An interesting web site with information about generating X rays was prepared by Grzegorz Jezierski

X Ray Generation

Introduction

X-Ray photons are electromagnetic radiation with wavelengths in the range 0.1 - 100 Å. X Rays used in diffraction experiments have typical wavelengths of 0.5 - 1.8 Å. X Rays can be produced by conventional generators, by synchrotrons, and by plasma sources. Electromagnetic radiation from nuclear reactions, called γ radiation, can also occur at the same energies as X rays, but γ radiation is differentiated from X ray radiation simply by the source of the radiation.

X rays are sometimes called Röntgen rays after their discoverer, Wilhelm Conrad Röntgen.¹ For this discovery, he received the first Nobel Prize in physics in 1901.

A great deal of information about the properties of X rays and X-ray generation is available at the X-Ray Data Book. Electromagnetic radiation is made up of waves of energy that contain electric and magnetic fields vibrating transversely and sinusoidally to each other and to the direction of propogation of the waves. Conventional generators are by far the most widely used sources of X rays in a laboratory setting.

Conventional Generators

X Rays are produced in labs by directing an energetic beam of particles or radiation, at a target material. X Rays for crystallographic studies are typically generated by bombarding a metal target with an energetic beam of electrons. The electrons are produced by heating a metal filament, emitting photo electrons. The electrons coming from the filament are then accelerated towards the target by a large applied electrical potential between the filament and the target. When the beam of electrons hits the target (or anode) a variety of events occur. This rapid deceleration of electrons causes the emission of X-ray radiation, photoelectrons, Auger electrons, and a large amount of heat. Actually two types of X rays are emitted in this process. X Rays are emitted in a continuous band of white radiation as well as a series of discrete lines that are characteristic of the target material.

Figure 1. X-ray Tube Schematic.²

White Radiation

Some of the collisions between the photo-electrons and the target result in the emission of a continuous spectrum of X rays called white radiaion or Bremsstrahlung. White radiation is believed due to the collision of the accelerated electrons with the atomic electrons of the target atoms. If all of the kinetic energy carried by an electron is converted into radiation, the energy of the X-ray photon would be given by

E_max = hν_max= eV

where h = Plank's constant, ν_max = the largest frequency, e = charge of an electron, V = applied voltage. This maximum energy or minimum wavelength is called the Duane-Hunt limit.

hν_max = hc/λ_min = eV

λ_min = hc / eV = 12398. / V (volts)

X-Ray White Radiation curves at
different applied voltages

Figure 2. White Radiation from an X-Ray Generator.² The intensity of the beam is plotted as a function of the wavelength of the radiation.

The majority of collisions that produce white radiation do not completely dissipate the kinetic energy of the electron in a single collision. Typically, these colliding electrons hit electrons in the target material with a glancing blow dissipating some energy as emitted X-ray photons. Then these photoelectrons hit other electrons in the target material emitting lower energy X-ray photons or hit valence electrons producing heat.

Thus the white radiation spectrum does have a minimum wavelength or maximum energy related to the kinetic energy of the incident radiation beam, and continues to longer wavelengths or lower energies until all of the kinetic energy is absorbed. The highest intensity of emitted white radiation spectrum is obtained at a wavelength that is about 1.5 time the minimum wavelength. The white radiation intensity curve may be fit to an expression of the form:

I_w = A i Z Vⁿ, n ~ 2

where i is the applied current, Z is the atomic number of the target, V is the applied voltage and A is a proportionality constant. The only type of diffraction experiment that uses white radiation is the Laue experiment.

Characteristic Radiation

When the energy of the electron beam is above a certain threshold value, called the excitation potential, an additional set of discrete peaks is observed superimposed on the white radiation curve. The energies of these peaks are characteristic of the type of target material.

These peaks are generated by a two-stage process. First an electron from the filament collides with and removes a core electron from an atom of the target. Then an electron in a higher energy state "drops down" to fill the lower energy, vacant hole in the atom's structure, emitting an X-ray photon. These emitted X-ray photons have energies that are equal to the difference between the upper and lower energy levels of the electron that filled the core hole. The excitation potential for a material is the minimum energy needed to remove the core electron.

