Dielectric Losses in NaCl Crystals Before and After Exposure to Ionizing Radiation

Yu. M. Annenkov

Over the past 15 years it has been reliably established that the dielectric properties of alkali-halide crystals are determined not only by the polarization of electronic and ionic displacement. The presence of peaks in $\operatorname{tg}\delta$ and dispersion in the frequency dependence of the dielectric permittivity indicates a certain concentration of polarizing defects in the NaCl-type structure, whose dimensions are larger than the lattice constant [1, 2].

The mechanism of dielectric relaxation in alkali halides has not been resolved unambiguously and remains a subject of discussion.

With the development of reactor engineering and particle-acceleration technology, experimenters have acquired new methods for generating structural defects.

Radiation exposure of materials has proved promising for expanding our knowledge of the structure of a real crystal. Therefore, in recent years the study of damage caused by irradiation has occupied an important place within solid-state physics.

The study of the dielectric properties of irradiated alkali-halide crystals usefully supplements information on the kinetics of formation of radiation defects, obtained mainly by methods of absorption spectroscopy.

Physical Concepts of Dielectric Losses in NaCl Crystals

The objects of study were artificial single crystals of NaCl grown from the melt. The temperature and frequency dependences of $\operatorname{tg}\delta$ were studied in the audio-frequency range at temperatures of 20–200°C. Preliminary experiments showed a significant influence of the hygroscopicity of the crystals on dielectric losses. Therefore, all measurements were carried out in an evacuated system at a vacuum of $10^{-3}$–$10^{-4}$ mm Hg.

Typical dependences of dielectric losses in NaCl crystals on temperature are shown in Fig. 1. Curve 1 characterizes

the temperature variation of the dielectric-loss angle at an electric-field frequency of 250 Hz. 51°C corresponds to the maximum of $\operatorname{tg}\delta$, whose position shifts toward higher temperatures with increasing frequency. Such behavior of the dispersion peak of the loss angle is typical of a relaxation process caused by dipole polarization and can be described by Debye’s theory.

Fig. 1. Dependence of $\operatorname{tg}\delta$ on temperature for NaCl crystals. 1—250 Hz, 2—500 Hz, 3—1000 Hz.

Separating the imaginary and real parts of the complex dielectric permittivity, we write Debye’s equation in the form

\[ K' = K'_{\infty} + \frac{K'_s - K'_{\infty}}{1+\omega^2 \tau_e^2}, \tag{1} \]

\[ K'' = \frac{(K'_s - K'_{\infty})\cdot \omega \tau_e}{1+\omega^2 \tau_e^2}, \tag{2} \]

where

$K'$—the real part of the complex dielectric permittivity,

$K''$—the imaginary part of the complex dielectric permittivity.

\[ \tau_e' = \tau \frac{K'_s + 2}{K'_{\infty}+2} \]
—the time constant of the relaxation process; \(\tag{3}\)

\[ \tau = 1/2\nu \cdot \exp(U/kT), \tag{4} \]

where

\(U\) — activation energy of the relaxation process,
\(\nu\) — frequency of vibration of the ion in the equilibrium position,
\(k\) — Boltzmann constant,
\(T\) — absolute temperature.

\(K'_{\infty}\) and \(K'_s\) are defined as the quantities \(K'\) at \(\omega \gg \tau_e\) and \(\omega \ll \tau_e\). For alkali-halide crystals one may take \(K'_s \simeq K'_{\infty}\) and write the formula for \(\operatorname{tg}\delta\) in the following form:

\[ \operatorname{tg}\delta = \frac{K''}{K'_{\infty}} = \frac{(K'_s-K'_{\infty})\cdot \omega\tau} {K'_{\infty}\cdot [1+(\omega\tau)^2]} . \tag{5} \]

Under the resonance condition \(\omega\tau = 1\), the dielectric-loss angle reaches its maximum value

\[ \operatorname{tg}\delta_{\max} = \frac{K'_s-K'_{\infty}}{2K'_{\infty}} . \tag{6} \]

Use of the Clausius–Mossotti equation makes it possible to determine \((K'_s-K'_{\infty})\) through the molecular parameters of the polarizing dipoles and thereby to estimate the number of relaxators (3)

\[ n = \frac{18\cdot \varepsilon_0\cdot kT\cdot K'_{\infty}\cdot \operatorname{tg}\delta_{\max}} {(Z\cdot e\cdot a)^2\cdot (K'_{\infty}+2)^2}, \tag{7} \]

\((Z\cdot e\cdot a)\) — the dipole moment of the orienting complexes.

We assume that \(z\cdot e\) is equal to the charge of the electron,
\(a\) — is of the order of the lattice constant,
\(\varepsilon_0\) — the dielectric constant in vacuum.

