ENERGY STORED IN ALKALI-HALIDE CRYSTALS UNDER IRRADIATION

E. K. ZAVADOVSKAYA, A. V. KUZMINA

Introduction

Under the influence of irradiation, defects are formed in the lattice of alkali-halide crystals. One type of defect is color centers. Energy, which is commonly called stored energy, is expended on the formation of color centers and other defects.

Knowledge of the laws governing the storage of energy and of its magnitude will make it possible to obtain information about the nature of lattice distortions under the influence of irradiation. No less important are data on the temperature stability of these distortions, as well as on which of them are responsible for changes in the various properties of alkali-halide crystals.

Many properties of ionic structures depend on the energy of the crystal lattice. Among ionic compounds, crystals with higher lattice energy possess greater mechanical, chemical, and thermal stability and higher dielectric strength.

It is of interest to compare the magnitude of the stored energy in alkali-halide crystals after $\gamma$-irradiation at room temperature with the lattice energy.

Stored energy after irradiation

in crystals of different chemical composition

One of the methods for determining stored energy is to measure the temperature difference between a reference crystal and an irradiated crystal during their simultaneous and uniform heating in a calorimeter [1]. In the course of annealing in this case, heat $Q$ is released. Figures 1 and 2 present the dependence of the rate of heat release on temperature after different doses of $\gamma$-irradiation in NaCl and KCl crystals.

The release of stored energy reaches a maximum at two temperatures. In an NaCl crystal the first maximum corresponds to $150^\circ\mathrm{C}$ ($kT = 3.6 \cdot 10^{-2}$ eV), and the second to a temperature of $250^\circ\mathrm{C}$ ($kT = 4.5 \cdot 10^{-2}$ eV). In a KCl crystal the first maximum is at a temperature of $130^\circ\mathrm{C}$ ($kT = 3.4^{-2}$ eV), and the second at a temperature of $130^\circ\mathrm{C}$ ($kT = 4.35 \cdot 10^{-2}$ eV).

In both cases the height of the first maximum (the low-temperature one) increases with increasing irradiation dose; the half-width remains un-

variable, while the height of the second (high-temperature) maximum does not change noticeably with the dose of γ-irradiation from a Co\(^{60}\) source.

The total amount of heat released in NaCl is considerably greater than in KCl. Figure 3 shows a plot of the stored energy in NaCl (1) and KCl (2) crystals as a function of the irradiation dose.

Fig. 1. Dependence of the rate of heat release on temperature after various doses of γ-irradiation in an NaCl crystal.

Fig. 2. Dependence of the rate of heat release on temperature after various doses of γ-irradiation in a KCl crystal.

Fig. 3. Dependence of the amount of stored energy in NaCl (1) and KCl (2) crystals on the dose of γ-irradiation.

As can be seen from the graph, the amount of stored energy in NaCl crystals increases with increasing irradiation dose much more rapidly than in KCl, and in magnitude at the maximum irradiation dose is 3.0 times greater than in KCl (1.8 cal/g for NaCl and 0.6 cal/g for KCl).

By the same method, the stored energy in LiF crystals was determined after x-ray and γ-irradiation at room temperature.

Figure 4 shows the dependence of the rate of heat release on temperature for LiF after x-ray irradiation with a dose of \(1.7 \cdot 10^5\) roentgens. In the spectrum of stored-energy release there are two max-

maximum. The first maximum is at a temperature of 230°C, while the second maximum is not completely recorded, since it lies beyond 400°C, the temperature up to which the crystals were annealed.

Fig. 4. Dependence of the rate of heat release on temperature in a LiF crystal after X-ray irradiation.

Fig. 5. Dependence of the rate of heat release on temperature after various doses of γ irradiation in a LiF crystal.

Figure 5 shows the dependence of the rate of heat release in LiF on temperature after various doses of γ irradiation. The rate of release of stored energy in LiF has a maximum at 230°C. The height of this maximum does not depend on the irradiation dose. As the dose of γ irradiation increases, the width of the peak increases. Table 1 gives the values of the stored energy in LiF after X-ray and γ irradiation at room temperature. As can be seen from Table 1, the magnitude of the stored energy in LiF crystals after exposure to ionizing radiation is very large: an order of magnitude greater than in NaCl and KCl crystals.

