X-rays Can Be Produced in Transitions Involving Inner Electrons in an Atom.

An interesting spider web site with information near generating 10 rays was prepared by Grzegorz Jezierski

X Ray Generation

Introduction

X-Ray photons are electromagnetic radiation with wavelengths typically in the range 0.1 - 100 Å. Ten Rays used in diffraction experiments have wavelengths of 0.v - 1.eight Å. Ten Rays can exist produced by conventional generators, by synchrotrons, and by plasma sources. Electromagnetic radiations from nuclear reactions, called γ radiation, can as well occur at the aforementioned energies as X rays, merely γ radiation is differentiated from 10 ray radiation by the fact that it originates from nuclear reactions.

X rays are sometimes called Röntgen rays after their discoverer, Wilhelm Conrad Röntgen.¹ He chosen these new rays Ten rays afterward the unknown quantity Ten in mathematics. These new rays had no accuse, and were much more penetrating than cathode rays discovered by Johann Hittorf in 1876. 10 Rays were able to laissez passer through a variety of objects. X rays could expose film. R&oml;ntgen institute that X rays could pass through the tissues of a living person and illustrate the bones and other tissues in the body. For this discovery he was awarded the Nobel Prize in physics in 1901.

Röntgen wanted to decide whether X rays were particles or waves. At the time it was known that waves were involved if a stream could be shown to exhibit reflection, refraction, or diffraction. Unfortunately, Röntgen was non able to verify whatsoever of these properties of X rays.

From slit measurements, the wavelength of Ten rays were calculated to exist on the order of Angstroms. Diffraction can occur when radiation is scattered off of an object with a echo spacing of approximately the same size as the wavelength of the radiation. Thus, Laue looked for an object with a repeat spacing on the order of Angstroms. Another quick calculation showed that crystals could have the needed lattice spacings. Forth with Friedrich and Knipping, Laue showed that X rays could be diffracted by a crystal of zinc blende.

A smashing bargain of information well-nigh the properties of X rays and X-ray generation is available at the X-Ray Information Book. Electromagnetic radiation is made up of waves of free energy that contain electric and magnetic fields vibrating transversely and sinusoidally to each other and to the management of propogation of the waves.

This graphic representation of an electromagnetic wave, showing its associated electrical (E) and magnetic (H) fields, moving forwards at the speed of light. (Copied from the CSIC web site.)

Conventional Generators

10 Rays are produced in labs by directing an energetic beam of particles or radiation, at a target textile. The energetic axle can exist electrons, protons, or other X rays. X Rays for crystallographic studies are typically generated past bombarding a metal target with an energetic axle of electrons. The electrons are usually produced by heating a metal filament which and then emits electrons. The electrons coming from the filament are then accelerated towards the target by a big applied electric potential between the filament and the target.

When the axle of electrons hits the target (or anode) a multifariousness of events occur. This rapid deceleration of electrons causes a variety of events including the emission of X-ray radiation, photoelectrons, Auger electrons, and a large corporeality of heat. Really 2 types of X rays are emitted in this process. A continuous band of white radiation is e'er emitted. If the free energy of the electron axle is sufficient and then a series of intense, detached lines that are characteristic of the target material are likewise observed.

Figure 1. X-ray Tube Schematic.²

White Radiations - Bremsstrahlung

Some of the collisions between the thermionic electrons and the target result in the emission of a continuous spectrum of X rays called white radiations or Bremsstrahlung. White radiation is believed due to the standoff of the accelerated electrons with the atomic nuclei 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. / Five (volts)

X-Ray White Radiation curves at different applied voltages

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

The majority of collisions that produce white radiation do non 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 every bit emitted 10-ray photons. Then these photoelectrons hit other electrons in the target material emitting lower energy Ten-ray photons or hit valence electrons producing heat.

Thus the white radiation spectrum does take a minimum wavelength or maximum free energy related to the kinetic energy of the incident radiations beam, and continues to longer wavelengths or lower energies until all of the kinetic free energy is absorbed. The highest intensity of emitted white radiations spectrum is obtained at a wavelength that is most 1.five time the minimum wavelength. The white radiation intensity curve may exist fit to an expression of the course:

I_{due west} = A i Z Vⁿ, northward ~ ii

where i is the applied electric current, Z is the atomic number of the target, 5 is the practical voltage and A is a proportionality abiding. The only type of diffraction experiment that uses white radiation is the Laue experiment.