Figure 3. Characteristic radiation from an X-ray generator.²

The characteristic lines in an atom's emission spectra are called K, L, M, ... and correspond to the n = 1, 2, 3, ... quantum levels of the electron energy states, respectively. When the two atomic energy levels differ by only one quantum level then the transitions are described as α lines (n = 2 to n = 1, or n = 3 to n = 2). When the two levels are separated by one or more quantum levels, the transitions are known as β lines (n = 3 to n = 1 or n = 4 to n = 2).

Figure 4. Electronic energy levels of an atom of the anode.²

Because all K lines (n = 1) arise from a loss of electrons in the n = 1 state, the Kα and Kβ lines always appear at the same time. The n = 2 and higher energy levels (L, M, N, O) are actually split into multiple energy levels causing the α and β transitions to split into a variety of closely spaced lines at high resolution. Thus, the observed Cu Kα line can be resolved at high scattering angle (high resolution) into Kα₁ and Kα₂ lines with separate wavelengths. The Kα₁ line is about twice as intense as the Kα₂ line. At low resolution (lower scattering angle) the Kα wavelength is considered as a weighted average of the Kα₁ and Kα₂ lines with λ(Kα_ave) = [2*(λ(Kα₁)) + λ(Kα₂)]/3. The Kα line is about 5 - 10 times as intense as the Kβ line.

The intensity of the Kα line can be approximately calculated by

I_k = B i (V - V_k)^1.5

where i = applied current, V_k = excitation potential of the target material, V = applied voltage. It can be shown that the ratio I_k / I_w is a maximum if the accelerating voltage is chosen to be about 4 times the excitation potential of the anode.

The wavelengths of characteristic X-ray lines were found to be inversely related to the atomic number of the atoms of the target material. Moseley found that

√(f) = K₁ [Z - σ]

where f is the frequency of the radiation, K₁ is a proportionality constant, Z is the atomic number of the target atom type, and σ is the shielding constant that typically has a value of just less than 1. Today this formula is more typically recast as

1/λ = K₂ [Z - σ]²

where λ is the wavelength of the radiation, K₂ is a proportionality constant, Z is the atomic number of the target atoms, and σ is the shielding constant.

The notation for describing the characteristic X-ray lines shown above was first presented by Siegbahn. In 1991, the International Union of Pure and Applied Chemists (IUPAC) recommended that X-ray lines be referred to by writing the initial and final levels separated by a hyphen, e.g. Cu K- L₃, rather than using the Siegbahn notation, e.g. Cu Kα₁, which is based on the relative intensities of the lines.³ A table of the correspondence between IUPAC and Siegbahn notations is given in the "International Tables for Crystallography," Vol. C.⁴ The Siegbahn notation remains common in the chemical and crystallographic literature.

The shape of the incident beam depends on the focal projection of the filament onto and the anode material. X-Ray beams that are parallel with wide projection of the filament have a focal shape of a line. X-Ray beams that are parallel with the narrow projection of the filament have an approximate focal shape of a square, which is usually labeled as a spot. These two focal projections are necessarily about 90 ° apart in the plane normal to the filament-anode axis. The X-ray beams emitted from the anode travel in a variety of angular directions from the anode surface. As the angle from the anode surface is increased, the intensity of the beam increases, but the spot also becomes less focused. Thus take-off angles are typically selected in the 3 - 6 ° range.

Two cartoons of an X-ray tube. Drawing a) shows the line and spot focus patterns of a typical sealed tube. Drawing b) shows the take-off angle of a tube.

The generation of X rays is very inefficient. In addition to white radiation and characteristic lines, laboratory sources also produce Auger electrons and photo-electrons. However, the vast majority of the power used in generating X rays results in the collision of accelerated electrons with valence electrons of the target material producing heat. A small fraction of the energy applied to the tube actually produces the characteristic radiation used in diffraction experiments.