Analysis of formula (7) leads to the conclusion that the concentration of dipoles causing the maximum in the temperature dependence of \(\operatorname{tg}\delta\) for NaCl crystals reaches \(2.3\cdot 10^{16}\ \mathrm{cm}^{-3}\).

The activation energy of the relaxation process, found from the displacement of the positions of the temperature peaks of \(\operatorname{tg}\delta\) upon changing the frequency, is \(0.68\ \mathrm{eV}\).

Comparison of the values of \(\operatorname{tg}\delta\) experimentally measured with those calculated from the electrical conductivity indicates that ionic conductivity is responsible for the dielectric losses at temperatures above \(80^\circ\mathrm{C}\) (1000 Hz).

In connection with this, there is a real possibility of determining the activation energy for the motion of free cation vacancies. It was found to be \(0.92\ \mathrm{eV}\).

The energy characteristics obtained by us for the relaxation and electrical-conductivity processes observed in NaCl crystals agree satisfactorily with the results of works [3, 4].

Thermal defects in alkali-halide crystals are prone to intensive aggregation. The simplest associate is a pair consisting of an anion and a cation vacancy. In addition, impurity rare-earth ions can combine with cation vacancies. Both types of defects are characterized by an effective dipole moment and, orienting in an alternating field, increase the dielectric losses.

It should be noted that cation vacancies are more mobile if they are bound to anion sites or divalent ions [5].

Comparison of the activation energy of the relaxation process (\(0.68\ \mathrm{eV}\)) with the activation energy for migration of free vacancies (\(0.92\ \mathrm{eV}\)) leads to the conclusion that dipole polarization is determined-

…by jumps of a cation vacancy, or around an impurity ion, or around an anion vacancy.

The dosed introduction of a divalent impurity into the crystals will probably make it possible to resolve unambiguously the question of the nature of the relaxation maximum of $\tg \delta$ observed by us.

For this purpose, the temperature dependences of dielectric losses in solid solutions NaCl—Mn were investigated. The introduction of an impurity into NaCl causes an increase of $\tg \delta$ over the entire temperature interval (Fig. 2), which indicates the appearance of a large number of weakly bound ions and cation vacancies.

Fig. 2. Dependence of $\tg \delta$ on temperature at a frequency of 1000 cps for NaCl—Mn crystals.
1 — NaCl + $2\cdot10^{-3}$ mol.% $\mathrm{Mn}^{++}$
2 — NaCl + $4\cdot10^{-3}$ mol.% $\mathrm{Mn}^{++}$
3 — NaCl + $5\cdot10^{-2}$ mol.% $\mathrm{Mn}^{++}$.

The maximum that occurs in the temperature dependence of $\tg \delta$ for pure specimens is regularly reproduced; moreover, a change in the manganese content in the crystal does not affect its amplitude. In the high-temperature region three additional peaks of $\tg \delta$ appear, associated with the presence of the activator.

Thus, in modeling the dipoles that cause relaxation in sodium chloride, we consider the associate of oppositely charged vacancies to be the more probable one.

Spectral analysis of the pure NaCl crystals studied shows the presence of random Ca and Mn ions in concentrations of approximately \(5 \cdot 10^{16}\ \text{cm}^{-3}\). This value is of the same order as the previously calculated number of relaxing dipoles. However, a considerable fraction of the impurity is located not at regular lattice sites but at weakened sites [6], and does not participate in the formation of “cation vacancy—divalent ion” complexes. Such a quantitative comparison also confirms the model of the relaxator as an associated pair of vacancies.

Dielectric losses in NaCl crystals after irradiation with ionizing radiation

The first stage of the formation of \(F\)-centers under the action of irradiation at room temperature is characterized by a considerable rate of the process and is due mainly to vacancies present before irradiation [7]. Thermal defects in alkali-halide crystals are predominantly in the associated state; therefore it is believed that irradiation leads to intensive destruction of vacancy bonds with subsequent generation of color centers.

Having detected dielectric relaxation in NaCl, caused, as we believe, by associated pairs of vacancies, one can use the dielectric-loss method to follow the change in the concentration of such formations after excitation of the crystal by radiation.

We chose x-ray irradiation and proton bombardment in order to compare the influence of different types of radiation on dielectric losses in NaCl crystals.

The single crystals studied were colored by x-rays from an RUP-2 apparatus (\(200\ \text{kV},\ 20\ \text{mA}\)). The absorbed energy was calculated from the experimentally obtained x-ray attenuation coefficient and varied from \(5 \cdot 10^{19}\ \text{eV}/\text{cm}^{3}\) to \(2 \cdot 10^{21}\ \text{eV}/\text{cm}^{3}\).

Irradiation with protons accelerated to \(4.1\ \text{MeV}\) was carried out on the cyclotron of the Scientific Research Institute of Technical Physics. The dose absorbed in the crystal varied from \(2 \cdot 10^{22}\ \text{eV}/\text{cm}^{3}\) to \(5 \cdot 10^{23}\ \text{eV}/\text{cm}^{3}\).

