4 Inelastic Interaction of X-rays with Matter

Amarjeet Singh

    Learning Outcomes

 

After studying this module, you shall be able to

  • Understand the electromagnetic spectrum and a window of x-rays in the entire spectrum.
  • Distinguish typical wavelength, frequency and energy associated with x-ray photons.
  • Understand the production of x-rays and various excitation process in a materials through interaction of photons with matter.
  • Learn X-ray absorption process and various measurement techniques (XANES, EXAFS, X-ray fluorescence).

    Introduction:

 

Wilhelm Conrad Roentgen discovered x-rays at the University of Wurzburg in 1895. In the twentieth century, x-rays have played an important role in gaining an understanding of matter on the atomic scale and quantum mechanics in general. The discovery of x-rays unfolded a new era of science. One of the major accomplishments was the exploration of the microscopic structural details of molecules, liquids and solids at length scales of inter-atomic distances. X-rays can penetrate thick objects that are opaque to visible light. The following diagram illustrates the range of frequencies, energy and wavelength for x-rays.

 

 

Fig: 3.1 Diagram illustrating soft and hard x-rays in the electromagnetic spectrum.

 

On the basic of penetrating power and applications the x-rays are usually categorized as soft x-rays and hard x-rays. On the basis of this property, atomic-resolution three-dimensional real-space imaging methods are used to obtain the invisible interior structure of objects. Several x-ray imaging techniques have been developed for this purpose. For example, real-space x-ray microscopy is similar to visible light microscopy, except that traditional refractive lenses are replaced by x-ray lenses such as zone plates. Lens less imaging gets rid of lenses altogether and instead reciprocal-space coherent diffraction patterns are recorded. They are subsequently inverted using computational algorithms to obtain a real-space image. These techniques allow the recording of high-resolution images that can be sensitive to elemental composition, chemical state, and state of magnetism.

 

 

Fig: 3.2 Several consequences of x-ray interaction with matter

 

The interaction of x-rays with matter results in several processes which are illustrated in the above diagram (Fig: 3.2). Two high energy x-rays can produce matter particles (a pair of positron and electron). A photon can be completely absorbed to produce a photoelectron. Inelastic scattering results in a partial loss of photon energy via Compton and Raman scattering. In an elastic scattering the photon is scattered without losing its energy. The exc itation of atoms and molecules results in decay process through fluorescence and Auger electrons. With the advent of high- intensity short-pulse x-ray sources, ultrafast processes have become accessible for investigations. These sources will allow the study of materials on time scales comparable to the motion of electrons circling around atoms, on spatial scales of inter-atomic bonds, and on energy scales that hold electrons in correlated motion with their neighbors. Ultra-short electromagnetic radiation sources are a critical tool for studying material properties, with the ultimate outlook of recording femtosecond movies of atomic and chemical processes. The earliest x-ray sources were x-ray tubes. Even though their light output is of relatively low brightness, x-ray tubes have enabled numerous important discoveries. The laser was invented more than half century ago and has led to steep progress in the optical sciences. Similarly, the advent of dedicated synchrotron sources around 1970 has enabled enormous ad vances in the x-ray sciences. We are now witnessing the emergence of short-pulse high- intensity x-ray sources such as x-ray free-electron lasers (XFELs), high- harmonic generators, x-ray lasers, and laser-plasma sources. With these new sources we are at the dawn of a very exciting time in x-ray science. One can expect progress of similar grandeur as resulted from the introduction of lasers and synchrotrons. Reversible interaction mechanisms of x-rays with matter, such as elastic x-ray scattering, are often used to probe materials. Since these interactions are usually relatively weak, a large photon flux is required to obtain sufficiently intense probe signals. Since the absorption of x-rays is typically much stronger than the elastic scattering strength, high- intensity x-ray radiation also modifies the structure of materials. How x-rays can be used to probe and modify matter. We will now provide examples for the application of x-ray–matter interaction and discuss methods to produce x-ray radiation. X-rays and their application in diverse disciplines including life sciences, crystallography, atomic physics, plasma physics, materials science, chemistry, and astronomy. X-ray radiation can be prepared to have a high spectral purity, which is useful for x-ray spectroscopy, a very short pulse duration, which enables time-resolved studies, and high intensity, which can lead to nonlinear x-ray–matter interaction phenomena. X-ray astronomy has enabled detailed studies of supernovae, pulsars, and black holes. Since the Earth’s atmosphere is opaque to x-ray radiation, x-rays can only be observed from outer space.

