THERMODEPOLARIZATION CURRENTS IN KCl AND KBr CRYSTALS AT LOW TEMPERATURES

Yu. M. Annenkov, V. F. Pichugin, V. V. Peshev

(Submitted by the Scientific Department of the RFIS Research Institute of the Russian Federation)

The present level of development of radiation physics has been achieved mainly through the use of spectroscopy and luminescence-analysis methods. A broad range of ionic processes is judged indirectly by experimenters, while a number of phenomena are not controlled at all.

The use of electrophysical research methods makes it possible to obtain very useful information about ionic processes occurring in dielectrics and provides the possibility of modeling defects that take part in these processes.

The most widespread methods for studying effects caused by ion migration are the investigation of the time function of the current of a dielectric placed in a constant electric field and the measurement of dielectric losses.

Recently experimenters have begun to devote increasing attention to a method based on a phenomenon formally analogous to thermally stimulated luminescence, which has been called the thermodepolarization method (TDP). The principal advantages of this method, in comparison with methods for analyzing absorption current and dielectric losses, are its high sensitivity and the possibility of obtaining, in a single experiment, information about diverse processes whose relaxation times differ by several orders of magnitude.

When a polarized dielectric is heated at a constant rate, at certain temperatures a current begins to flow in it, caused by depolarization processes. For analysis of depolarization currents one may use the theory of thermoluminescence, which describes processes characterized by first-order kinetics [1]

\[ i(T)=N_{\alpha}\frac{p^{2}\alpha\varepsilon_{p}}{kT_{p}} \left[\tau_{0}\exp\left(\frac{E}{kT}\right)\right]^{-1} \cdot \exp\left( -\int_{T_{0}}^{T} \left[ \beta\tau_{0}\exp\left(\frac{E}{kT'}\right) \right]^{-1}dT' \right), \tag{1} \]

where \(N_{\alpha}\) is the number of dipoles, \(p\) is the dipole moment,
\(T_{p}\) is the polarization temperature, \(T_{0}\) is the cooling temperature,
\(\beta\) is the heating rate,
\(\alpha\) is a geometric factor depending on the possible orientation of the dipole, \(\varepsilon_{p}\) is the strength of the polarizing field, \(\tau_{0}\) is the frequency factor,
\(E\) is the activation energy of relaxation.

It follows from expression (1) that the function of the depolarization current on temperature has a maximum. From the extremum condition for the dependence \(i=f(T)\), the temperature corresponding to the maximum value of the current is readily determined:

\[ T_m=\left\{\frac{\beta E\tau(T_m)}{k}\right\}^{1/2}. \tag{2} \]

Here \(\tau=\tau_0 \exp(E/kT)\) is the relaxation time. The activation energy of relaxation is given by the slope of \(\ln i(T)\) as a function of \(kT\) in the temperature interval below \(T_m\):

\[ \ln i(T)=\mathrm{const}-E/kT. \tag{3} \]

All of the above pertains to a process with a single relaxation time. If \(n\) polarization phenomena characterized by different relaxation times develop in a dielectric, then the TDP spectrum will consist of \(n\) bands.

Thus, the TDP method may be useful in the study of polarization phenomena in ionic crystals and, possibly, will make it possible experimentally to detect dipole relaxation in alkali-halide crystals; this is of extremely great importance for the radiation physics of ionic structures.

We know of only a limited number of works devoted to the study of thermodepolarization in alkali-halide crystals [1–5]. These works present some data on the investigation of TDP spectra at temperatures close to room temperature, and the nature of the observed effects has not been unambiguously proved. In addition, it is of interest to carry out studies in the region of lower temperatures. In this connection, we investigated TDP processes in alkali-halide crystals in the temperature range from 80 to 300 K, with the aim of elucidating the spectrum of thermodepolarization currents and establishing the nature of the observed peaks.

This article presents the results of measurements of depolarization currents under a linear increase of temperature in KCl and KBr crystals, both “pure” and with SrCl\(_2\), PbCl\(_2\), and KOH impurities. An SP-1M electrometer with a current sensitivity of \(2\cdot10^{-14}\) A was used as the recording instrument. During the experiments, a vacuum no worse than \(10^{-3}\) torr was maintained in the cryostat. The temperature was measured with a copper–constantan thermocouple, and the rate of linear heating was \(0.1\ \mathrm{K\,s^{-1}}\).