Sealed-tube X-ray generators use a stationary anode. These tubes are limited in the power that can be applied to the tube by the amount of heat that can be dissipated through water cooling. One way to increase the heat dissipating ability of the system, and thus increase the X-ray beam intensity, is to move or rotate the anode surface so that the beam of electrons continually hits a new region of the anode. These rotating-anode generators typically yield about 5 times the flux of X-rays as is routinely produced by sealed-tube generators with normal-focus X-ray tubes.

Because macromolecular crystallographers need the most intense beam available, they typically use rotating-anode X-ray generators. Rotating-anode generators require a considerable amount of maintenance to replace filaments, and repair or replace the anode bearings as well as vacuum and water seals. To keep from burning the filament, it must remain in a high vacuum. The anode with its constant flow of cooling water must be continuously rotating at speeds of 6000 rpm or more. Special ferro-fluidic seals are used to maintain the vacuum along the rotating shaft of the anode. Sealed-tube sources with their minimal maintenance requirements are generally quite adequate for most small molecule needs.

Another type of sealed-tube source that produces beam fluxes comparable to rotating-anode systems is a micro-focus generator. Because heat dissipates rather quickly in a metal block, manufacturers have found that when the focal size is reduced to 10-300 μm then the power can be increased to make the beam flux much higher than for normal- or even fine-focus sealed tube sources. One of the great advantages of a micro-focus radiation source is that the electrical power needs are in the range of 30-80 Watts not the 2-3 kWatts that are required of a typical sealed tube generator, or the 3-12 kWatts required by a rotating anode generator.

Other Sources

There are other sources of X-ray photons that have special applications in the laboratory. Synchrotrons produce the highest flux sources available. Unfortunately, because synchrotrons are very expensive to build and maintain, there are few such sources available throughout the world. Web links to many of the world's synchrotrons are listed on the links page.

Certain radioactive materials decay to produce photons with energies in the X-ray region (e.g., ⁵⁵Fe). The flux of photons of this radioactive material is so low that it is not used as a source of X-rays for diffraction experiments. However, small samples of ⁵⁵Fe are often used to test the functioning of X-ray detectors.

A new method of generating X rays that is not yet commercially available uses an electron-impact beam impinging on a stream of liquid gallium.⁵ These authors have already reported achieving beam fluxes greater that modern rotating anodes, with the theoretical capability of increasing this flux by another 3 orders of magnitude.

As a side note, X rays may also be produced by very different means, for example, when doing such simple tasks as unrolling adhesive tape from a tape dispenser. Tribologists found that low energy X rays were emitted even when unrolling the tape at rather slow rates of a few centimeters per second.⁶

Choice of Radiation

Most X-ray tubes used for diffraction studies have targets (anodes) made of copper or molybdenum metal. The characteristic wavelengths and excitation potentials for these materials are shown below. Copper radiation is preferred when the crystals are small or when the unit cells are large. Copper radiation (or softer) is required when the absolute configuration of a compound is needed and the compound only contains atoms with atomic numbers & 10. A copper source is preferred for most types of powder diffraction.

Molybdenum radiation is preferred for larger crystals of strongly absorbing materials and for very high resolution, sin (θ) / λ < 0.6 Å, data. The scintillation point detectors, often used in small molecule diffraction, have somewhat higher quantum efficiencies for molybdenum radiation than for copper radiation. Because the diffraction spots are closer together for molybdenum radiation than for copper radiation, molybdenum is the preferred radiation source when using area detectors to study small molecules. The solid angle coverage of most area detectors is such that with molybdenum radiation, it is usually possible to collect an entire data set with the detector sitting at a single position. However, because a brighter incident beam of X-rays is produced from a copper tube than from a molybdenum tube at the same power level, very small crystals of even strongly absorbing materials will often yield better diffracted intensities from copper radiation than from molybdenum radiation.

