The discovery of X-rays

© Engineer Xavier Borg - Blaze Labs Research

The discovery of X-rays

In November 1895, Wilhelm Röntgen discovered X-rays while working at the University of Wurzburg, Germany. Röntgen was investigating cathode rays in different types of evacuated glass tubes and trying to determine their range in air. He noticed that while the rays were being produced, a screen coated in fluorescent barium platinocyanide would glow. He was intrigued because the screen was too far from the tube to be affected by the cathode rays. He assumed unkown rays, X-rays, were being emitted from the walls of the tube while the cathode ray tube was running. To his amazement, Röntgen found that the rays could pass straight through his hand and cast shadows of his bones on the fluorescent screen. He spent several weeks privately investigating the rays before publishing his results at the end of the year.

Röntgen's paper described many of the properties of X-rays. He showed that they were:

  • very penetrating and were able to pass through materials that are opaque to visible light.
  • invisible to the human eye.
  • would cause many types of material to fluoresce and could be recorded on photographic paper.
  • they moved in straight lines like visible light and hence called rays.

  • One physicist who studied the rays was Max von Laue in Germany. Laue believed that X-rays were similar to light waves and not some form of tiny particle. In 1905 Charles Barkla in Edinburgh had shown that X-rays could be polarised, but the rays could not be made to refract. If they were waves, they must have a very short wavelength. Von Laue's colleague, Wilhelm Wien, calculated that the wavelength should be around one hundredth of a nanometre, ten thousand times shorter than the wavelength of visible light. Von Laue had been studying the diffraction of light using narrow slits and wondered if X-rays could also be diffracted if the slits were small enough.

    Huygen's Principle

    The reason for the diffraction effect was explained by the Dutch physicist and mathematician Christian Huygens in 1678. He showed that any wave can be thought of as spreading spherically at every point along its wavefront. All these little spherical 'wavelets' are constantly interacting, so can maintain a planar (or flat) wavefront. But if this wavefront is interrupted by an obstacle the wave spreads spherically at the points where it has been broken. Diffraction gratings work by splitting a planar wavefront at many regular points. The wavelets which pass through the gaps in the grating will spread spherically and interfere with each other. When several wavelets are in phase with each other they will add together and produce a strong signal in a detector, and if they are out of phase they will cancel out and produce a very weak signal. Diffraction patterns made with light will show successive bright and dark areas demonstrating the differences in phase between several wavelets.

    Von Laue's Crystals
    The spacing of slits in a diffraction grating has to be comparable to the wavelength of the waves being diffracted. Von Laue realised that a crystal could be used as a diffraction grating for X-rays. In 1850 Bravais had suggested that a crystal is arranged as a lattice, and the distance between molecules in a solid is around a tenth of a nanometre. If the X-rays were a wave the atoms in a crystal should cause them to diffract.X-rays were allowed into a lead box containing a crystal, with sensitive film behind and to the sides. When the films were developed there was a large central point from the incident X-rays, but also many smaller points in a regular pattern. These could only be due to the diffraction of the incident beam and the interference of many beams.

    Von Laue published his discovery in 1912, more than ten years after the discovery of X-rays. By using a crystal as a diffraction grating, von Laue had proved the X-rays were not particles, but waves of light with very small wavelengths.

    Lawrence Bragg in Cambridge

    Von Laue had proved that X-rays were waves by diffracting them with a crystal. He had recorded his results photographically, with bright spots showing points where many X-rays were in phase with each other. There were a large number of points where these spots appeared to be 'missing'. Diffracted beams of X-rays were expected in these directions, but didn't seem to occur. Von Laue suggested that the X-rays must contain only certain wavelengths to account for the missing diffracted beams.

    William Lawrence Bragg wasn't convinced by this explanation. In the Autumn of 1912 Lawrence Bragg had just received his degree in Natural Sciences from Cambridge and he began investigating Von Laue's X-ray patterns. Lawrence Bragg thought that X-rays must be made up of a continuous spectrum of all possible wavelengths in the same way that white light is made of a spectrum of all the possible colours. If this was true then the 'missing' directions of diffraction wouldn't be due to the wavelength of the X-rays, but due to some property of the crystal being examined.

