Spectrometric Methods in Materials Defectoscopy

V. I. Gorbunov, V. B. Kuznetsov, V. K. Kuleshov, Yu. B. Yanketevich

(Presented by the scientific seminar of the Research Institute of Nuclear Physics, Electronics, and Automation)

The wide application of radiation methods of inspection has made it necessary to study in detail the features of the passage and detection of $\gamma$-radiation from various sources. The initial energy spectrum of a radiation source is transformed in a definite way in the absorber and in the radiation detector. It is obvious that, in order to select the parameters of the source, the inspection geometry, and the detector parameters, as well as to determine the capabilities of one or another method of radiation defectoscopy, it is necessary to know the energy spectrum of $\gamma$-quanta after various absorbers and the pulse spectrum at the output of a detector that registers $\gamma$-radiation.

Fig. 1. Spectrum of radiation from the isotope Co$^{60}$.

In the present work an attempt has been made to generalize the theoretical and experimental material available in the literature and obtained by the authors over a wide range of $\gamma$-quantum energies. This range includes bremsstrahlung from X-ray apparatuses, gamma radiation from radioactive isotopes, and bremsstrahlung from a betatron.

A number of works [1, 2] have been devoted to the study of the output spectra of X-ray apparatuses, isotopes, and betatrons. It is known that the energy spectrum of the radiation of radioactive isotopes consists of one or several monoenergetic lines (Fig. 1). In contrast to

Fig. 2. Spectrum of radiation generated by an X-ray apparatus (2).

isotopes, the bremsstrahlung radiation of X-ray apparatuses and the betatron is characterized by a so-called “white,” i.e., continuous, spectrum. The shape of this spectrum does not change appreciably when the maximum energy of the bremsstrahlung radiation of the X-ray apparatus is changed (Figs. 2, 3).

Fig. 3. Bremsstrahlung spectrum of a betatron (1) with \(E_{\max}=10\) MeV.

The form of the energy spectrum beyond the absorber will depend on the properties of the absorber itself [3], on the dimensions and geometry of the region in which the radiation is detected. These propositions can be explained by a concrete consideration of the passage of radiation from the above-mentioned sources through matter.

Transmission Spectra

1. $\gamma$-radiation of radioactive isotopes. The greatest amount of information on the transmission of $\gamma$-radiation from radioactive isotopes through an absorber relates to Co$^{60}$, which is widely used in defectoscopy [4, 10, 11].

As already noted, Co$^{60}$ has two monochromatic lines with energies of 1.17 and 1.33 MeV. For this energy of $\gamma$-quanta, the cross sections of elementary processes have been found, such as Compton and Rayleigh scattering, the photoelectric effect, and pair production. However, in defectoscopy it is necessary to know the law of propagation of a beam of $\gamma$-quanta in an absorber, since the presence of secondary processes (multiple scattering, bremsstrahlung of electrons, etc.) leads to significant deviations from the elementary laws of propagation of $\gamma$-quanta.

Secondary processes are especially noticeable when radiation is detected under “broad-beam” conditions, at absorber thicknesses equal to several mean free paths of quanta of the given energy.

A “broad beam” is usually used in the radiographic and visual method, whereas a “narrow beam” is used mainly in scintillation $\gamma$-defectoscopy. One should distinguish between the concepts of “narrow beam” and “clean geometry,” since under “narrow-beam” conditions there is a possibility of recording secondary photons, although to a lesser extent than under “broad-beam” conditions. Thus, the geometry of a “narrow beam” is, as it were, intermediate between “clean geometry,” under which any interaction removes the quantum completely from the beam, and a “broad beam,” or so-called “poor geometry.”

It is known that for $\gamma$-radiation with an energy of about 1 MeV, the most characteristic process is Compton scattering. For example, the average number of Compton-scattering processes in water exceeds the average number of photoabsorptions by a factor of 14 [3]. In each interaction process the photon energy decreases. This decrease in Compton scattering is, on average, considerably smaller for low photon energies than for high photon energies. Therefore, in the low-energy part of the spectrum there occurs, as it were, an accumulation of the number of photons, although it is limited from below by photoabsorption. In this case the attenuation of primary photons will to some extent be compensated by the accumulation of secondary photons. Then the transmission spectrum is

\[ I_{\mathrm{tr}} = I_0 + I_{\mathrm{sc}}, \tag{1} \]

where $I_0$ is the energy spectrum of the radiation source;

$I_{\mathrm{sc}}$ is the spectrum of scattered radiation, taking into account both singly and multiply scattered photons.

