ON FLAW DETECTION AND THICKNESS MEASUREMENT OF MATERIALS USING AN ELECTRON BEAM

B. A. Kononov, Yu. M. Stepanov

(Presented by the scientific seminar of the Faculty of Physics and Engineering)

The detection of hidden cavities, cracks, inclusions, etc., in materials and products is the subject of flaw detection, which is used in various branches of industry. In radiation flaw detection, electromagnetic radiation is at present used mainly—bremsstrahlung, X-ray, and gamma radiation. The presence of a defect is judged from the change in the intensity of the radiation that has passed through different regions of the specimen. The detectability of a defect is determined mainly by the resolving power of the detector and is usually about 1% of the thickness of the product being inspected, in rare cases reaching tenths of a percent. This limit is due to the difficulty of measuring the radiation intensity with high accuracy.

When inspecting products of small thickness made of light materials, the sensitivity of a radiation flaw detector can be increased by approximately a factor of 10 if, for transillumination of the product, a narrow monochromatic beam of electrons is used and the change in its spectral composition after the absorber is observed.

The scheme of such a spectrometric electron flaw detector is shown in Fig. 1. The electron source 1 must produce a narrow monoenergetic beam of particles of high intensity with energies from one to several tens of MeV. The electron source may be a betatron, microtron, high-voltage accelerator, linear accelerator with a particle separator, etc. The specimen under inspection 2 is moved in space perpendicular to the radiation beam. The spectrometric detector 3—a magnetic spectrometer, for example—records the change in the energy of the electrons that have passed through absorber 2 and sends a signal to the recording device 4—a self-recording instrument or any other recording device.

Fig. 1. Scheme of a spectrometric electron flaw detector: 1—electron source, 2—specimen under inspection, 3—spectrometer, 4—recording device.

The operating principle of the spectrometric electron flaw detector is based on the almost linear dependence of the energy loss of electrons on the thickness of the material traversed, given, for example, by the well-known Landau formula for the probable energy loss [1]:

\[ \Delta E_{\mathrm{B}} = ax \left[\ln \frac{2mv^2 ax}{I^2(1-\beta^2)} - \beta^2 + 0.37 \right], \]

where \(m\) and \(v\) are the mass and velocity of the electron,
\(\beta = v/c\), \(c\) is the velocity of light in vacuum,
\(I\) is the mean excitation potential of an atom of the substance,
\(x\) is the thickness in cm,
\(a = 0.154 Z/A \, \rho/\beta^2\),
\(Z, A, \rho\) are the atomic number, atomic weight, and density of the substance.

In other words, \(\Delta E_{\mathrm{B}} \sim x \ln x\), and, consequently, a change in absorber thickness or, what is the same thing, the presence of a defect can easily be detected by measuring the energy of the electrons that have passed through the material.

As a result of fluctuations in energy losses as the electrons penetrate into the substance, their energy spectrum will broaden. Figure 2 shows

Fig. 2. Spectrum of a monochromatic electron beam before the absorber (1) and after passing through 1.561 and 2.699 g/cm² of aluminum (2 and 3, respectively). 4 — displacement of the curve when a defect appears

the shape of the spectrum of a monochromatic electron beam with an energy of \(53.61 \pm 0.01\) MeV before the absorber (curve 1) and after passing through 1.561 and 2.699 g/cm² of aluminum (curves 2 and 3, respectively) [2]. The ordinates of 2 and 3 have been increased by factors of 20 and 40, respectively. The change in electron energy behind the absorber can be recorded by the change in the position of the maximum along the abscissa axis, but still better by the change in the position of the point corresponding to an ordinate half the maximum and lying in the region of greatest steepness of the curve. In the first case, to find the maximum of the curve it is necessary to make several measurements, changing the current in the spectrometer coils and recording the counting rate. In the second case, fluctuations in absorber thickness will cause changes in the counting rate due to the displacement of the curve and the change in the position of the maximum (for example, when the thickness decreases or a cavity appears, the curve shifts to the right—Fig. 2, curve 4). The measured val-

...of electron energies in the example given (Fig. 2, curves 2 and 3) correspond to \(51.33 \pm 0.02\) and \(49.58 \pm 0.04\) MeV.

As the thickness of the absorber increases, the maximum of the energy-loss distribution curve decreases, the half-width increases, and the steepness of the right-hand front decreases. As a result, the accuracy of determining \(\Delta E_{\mathrm{B}}\), and consequently also \(\Delta x\), decreases. For energies of the order of 50 MeV, the proposed method will give high resolution for thicknesses up to 2 cm in the case of Al or a lighter substance; the limiting sensitivity of the flaw detector is determined by the accuracy of the energy measurement and, for a high-resolution magnetic spectrometer, amounts to as much as \(10^{-4}\).

A drawback of the method is the possibility of inspecting only comparatively thin layers of light substances and the complexity of the apparatus.

We have investigated the possibility of detecting defects in small thicknesses of light materials by radiographing the latter with a broad beam of monochromatic electrons with energies from 3 to 9 MeV onto X-ray film. As the experiments performed have shown, in this way it is possible to detect only sharply defined defects (cavities, cracks, etc.) lying on the surface of the specimen facing the film, on which an image arises not of the entire defect, but only of its boundaries. The image of the boundaries is formed in this case owing to the different scattering of electrons by regions of the absorber on either side of the defect boundaries. Figure 3 schematically shows images

Fig. 3. Diagram of the formation of images of large (\(a\)) and small (\(b\)) defects when radiographed with a broad electron beam

of large (\(a\)) and small (\(b\)) defects. The density of blackening of the film that should be expected from the ionization-distribution curves over the depth of the specimen is shown by a dashed line. In view of the strong scattering of electrons, internal defects are revealed only very weakly.

In radiation methods of thickness measurement, radiation from radioactive isotopes is currently used. The use of monochromatic electron beams for these purposes makes it possible to obtain greater sensitivity.

If the radiation intensity is measured by an ionization chamber of small volume, then the dependence of the chamber current on the absorber thickness has the form shown in Fig. 4 [3]. The absorber thickness is plotted in fractions of the extrapolated range. Calculation shows that the minimum relative error in measuring the thickness in this case is half the relative error in measuring the ionization current in

at the maximum of the curve. To obtain the same sensitivity when using electromagnetic or beta radiation with the energy optimal for the given thickness, the current in the chamber at zero thickness must be 5–6 times greater, i.e., a considerably higher radiation intensity is required.

Fig. 4. Dependence of the ionization-chamber current on the thickness of an aluminum absorber under irradiation by monochromatic electrons with energies from 2 to 6 MeV.

In this way it is possible to monitor thicknesses up to \(7\text{–}8\ \mathrm{g/cm^2}\) at electron energies up to \(20\ \mathrm{MeV}\).

LITERATURE

1. L. Landau. J. of Physics (USSR), vol. VIII, No. 4, 201 (1944).
2. H. Breuer. Z. Phys. 180, 209 (1964).
3. V. N. Rudenko. Dissertation, TPI, Tomsk, 1964.