# 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 [1] the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science.[2][3]

## Basic principles

Principle of X-ray standing wave measurements

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.[4]

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 [2][3]

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

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.

X-ray reflectivity from the ubiquitous phase problem of X-ray crystallography. Therefore, and with a sufficiently large number of Fourier components being measured, XSW data can be used to establish the distribution of the different atoms in the unit cell (XSW imaging) [5]

## Selected applications

which require ultra-high vacuum conditions

which do not require ultra-high vacuum conditions