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# X-ray standing waves

## The X-ray standing wave technique

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 the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science.

## 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 - as 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.

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 Yp is described by

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

where R is the reflectivity and ν is the relative phase of the interfering beams. The characteristic shape of Yp can be used to derive precise structural information about the surface atoms via the two parameters fH (coherent fraction) and PH (coherent position). Since the emitting atoms are located in the near field, XSW measurements do not suffer from the ubiquitous phase problem of X-ray crystallography.

## Selected Applications

which require ultra-high vacuum conditions

which do not require ultra-high vacuum conditions