X-ray Standing Waves - Basic Principles

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.

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 is described by

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

Since the emitting atoms are located in the near field, this technique does not suffer 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)