X-ray Raman scattering
Encyclopedia
X-ray Raman scattering is non-resonant inelastic scattering
of x-ray
s from core electron
s.
It is analogous to Raman scattering
, which is a largely used tool in
optical spectroscopy, with the difference being that the wavelengths of the
exciting photons fall in the x-ray regime and the corresponding excitations
are from deep core electrons.
XRS is an element-specific spectroscopic
tool for studying the electronic structure
of matter
. In particular, it probes the excited-state density of states
(DOS) of an atomic species in a sample.
process, in which a high-energy x-ray photon gives energy to a core electron, exciting it to an unoccupied state. The process is in principle analogous to x-ray absorption (XAS), but the energy transfer plays the role of the x-ray photon energy absorbed in x-ray absorption, exactly as in
Raman scattering in optics vibrational low-energy excitations can be observed
by studying the spectrum of light scattered from a molecule.
Because the energy (and therefore wavelength) of the probing x-ray can be chosen
freely and is usually in the hard x-ray regime, certain constraints
of soft x-rays in the studies of electronic structure of the material are
overcome. For example, soft x-ray studies may be surface sensitive and they require a vacuum environment. This makes studies of many substances, such as numerous liquids impossible using soft x-ray absorption. One of the most notable applications in which x-ray Raman scattering is superior to soft x-ray absorption is the study of soft x-ray absorption edges in high pressure
. Whereas high-energy x-rays may pass through a high-pressure apparatus like a diamond anvil cell
and reach the sample inside the cell, soft x-rays would be absorbed by the cell itself.
proposed that a similar effect should be found also in the x-ray regime. Around the same time, B. Davis and D. Mitchell reported in 1928 on the fine-structure of the scattered radiation from graphite and noted that they had lines that seemed to be in agreement with carbon K shell energy. Several researchers attempted similar experiments in the late 1920s and early 1930s but the results could not always be confirmed. Often the first unambiguous observations of the XRS effect is credited to K. Das Gupta (reported findings 1959) and Tadasu Suzuki (reported 1964). It was soon realized that the XRS peak in solids was broadened by the solid-state effects and it appeared as a band, with a shape similar to that of a XAS spectrum. The potential of the technique was limited until modern synchrotron light
sources became available. This is due to the very small XRS probability of the incident photons, requiring radiation with
a very high intensity
. Today, the XRS technique is rapidly growing in importance. It can be used to study near-edge x-ray absorption fine structure
(NEXAFS or XANES) as well as extended x-ray absorption fine structure
(EXAFS).
which has a cross section
of
.
Here,
is the
Thomson cross section
, which signifies that the
scattering is that of electromagnetic waves from electrons. The physics
of the system under study is buried in the dynamic structure factor
, which is a function of momentum transfer 
and energy transfer
. The dynamic structure factor
contains all non-resonant electronic excitations, including
not only the core-electron excitations observed in XRS but also e.g. plasmon
s,
the collective fluctuations of valence electron
s,
and Compton scattering
.
at small momentum transfers
the XRS contribution of
the dynamic structure factor is
proportional to the x-ray absorption spectrum. The main difference is that
while the polarization vector of light couples to momentum of the
absorbing electron in XAS, in XRS the momentum of the incident photon
couples to the charge of the electron. Because of this, the momentum transfer
of XRS plays the role of photon polarization of XAS.
X-ray scattering techniques
X-ray scattering techniques are a family of non-destructive analytical techniques which reveal information about the crystallographic structure, chemical composition, and physical properties of materials and thin films...
of 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...
s from core electron
Core electron
Core electrons are the electrons in an atom that are not valence electrons and therefore do not participate in bonding. An example: the carbon atom has a total of 6 electrons, 4 of them being valence electrons. So the remaining 2 electrons must be core electrons.They are so tightly bound to the...
s.
It is analogous to Raman scattering
Raman scattering
Raman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa Krishnan in liquids, and by Grigory Landsberg and Leonid Mandelstam in crystals....
, which is a largely used tool in
optical spectroscopy, with the difference being that the wavelengths of the
exciting photons fall in the x-ray regime and the corresponding excitations
are from deep core electrons.
XRS is an element-specific spectroscopic
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
tool for studying the electronic structure
Electron configuration
In atomic physics and quantum chemistry, electron configuration is the arrangement of electrons of an atom, a molecule, or other physical structure...
of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
. In particular, it probes the excited-state density of states
Density of states
In solid-state and condensed matter physics, the density of states of a system describes the number of states per interval of energy at each energy level that are available to be occupied by electrons. Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not...
(DOS) of an atomic species in a sample.