 

Absorption of x-rays:

 

When the x-rays hit a sample, the oscillating electric field of the electromagnetic radiation interacts with the electrons bound in an atom. Either the radiation will be scattered by these electrons or absorbed and excite the electrons.

 

Fig: 3.3 Illustration of x-ray absorption

 

A narrow parallel monochromatic x-ray beam of intensity I0 passing through a sample of thickness x will get a reduced intensity I according to the expression:

 

 

where µ is the linear absorption coefficient, which depends on the types of atoms and the density of the material. At certain energies where the absorption increases drastically and gives rise to an absorption edge. Each such edge occurs when the energy of the incident photons is just sufficient to cause excitation of a core electron of the absorbing atom to a continuum state, i.e. to produce a photoelectron. Thus, the energies of the absorbed radiation at these edges correspond to the binding energies of electrons in the K, L, M, etc, shells of the absorbing elements. The absorption edges are labeled in the order of increasing energy, K, LI, LII, LI II, M etc. corresponding to the excitation of an electron from the 1s (2S1/2), 2s (2S1/2), 2p (2P1/2), 2p (2P3/2), 3s (2S1/2) orbital (states), respectively.

Fig: 3.4 Absorption lines from different orbitals and absorption edge in the spectrum

 

X-ray absorption edge:

 

An absorption edge by itself is of little value beyond elemental identification. However, if one examines any of the edges in Figure 3.4 in more detail, they are found to contain a wealth of information. This is illustrated by the schematic absorption edge shown in figure 3.5. The absorption edge is not simply a discontinuous increase in abso rption, as suggested by figure 3.4, but in fact shows significant structure both in the immediate vicinity of the edge jump and well above the edge. The structure in the vicinity of the edge is sometimes referred to as X-ray absorption near-edge structure (XANES). The oscillations above the edge, which can extend for 1,000 eV or more, are often referred to as extended X-ray absorption fine structure (EXAFS).

 

Fig: 3.5 Illustration of x-ray absorption edge

 

The distinction between XANES and EXAFS is arbitrary, since the same fundamental physical principles govern photo-absorption over the entire XAS region and there is ambiguous definition that distinguishes between ‘‘near-edge’’ and ‘‘extended’’ structure. In an attempt to emphasize the essential similarity of these regions, the term XAFS (X-ray absorption fine structure) has gained some currency as a reference to the entire structured absorption region. Nevertheless, the terms EXAFS a nd XANES remain the most widely used, with some justification, since the XANES and EXAFS regions are generally analyzed differently. The XANES region is sensitive to oxidation state and geometry, but is not, in most cases, analyzed quantitatively. The EXAFS region is sensitive to the radial distribution of electron density around the absorbing atom and is used for quantitative determination of bond length and coordination number.

 

X-ray fluorescence:

 

Absorption of an ionizing X-ray results in photoelectron ejection, leaving behind a highly excited core-hole state. This can relax by a variety of mechanisms, with the two most important being emission of an Auger electron and X-ray fluorescence. For lower-energy excitation, Auger emission can be the dominant relaxation process. For higher-energy excitation (e.g., for the K edges of elements with atomic numbers greater than 40), X-ray fluorescence is the primary relaxation process, with X-ray fluorescence yields approaching 1. For light elements, the X-ray fluorescence spectrum is quite simple. However, for heavy elements, a large number of X-ray emission lines are observed. The nomenclature associated with X-ray fluorescence lines predates a modern, quantum understanding of the origins of X-ray fluorescence and consequently there is not a simple relationship between the names of different emission lines and the origin of the line. Some of the possible emission lines are shown in figure 3.6. Like all emission spectroscopy, X-ray fluorescence is governed by a series of selection rules. Consequently, only certain transitions, referred to as ‘‘diagram lines,’’ are allowed. As with other spectroscopies, a variety of forbidden transitions (nondiagram lines) is also observed, and can yield important information. Each element has unique ‘‘characteristic’’ X-ray emission energies which are, in most cases, well resolved from neighboring emission lines.

