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X-ray standing waves
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X-ray standing waves : ウィキペディア英語版
X-ray standing waves
The X-ray standing wave (XSW) technique can be used to study the structure of surfaces and interfaces with high spatial resolution and chemical selectivity. Pioneered by B.W. Batterman in the 1960s 〔B. W. Batterman and H. Cole, ''Dynamical Diffraction of X Rays by Perfect Crystals'', (Rev. Mod. Phys. 36 (1964) 681 )〕 the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science.〔J. Zegenhagen, ''Surface structure determination with X-ray standing waves'' ( Surf. Sci. Rep. 18(7/8) (1993) 199 )〕〔D. P. Woodruff, ''Surface structure determination using x-ray standing waves'', ( Rep. Prog. Phys. 68(4) (2005) 743 )〕
== Basic principles ==

An X-ray interference field created by Bragg reflection provides the length scale against which atomic distances can be measured. The spatial modulation of this field described by the dynamical theory of X-ray diffraction undergoes a pronounced change when the sample is scanned through the Bragg condition. Due to a relative phase variation between the incoming and the reflected beam the nodal planes of the XSW field shift by half a lattice constant.〔J. Als-Nielsen and D. McMorrow, ''Elements of Modern X-ray Physics'', John Wiley & Sons, Ltd. (2000)〕
Depending on the position of the atoms within this wave field the element specific absorption of X-rays varies in a characteristic way. Therefore, measurement of the photo yield – via X-ray fluorescence or photoelectron spectroscopy – can reveal the position of the atoms relative to the lattice planes.
For a quantitative analysis the normalized photo yield Y_p is described by 〔〔

Y_(\Omega) = 1 + R + 2C \sqrt f_H \cos (\nu - 2\pi P_H ),

where R is the reflectivity and \nu is the relative phase of the interfering beams. The characteristic shape of Y_p can be used to derive precise structural information about the surface atoms because the two parameters f_H (coherent fraction) and P_H (coherent position) are directly related to the Fourier representation of the atomic distribution function.

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