Feature Radiation

When the energy of the electron beam is above a sure threshold value, chosen the excitation potential, an boosted 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 procedure. First an electron from the filament collides with and removes a core electron from an atom of the target. Then an electron in a college energy country drops down to fill the lower energy, vacant pigsty in the atom's structure, emitting an X-ray photon. These emitted Ten-ray photons have energies that are equal to the difference between the upper and lower energy levels of the electron that filled the cadre hole. The excitation potential for a cloth is the minimum energy needed to remove the core electron.

Effigy three. Feature radiation from an X-ray generator.²

The characteristic lines in an cantlet's emission spectra are called Yard, L, Thou, ... and correspond to the n = 1, 2, 3, ... quantum levels of the electron energy states, respectively. When the two diminutive energy levels differ by only ane quantum level then the transitions are described as α lines (north = two to n = 1, or n = 3 to n = 2). When the 2 levels are separated by 1 or more breakthrough levels, the transitions are known as β lines (n = 3 to n = 1 or north = four to northward = 2).

Figure iv. Electronic energy levels of an atom of the anode.

Considering 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 fourth dimension. The n = 2 and college energy levels (Fifty, Thousand, N, O) are actually divide into multiple energy levels causing the α and β transitions to split into a variety of closely spaced lines at loftier resolution. Thus, the observed Cu Thousandα line can be resolved at high scattering angle (high resolution) into One thousandα₁ and Kα_two lines with separate wavelengths. The 1000α₁ line is about twice as intense as the Yardα_two line. At low resolution (lower scattering bending) the Yardα wavelength is considered as a weighted average of the Thousandα_ane and Kα_two lines with λ(Grandα_ave) = [2*(λ(Kα_ane)) + λ(Kα₂)]/iii. The Kα line is nearly v - 10 times every bit intense equally the Grandβ line.

The intensity of the Kα line can exist approximately calculated by

I_grand = B i (Five - 5_thousand)^i.5

where i = practical electric current, 5_{one thousand} = excitation potential of the target material, Five = applied voltage. It can exist shown that the ratio I_chiliad / I_w is a maximum if the accelerating voltage is chosen to exist about 4 times the excitation potential of the anode.

The wavelengths of feature X-ray lines were establish to exist inversely related to the diminutive number of the atoms of the target fabric. Moseley found that

√(f) = K₁ [Z - σ]

where f is the frequency of the radiation, One thousand₁ is a proportionality abiding, Z is the diminutive number of the target cantlet type, and σ is the shielding constant that typically has a value of just less than one. Today this formula is more typically recast as

one/λ = K₂ [Z - σ]²

where λ is the wavelength of the radiations, K_two 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 Ten-ray lines shown above was first presented past 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 concluding levels separated past a hyphen, e.g. Cu Chiliad- L ₃, rather than using the Siegbahn notation, eastward.1000. Cu Kα₁, which is based on the relative intensities of the lines.^three 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 mutual in the chemic and crystallographic literature.

The shape of the incident beam depends on the focal projection of the filament onto and the anode textile. 10-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 project of the filament accept an approximate focal shape of a square, which is usually labeled equally a spot. These two focal projections are necessarily near 90 ° autonomously 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 as well becomes less focused. Thus take-off angles are typically selected in the 3 - 6 ° range.

Two cartoons of an X-ray tube. Cartoon 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 10 rays is very inefficient. In addition to white radiation and characteristic lines, laboratory sources too produce Auger electrons and photo-electrons. Withal, the vast majority of the power used in generating 10 rays results in the collision of accelerated electrons with valence electrons of the target material producing estrus. A small fraction of the energy practical to the tube really produces the characteristic radiation used in diffraction experiments.

Sealed-tube X-ray generators use a stationary anode. These tubes are express in the power that can be applied to the tube past the amount of rut that can exist dissipated through water cooling. 1 way to increase the estrus dissipating power of the system, and thus increase the Ten-ray axle intensity, is to move or rotate the anode surface and 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 10-rays equally is routinely produced past sealed-tube generators with normal-focus X-ray tubes.

Considering macromolecular crystallographers demand the most intense axle available, they typically apply rotating-anode 10-ray generators. Rotating-anode generators require a considerable amount of maintenance to replace filaments, and repair or replace the anode bearings as well equally 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 acceptable for most small-scale 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 cake, manufacturers have found that when the focal size is reduced to x-300 μm then the power can be increased to brand the beam flux much higher than for normal- or fifty-fifty fine-focus sealed tube sources. 1 of the not bad advantages of a micro-focus radiations source is that the electrical power needs are in the range of 30-80 Watts not the ii-3 kWatts that are required of a typical sealed tube generator, or the 3-12 kWatts required by a rotating anode generator.

