The

X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...

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 radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in ...

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

Basic principles

An X-ray standing wave (XSW) field is created by interference between an X-ray beam impinging on a sample and a reflected beam. The reflection may be generated at the

Bragg condition In physics and chemistry , Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in ...

for a crystal lattice or an engineered multilayer

superlattice A superlattice is a periodic structure of layers of two (or more) materials. Typically, the thickness of one layer is several nanometers. It can also refer to a lower-dimensional structure such as an array of quantum dots or quantum wells. Disc ...

; in these cases, the period of the XSW equals the periodicity of the reflecting planes.

X-ray reflectivity X-ray reflectivity (sometimes known as X-ray specular reflectivity, X-ray reflectometry, or XRR) is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers.J. ...

from a mirror surface at small incidence angles may also be used to generate long-period XSWs. The spatial modulation of the XSW 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 reflected beams, the nodal planes of the XSW field shift by half the XSW period. Depending on the position of the atoms within this wave field, the measured element-specific absorption of X-rays varies in a characteristic way. Therefore, measurement of the absorption (via

X-ray fluorescence X-ray fluorescence (XRF) is the emission of characteristic "secondary" (or fluorescent) X-rays from a material that has been excited by being bombarded with high-energy X-rays or gamma rays. The phenomenon is widely used for elemental analysis ...

photoelectron The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid sta ...

yield) can reveal the position of the atoms relative to the reflecting planes. The absorbing atoms can be thought of as "detecting" the phase of the XSW; thus, this method overcomes the

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

of X-ray crystallography. For quantitative analysis, the normalized fluorescence or photoelectron yield

Y_p

is described by

Y_(\Omega) = 1 + R + 2C \sqrt 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. Therefore, 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).

Experimental considerations

XSW measurements of

single crystal In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.RIWD. "Re ...

surfaces are performed on a

diffractometer A diffractometer is a measuring instrument for analyzing the structure of a material from the scattering pattern produced when a beam of radiation or particles (such as X-rays or neutrons) interacts with it. Principle Because it is relatively eas ...

. The crystal is rocked through a Bragg diffraction condition, and the reflectivity and XSW yield are simultaneously measured. XSW yield is usually detected as

(XRF). XRF detection enables ''in situ'' measurements of interfaces between a surface and gas or liquid environments, since hard X-rays can penetrate these media. While XRF gives an element-specific XSW yield, it is not sensitive to the chemical state of the absorbing atom. Chemical state sensitivity is achieved using

detection, which requires

ultra-high vacuum Ultra-high vacuum (UHV) is the vacuum regime characterised by pressures lower than about . UHV conditions are created by pumping the gas out of a UHV chamber. At these low pressures the mean free path of a gas molecule is greater than approximately ...

instrumentation. Measurements of atomic positions at or near single crystal surfaces require substrates of very high crystal quality. The intrinsic width of a Bragg reflection, as calculated by dynamical diffraction theory, is extremely small (on the order of 0.001° under conventional X-ray diffraction conditions). Crystal defects such as mosaicity can substantially broaden the measured reflectivity, which obscures the modulations in the XSW yield needed to locate the absorbing atom. For defect-rich substrates such as metal single crystals, a normal-incidence or back-reflection geometry is used. In this geometry, the intrinsic width of the Bragg reflection is maximized. Instead of rocking the crystal in space, the energy of the incident beam is tuned through the Bragg condition. Since this geometry requires soft incident X-rays, this geometry typically uses XPS detection of the XSW yield.

Selected applications

Applications which require

conditions: *

Physisorption Physisorption, also called physical adsorption, is a process in which the electronic structure of the atom or molecule is barely perturbed upon adsorption. Overview The fundamental interacting force of physisorption is Van der Waals force. Even ...

and

chemisorption Chemisorption is a kind of adsorption which involves a chemical reaction between the surface and the adsorbate. New chemical bonds are generated at the adsorbent surface. Examples include macroscopic phenomena that can be very obvious, like cor ...

studies *

Diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...

of dopants in crystals *

Superlattice A superlattice is a periodic structure of layers of two (or more) materials. Typically, the thickness of one layer is several nanometers. It can also refer to a lower-dimensional structure such as an array of quantum dots or quantum wells. Disc ...

s and

Quasi-crystal A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical cr ...

characterization Applications which do not require ultra-high vacuum conditions: * Langmuir-Blodgett films *

Self-assembled monolayers Self-assembled monolayers (SAM) of organic molecules are molecular assemblies formed spontaneously on surfaces by adsorption and are organized into more or less large ordered domains. In some cases molecules that form the monolayer do not interact ...

* Model

heterogeneous catalysts In chemistry, heterogeneous catalysis is catalysis where the phase of catalysts differs from that of the reactants or products. The process contrasts with homogeneous catalysis where the reactants, products and catalyst exist in the same phase. P ...

* Buried interfaces

Basic principles

Experimental considerations

Selected applications

See also

References

Further reading