Accordingly, the accumulation factor is

\[ B = \frac{N_{\mathrm{tr}}}{N_0}, \tag{2} \]

where $N_{\mathrm{tr}}$ is the total number of quanta, scattered and unscattered, incident on the detector;

$N_0$ is the number of quanta of primary energy that have passed through the absorber layer in the direction of the detector.

As can be seen from Fig. 4, the line spectrum of the radiation source, after passing through the absorber, has become continuous. Study of the details of this spectrum shows that in the low-energy region there is a peak of multiple scattering, whose position depends on the atomic number of the absorber (100–120 keV for Al and 200–240 keV for Pb). In addition, there is a transition region in the energy range

300 \(K_{\gamma}-1M_{\gamma}\), caused mainly by singly and doubly scattered quanta [4]. The area under the multiple-scattering peak and the transition region is precisely what characterizes the magnitude of the build-up factor. It is also important to note the fact that the value “\(B\)” for an absorber of a given

Fig. 4. Energy spectrum of \(Co^{60}\) radiation after passage through an absorber.

thickness, density, and composition is a function of the detector irradiation field, i.e., it depends on the conditions under which the beam of \(\gamma\)-quanta is detected. When a scintillation counter is used as the detector, the irradiation field of the crystal is determined by the shape and dimensions of the collimator aperture.

Fig. 4a. Dependence of the build-up factor on the collimator diameter. Radiation source \(Co^{60}\).

To reduce the build-up factor and, consequently, to increase the sensitivity of the flaw detector, it is necessary to use small collimator apertures. On the other hand, however, this leads to a substantial reduction in inspection productivity, which is highly undesirable. Therefore, in real installations one has to make a compromise,

choosing intermediate dimensions for the collimator aperture. We have carried out studies of the magnitude of the accumulation factor as a function of the detector irradiation field. The measurements were performed on a scintillation spectrometer with a NaI (Tl) crystal of dimensions \(80 \times 80\) mm and an FEU-24. The measurement results are presented in Fig. 4a. Analysis of these data shows that there are possibilities for eliminating—although not completely—the influence of quantum accumulation on the sensitivity of flaw detectors; this is achieved, however, at the cost of reduced inspection productivity. In [5] another variant of partial elimination of accumulation is noted—amplitude discrimination of the pulses of the scintillation detector. By setting the discrimination threshold beyond the multiple-scattering peak, one can substantially improve the “quality” of the recorded spectrum. A detailed consideration of the question of choosing the optimum discrimination threshold in a scintillation flaw detector with a \(Co^{60}\) source may be found in these same works.

Bremsstrahlung of X-ray Apparatus and Betatrons

The continuous bremsstrahlung spectra of betatrons and X-ray apparatus differ in their transformation when passing through a layer of absorber. This is explained by the fact that in the energy region 50—

Fig. 5. “Hardening” of the continuous radiation spectrum of an X-ray apparatus.

400 keV, for most materials the curve \(\mu=\tau(E)\) decreases smoothly with increasing energy, while in the energy range 1–30 MeV, in materials with large \(Z\), an inflection of the curve is observed, causing a mini-

low absorption coefficient \(\mu\). Therefore, the transmission spectra of a beam of bremsstrahlung quanta from an X-ray apparatus under conditions of “clean geometry” reflect the process of filtration, or “hardening,” of the primary beam (Fig. 5) up to \(E_{\max}\).

In the case of a betatron with an energy from 10 to 30 MeV, for example for steel, the transmission spectrum narrows near the energy corresponding to \(\mu_{\min}\) when the thickness of the steel is increased above 50 cm (Fig. 6).

Fig. 6. Change in the spectral composition of betatron bremsstrahlung after passage through steel barriers of different thicknesses.

The spectra were obtained by recalculating the output spectrum of a betatron with \(E_{\max}=30\) MeV for conditions of “clean geometry” using the absorption coefficients of monoenergetic quanta.

A qualitative consideration of the interaction processes of bremsstrahlung quanta generated by an X-ray apparatus shows that in this case, in addition to Compton scattering, it is also necessary to take into account Rayleigh (coherent) scattering, which makes a substantial contribution to the accumulation of quanta. It should be noted that there is a sharply pronounced dependence of the build-up factor on the atomic number of the absorber, since in this energy range the cross section depends very strongly on \(Z\), and, moreover, during scattering a quantum either does not lose its energy at all or loses only a small part of it.