 

Measure ment of x-ray absorption:

 

In the simplest case, measurement of an X-ray absorption spectrum involves only measurement of the incident and the transmitted X-ray flux. This can be accomplished, for example, with an

 

Fig: 3.6  Nomenclature for selected X-ray emission lines.

 

ionization chamber in front of and behind the sample, using eqn 1 to convert to absorption coefficient. This approach is limited to moderately concentrated samples (greater than 500 ppm) and, depending on the energy of the absorption edge, even these concentrations may not be accessible. For example, sulfur or chlorine containing solvents are nearly opaque to lower energy X-rays and thus interfere with XAS measurements. To avoid the limitations of absorption, XAS spectra are frequently measured as fluorescence excitation spectra. This is particularly important for dilute samples such as catalysts, biological samples, or environmental samples. The basic experimental geo metry is illustrated in Figure 2.7. Providing the sample is dilute (absorbance due to the element of interest is much smaller than the background absorbance) or thin (total absorbance), the intensity of the fluorescence X-rays is proportional to the X-ray absorption cross-section (see figure 3.7). In most cases, the sample will emit a variety of X-rays, both the fluorescence X-rays of interest and a background of scattered X-rays. In order to have good sensitivity, the fluorescence detector needs some kind of energy resolution to distinguish between the signals and background X-rays. In some cases, energy resolution can be provided by a simple low-pass filter although for the ultimate sensitivity it is necessary to use higher resolution in order to more effectively exclude background radiation. This is typically an energy-resolving solid-state fluorescence detector, although recent advances with wavelength resolving detectors (i.e., multilayer diffraction gratings) may be important in special cases. In principle, any physical property that changes in proportion to X-ray absorption could be used to measure XAS spectra. In addition to X-ray fluorescence, properties that have been used include photoconductivity, optical luminescence, and electron yield, although only the latter is widely used. Electron yield detection of XAS is particularly important for studies of surfaces. Since the penetration depth of an electron through matter is quite small, electron yield can be used to make XAS measurements surface sensitive. Although XAS can be studied for virtually any X-ray absorption edge, experiments are simplest.

 

 

Fig: 3.7 Typical experimental apparatus for XAS measure ments. Incident and transmitted intensities are typically measured using an ion chamber; a variety of detectors can be used to measure X-ray fluorescence intensity for dilute samples.

 

To avoid the limitations of absorption, XAS spectra are frequently measured as fluorescence excitation spectra. This is particularly important for dilute samples such as catalysts, biological samples, or environmental samples. The basic experimental geometry is illustrated in Figure 1.2.7 provided the sample is dilute or thin the intensity of the fluorescence X-rays is proportional to the X-ray absorption cross-section. In most cases, the sample will emit a variety of X-rays, both the fluorescence X-rays of interest and a background of scattered X-rays. In order to have good sensitivity, the fluorescenc e detector needs some kind of energy resolution to distinguish between the signals and background X-rays. In some cases, energy resolution can be provided by a simple low-pass filter although for the ultimate sensitivity it is necessary to use higher resolution in order to more effectively exclude background radiation. This is typically an energy-resolving solid-state fluorescence detector, although recent advances with wavelength resolving detectors may be important in special cases. In principle, any physical property that changes in proportion to X-ray absorption could be used to measure XAS spectra. In addition to X-ray fluorescence, properties that have been used include photoconductivity, optical luminescence, and electron yield, although only the latter is widely used. Electron yield detection of XAS is particularly important for studies of surfaces. Since the penetration depth of an electron through matter is quite small, electron yield can be used to make XAS measurements surface sensitive.

