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

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 .

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

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

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 $R$ (green) and photo yield $Y_p$ (red) for different coherent positions $P_H = H.r$

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)

Selected applications

which require ultra-high vacuum conditions

• Physisorption and chemisorption studies
• Diffusion of dopants in crystals
• Superlattices and Quasi-crystal characterization

which do not require ultra-high vacuum conditions

• Langmuir-Blodgett films
• Self-assembled monolayers
• Buried interfaces

See also

• List of surface analysis methods