Dynamical theory of diffraction

The key here was the theory. The pioneers familiarity with both the kinematic and the dynamic theory of diffraction and with the real structure of real crystals (the subject-matter of Lai s review cited in Section 4.2.4) enabled them to work out, by degrees, how to get good contrast for dislocations of various kinds and, later, other defects such as stacking-faults. Several other physicists who have since become well known, such as A. Kelly and J. Menter, were also involved Hirsch goes to considerable pains in his 1986 paper to attribute credit to all those who played a major part. 

In this chapter we discuss the computational implementation of the dynamical theory of diffraction Takagi-Taupin theory, the solution for grids and thin layers, HRXRD simulation, deviation parameters, strategies, effect of strain, dislocation and defect arrays. We then give a number of examples of simulations. 

G.30 B. E. Warren. X-Ray Diffraction (Reading, Mass. Addison-Wesley, 1969). Excellent advanced treatment, in which the author takes pains to connect theoretically derived results with experimentally observable quantities. Stresses diffraction effects due to thermal vibration, order-disorder, imr>erfect crystals, and amorphous materials. Includes a treatment of the dynamical theory of diffraction by a perfect crystal. 

G.43 Leonid V. Azaroff Roy Kaplow N. Kato Richard J. Weiss A. J. C. Wilson and R. A. Young. X-Ray Diffraction (New York McGraw-Hill, 1974). Advanced treatments of atomic scattering, kinematical and dynamical theories of diffraction, powder diffractometry, and single-crystal intensities. 

Takagi, S. (1969). A Dynamical Theory of Diffraction for a Distorted Crystal. J. Phys. Soc. Japan 26, 1239-1253. 

For the case of oblique incidence, first- and higher-order diffractions are permitted. The polarization becomes elliptical in this case. Precise measurements of the reflection spectrum for the obhque incidence of this hght were given in [19]. First- and second-order reflection spectra were calculated and observed. The analytical solution of Maxwell s equations by the dynamical theory of diffraction [20] is in good agreement with experimental data [19]. The exact solution of Maxwell s equations has not been yet developed, because the theory is very complicated. 

The analysis and interpretation of diffraction patterns and other data from these new instruments required advanced mathematical skills. The first theoretical physicist to join the Institute was Gert Moliere, who arrived at the Institute shortly after completing his doctorate under Max von Laue in 1935 and remained in Dahlem until around 1940. During this time, he formulated a quantum mechanical account of X-ray diffraction in metals based on Laue s classical dynamic theory of diffraction, in which crystals were treated as continuous dielectrics. In... 

The behavior of diffracted electrons from crystals is best described by simple 2-beam dynamical theory of electron... 

For readers learning electron diffraction, there are a number of books on electron diffraction for materials characterization [1,2,3,4]. Most of these books focus on crystals since many polycrystalline materials are perfect single crystals in an electron microscope because of the small electron probe. Full treatment of the dynamic theory of electron diffraction is given in several special topic books and reviews [5,6,7,8]. 

Authier A. (2001). Dynamical Theory of X-Ray Diffraction. Oxford University Press. 

In HRTEM studies of complex catalyst structures, complementary multislice image simulations using the dynamical theory of electron diffraction (Cowley 1981) may be necessary for the nanostructural analysis and to match experimental images with theory. 

Dynamical theory of electron diffraction is a solution of the Schrodinger equation provided... 

If k is the wavevector of the incident wave in vacuum, then K is the magnitude of k after correction for the mean inner potential Uq of the crystal. The fact that K is different from k means that the crystal has a refractive index, and it is clear that the mean refractive index n must be related to Uq. Direct measurements show that n is of the order of 1 x 10 In the dynamical theory of electron diffraction, which we develop in this chapter, we formally make all the Fourier components Kg complex quantities, that is, we replace Kg by Vg + iV. The full physical significance of the procedure will become clear in due course, but for the moment it will be helpful to consider the consequences of making Kq complex. If Kq is complex, then the mean refractive index n must also be complex, and so we write n = n +in". 

The following account of the dynamical theory of electron diffraction is based on the treatment of the formally similar theory of x-ray diffraction given by Batterman and Cole (1964). 

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