Figures 1 (curve 1) and 2 show typical curves of thermodepolarization currents for pure KCl and KBr crystals. It is seen from the figures that the spectra have a complex nature and consist of three bands for KCl and five for KBr. It is known that in ionic crystals the establishment of dipole-orientational polarization, interlayer polarization, and also the formation of space charge due to migration of point defects are possible.

Since the studies were carried out on single-crystal samples, interlayer polarization is unlikely to occur. Space charge, as shown in [2, 5], is formed only at temperatures substantially above room temperature. At room and lower temperatures the contribution of space charge to thermionic currents will be very small; it may be neglected.

Consequently, it makes sense to consider only dipole-orientational polarization. It may be caused by various defects of the crystal lattice, among which one should first of all note complexes of the type “Me\(^{++}\)—cation vacancy”

\((Me^{++}V_k)\); hydroxyl-group ions \(\mathrm{OH^-}\) and associates of oppositely charged vacancies—dipoles \((V_a V_k)\). It should be assumed that the activation energy of relaxation is minimal for the dipole and maximal for the complex \(Me^{++}V_k\). Therefore the TDP spectra for alkali-halide crystals can be conventionally divided into three regions: a low-temperature region (80–180 K), in which the TDP current peaks can possibly be explained by relaxation of dipoles; a middle-temperature region (180–190 K), in which the TDP peaks are most likely due to the \(\mathrm{OH^-}\) group; and a high-temperature region (190–300 K), where dielectric relaxation of impurity complexes of the type \(Me^{++}V_k\) should be observed.

Fig. 1. Dependence of the depolarization current on temperature for KCl crystals (1) and \(\mathrm{KCl} + 0.25\ \mathrm{mol}\%\, \mathrm{SrCl_2}\).

Fig. 2. Dependence of the depolarization current on temperature for KBr crystals.

The experimental data made it possible to calculate the activation energies of the processes responsible for the maxima of the TDP current in the crystals studied (Table 1).

In the works of a number of authors [6], from measurements of dielectric losses, as well as from theoretical studies [7], the activation energies of polar formations in alkali-halide crystals were found. The satisfactory agreement of the data obtained by us and the literature data on the magnitudes of the activation energies of polarization processes in KCl and KBr crystals made it possible to propose probable models of relaxators responsible for the TDP bands (Table 1).

Table

To check the assumptions put forward, experiments were carried out with KCl and KBr crystals doped with various impurities. The introduction of \(0.025\ \mathrm{mol}\%\, \mathrm{SrCl_2}\) into KCl (Fig. 1, curve 2) leads to an increase of the peak with \(T_m = 221\) K by approximately a factor of 100. This confirms the conclu-

…evidence that this relaxation-current peak is due to the complex \(Sr^{++}V_k\). The increase of the band at \(T_m = 173\ \mathrm{K}\) with increasing concentration of the divalent cation-substituting impurity in the crystal can be explained by the generation of dipoles for the elimination of elastic stresses in the lattice arising from the difference in the ionic radii of the impurity and host cations.

Fig. 3. Dependence of the depolarization current on temperature for crystals of KBr \(+0.02\ \mathrm{M}\%\) KOH (1) and KBr \(+0.01\ \mathrm{M}\%\) PbCl\(_2\) (2).

The addition of KOH to KBr is accompanied by such a sharp increase of the band with \(T_m = 182\ \mathrm{K}\) that it dominates over the entire temperature interval (Fig. 3, curve 1). When KBr crystals are doped with lead ions, the band with \(T_m = 212\ \mathrm{K}\) increases and a band with \(T_m = 166\ \mathrm{K}\) appears (Fig. 3, curve 2).

It is known [8] that the introduction of KOH into a melt of alkali-halide crystals purifies the compounds from divalent cation-substituting impurities. Therefore, when lead is introduced into KBr, the band for which the relaxation of \(OH^{-}\) is responsible should decrease, and when KOH is introduced into KBr the concentration of \(Me^{++}V_k\) complexes should decrease, which is manifested in the TDP spectra. The good agreement between the value of the activation energy of the dipoles calculated by Dekker [7] and that determined by us for the band with \(T_m = 166\ \mathrm{K}\) allows one to assume that this band is due to the relaxation of neutral vacancy–dipole pairs.

Thus, the experiments performed confirm the models we proposed for the relaxators responsible for the appearance of depolarization-current maxima (Table 1).

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