Handbook of Modern Coating Technologies

Production and characteristics of X-rays

The laboratory sources of X-rays include radioactive materials, X-ray tubes, and synchrotron radiation. X-rays are generally in the form of continuous spectrum radiation and characteris­tic radiation. Following subsections briefly describe the technique for production of X-rays, primarily from the perspective of X-ray tubes, which serve as the most common source in their laboratory production for application in the field of materials science.

  • Emission of continuous spectrum radiation

Continuous spectrum or "white” X-rays are generally produced in an X-ray tube through rapid deceleration of charged particles (namely, electrons) possessing sufficient kinetic energy. For this purpose, an electron beam, accelerated to an energy level of around 5 keV is bombarded onto some metal target placed inside the X-ray tube. The radiation thus resulting from sudden deceleration of charged particles is also known as bremsstrahlung—which means "braking radiation” in German. Since only a tiny fraction of the total kinetic energy of all incident electrons gets converted into X-rays, with the remaining energy converting into heat, the target metal generally requires cooling by water for continuous operation.

As various electrons hit the target atoms at different locations, they lose different fractions of their kinetic energies in each collision. As a result, the emitted X-rays comprise of a con­tinuous spectrum of different wavelengths, whose intensity varies with wavelength and drops to zero at a limiting short wavelength (ASWL), which is independent of the target material and corresponds to conversion of entire kinetic energy to radiative energy in a single step, as described by Duane—Hunt law:

hc

A SWL

K.E. 5 Ve =

hc

5 ve

6.63 X 10234 X 3 X 108
6000 X 1.6 X 10219
5 2.075 X 10
10
m

As an example, the short wavelength corresponding to an accelerating voltage of 6 kV works out be around 0.2 nm, as calculated below:

On increasing the tube voltage (V), the kinetic energy of bombarding electrons will also increase, thereby leading to a lower value of ASWL. The corresponding distribution of inten­sity over different wavelengths also shifts toward higher energy (i.e., shorter wavelength), as schematically shown in Fig. 32.

'o

75
50
25
0.00
0.05
0.10
0.15             0.20              0.25             0.30
0
Wavelength (nm)
FIGURE 3-2 Spectrum of X-rays emitted from molybdenum target superimposed with plot of mass absorption coefficient pertaining to a suitable в-filter.
100

:-д

<u

c

■-V

  • Emission of characteristic radiation

As the accelerating voltage is further increased, electrons in the incident beam gain sufficient energy to knock-out orbital electrons from the atoms of the target material. The vacancy thus formed is immediately filled by an electron from some neighboring shell, thereby emitting a photon of radiation, whose energy equals the difference between energy levels of the two shells. Since different pairs of shells could be involved in this process, therefore, the emitted X-rays comprise of multiple characteristic peaks, namely, Ka, Кв, and La for electron transi­tions from L to K, M to K, and M to L shells, respectively.

Thus at high accelerating voltages, the radiation will comprise of two components—first, white X-rays, which are produced as a consequence of rapid deceleration of the bombarding electrons, and second, characteristic radiation, whose wavelengths depend on energy levels of the target metal. With further increase in accelerating voltage, the intensity of characteris­tic radiation increases much more rapidly in comparison to that of the white radiation. The wavelengths of Ka characteristic radiation for the commonly used target metals, namely, Cr, Cu, Mo, and W are 0.229, 0.154, 0.071, and 0.021 nm, respectively, while their corresponding excitation potentials are 6, 9, 20, and 70 kV, respectively. For details concerning characteristic wavelengths of various elements, the reader can refer to Table 4.2.2.4 in Ref. [27]. Information regarding construction and operation of X-ray tubes can be found in Ref. [28].