The distinctive feature of the process of build-up of betatron bremsstrahlung quanta is that it is produced mainly by single-scattered ...

quanta scattered through a small angle, as well as quanta scattered two or more times through very small angles. In addition, the bremsstrahlung of secondary charged particles also makes some contribution to the accumulation. However, the details of the interaction processes of a betatron bremsstrahlung beam with various absorbers have not at present been studied. In this sense, work [6] is of some interest; it presents spectral distributions of betatron bremsstrahlung with \(E_{\max}=10\) MeV that has passed through a layer of lead (Fig. 7).

Fig. 7. Spectrum of \(\gamma\)-quanta that passed through a layer of lead 15.2 cm thick. The maximum energy of the primary quanta is 10 MeV. Points are the distribution of pulses of a NaI(Tl) detector in different series. The histograms are the photon spectrum obtained with allowance for the detector resolution. The solid curve is the spectrum of singly scattered photons.

Instrumental Spectra

When $\gamma$-quanta with energies from 0 to 30 MeV interact with the substance of a scintillation crystal, photoelectrons, Compton electrons, and electron–positron pairs are formed in the latter. Other nuclear processes, because of their small cross section, may be neglected. The charged particles formed transfer their energy to the crystal, producing a light flash whose amplitude is proportional to the energy of the secondary particle absorbed in the crystal. Thus, in the case of the photoelectric effect and the pair-production effect, if the escape of fluorescent radiation and the bremsstrahlung radiation of the pairs are neglected, the amplitude of the scintillation may be taken to be proportional to the energy of the $\gamma$-quantum. In the case of the Compton effect, the $\gamma$-quantum does not leave all its energy in the crystal and does not determine the energy of the incident $\gamma$-quantum, since the scattered quantum may leave the crystal. In view of this, the amplitude distribution of pulses recorded from the photomultiplier, in the case of monoenergetic $\gamma$-radiation, will consist of a peak corresponding to complete absorption in the crystal and of a continuous distribution caused by Compton scattering in the scintillation crystal.

Consequently, the transmission spectrum in a scintillation crystal is transformed into a spectrum of electron energies and then into a spectrum of amplitudes of light flashes. The pulse spectrum at the output of a scintillation detector is called the “instrumental spectrum.” The transformation of the true radiation spectrum into the instrumental spectrum proceeds according to the following law [4, 7, 8]:

\[ N(E)=\int_{0}^{E_{\max}} I(E')R(E',E)\,dE', \tag{3} \]

where $I(E')$ is the true energy spectrum of quanta incident on the crystal;

$N(E)$ is the measured amplitude distribution;

$R(E',E)$ is the sensitivity function of the crystal.

In this transformation the principal role is played by $R(E,E')$. Let us consider what parameters determine the form of this function.

\[ R(E',E)=Y(E')\cdot k(E',E), \tag{4} \]

where $Y(E')$ is the efficiency of the spectrometer;

$k(E',E)$ is the probability that a pulse will appear in the interval from $E$ to $E+dE$ under the condition that a quantum with energy between $E'$ and $E'+dE'$ interacts with the crystal.

\[ Y(E')=1-e^{-\psi_k h}, \tag{5} \]

where $\psi_k$ is the total absorption coefficient,

$h$ is the height of the crystal.

In turn,

\[ k(E',E)=P(E')\delta(E-E')+L(E',E), \tag{6} \]

where $L(E',E)$ is the probability of Compton scattering in the crystal, characterizing the continuous Compton distribution in the instrumental spectrum;

$P(E')$ is the photo-fraction, or the ratio of the area under the “total-energy peak” to the total area under the Compton distribution and the “total-energy peak.”

These two functions are the most important characteristics of a scintillation detector. Let us consider in greater detail the relationship of these two functions in the instrumental spectrum. Figure 8 shows the pulse spectrum from the isotope Co\(^{60}\), obtained with a scintillation crystal measuring \(40 \times 50\) mm. Analysis of the shape of this spectrum, typical of the crystals currently used in defectoscopy, shows that the area under the Compton distribution considerably exceeds the area under the full-energy peak.

Fig. 8. Instrumental spectra of the isotope Co\(^{60}\), obtained with crystals of different sizes.