Table 1

Magnitude of the stored energy in LiF crystals after gamma and X-ray irradiation

The magnitude of the stored energy can be measured from the difference in the heats of solution of irradiated and unirradiated samples during their simultaneous dissolution in a microcalorimeter [3]: \(\Delta Q = Q_{\text{unirr}} - Q_{\text{irr}}\).

Table 2 gives the values of the stored energies obtained by the dissolution method in NaCl, KCl, KBr, and KJ crystals after various doses of gamma irradiation at room temperature [4].

In crystals with a higher lattice energy, the magnitude of the stored energy is also larger (Table 2).

The magnitude of the stored energy obtained by this method is somewhat higher than that obtained by the annealing method. In explaining this

Table 2

Magnitude of the stored energy after γ-irradiation at room temperature, determined by the dissolution method in NaCl, KCl, KBr, and KJ crystals

differences, it should be taken into account that alkali-metal atoms may appear in irradiated crystals. Therefore it is necessary to introduce into the measurement results an energetic addition \(\Delta Q_{\text{chem}}\).

According to Phelps [5], this correction has a sign opposite to the sign of the stored energy. The dependence on the γ-irradiation dose of the difference of the heats of dissolution is shown in Fig. 6 for NaCl and KJ crystals.

After smaller irradiation doses this difference has a large value and is positive. With increasing irradiation dose, the difference of the heats of dissolution decreases; after a dose of \(3.75 \cdot 10^8\) roentgens for NaCl it is equal to zero, and with a further increase in irradiation dose this difference becomes negative and increases in absolute value. A positive value of the difference of the heats of dissolution means that the heat of dissolution of the irradiated crystal is less than that of the unirradiated one. A negative value of this difference indicates that the heat of dissolution of the irradiated crystal is greater than that of the unirradiated one. This phenomenon can be explained as follows. In the experiments, the difference of the heats of dissolution is measured:

\[ Q_{\text{unirr}} - Q_{\text{irr}} = \Delta Q. \]

This difference can be decomposed into two components: \(\Delta Q_{\text{stored}}\)—the change in the free energy in the crystal under the influence of irradiation, i.e., the stored energy, and \(\Delta Q_{\text{chem}}\)—a correction that must be introduced into the calorimetric measurements in order to take into account changes in the chemical composition of the irradiated crystals. The correction \(\Delta Q_{\text{chem}}\) has a sign opposite to that of the stored energy \(\Delta Q_{\text{stored}}\). It is possible that, with increasing irradiation dose, this \(\Delta Q_{\text{chem}}\) becomes equal to and even greater than the stored energy, which explains the change in sign of the difference of the heats of dissolution.

Fig. 6. Dependence of the difference of the heats of dissolution of unirradiated and irradiated NaCl and KJ crystals, \(\Delta Q = Q_{\text{unirr}} - Q_{\text{irr}}\), on the γ-irradiation dose.

The stored energy in NaCl under the influence of plastic deformation at room temperature was measured by A. I. Garber [6]. With a compressive deformation of 6.64% and a maximum stress of \(1.02\ \text{kg}/\text{mm}^2\), the stored energy obtained by him was equal to \(0.096\ \text{kcal}/\text{g}\) \((2.5 \cdot 10^{17}\ \text{eV})\).

Assuming that there is a linear dependence between the amount of stored energy and the relative deformation, a stored-energy value in NaCl of about 1 cal/g can be obtained at a relative deformation of \(\sim 40\%\), unattainable at room temperatures.

K. Kobayashi [1] irradiated NaCl with protons of energy 350 MeV and then measured the energy released on heating the crystals from room temperature to \(400^\circ\)C. In these experiments, two maxima of heat release in the irradiated crystals were also observed.

Stored energy calculated per one F-center

In the experiments of K. Kobayashi [1] and in the present work the crystals were strongly colored. The density of F-centers, determined by extrapolation, was \(3.6 \cdot 10^{18}\ \text{cm}^{-3}\) for an irradiation dose of \(3.5 \cdot 10^8\) roentgens.

The results of measurements of the absorption spectra, shown in Fig. 8, demonstrated that at room temperature the \(V\)-band in NaCl and KCl crystals is small in comparison with the \(F\)-band; therefore, assuming that the energy is stored in the form of \(F\)-centers, we calculated the energy stored by an \(F\)-center and found it to be \(8.3 \pm 1.5\) eV.

The total stored energy, calculated per one \(F\)-center from the data of K. Kobayashi, was equal to 4.3 eV.

