DISTRIBUTION OF COLOR DENSITY AND ABSORBED ENERGY OF FAST ELECTRONS IN ALKALI-HALIDE CRYSTALS

B. A. Kononov, O. B. Evdokimov
(Presented by the scientific seminar of the Faculty of Physics and Technology)

Introduction

When electrons pass through a substance, their energy decreases; therefore, one may expect differences between the distribution of energy losses of the electron beam and the distribution of changes in properties. In general, it would be of interest to compare the spatial variation of one property or another along the length of a crystal with the spatial distribution of those energy losses along the path of the electrons which take a direct part in changing the given property and can be measured. In particular, a comparison of this kind is possible by comparing the ionization energy losses of fast electrons with the change in the number of \(F\)-centers along the path of the electron flux. In this case the concentration of \(F\)-centers must lie within the limits of the first stage of their accumulation, when the formation of new vacancies due to elastic interaction with the nuclei of the substance is still insignificant, and the basic process is the filling of anion vacancies already present in the crystal by slow electrons formed in the process of ionization of the crystal atoms.

Below we report the results of such experiments for NaCl and LiF crystals.

Experimental studies and results

NaCl and LiF crystals were irradiated with a collimated beam of electrons with an energy of 6 MeV from a betatron. The exposure dose was monitored by a transmission chamber at the entrance to the collimator. The chamber was calibrated by means of a Faraday cylinder, which during calibration was placed in the position of the crystal.

The crystal under study, with dimensions \(30 \times 18 \times d\ \text{mm}^3\) (where the crystal thickness was \(d = 1.5\text{–}2\ \text{mm}\)), was placed along the electron beam at the center of the collimator; two crystals of the same substance were adjoined to its sides (dimensions \(30 \times 18 \times 15\ \text{mm}^3\)) in order to reduce the leakage of fast electrons from the crystal and to facilitate measurement of the distribution of absorbed energy. After irradiation, the crystal, together with a special carriage, was placed in the cuvette chamber of an SF-4 spectrophotometer perpendicular to the light beam. At the entrance to the cuvette chamber, an additional slit 1 mm wide and 2 mm high was installed near the carriage with the crystal. Measurement of the distribution of the absorption coefficient at the maximum of

The $F$-band was carried out by moving the carriage with the aid of a special micrometer screw with a division value of 10 μm in a direction perpendicular to the light beam.

The method for measuring the distribution of absorbed energy by the ionization method was taken from [1]. A miniature ionization chamber was used, with walls made of the material of the crystal under investigation. The dimensions of the chamber were $20 \times 18 \times 16\ \mathrm{mm}^3$; the larger dimension was placed along the electron beam. The working volume of the chamber, $2 \times 2 \times 1\ \mathrm{mm}^3$, was located at the center of the front wall of the chamber. The ionization distribution was measured at those points at which the distribution of the absorption coefficient $\alpha_F$ at the maximum of the $F$-band was subsequently measured.

Figure 1 shows the relative distribution of $\alpha_F$ over the depth of a NaCl crystal (curve 1) (the coloration maximum corresponds to $\alpha_F = 3.3\ \mathrm{cm}^{-1}$) and the distribution of absorbed energy at the same points (curve 2). Curves 1 and 2 have been conditionally superposed at the maximum of curve 2. Since curves 1 and 2 in Fig. 1 do not coincide, it follows that there is no proportionality between the value of the absorption coefficient $\alpha_F$ and, consequently, between the number density of $F$-centers and the magnitude of ionization over the depth of the crystal. The same result is observed at electron energies $E = 9\ \mathrm{MeV}$ and $3\ \mathrm{MeV}$ for NaCl crystals, and also for LiF and KBr at $E = 6\ \mathrm{MeV}$. The data for LiF, $E = 6\ \mathrm{MeV}$, are shown in Fig. 2.

Fig. 1. Distribution of the relative value of the absorption coefficient at the maximum of the $F$-band (curve 1) and of absorbed energy, measured by the ionization method, over the depth of the crystal (curve 2), NaCl.

Fig. 2. Distribution of the relative value of the absorption coefficient at the maximum of the $F$-band (curve 1) and of absorbed energy over the depth of the LiF crystal (curve 2).