This fact has an adverse effect on the efficiency of recording \(\gamma\)-radiation beyond the absorber; therefore it is of interest to examine the dependence of the ratio \(P(E')\) and \(L(E', E)\) on the energy of the \(\gamma\)-quanta and on the crystal dimensions. At \(\gamma\)-quantum energies up to 200 keV, the principal contribution to the interaction in NaI(Tl) is the photoeffect, and the photo-contribution by area exceeds the area under the continuous distribution by several times. As the energy is increased to 1 MeV, the photoeffect ceases to be the dominant type of interaction, and this accounts for the large area under the continuous distribution in comparison with the photo-contribution. In the energy region above 2 MeV, the photo-contribution begins to increase because of pair production. Thus, detection of radiation in the range 0.5–2 MeV is associated with certain difficulties.

As indicated above, the transmission spectrum of Co\(^{60}\) radiation contains a peak of multiple scattering, which causes an accumulation of quanta and carries no information about the quality of the inspected product, unlike radiation singly scattered into the small solid angle of the collimator. The use of amplitude discrimination in this case makes it possible to remove a significant fraction of the multiply scattered radiation and thereby increase the sensitivity of inspection.

However, when the level of the Compton distribution in the instrumental spectrum is high, discrimination does not lead to the desired results, since a substantial portion of the primary quanta forming the region below the discrimination threshold is lost. At the same time, the level of the continuous distribution in the instrumental spectrum affects the actual recording efficiency of the detector. The point is that not all quanta that have interacted with the crystal will be recorded-

In addition, a large contribution of Compton scattering in the crystal, as it were, reduces its efficiency. The actual registration efficiency of a crystal + PMT scintillation detector is given by the following expression:

\[ \varepsilon_0 = Y(E)\cdot \nu (1-\eta), \tag{7} \]

where \(\nu\) is a coefficient taking into account the sensitivity threshold of the photocathode and the self-absorption of light quanta in the crystal;

\(\eta\) is the fraction of energy carried away by secondary particles and photons owing to the small dimensions of the crystal;

\[ \eta = \frac{\Delta J_T}{J_n}, \tag{8} \]

where \(\Delta J_T\) is the radiation intensity carried out of the crystal by quanta that have interacted;

\(J_n\) is the intensity of the radiation that has interacted with the crystal.

It should be noted that formula (7) is valid only in the case of the current mode of the scintillation detector, since in the case of the counting method of registering \(\gamma\)-quanta with amplitude normalization,

\[ \varepsilon_0 = Y(E)\cdot f_n, \tag{9} \]

where \(f_n\) is a coefficient taking into account the discrimination threshold in the instrumental spectrum.

To a certain extent this explains some advantages of the counting method in comparison with the current method, since here the energy carried out of the crystal by secondary particles plays no role, whereas for the current mode the greatest possible light collection from the crystal is essential. This light collection depends on the fraction of energy absorbed by the crystal at each interaction of a \(\gamma\)-quantum and determines the minimum radiation intensity that can be stably measured by the given crystal.

The actual registration efficiency depends on the energy of the radiation being detected not only through the absorption coefficient of the crystal, but also through the coefficients \(\nu\) and \(\eta\). Thus, in the case of detecting X-radiation, the most important factor is that taken into account by the coefficient \(\nu\), since the photoeffect predominates here over scattering, and, on the other hand, the number of light photons produced by low-energy \(\gamma\)-quanta is small, and the effect of self-absorption in the crystal becomes substantial. If, however, the energy of the \(\gamma\)-quanta lies in the range \(0.5\)—\(1\ \mathrm{MeV}\), it is necessary to take both coefficients into account, since the fraction of energy carried out of the crystal begins to increase. In registering the hard bremsstrahlung of a betatron, the dominant factor is the removal of energy from the crystal, while self-absorption of light photons can most often be neglected.

Accordingly, it is necessary to know, on the one hand, the dependence of the photocontribution, characterizing the fraction of completely absorbed quanta and, consequently, the fraction of energy carried out of the crystal, and, on the other hand, the dependence of self-absorption on the dimensions of the scintillation crystal.

In the present work we consider only the first question.

Conclusion

The materials considered in the present article are of definite interest from the standpoint of using the possibilities

…spectrometry of bremsstrahlung and gamma radiation for the needs of practical defectoscopy.

The study and analysis of radiation spectra obtained behind absorbers of various thicknesses and densities, as well as analysis of instrumental spectra, make it possible to approach correctly the question of the optimal conditions for radiographic inspection of materials and products and thereby to significantly expand the possibilities of inspection by radiography.

It may be hoped that the use, proposed by the authors, of the spectrometric method for the purposes of defectoscopy by radiography will prove to be the most promising from the standpoint of solving problems of nondestructive inspection of materials and products by gamma radiation.

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