Figure 3 gives the dependences of \(\operatorname{tg}\delta\) on temperature for NaCl crystals irradiated with x-rays and protons. With increasing energy of the x-radiation absorbed by the crystals, in the temperature range from \(20^\circ\text{C}\) to \(110^\circ\text{C}\), \(\operatorname{tg}\delta\) decreases; at the same time the amplitude of the peak observed for uncolored specimens increases.

Proton bombardment qualitatively reproduces the picture of radiation damage to crystals by x-rays. However, increasing the absorbed dose of proton radiation from \(2 \cdot 10^{22}\ \text{eV}/\text{cm}^{3}\) to \(5 \cdot 10^{23}\ \text{eV}/\text{cm}^{3}\) does not affect the magnitude of the effect. With increasing frequency, the position of the \(\operatorname{tg}\delta\) peak in irradiated NaCl single crystals shifts according to the same regularity as for specimens not disturbed by radiation (Fig. 4).

After x-irradiation of sodium chloride, the absorption spectrum has \(F\)-, \(V_{3}\)-, and weak \(M\)-bands. Proton bombardment causes the appearance of analogous absorption bands, but more intense ones.

Fig. 3. Temperature variation of $\mathrm{tg}\,\delta$ at a frequency of 1000 Hz for NaCl crystals.
○—○ — unirradiated specimens.
Specimens irradiated with X-rays:
□—□ — $2.5 \cdot 10^{20}$ eV/cm³;
△—△ — $5.0 \cdot 10^{20}$ eV/cm³;
×—× — $1.2 \cdot 10^{21}$ eV/cm³;
●—● — after proton irradiation ($1.0 \cdot 10^{23}$ eV/cm³).

Fig. 4. Temperature dependences of $\lg \delta$ for crystals irradiated with X-rays and gamma rays ($1.0 \cdot 10^{23}$ eV/cm³) in NaCl.
1 — 50 Hz; 2 — 500 Hz; 3 — 1000 Hz; 4 — 5000 Hz.

At temperatures above \(110^\circ\mathrm{C}\), the values of \(\operatorname{tg}\delta\) in irradiated and unirradiated specimens coincide completely.

Heating NaCl crystals damaged by X-rays and protons to \(200^\circ\mathrm{C}\) eliminates the coloration, and upon repeated measurement of the dielectric losses in the temperature course the \(\operatorname{tg}\delta\) maximum is reproduced, with the same amplitude and half-width values as were observed in the unirradiated specimens.

Fig. 5 illustrates the temperature dependence of \(\operatorname{tg}\delta\) at 50 Hz for X-rayed and unirradiated NaCl crystals. Since, at the chosen measurement frequency, \(\operatorname{tg}\delta\) in the temperature range above \(60^\circ\mathrm{C}\) is determined by ionic conductivity, the results presented in Fig. 5 clearly show the change in the electrical conductivity of the crystals under study due to X-irradiation.

Fig. 5. Dependence of \(\operatorname{tg}\delta\) on temperature for
1 — unirradiated NaCl crystals,
2 — crystals irradiated with X-rays
\((5.0 \cdot 10^{20}\ \mathrm{eV/cm^3})\).
(The doses of proton and X-ray irradiation correspond to the energy absorbed by the crystals).

Radiation exposure causes an increase in the resistance of NaCl single crystals in the temperature range \(60\text{–}110^\circ\mathrm{C}\). At higher temperatures, the values of the electrical conductivity in irradiated and unirradiated specimens coincide.

Thus, the action of protons and X-rays on NaCl causes the appearance of identical defects, which is in agreement with the theory of energy loss by a charged particle in a substance—

[8]. Radiation increases the number of associated vacancy pairs responsible for dielectric relaxation, and decreases the concentration of free cation vacancies.

The vacancy pairs produced in excess by irradiation are thermally unstable and are destroyed at a temperature close to \(110^\circ\mathrm{C}\). Moreover, at this same temperature the number of free cation vacancies, which determine the electrical-conduction process, increases to the value in an unirradiated crystal.

This fact indicates that ionizing radiation does not generate cation vacancies. The process of radiation damage is probably reduced to the creation of anion vacancy–interstitial pairs. Some of the anion vacancies capture electrons, forming \(F\)-centers; another part associates with free cation vacancies, removing them from the conduction process and increasing the amplitude of the relaxation maximum that occurs in unirradiated crystals.

The low thermal stability of vacancy pairs formed in excess as a result of irradiation is probably connected with the fact that the dipoles are located near interstitial halide ions. At a sufficiently high temperature the latter take up their normal positions, thereby releasing the cation vacancies.

The proposed process of thermal annealing of radiation defects must proceed in parallel with the destruction of some hole color centers.

References

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