The X-ray standing wave technique

The X-ray

X-ray

X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

 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

Synchrotron light

A synchrotron light source is a source of electromagnetic radiation produced by a synchrotron, which is artificially produced for scientific and technical purposes by specialized particle accelerators, typically accelerating electrons...

 has stimulated the application of this interferometric technique

Interferometry

Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...

 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 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

X-ray fluorescence

X-ray fluorescence is the emission of characteristic "secondary" X-rays from a material that has been excited by bombarding with high-energy X-rays or gamma rays...

 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

Fourier series

In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

 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

Phase problem

In physics the phase problem is the name given to the problem of loss of information concerning the phase that can occur when making a physical measurement. The name itself comes from the field of x-ray crystallography, where the phase problem has to be solved for the determination of a structure...

 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
  Physisorption
  Physisorption, also called physical adsorption, is a process in which the electronic structure of the atom or molecule is barely perturbed upon adsorption...
  
   and chemisorption
  Chemisorption
  Chemisorption is a sub-class of adsorption, driven by a chemical reaction occurring at the exposed surface. A new chemical species is generated at the adsorbant surface...
  
   studies
• Diffusion
  Diffusion
  Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
  
   of dopants in crystals
• Superlattice
  Superlattice
  Superlattice is a periodic structure of layers of two materials. Typically, the thickness of one layer is several nanometers.- Discovery :Superlattices were discovered early in the 20th century through their special X-ray diffraction patterns....
  
  s and Quasi-crystal characterization

which do not require ultra-high vacuum conditions

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