxÞ dx where c012 ðxÞ ¼ expð2pixD=kZS Þ: The overall complex degree of partial coherence is obtained by integrating over all source points, in the form Z1 c12 ðD; 0Þ ¼ IðxÞ expð2pixD=kZS Þdx ð2:43Þ À1 Extending this to a two-dimensional source, we have c12 À Á 1 Dx ; Dy ; 0 ¼ Io R1 Z1 Â À Á Ã Iðx; yÞ exp 2pi xDx þ yDy =kZS dxdy ð2:44Þ À1 where Io ¼ À1 Iðx; yÞdxdy is the integrated source intensity.
A useful approximation is as follows: À Á 1 2 2 / ~ k ¼ A kx ; ky pﬃﬃﬃﬃﬃﬃ eÀðkz Àko Þ =2rk ; ð2:32Þ r 2p qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ À Á 2 where A kx ; ky ¼ 1=pkmax for kx2 þ ky2 kmax and 0 otherwise. This model assumes that momentum is uniformly distributed within a disk along the x direction and y direction and has a Gaussian distribution along the z direction around the mean value of ko ¼ 1=k. The Fourier transform in the integral of Eq. 31) has the property that a broadly distributed function gives rise to a narrowly distributed Fourier spectrum or vice versa in a reciprocal relationship.