    Lawrence Bragg thought of each plane of atoms in a crystal as a reflecting surface. The X-rays would hit each plane of atoms in turn, reflecting first off the surface layer, then the one below it, and so on. If the X-rays reflected off all the surfaces were in phase, with their peaks and troughs all aligned, then a very strong signal could be measured from the reflection.

    Bragg's Law

    An X-ray which reflects from the surface of a substance has travelled less distance than an X-ray which reflects from a plane of atoms inside the crystal. The penetrating X-ray travels down to the internal layer, reflects, and travels back over the same distance before being back at the surface. The distance travelled depends on the separation of the layers and the angle at which the X-ray entered the material. For this wave to be in phase with the wave which reflected from the surface it needs to have travelled a whole number of wavelengths while inside the material. Bragg expressed this in an equation now known as Bragg's Law:

    When n is an integer (1, 2, 3 etc.) the reflected waves from different layers are perfectly in phase with each other and produce a bright point on a piece of photographic film. Otherwise the waves are not in phase, and will either be missing or feint.

    The X-ray Spectrometer

    To examine the reflection of X-rays from crystals at various angles, Bragg's father developed the X-ray spectrometer in Leeds. X-rays were passed through slits to produce a narrow beam, which fell on a crystal at the centre of the spectrometer. The reflected beam was then measured in an ionisation chamber, finding the strength as well as direction of reflected beams.

    By changing the angle of the incident X-rays, W.H. Bragg measured the reflections at different angles from the faces of the crystal. He found that very strong reflections occured at certain angles. These strong reflections depended on the spacing of the planes of atoms inside the crystal, according to his son Bragg's Law. By measuring all the angles at which strong reflections occurred, the Braggs worked out the arrangement of individual atoms inside the crystals.

    W.H. Bragg continued to study X-rays and improve the X-ray spectrometer, while his son Lawrence analysed the arrangements of atoms inside different crystals. Together they created the science of X-ray crystallography.

    Generating X-rays

    This mechanism operates in all EM sources. It originates from the acceleration of electrons in Coulomb collisions with other electrons and with ions and nuclei. It comes from the German, 'brems' for braking, and 'strahlung' for radiation. The most common situation is the emission from a hot gas as the electrons collide with the nuclei, due to their random thermal motions. This is called 'thermal bremsstrahlung'. Bremsstrahlung can also occur when a beam of particles decelerates on encountering an obstacle. "Braking radiation" is the main way very fast charged particles lose energy when traveling through matter. Radiation is also emitted when charged particles are accelerated. In this case, the acceleration is caused by the electromagnetic fields of the atomic nuclei of the medium. These bremsstrahlung photons have a continuous spectrum with a broad peak of intensity, for photons with roughly half the incident electron energy, and are more numerous in directions perpendicular to the electrons' acceleration vector.

    X-rays and shorter wavelengths can be easily generated by striking an anode with highly accelerated electrons within a high voltage gradient.

    The higher the temperature of the cathode, the more electrons are released. We measure the level of current in milliamperes (mA). Increasing the current increases the number of electrons emitted from the cathode. This, in turn, increases the intensity of the rays produced.

    Increasing the voltage (in kV), increases the speed of the electrons that strike the target. Higher potential difference settings produce shorter wavelength EM rays.

    Doubling the tube current, doubles the quantity of heat produced. Heat production also varies almost directly with varying kVp. It is known that aluminium has got low Bremsstrahlung radiation levels, but there are other ways that it can emit short wavelength radiation.

    The efficiency (not intensity) of x-ray & gamma ray production is independent of the hv current. Regardless of what current is selected, the efficiency of x-ray produciton remains constant. The efficiency of x-ray production increases with increasing projectile-electron energy. It may vary from 1% to 70% depending on the potential difference.