Discussion of the Results

The absence of proportionality between the concentration of ions and the density of the $F$-centers formed (absorption coefficient) may be caused by a number of reasons. These include the influence

intensity (whose distribution in relative units is characterized by curves 2 in Figs. 1 and 2), different average directions of the electrons with respect to the crystal lattice at different depths of the crystal, and phenomena associated with changes in the energy composition of the electrons with depth. According to [2], when the number of electrons incident on the crystal surface per unit time is decreased, a decrease is observed in the efficiency of formation of \(F\)-centers in the first stage of accumulation. This gives grounds to suppose that the observed deviation from proportionality between the density of \(F\)-centers and the ion density with depth in the crystal is not connected with the influence of intensity, since curve 1 in Figs. 1 and 2 lies above curve 2.

The influence of a change in the angle between the trajectories of fast electrons and the crystal lattice is evidently excluded, since the role of atomic displacements at the stage of coloration under consideration is not significant.

To each point of the crystal, for a given energy of the primary electrons and a given experimental geometry, there corresponds unambiguously a definite electron spectrum. As the electron flux penetrates into the crystal, the mean electron energy in the spectrum decreases and the number of slow electrons becomes larger. In this same direction we have found an increase in the efficiency of formation of the number of \(F\)-centers per unit volume, calculated per ion formed; their relative distribution with depth is given by curves 2 in Figs. 1 and 2. The relative increase of this efficiency with depth in the crystal (i.e., in the direction of decreasing mean energy of the electron spectrum) is shown in Fig. 3. Qualitatively analogous results are obtained for LiF and KBr; moreover, for KBr the increase in efficiency with depth in the crystal is still more substantial. The larger number of \(F\)-centers per one ion formed in the first stage of their accumulation in the direction of decreasing mean energy of the electron spectrum may be caused by a number of reasons. An increase in the specific ionization losses may lead to the fact that

Fig. 3. Relative increase in the efficiency of formation of \(F\)-centers with depth in an NaCl crystal.

a) with an increase in \(dE/dx\), the role of thermal phenomena in the track in breaking vacancy bonds increases more rapidly than the number of ions per unit volume increases;

b) the same occurs also owing to the participation of electron energy losses in excitation and to an increase in the share of these losses in the total ionization losses.

There are as yet no grounds for expecting an increase in the probability of capture of slow electrons by an anion vacancy with increasing \(dE/dx\).

For a qualitative verification of assumptions a) and b), measurement of the distribution of absorbed energy through the crystal was carried out by a scintillation method.

Preliminary results were obtained in a geometry different from the preceding one. The diameter of the paraffin collimator was 40 mm. The miniature chamber was borrowed from [1]. In measurements by the scintillation method, the air volume of the chamber is replaced by an (air-equivalent) plastic scintillator based on polystyrene + 2% p-terphenyl + 0.1% POPOP. The light flux was led by a plexiglass light guide 20 cm long to an FEU-12 photomultiplier placed behind lead shielding. The photocurrent of the photomultiplier was measured with a galvanometer.

Figure 4 gives the results of measuring the distribution of absorbed energy by the scintillation (curve 1) and ionization (curve 2) methods under identical conditions. In organic scintillators the scintillation process is due to excitation of their molecules, so that the light flux is proportional to the loss of electron energy for excitation of molecules, with a correction for the nonlinearity of the light yield with energy at small electron energies.

Fig. 4. Distribution of absorbed energy through the crystal, measured by the scintillation (curve 1) and ionization methods (curve 2).

Thus, curve 2 in Fig. 4 characterizes the relative distribution of losses to ionization, while curve 1 characterizes, to within the linearity of the light yield with electron energy, the relative distribution of losses to excitation. Introducing a correction for the decrease of the specific light yield at small electron energies will naturally lead to a rise of curve 1. This correction will be the larger, the deeper in the crystal the point under consideration is. The exact magnitude of the correction requires knowledge of the electron spectrum at different depths in the crystals.

The relative positions of curves 1 and 2 in Fig. 4 support the assumption that the losses of electron energy to excitation of atoms of the substance participate in the process of formation of \(F\)-centers, at least at low densities of \(F\)-centers. The relative positions of curves 1 and 2 suggest that, as the electron energy decreases, the fraction of losses to excitation in the total ionization losses of the electrons increases.

Conclusions

1. The distribution of the density of \(F\)-centers with depth in alkali-halide crystals within the first stage of their accumulation does not coincide with the distribution of ions formed as a result of irradiation by fast electrons.

2. The observed phenomenon can be explained by the participation of losses of electron energy to excitation in the process of formation of \(F\)-centers.

LITERATURE

1. B. A. Kononov, V. N. Rudenko. Proceedings of the Conference “Effect of Radiation on the Properties of Materials,” Novosibirsk, issue 2, 1963.

2. W. A. Sibley, E. Sonder, J. Appl. Phys. 34, No. 8, 2366, 1963.