Description
XRS is an inelastic x-ray scatteringX-ray scattering techniques
X-ray scattering techniques are a family of non-destructive analytical techniques which reveal information about the crystallographic structure, chemical composition, and physical properties of materials and thin films...
process, in which a high-energy x-ray photon gives energy to a core electron, exciting it to an unoccupied state. The process is in principle analogous to x-ray absorption (XAS), but the energy transfer plays the role of the x-ray photon energy absorbed in x-ray absorption, exactly as in
Raman scattering in optics vibrational low-energy excitations can be observed
by studying the spectrum of light scattered from a molecule.
Because the energy (and therefore wavelength) of the probing x-ray can be chosen
freely and is usually in the hard x-ray regime, certain constraints
of soft x-rays in the studies of electronic structure of the material are
overcome. For example, soft x-ray studies may be surface sensitive and they require a vacuum environment. This makes studies of many substances, such as numerous liquids impossible using soft x-ray absorption. One of the most notable applications in which x-ray Raman scattering is superior to soft x-ray absorption is the study of soft x-ray absorption edges in high pressure
High pressure
High pressure in science and engineering is studying the effects of high pressure on materials and the design and construction of devices, such as a diamond anvil cell, which can create high pressure...
. Whereas high-energy x-rays may pass through a high-pressure apparatus like a diamond anvil cell
Diamond anvil cell
A diamond anvil cell is a device used in scientific experiments. It allows compressing a small piece of material to extreme pressures, which can exceed 3,000,000 atmospheres ....
and reach the sample inside the cell, soft x-rays would be absorbed by the cell itself.
History
In his report of finding of a new type of scattering, Chandrasekhara Venkata RamanChandrasekhara Venkata Raman
Sir Chandrasekhara Venkata Raman, FRS was an Indian physicist whose work was influential in the growth of science in the world. He was the recipient of the Nobel Prize for Physics in 1930 for the discovery that when light traverses a transparent material, some of the light that is deflected...
proposed that a similar effect should be found also in the x-ray regime. Around the same time, B. Davis and D. Mitchell reported in 1928 on the fine-structure of the scattered radiation from graphite and noted that they had lines that seemed to be in agreement with carbon K shell energy. Several researchers attempted similar experiments in the late 1920s and early 1930s but the results could not always be confirmed. Often the first unambiguous observations of the XRS effect is credited to K. Das Gupta (reported findings 1959) and Tadasu Suzuki (reported 1964). It was soon realized that the XRS peak in solids was broadened by the solid-state effects and it appeared as a band, with a shape similar to that of a XAS spectrum. The potential of the technique was limited until modern 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...
sources became available. This is due to the very small XRS probability of the incident photons, requiring radiation with
a very high intensity
Intensity (physics)
In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...
. Today, the XRS technique is rapidly growing in importance. It can be used to study near-edge x-ray absorption fine structure
XANES
X-ray Absorption Near Edge Structure , also known as Near edge X-ray absorption fine structure is a type of absorption spectroscopy. NEXAFS also at times used the abbreviation EXAFS....
(NEXAFS or XANES) as well as extended x-ray absorption fine structure
Extended X-Ray Absorption Fine Structure
X-ray Absorption Spectroscopy includes both Extended X-Ray Absorption Fine Structure and X-ray Absorption Near Edge Structure . XAS is the measurement of the x-ray absorption coefficient of a material as a function of energy...
(EXAFS).
Brief theory of XRS
XRS belongs to the class of non-resonant inelastic x-ray scattering,which has a cross section
Cross section (physics)
A cross section is the effective area which governs the probability of some scattering or absorption event. Together with particle density and path length, it can be used to predict the total scattering probability via the Beer-Lambert law....
of
.Here,
is theThomson cross section
Thomson scattering
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering...
, which signifies that the
scattering is that of electromagnetic waves from electrons. The physics
of the system under study is buried in the dynamic structure factor
, which is a function of momentum transfer and energy transfer
. The dynamic structure factorcontains all non-resonant electronic excitations, including
not only the core-electron excitations observed in XRS but also e.g. plasmon
Plasmon
In physics, a plasmon is a quantum of plasma oscillation. The plasmon is a quasiparticle resulting from the quantization of plasma oscillations just as photons and phonons are quantizations of light and mechanical vibrations, respectively...
s,
the collective fluctuations of valence electron
Valence electron
In chemistry, valence electrons are the electrons of an atom that can participate in the formation of chemical bonds with other atoms. Valence electrons are the "own" electrons, present in the free neutral atom, that combine with valence electrons of other atoms to form chemical bonds. In a single...
s,
and Compton scattering
Compton scattering
In physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...
.
Similarity to x-ray absorption
It was shown by Yukio Mizuno and Yoshihiro Ohmura in 1967 thatat small momentum transfers
the XRS contribution ofthe dynamic structure factor is
proportional to the x-ray absorption spectrum. The main difference is that
while the polarization vector of light couples to momentum of the
absorbing electron in XAS, in XRS the momentum of the incident photon
couples to the charge of the electron. Because of this, the momentum transfer
of XRS plays the role of photon polarization of XAS.