Other Sources

Synchrotron Radiation Sources

In 1943, Dmitri Ivanenko and Isaak Pomeranchuk predicted that electrons traveling at relativistic speeds when directed through a magnetic field would emit radiations. This prediction was observed in the lab in 1946 by scientists at GE. A synchrotron radiations source is a very intense, tunable source of radiation with wavelengths from difficult X-rays through visible moving ridge, to microwaves. Considering it is so costly to maintain big quantities of electrons traveling at near the speed of light in a high vacuum storage band, few of these radiations sources are congenital.

To make the best use of this type of radiation, synchrotrons are shaped roughly as rings with ports that emit the photons located at near each bend of the ring. The radiations from each of these ports is and so directed to 1 or more experimental chambers. Synchrotron radiation is used in crystallography to collect data on biological macromolecules, on tiny small-molecule unmarried crystals, and on various polycrystalline materials. In add-on, synchrotron radiation in X-ray energies is used in a variety of scattering and absorption studies likewise equally a multitude of physics experiments. Aside from the very loftier flux, synchrotron radiation likewise has the added do good of existence tunable to a specific wavelength.

In most synchrotrons, electrons are generated by an electron gun, then accelerated starting time past a linear accelerator, linac, then transferred to a booster band where they are accelerated by resonating rf cavities until the energies are 3-6 Gev and the speeds of the electrons are near the speed of light. These electrons are and so directed into the main storage ring. When radiations is emitted, the electrons loose free energy. The electrons are reenergized by resonating rf cavities located in the straight parts of the storage ring.

Two types insertion devices, devices to send radiations beams towards an instrument, are used in the straight parts of the storage ring to heave the flux of radiations. Wigglers are a series of electromagnetic plates with opposite accuse. Undulators are similar to wigglers with lower energy practical to the plates, only the plates are spaced to give optimum intensity to particular wavelengths and their harmonics.

Fluid Anodes

The main trouble limiting brightness in laboratory-based X-ray sources is the removal of heat. A new type of X ray source, that offers a novel solution to this problem, uses a liquid metal, gallium anode.⁵ The scientists that developed this source accept already reported achieving axle brightnesses greater that modern rotating anodes, with the theoretical capability of increasing this flux by another three orders of magnitude. A Swedish company, Excillum, is currently producing these sources.

Carbon-Nanotube Cathodes

A new blazon of tube that utilizes carbon nanotubes as the cathode are near likely to be developed as portable and miniature X-ray sources.⁶ As of this writing, these sources are not commercially bachelor.

Medical X Rays

X Rays for medical apply are generally produced by one of two methods. Diagnostic X rays for examining bones and teeth are usually produced by sealed tube equipment with a tungsten target. 10 Rays for CT (computed tomography) scans and radiation therapy are produced past a linear accelerator, linac. Electrons from an electron gun are accelerated through the linac by a series of charge plates. These electrons then collide with a target giving off Bremsstrahlung. The medical X rays from sealed tube equipment take typical energies of 50-80 kev. The 10 rays from CT or tomography equipment typically have energies around iv-8 Mev.

Choice of Radiations

Most X-ray tubes used for diffraction studies have targets (anodes) made of copper or molybdenum metal. The feature wavelengths and excitation potentials for these materials are shown below. Copper radiation is preferred when the crystals are small-scale or when the unit cells are large. Copper radiation (or softer) is required when the accented configuration of a compound is needed and the compound but contains atoms with atomic numbers < 10. A copper source is preferred for most types of powder diffraction. Chromium anodes are sometimes used to enhance anomalous scattering furnishings for some macromolecular samples.

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 bespeak detectors, often used in small molecule diffraction, take somewhat higher breakthrough 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 near 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 10-rays is produced from a copper tube than from a molybdenum tube at the same power level, very modest crystals of even strongly absorbing materials will oft yield ameliorate diffracted intensities from copper radiations than from molybdenum radiations.

Occasionally, other types of target materials, due east.g. Cr, Iron, W, or Ag, are called for specialized diffraction experiments. Sources with Cr or Fe targets are often called when protein crystals are very small or when dissonant differences need to be enhanced. When samples are very strongly absorbing or when extremely high resolution data are needed and so X-ray tubes with sources such as W or Ag are commonly selected.

