Diffraction dynamical theory

Dederichs, P.H. (1972) Dynamical diffraction theory by optical potential methods, Solid State Phys., 27, 125. 

For particles of heavy atoms such as Au or Pt it is not sufficient to assume that the calculations of diffraction patterns can be made by use of the simple, single-scattering, kinematical approximation. This leads to results which are wrong to a qualitatively obvious extent (16). The calculations must be made using the full dynamical diffraction theory with the periodic... 

The method of strueture analysis developed by the Soviet group was based on the kinematieal approximation that ED intensity is directly related (proportional) to the square of structure factor amplitudes. The same method had also been applied by Cowley in Melbourne for solving a few structures. In 1957 Cowley and Moodie introdueed the -beam dynamical diffraction theory to the seattering of eleetrons by atoms and crystals. This theory provided the basis of multi-sliee ealeulations whieh enabled the simulation of dynamieal intensities of eleetron diffraetion patterns, and later electron microscope images. The theory showed that if dynamical scattering is signifieant, intensities of eleetron diffraetion are usually not related to strueture faetors in a simple way. Sinee that day, the fear of dynamical effects has hampered efforts to analyze struetures by eleetron diffraction. 

A.AUTHIER, in X-ray and neutron dynamical diffraction theory and applications, eds. A.AUTHIER, S.LAGOMARSINO B.K.TANNER (Plenum Press, New York, 1997),p. 1. 

The dynamical diffraction theory is very accurate and highly practical, but no theoiy provides a perfect description of the complexity of real specimens. What are the limitations and approximations, and how serious are they ... 

Around the defect, enhanced scattering was observed and this loss of extinction is the origin of the name. The exact nature of the images can only be explained using dynamical diffraction theory and we will return to this in a later section. 

Lateral shifts are also due to depth penetration and refer to a shift in the exit location of an X-ray at the crystal surface. This results in a transverse shift at the detector, typically 10%-100% of refractive index corrections [20]. While ray-tracing can adequately describe geometrical effects outside the crystal, the effects of depth penetration and lateral shifts require full dynamical diffraction theory. 

Experimental reflection curves from LSMs compare well with predictions from dynamical diffraction theory, and peak reflectivities are as high as 80%. Therefore, a well-defined standing wave can be produced (Fig. 27). 

The rocking width or Darwin width mono of a perfect crystal is derivable from dynamical diffraction theory as... 

Authier, A., Lagomarsino, S., and Tanner, B.K. (1997). X-Ray and Neutron Dynamical Diffraction, Theory and Applications, vol. 357, Plenum Publishing Corporation. 

Following the observations of Batterman, a quantitative explanation of the fluorescence yield has been based on the dynamical diffraction theory of von Laue and Ewald (Laue 1960). The formal theory for the Bragg diffraction XSW technique has been described by Afanas ev et al. (1978), Takahashi and Kikuta (1979), Hertel et al. (1985) and Bedzyk and Materlik (1985), as well as in a review by Zegenhagen (1993). The theory of dynamical X-ray diffraction has been reviewed by Laue (I960), Batterman and... 

From dynamical diffraction theory (Batterman and Cole 1964), the E-field amplitude ratio is defined as... 

From dynamical diffraction theory, the relative phase, v, of the standing wave field decreases by n radians as the incident angle is scanned from the low-angle side to the high-angle side of the rocking curve (i. e., from rf = 1 to ( = -1). According to Equation... 

To produce XSW data that can be analyzed quantitatively by X-ray diffraction theory, it is necessary to achieve an analytically well-defined XSW field. A first test of meeting this condition is to determine if the angular dependence of the measured reflectivity curve closely matches the ideal reflectivity calculated with dynamical diffraction theory. This, of course, includes a convolution with the emittance function... 

The TER condition is the zeroth-order Bragg diffraction condition, or the condition when H = 0 and dH = oo. Therefore, the derivations from dynamical diffraction theory for Bragg diffraction can be applied to the case of TER by substituting F0 for FH. In which case, Equation (10) becomes... 

As stated earlier, the postmonochromator optics should prepare the incident beam in a way that avoids angle and wavelength averaging effects that would smear (or reduce the fringe visibility of) the XSW. Figure 12a shows the X vs. DuMond diagram for the APS undulator source at E7 = 12.50 keV, the Si(lll) monochromator, and the pair of Si(004) postmonochromator reflections. The slanted stripes represent the conditions where Bragg diffraction is allowed on the basis of dynamical diffraction theory. The... 

Finally, the other type of physical method, in an active state of development during the last few years, is that of multibeam reflection methods. These methods are based on the N beam diffraction effect (N>1, integer), which occurs when N nodes of the reciprocal lattice diffract for a unique incident beam. These simultaneous reflections are very well known processes and can be treated in accordance with dynamic diffraction theory. 

Delille D, Pantel R, Van Cappellen E (2001) Crystal thickness and extinction distance determination using energy filtered CBED pattern intensity measurement and dynamical diffraction theory fitting. Ultramicroscopy 87 5-18... 

To determine the structural parameters of these M-plane MQWs by HRXRD, we follow the same procedure as employed in Ref. 67. Symmetric X-ray o)-20 scans were taken with a Philips X Pert PRO triple-axis diffractometer with a GuXai source, a Ge(220) hybrid monochromator, and a Ge(220) three-bounce analyzer crystal. We first analyzed the angular positions of the satellite peaks kinematically based on the nominal growth times to obtain the structural parameters of the sample, implicitly assuming that segregation does not occur. Next, we employed simulations based on the dynamical diffraction theory [67] and varied the kinematically obtained parameters, until the intensity of the satellites matched the experiment in addition to their position. The simulations were performed for perfect interfaces and are convoluted with the instrumental resolution (25 ) only. As an example. Figure 6.15 shows (o-20 scans for sample MQW-A across the (a) GaN(nOO) and (h) GaN(2200) reflection. 

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