    Characteristic Radiation

    If the projectile electron interacts with an inner-shell electron of the target atom, rather than an outer-shell electron, characteristic x-radiation can be produced. Characteristic x-radiation results when the interaction is sufficiently violent to ionize the target atom, by the total removal of the inner-shell electron. Excitation of a inner (K)-shell electron does not immediately produce characteristic x-radiation.

    When the projectile electron ionizes a target atom by removal of a K-shell electron, a temporary electron hole is produced in the K shell. This is a highly unnatural state for the target atom, and is corrected by an outer-shell electron falling into the hole in the K shell. The transition of an orbital electron from an outer shell to an inner shell is accompanied by the emission of an x-ray photon. Photons of this sort have energies that are, of course, characteristic of the anode material, and are emitted from the atom with equal probability in all directions. This x-ray has energy equal to the difference in the binding energies of the orbital electrons involved (K-L).

    A K-shell elctron is removed from a tungsten atom and is repleced by an L shell electron. What is the energy of the characteristic x-ray that is emitted?

    For tungsten, K electrons have binding energies of 69.5 keV, and L electrons are bound by 12.1 keV. Therefore, the characteristic x-ray emitted has energy of: 69.5 - 12.1 = 57.4 keV

    In summary, characteristic x-rays are produced by transitions of orbital electrons from outer to inner shells. Since the electron binding energy for every element is different, the characteristic x-rays produced in the various elements are also different. This type of x-radiation is called characteristic radiation, because it is characteristic of the target element. The effective energy characteristic x-rays increases with increasing atomic number of the target element.

    X-rays and accelerated ions in air

    When an electron hits the target so hard on its inner shell, the target material will radiate an EM wave of energy, equal to the energy difference between the innermost and the next shell called K & L1 respectively.

    Luckily for us, the air molecules in the atmosphere make it impossible for any electron to travel the whole path from emitter to collector without any collision, in fact there would be millions of such collisions and the electrons can never obtain very high speeds, enough to generate any radiation upon impact. My latest tests for radiation within EHD thrusters confirmed no radiation when thrusters are powered in air. However, in vacuum, they would certainly work in a similar way to an x-ray tube.

    The following calculations apply only in pure vacuum.

    For aluminium (our foil target), K = 1.56 keV , and L1 = 0.118 keV
    The energy difference between the two shells is 1.442 keV.

    So, when a charge of sufficient energy hits the aluminium foil, an energy packet of 1.442 keV will be released.

    Using E = hf
    1.442E3 x e/h = f

    This gives f = 3.486E17 Hz, which happens to be the so called 'soft X-ray' band.

    Alternatively, knowing the atomic number for Al (Z=13), approximate values can be found. Energy released by an electron shift from L to K = (Z-1)2 * 10.2 eV = 1.46 keV, and f=E/h gives 3.55E17 Hz.

    AL EM spectrum

    Maximum radiation frequency
    max frequency

    As discussed, we have two kinds of radiation mechanisms radiating within the x-ray & gamma ray band. The resulting radiation will be similar to the above diagram. The characteristic radiation peaks will be added over a background noise floor, which is due to the Bremsstrahlung mechanism. The wavelengths of the characteristic lines are independent of the pd - they are just characteristic of the metal target. The background radiation cuts off sharply at A or B as the wavelengths diminish down to a certain point at which maximum radiation frequency occurs. This maximum limit for the radiation frequency will depend only upon the voltage across the electrodes, and is independent of the metal target characteristics.

    hf(max) = eV
    f(max)= eV/h

    Conversely, if we need to know the minimum pd required to reach a particular maximum radiation frequency we use:

    V(min)= f(max)h/e

    So, suppose we need to reach the Gamma radiation band at 3E19 Hz, then

    V(min) = 3E19 x 6.62e-34/ 1.6e-19
    V(min) = 124 kV

    Note that when operating pulsed dc supplies, sharp spikes on the secondary might reach higher hv values than the nominal output, and the duration of these spikes is significant at such frequencies.