Occasionally, other types of target materials, e.g. Cr, Fe, W, or Ag, are chosen for specialized diffraction experiments. Sources with Cr or Fe targets are often chosen when protein crystals are very small or when anomalous differences need to be enhanced. When samples are very strongly absorbing or when extremely high resolution data are needed then X-ray tubes with sources such as W or Ag are usually selected.

Table 1. Selected X-Ray Wavelengths and Excitation Potentials.
	Cr	Fe	Cu	Mo
Z	24	26	29	42
Kα₁, Å	2.28962	1.93597	1.54051	0.70932
Kα₂, Å	2.29351	1.93991	1.54433	0.71354
Kα_ave, Å	2.29092	1.93728	1.54178	0.71073
Kβ, Å	2.08480	1.75653	1.39217	0.63225
β filter	Ti	Cr	Ni	Nb
Resolution, Å	1.15	0.95	0.75	0.35
Excit. Pot. (kV)	5.99	7.11	8.98	20.0

Monochromatization and Collimation of X Rays

Nearly all of the data collection experiments require that the energy of the X-ray radiation be limited to as narrow a band of energies (and hence wavelengths) as possible. Using a narrow wavelength band of X rays significantly reduces the fluorescent radiation given off by the sample and makes absorption corrections much simpler to perform. It has been noted that when the applied voltage for K excitation occurs, both the Kα and Kβ lines as well as the white radiation curve are observed. Usually the Kα band is selected for diffraction experiments because of its greater intensity.

Also, typical data collection methods require that the incident beam be a parallel beam of photons. To assure that the beam is as parallel as possible (lacking divergence), the incident beam path is collimated to produce an incident beam that is about 0.5 mm in diameter.

Filters

When the energy of a photon beam is just above the excitation potential or absorption edge of a material, that material strongly absorbs the given photon beam. If another substance can be found that has an absorption edge between the Kα and Kβ lines of the incident photon beam, this other substance can be used to significantly reduce the intensity of the Kβ line relative to the Kα line. The absorption edges of elements with Z_Filter = Z_Target - 1 (or - 2) meet this requirement. The thickness of the filtering material is usually chosen to reduce the intensity of the Kβ line by a factor of 100 while reducing the intensity of the Kα line by a factor of 10 or less.

The absorption of X rays follows Beer's Law:

I / I^o = exp(-μ × t)

where I = transmitted intensity, I^o = incident intensity, t = thickness of material, μ = linear absorption coefficient of the material. The linear absorption coefficient depends on the substance, its density, and the wavelength of radiation. Since μ depends on the density of the absorbing material, it is usually tabulated as the mass absorption coefficient μ_m = μ / ρ.

Monochromators

An alternative way to produce an X-ray beam with a narrow wavelength distribution is to diffract the incident beam from a single crystal of known lattice dimensions. X-Ray photons of different wavelengths are diffracted from a given set of planes in a crystal at different scattering angles according to Bragg's Law. Therefore a narrow band of wavelengths can be chosen by selecting a particular scattering angle for the monochromator crystal. Crystal monochromators need to have the following properties.

The crystal must be mechanically strong and stable in the X-ray beam.
The crystal must have a strong diffracted intensity at a reasonably low scattering angle for the wavelength of the radiation being considered.
The mosaicity of the crystal, which determines the divergence of the diffracted beam and the resolution of the crystal, should be small.

A variety of geometries are possible for crystal monochromators. Most monochromators are cut with one face parallel to a major set of crystal planes. These monochromators are then oriented to diffract Kα lines from this major set of planes. Some monochromators are cut at an angle to the major set of planes in order to produce a diffracted beam with a smaller divergence. By properly curving the monochromator crystal, the diffracted beam may be focused onto a very small area. This curving may be achieved either by bending or grinding or both bending and grinding. Curved monochromators are usually reserved for special applications such synchrotrons.

