ON THE CHOICE OF OPTIMAL SCINTILLATOR DIMENSIONS FOR FLAW DETECTION IN PRODUCTS

V. I. GORBUNOV, V. K. KULESHOV

(Presented by the scientific seminar of the Scientific Research Institute of Electronics)

The work investigates the influence of the height of cylindrical scintillation crystals NaI (Tl) and CsI (Tl) on the relative light output. It has been established that, for a flaw detector with a maximum energy of 70 keV, the crystals optimal with respect to light output are those having a height \(h = 0.8\) mm.

The type of crystal treatment has a noticeable effect on the light output.

For measuring low-intensity hard radiation by the scintillation method, it is important to determine the optimal dimensions of the scintillator.

In radiation flaw detection this problem is now solved from two sides, between which a compromise is chosen:

1) the scintillator is calculated for the maximum absorbed energy;

2) the scintillator dimensions are determined from the standpoint of a minimum of optical losses in it.

Both solutions can be found both theoretically [1, 2, 3] and experimentally.

We have experimentally investigated the dependence of the light output of scintillators on their dimensions for energies from 30 keV to 30 MeV.

In the present article, results are presented on the investigation of the dependence of the light output on the height of NaI (Tl) and CsI (Tl) scintillators for x-radiation from a URPO-70-4 tube.

The CsI (Tl) crystals were treated as follows. In all specimens the side surface was matted. The end faces were ground first on fine emery paper and then on silk fabric. For better grinding, cerium oxide diluted in ethyl alcohol was used. During grinding, glass-like transparency was achieved. If it was necessary to reduce the crystal by large thicknesses, it was simply sawed with a thread moistened in water. Then treatment was carried out in the same sequence.

Matting of the surface was carried out with emery paper.

Treatment of NaI (Tl) crystals differs in no way from that described above for CsI (Tl). However, there are differences in their use, associated with the fact that NaI (Tl) possesses fairly high hygroscopicity. The latter leads to the fact that, at least, ground ...

surfaces had to be protected during the experiment from the deposition of moisture from the air. For this purpose, glass plates were glued onto especially important surfaces by means of silicone oil having a refractive index close to that of NaI (Tl).

The investigated CsI (Tl) and NaI (Tl) crystals were placed in a light-tight case connected to a light guide, which excluded the entry of extraneous light into the recording device.

The block diagram of the setup is shown in Fig. 1. As the scintillator-light detector, an FEU-17 was used, whose spectral sensitivity lies in a region close to the emission spectra of the crystals being investigated.

1. RUM-70 X-ray unit
2. Lead collimator
3. Scintillator
4. Light guide
5. UM-2 monochromator
6. Phototube attachment with FEU
7. Amplifier
8. Recording device
9. Power-supply unit.

Fig. 1. Block diagram of the setup.

Recording was carried out by mean current. The signal from the FEU, through a direct-current amplifier, was fed to the indicating device—a V2-3 lamp voltmeter.

To avoid noise associated with the direct incidence of X-radiation on the FEU, a UM-2 monochromator was used. The use of the monochromator in this case is also useful in the sense that it makes it possible to attenuate the light flux and not overload the FEU.

The principal error in measuring the dependence of the light output of scintillators according to the indicated scheme is associated with instability of the mains and, consequently, with considerable instability of the radiation intensity of the X-ray tube. Therefore, despite the fact that the power supply of the FEU and of the amplifier is stabilized, the readings on the recording instrument change considerably with time. To avoid this error, we measured the dependences of the light output of scintillators on the intensity of the exciting X-radiation for different thicknesses (Fig. 2). Since the elements of the circuit—the scintillator, FEU, amplifier, and recording instrument—are linear, the dependence of the light outputs on the intensity of the X-radiation is also linear. The slope of the straight lines depends only on the length of the crystal.

From points of equal intensity taken from these straight lines, the dependences of the light output on the length of the crystal are constructed (Figs. 3, 4). From the graphs

![Graph with vertical axis labeled “\(J_{\mathrm{sv}}\), relative units” and horizontal axis labeled “mA”; three straight-line dependences marked \(0.8\) mm, \(5.73\) mm, and \(8.4\) mm.]

Fig. 2. Dependence of the light output of a CsI(Tl) scintillator on the intensity of the exciting X-ray radiation for various thicknesses (the numbers indicate the scintillator thicknesses; along the abscissa axis are plotted the intensities of the exciting radiation; along the ordinate axis—the light output in relative units).

![Graph with vertical axis labeled “\(J_{\mathrm{sv}}\), relative units” and horizontal axis labeled “mm”; curve labeled “CsJ(Te)”.]

Fig. 3. Dependence of the light output of a CsI(Tl) scintillator on its thickness (along the abscissa axis are plotted the thicknesses; along the ordinate axis—the light output in relative units).

from Figs. 3 and 4 one can determine the optimum height of the CsI(Tl) and NaI(Tl) scintillators for a flaw detector based on the URPO-70-4.

Within the limits of experimental error, a height \(h = 0.8\) mm may be taken as optimum for both types of scintillators. As can be seen, the curves have a sharply pronounced maximum. The increase in light output at small lengths can be explained by an increase in the number of absorbed and registered radiation quanta, whereas the decrease in light output with a further increase in height is explained purely by the phototechnical properties of scintillation crystals: the coefficient of absorption of their own radiation, reabsorption, the effect of total internal reflection, and absorption in the reflector.

Fig. 4. Dependence of the light output of the NaI(Tl) scintillator on its thickness (thicknesses are plotted along the abscissa axis; light output in relative units is plotted along the ordinate axis).