  • Absorption and filtration of characteristic radiation

The phenomenon of absorption can be understood by considering the process of interaction of X-rays with crystalline materials. The energy is removed from incident beam through two differ­ent mechanisms—first, through scattering (discussed in Section 3.6) and second through pure absorption, which includes various thermal and nonthermal processes. Nonthermal effects may
include ionization of atoms, thereby producing (3-rays, which in-turn might lead to emission of X-rays of longer wavelengths—a phenomenon known as fluorescence, commonly encountered when irradiating ferrous substrates with Cu Ka radiation. A portion of the incident energy could also be absorbed by free electrons and reemitted as radiation of longer wavelength—a phenom­enon known as Compton effect. As a consequence, the transmitted beam gets reduced in inten­sity both due to scattering as well as absorption through the various processes described above. The term "absorption” therefore signifies reduction in residual intensity of incident beam, which happens due to cumulative effect of pure absorption, along with scattering, even though the latter phenomenon just redirects energy in some other direction.

Rontgen found that the residual intensity (I) of X-rays on passing through a material of thickness t and linear absorption coefficient (p), is progressively reduced according to the fol­lowing relationship:

(3.1)

= — p dx I p

.I = I0e p t |l0 : Incident intensity

The linear absorption coefficient (p) corresponding to a given wavelength of incident X-rays is proportional to density (p) of the material, regardless of its physical state. The ratio р/р is a constant, known as mass absorption coefficient of the material and its values (in cm2/g) for vari­ous materials have been tabulated in Table 4.2.4.3 in Ref. [27]. The mass absorption coefficient for compound materials can be calculated as weighed averages of the coefficients of their con­stituent elements.

The absorption of X-rays by a material decreases with decreasing wavelength (i.e., increasing energy). However, similar to the phenomenon of emission/absorption lines observed in visible spectra of various materials, there is a sudden increase in the absorption of X-rays, whenever their energy matches with some characteristic emission wavelength (namely, Ka and Kf3) of the absorbing material. Owing to the shape of its appearance on the wavelength versus absorption graph, this abrupt rise in absorption with decreasing wavelength (increasing energy) is known as absorption edge, as shown with dotted curve in Fig. 32. The absorption edge wavelength corre­sponding to a particular transition state (namely, Ka and Kf3) for different elements increases with increasing atomic number.

The XRD measurements usually require an intense, collimated, and highly monochro­matic beam. As a consequence, it is generally the most prominent, Ka peak that finds appli­cation in production of X-rays for application in diffraction analysis, while the neighboring K/3 peak is filtered using an absorbing thin foil (or coating) of a metal (or its compound) hav­ing atomic number one or two less than that of the target metal emitting the characteristic Ka radiation. The guiding principle for selection of the absorbing material is that its absorp­tion edge should be located within the Ka and K/3 emission lines of the X-ray source mate­rial. For example, when the radiation originating from a Cu target is passed through 20 pm thick Ni filter, the intensity of Ka peak would get attenuated to 42% of incident intensity, while that of the K/3 peak (which is just covered by the absorption edge) will get reduced to
a mere 0.63% of the original intensity, as depicted schematically in Fig. 33. Accordingly such filters are known as в-filters. Similarly foils of Ti and Nb act as ^-filters for Ka charac­teristic radiation of Cr and Mo respectively. The в-filters are usually placed between the specimen and detector, so as to further improve signal-to-noise ratio by removing unwanted radiation produced by fluorescence of specimen.

  • Total external reflection of X-rays

Any kind of electromagnetic radiation incident onto a surface in general undergoes a combi­nation of specular reflection, diffuse reflection and refraction. For X-rays, the refractive index of a material is slightly less than unity. Accordingly, as the angle of incidence (0, measured from surface tangent) of X-rays is decreased, a stage of total external reflection (similar to the familiar case of total internal reflection of light in optical fibers) is reached, wherein the inci­dent X-rays stop penetrating into the material and begin to undergo near total specular reflection from the surface. This happens both for crystalline as well as noncrystalline materi­als. The angle at which this occurs is known as the critical angle (0c) for total reflection and is given (in radians) by the following expression:

ec 5 A^/2.7 X 10up                                             (3.2)

where A0 is the wavelength of incident monochromatic beam of X-rays in meters and p is the density of material in kg/m3. The phenomenon of total external reflection finds

Wavelength

FIGURE 3-3 Schematic showing application of в-filter for monochromatization.

 

 

application in grazing-incidence techniques, discussed in Section 3.10.3. It is also used in fabrication of X-ray focusing equipment.

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