Table ane. 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	ane.54433	0.71354
Grandα_ave, Å	2.29092	ane.93728	1.54178	0.71073
Kβ, Å	two.08480	one.75653	one.39217	0.63225
β filter	Ti	Cr	Ni	Nb
Resolution, Å	1.15	0.95	0.75	0.35
Excit. Pot. (kV)	5.99	vii.xi	8.98	20.0

Monochromatization and Collimation of X Rays

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

Also, typical data collection methods crave that the incident beam be a parallel beam of photons. To assure that the beam is as parallel as possible (lacking divergence), the incident axle path is collimated to produce an incident beam that is about 0.five mm in diameter for normal focus sources and 0.1-0.3 mm for micro focus sources.

Filters

When the free energy of a photon beam is simply above the excitation potential or absorption border of a material, that fabric strongly absorbs the given photon beam. If another substance can be institute that has an assimilation border between the Kα and Gβ lines of the incident photon axle, this other substance tin can be used to significantly reduce the intensity of the Kβ line relative to the Thouα line. The absorption edges of elements with Z_Filter = Z_Target - 1 (or - 2) encounter this requirement. The thickness of the filtering material is usually chosen to reduce the intensity of the Kβ line past a factor of 100 while reducing the intensity of the Kα line by a cistron of ten 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 normally tabulated as the mass absorption coefficient μ_m = μ / ρ.

Monochromators

An alternative way to produce an X-ray axle with a narrow wavelength distribution is to diffract the incident axle 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'southward 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 stiff and stable in the X-ray beam.
The crystal must have a stiff diffracted intensity at a reasonably depression handful 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 so oriented to diffract Kα lines from this major set up 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 departure. By properly curving the monochromator crystal, the diffracted beam may exist focused onto a very small area. This curving may be accomplished either past bending or grinding or both bending and grinding. Curved monochromators are ordinarily reserved for special applications such synchrotrons.

Graphite crystals cut on the (0002) face are the most common crystals used as monochromators in Ten-ray diffraction laboratories. Other special purpose monochromator materials include germanium and lithium fluoride. In all commercially available unmarried-crystal instruments, the monochromator is placed in the incident beam path. Powder diffraction instruments with a indicate 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 exist bathed in the incident beam at all times. Incident-axle collimators are usually manufactured with two narrow regions. The region closest to the X-ray source carries out the collimation functions. The 2d narrow region has a slightly larger diameter than the showtime 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 role to remove any stray radiation from hit the detector.

The left stop of the collimator shown is mounted on the Ten-ray tube (or incident beam monochormator). The minor yellow-colored region at the left is the function of the collimator where the size of the beam is determined. The greenish region at the right is chosen to accept an opening slightly larger than the region fatigued in yellow. This green region removes the parasitic radiations.

Recently, manufacturers have been selling metallic collimators with a single or multiple glass capillaries. These glass capillaries redirect much of the Ten-ray beam that would otherwise exist 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 iv.

When a very intense and very modest point source is needed, such as in protein crystallography, 10-ray mirrors may be used to shape the incident beam. Mirrors are sometimes made from materials that human action every bit beta filters for the radiations in use. Mirrors are primarily used with very brilliant 10-ray sources such as rotating-anode generators or synchrotrons.

Mirrors

10-ray mirrors are sometimes used in the incident axle to shape the beam as is done past a collimator. Even with Cu radiation, the spots in protein diffraction patterns are frequently very shut 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 Mα radiation making the beam approximately monochromatic. Monochromators significantly reduce the intensity of the incident axle; omitting the monochromator maximizes the incident beam flux.

Soller Slits

Pulverization diffraction experiments normally crave a line-shaped incident beam that is produced from a pair of parallel pocketknife edges. A set up of Soller slits are used in the beam path after the knife edges to remove parasitic radiations that scatters from the edges of the blades. Soller slits are a prepare of parallel thin foil sheets that blot virtually all of the Ten rays non traveling parallel to the metallic sheets.

Multi-Layer Optics

These optics human activity somewhat equally X-ray mirrors that both focus the 10-ray beam and selectively absorb the Kβ wavelengths producing an intense beam of 1000α radiation.

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 Telescopic, Potential and Applications of X-ray Analysis in International Union of Crystallographers Educational activity Pamphlets available at: http://www.iucr.org/pedagogy/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 nine keV electron-impact liquid-gallium-jet x-ray source., Rev. of Sci. Inst., 2008, 79, 016102-3. doi: 10.1063/1.2833838
See web page and associated references at: Grzegorz Jezierski's web page

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