The results obtained make it possible, as a first approximation, to determine the effective coefficients of self-absorption for the crystals under investigation.

For the calculation the following restrictions are introduced:

a) the radiation is assumed to be monochromatic, having an energy corresponding to the effective energy of the X-ray radiation of the tube, determined from the generally accepted relation

\[ E_{\text{eff}} = \frac{2}{3} E_{\max}, \]

where \(E_{\text{eff}}\) is the effective energy of the X-ray radiation of the tube;
\(E_{\max}\) is the maximum energy in the energy spectrum of the tube.
In our case \(E_{\max} = 70\) keV; consequently, \(E_{\text{eff}} = 47\) keV;

b) the principal interaction mechanism is the photoelectric effect;

c) the photoelectrons formed as a result of the photoelectric effect are absorbed at the point.

Taking into account the assumptions given above, from Fig. 5 one can obtain the following expressions for the light flux \(I_{\text{light}}\) from the rear wall of the crystal:

\[ I_{\text{light}}=\alpha\mu\cdot I_0\cdot \int_0^L e^{-\mu x}\cdot e^{-\nu(L-x)}\cdot dx, \tag{1} \]

Fig. 5. Dependence of the ratio of the light output of a matted CsI(Tl) scintillator to the light output of an unmatted one on its thickness (thicknesses are plotted on the abscissa axis; the ratio of light outputs on the ordinate axis).

where \(I_0\) is the flux of \(\gamma\)-quanta incident on the front wall of the crystal;

\(I_0\cdot e^{-\mu x}\) is the flux of \(\gamma\)-quanta that have traversed a distance \(x\) inside the crystal;

\(\mu\cdot I_0\cdot e^{-\mu x}\cdot dx\) is the number of \(\gamma\)-quanta absorbed over the interval \(dx\);

\(\alpha\) is the conversion efficiency of the crystal;

\(\mu\) is the absorption coefficient of X-radiation for the given energy;

\(\nu\) is the effective absorption coefficient of the scintillator’s own radiation;

\(e^{-\nu(L-x)}\) is the attenuation coefficient of the light flux along the path \((L-x)\);

\(L\) is the length of the crystal.

As a result of integrating expression 1, we obtain

\[ I_{\text{light}}=\alpha\cdot \mu\cdot I_0\frac{\exp(-\nu L)}{(\mu-\nu)}\cdot \left[1-e^{-L(\mu-\nu)}\right], \tag{2} \]

from which it is seen that the maximum light output is obtained when the condition

\[ \nu\cdot e^{-\nu L_0}=\mu\cdot e^{-\mu L_0}, \tag{3} \]

is satisfied, where \(L_0\) is the crystal length at which the maximum scintillator light output is observed for the given \(\mu\) and \(\nu\).

Taking the known values of \(L_0\) (\(\approx 0.8\ \text{mm}\)), we find, for example, for NaI(Tl) \(\nu\approx 0.380\ \text{cm}^{-1}\).

It is clear that the coefficient obtained is very far from the true value, and determining it in this way is of interest, most likely, only from the methodological standpoint.

The main error in the calculation is obtained chiefly because the spectral distribution of X-ray \(\gamma\)-quanta by energy is not taken into account.

As was already said above, the coefficient \(\nu\) taken by us for the calculation takes into account not only the crystal’s own absorption, but also absorption in the reflector, reabsorption, etc. Thus, \(\nu\) depends on the type of reflector. It is natural to suppose that the value of \(\nu\) is affected by the type of treatment of the scintillator surfaces. It has repeatedly been pointed out in the literature [4] that the light output of scintillators depends noticeably on the treatment of their surfaces. We have established that the treatment of the front base of the specimens under study has the most noticeable influence. Thus, for example, the light output of matted CsI (Tl) crystals \(30 \times 6\) increases by a factor of 2.5 in comparison with the light output of the same specimen having a transparent front base. For NaI (Tl) crystals \(30 \times 5\), in an analogous experiment the light output changes by a factor of 1.5.

But the most interesting point is that, for differently treated specimens, the course of the dependence of light output on height changes.

Fig. 6. Explanatory diagram for deriving formula (3).

In Fig. 6 the dependence is presented of the ratio of the light outputs of CsI (Tl) specimens whose front bases are matted to the light outputs of the same specimens with transparent front bases.

As can be seen, this ratio increases with decreasing height, which clearly confirms the assumption that \(\nu\) depends on the type of treatment of scintillators.

From the above, the following conclusions may be drawn.

The light output of scintillators depends in a definite way on the height and type of treatment.

For each energy of the radiation being recorded there is a definite height that is optimal from the standpoint of maximum light output. It is determined by the coefficients $\mu$ and $\nu$. The coefficient $\nu$ depends, among other things, on the type of surface treatment of the scintillators.

REFERENCES

1. V. I. Gorbunov, V. B. Kuznetsov, V. K. Kuleshov, Yu. B. Yankelevich. Calculation of the optimal parameters of a scintillation crystal in beta-ray flaw detection of materials. Reports at the All-Union Conference on Nuclear Spectroscopy, 1964. February 14–21. Tbilisi.

2. L. S. Kukushkin and A. M. Ratner. ZhTF, XXVIII, 2, 345–350, 1958.

3. A. M. Ratner and L. S. Kukushkin. ZhTF, XXVIII, 5, 1121–1125, 1958.

4. D. Birks. Scintillation Counters. Foreign Literature Publishing House, 1955.