Graphite crystals cut on the (0002) face are the most common crystals used as monochromators in X-ray diffraction laboratories. Other special purpose monochromator materials include germanium and lithium fluoride. In all commercially available single-crystal instruments, the monochromator is placed in the incident beam path. Powder diffraction instruments with a point detector typically place a monochromator in the diffracted beam path to remove any fluorescent radiation from the sample. Crystal monochromators systematically alter the polarization of the incident beam, requiring different geometric corrections be applied to the intensity data.

Collimators

Collimators are objects inserted in the incident- or diffracted-beam path to shape the X-ray beam. Metal tubes are typically used in single-crystal experiments. The inside radius of the collimators is typically chosen to be somewhat larger than the size of the sample so that the sample may be bathed in the incident beam at all times. Incident-beam collimators are usually manufactured with two narrow regions. The region closest to the X-ray source carries out the collimation functions. The second narrow region has a slightly larger diameter than the first and is used to remove the "parasitic" radiation that takes a bent path due to interaction with the edge of the first narrow region of the collimator. Diffracted beam collimators only function to remove any stray radiation from hitting the detector.

The left end of the collimator shown is mounted on the X-ray tube (or incident beam monochormator). The small yellow-colored region at the left is the part of the collimator where the size of the beam is determined. The green region at the right is chosen to have an opening slightly larger than the region drawn in yellow. This green region removes the "parasitic" radiation.

Recently, manufacturers have been selling metal collimators with a single or multiple glass capillaries. These glass capillaries redirect much of the X-ray beam that would otherwise be blocked by the collimator. Such capillary inserts in a collimator have been shown to increase the intensity of the incident beam by a factor of between two and four.

When a very intense and very small point source is needed, such as in protein crystallography, X-ray mirrors may be used to shape the incident beam. Mirrors are sometimes made from materials that act as beta filters for the radiation in use. Mirrors are primarily used with very bright X-ray sources such as rotating-anode generators or synchrotrons.

Powder diffraction experiments usually require a line-shaped incident beam that is produced from a pair of parallel knife edges. A set of Soller slits are used in the beam path after the knife edges to remove parasitic radiation that scatters from the edges of the blades. Soller slits are a set of parallel thin foil sheets that absorb nearly all of the X rays not traveling parallel to the metal sheets.

X-ray mirrors are sometimes used in the incident beam to shape the beam as is done by a collimator. Even with Cu radiation, the spots in protein diffraction patterns are often very close together. The mirrors act to focus the incident beam into an very small cross section producing very sharp spots in the diffraction pattern. Mirrors are often constructed to absorb more of the Kβ radiation than the Kα radiation making the beam approximately monochromatic. Monochromators significantly reduce the intensity of the incident beam; omitting the monochromator maximizes the incident beam flux. Macromolecular structures are crystalline to only low resolution. The Kβ and Kα peaks are generally not separated at these low scattering angles.

References

Wilhelm Conrad Röntgen, "Über eine neue Art von Strahlen" (On a New Kind of Rays) presented to the Würzburg Physical and Medical Society, 1895. Translated by Arthur Stanton, Nature, 1896, 53, 274-276.
Michael Liang, 1997, "An Introduction to the Scope, Potential and Applications of X-ray Analysis" in International Union of Crystallographers Teaching Pamphlets available at: http://www.iucr.org/education/pamphlets.
R. Jenkins, R. Manne, J. Robin, & C. Senemaud, Pure and Appl. Chem., 1991, 63, 735-746.
"International Tables for Crystallography, Vol. C," 1995 Kluwer: Boston, p 167.
M. Otendal, T. Tuohimaa, U. Vogt, and H. M. Hertz, A 9 keV electron-impact liquid-gallium-jet x-ray source., Rev. of Sci. Inst., 2008, 79, 016102-3. doi: 10.1063/1.2833838
C. G. Camara, J. V. Escobar, J. R. Hird, and S. J. Putterman, Correlation between nanosecond X-ray flashes and stick-slip friction in peeling tape. Nature, 2008, 455, 1089-1092. doi: 10.1038/nature07378

Dept. of Chemistry & Biochemistry | University of Oklahoma

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Last modified May 16, 2011
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