Phelps et al. [5] obtained a value of the energy stored by one \(F\)-center after x-ray irradiation equal to \(9.2 \pm 0.2\) eV. The stored energy was determined by the method of dissolution in a differential calorimeter. To the measured value of the energy stored by one \(F\)-center (5.5 eV), a correction \(\Delta Q_{\text{chem}} = 3.7\) eV was added. The value they obtained is close to the theoretical value of the energy of formation of an \(F\)-center, equal to 9.6 eV per \(F\)-center [9].

Table 3 gives the values of stored energy, calculated per one \(F\)-center, in crystals of different chemical composition, according to the results of the present work and those of other authors.

Table 3

Value of the stored energy, calculated per one F-center, in crystals of different chemical composition, according to the results of the present work and other authors

The values of the stored energy, calculated per one \(F\)-center, obtained in the present work, correlate with the values of the energy absorbed in the listed crystals for the formation of one \(F\)-center after irradiation with X-rays at room temperature, according to the data of work [7], given in Table 4.

Table 4

Magnitude of the energy absorbed for the formation of one \(F\)-center after X-ray irradiation at room temperature

Results of microhardness measurements in NaCl, KCl, KBr, and KJ crystals after gamma irradiation at room temperature

Figure 7 gives the results of microhardness measurements in NaCl, KCl, KBr, and KJ crystals after different doses of gamma irradiation. The greatest change in microhardness is observed in NaCl crystals. Their microhardness increases rapidly with increasing irradiation dose. In the KCl crystal an increase in microhardness is also observed, but at a lower rate. In KBr crystals the microhardness increases, but is already close to saturation. In KJ crystals the microhardness changes only slightly.

Figure 8 gives the results of measurements of the absorption spectra in alkali-halide crystals NaCl, KCl, KBr, and KJ after different doses of \(\gamma\)-irradiation. As is evident from the absorption spectra, in NaCl and KCl crystals the \(F\)-band is considerably larger in magnitude than the \(V\)-band. The \(M\)-band in these crystals is also small. The concentration of \(M\)-centers is less than \(5\%\) of the concentration of \(F\)-centers. In KBr and KJ crystals the concentration of \(F\)- and \(V\)-centers is much lower than in NaCl and KCl.

Fig. 7. Dependence of microhardness in NaCl, KCl, KBr, and KJ crystals on the dose of \(\gamma\)-irradiation.

The magnitude of the stored energy, as was shown earlier, also decreases significantly from NaCl to KJ. Thus, \(F\)-centers or other defects whose formation is associated with the formation of \(F\)-centers are responsible for the increase in microhardness.

The data we obtained on microhardness measurements do not co-

agree with the results of E. L. Andronikashvili et al. [8]. In their work the microhardness of a KCl crystal decreased with increasing concentration of F-centers formed under the action of X-ray irradiation. A possible explanation of this discrepancy may be that in the work of E. L. Andronikashvili et al. a much smaller dose interval and a lower intensity of ionizing radiation were investigated.

Fig. 8. Absorption spectra in NaCl, KCl, KBr, and KJ crystals after γ-irradiation at room temperature.
1 — irradiation dose \(1.5 \cdot 10^8\) roentgens,
2 — irradiation dose \(2.5 \cdot 10^8\) roentgens,
3 — irradiation dose \(3.5 \cdot 10^8\) roentgens,
4 — irradiation dose \(5.0 \cdot 10^8\) roentgens.

Conclusions

As a result of measurements of the stored energy in alkali-halide crystals LiF, NaCl, KCl, KBr, and KJ, the following conclusions may be drawn.

1. The magnitude of the stored energy depends on the chemical composition of the crystals, which is expressed in the fact that in crystals with a higher lattice energy the magnitude of the stored energy is greater.

2. The magnitude of the energy stored by one \(F\)-center also depends on the chemical composition of the crystals. In crystals with a higher lattice energy the magnitude of the energy stored by one \(F\)-center is smaller. This means that:

a) in NaCl crystals the principal contribution to the magnitude of the stored

energy is contributed by \(F\)-centers, since the amount of stored energy calculated per one \(F\)-center is close to the theoretical value of the energy of formation of an \(F\)-center.

b) In crystals with a lower lattice energy, the main contribution to the stored energy is made by other, more complex defects, which are complex aggregates that cannot be detected by the optical method.

In conclusion, the authors consider it their pleasant duty to express their sincere gratitude to Professor Doctor Aleksandr Akimovich Vorob’ev for valuable comments and advice in carrying out this work.

REFERENCES

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