 

Although XAS can be studied for virtually any X-ray absorption edge, experiments are simplest when they can be performed at atmospheric pressure. This limits the accessible X-ray energies to those greater than approximately 5 keV (for air) or 2 keV (for a He atmosphere). Lower energy measurements (i.e., measurements of the K edges for elements lighter than phosphorus) require that the sample be in vacuum in order to avoid excessive attenuation of the incident X-ray beam. Similarly, it is difficult, although not impossible, to make XAS measurements at energies above approximately 30 ke. However, this does not limit XAS significantly, since elements that are heavy enough to have K edge energies >30 keV have readily accessible L edge energies (the L edge for Sn is at 4 keV). This means that XAS spectra can be measured for virtually every element, although measurements for elements lighter than phosphorus generally require that the sample be made vacuum compatible. X-ray absorption spectra can be measured for solids, liq uids, or gases and do not require that samples have long-range order (i.e., be crystalline) or that samples possess particular magnetic properties (e.g., nonzero electron spin or specific isotopes). Measurements can be made at low temperature for studies of unstable samples, or at high temperature and/or pressure, for example for studies of catalysts under reaction conditions or of geochemical samples under conditions that approximate the inner mantle. This flexibility, combined with near universality, has made XAS a widely utilized technique in all areas of coordination chemistry.

 

The critical experimental detail that limits the utility of XAS, and that accounts for XAS having been an obscure technique prior to about 1975, is the need for an intense, tunable X-ray source. Conventional X-ray sources work much the same as the X-ray tube that was invented by Rontgen: an electron beam strikes a target which emits both ‘‘characteristic’’ radiation (X-ray fluorescence lines) and a broad continuous background of bremsstrahlung radiation. Only the latter is useful for XAS, since XAS measurements require a broad band of X-ray energies. The intensity of monochromatic radiation that can be obtained from the bremsstrahlung radiation is too low for most XAS measurements.

    Value Addition:

 

Do You Know?

  1. Wilhelm Roentgen was already working on the effects of cathode rays during 1895, before he actually discovered X-rays. His experiments involved the passing of electric current through gases at extremely low pressure. On November 8, 1895 while he was experimenting, he observed that certain rays were emitted during the passing of the current through discharge tube. His experiment that involved working in a totally dark room with a well covered discharge tube resulted in the emission of rays which illuminated a barium platinocyanide covered screen. The screen became fluorescent even though it was placed in the path of the rays, two meters away from discharge tube.
  2. He continued his experiments using photographic plate to capture the image of various objects of random thickness placed in the path of the rays. He generated the very first “roentgenogram” by developing the image of his wife’s hand and analyzed the variable transparency as showed by her bones, flesh and her wedding ring. Based on his subsequent research and experiments, he declared that X-ray beams are produced by the impact of cathode rays on material objects.
  3. His discovery revolutionized the entire medical profession and set foundation for diagnostic radiology. In 1901, Roentgen received the first ever Nobel Prize in Physics. This was a true acknowledgement of his remarkable discovery which was going to be highly beneficial for mankind in the coming years.

    4. Suggested Reading

 

For More Details (on this topic and othe r topics discussed in Text Module) See

  1. Neil W. Ashcroft and N. David Mermin, Solid State Physics, Thomson Brooks/Cole, Eastern Press Bangalore (India) 2005
  2. Charles Kittel, Introduction to Solid State Physics, John Wiley & Sons, Singapore 1999
  3. X-ray Absorption Spectroscopy, J. E. Penner-hahn, MI, USA Page 159-186)

    Glossary:

 

Inelastic Scatte ring:

 

When a particle of radiation shares energy with the matter in the scattering process it is called inelastic scattering. The outgoing particle may come out with less or more energy than its initial energy.

    XAS: X-ray absorption spectroscopy

 

XANES: X-ray absorption near edge structure

 

EXAFS: Extended x-ray absorption fine structure

 

Fluorescence:

 

When a high energy radiation interact with matter with a process of collision, it excites atoms and molecules to higher energy state. On de-excitation, the matter emits radiation which has lower energy than the incident quanta of radiation.