On the Question of the Influence of X-Rays on Electrical Conductivity

A. D. Shchelokov

In connection with the wide use of ionizing radiations in technology, medicine, agriculture, and scientific research, the question of the influence of ionizing radiations on various properties of materials has acquired great importance. In particular, the question of changes in the electrical conductivity of insulators in a radiation field is of great interest; in this field some insulators lose their insulating properties [1-10, 12, 13], while others, on the contrary, improve them under prolonged irradiation [11].

In the present work, the change in the electrical conductivity of NaCl crystals in the field of action of X-radiation was studied as a function of temperature.

Measurement Method

The electrical conductivity of NaCl was measured with an SG-1M electrometer (a combination string electrometer with a quadrant) by the method of constant deflection according to the circuit shown in Fig. 1.

Fig. 1. Schematic of the measuring apparatus. O—sample with electrodes; T—differential thermocouple; v—guard ring; \(U_{\text{sam}}\)—voltage applied to the sample; \(P_1\)—relay switch; \(R^*\)—measuring resistances from \(10^5\) to \(10^{12}\ \Omega\); E—SG-1M string electrometer; \(P_2\)—switch; \(B_1\) and \(B_2\)—BAS-80 batteries; \(r\)—protective resistances of 3 megohms each; K—relay key for grounding the electrometer filament; KE—electrometer housing; \(R\)—resistance of \(10^{10}\ \Omega\), short-circuiting the rectifier when it is disconnected from the sample; \(\mu A\)—microammeter; \(R_g\)—beam of X-rays.

The specimens were prepared from natural single crystals of NaCl in the form shown in Fig. 2.

A specimen of the indicated form was chosen for the purpose of reducing to a minimum the leakage currents through the ionized air between the electrodes during irradiation.

The thickness of the specimen was 0.48 mm.

The electrodes on both sides of the specimen \(ab\) were made of aquadag. The guard ring was a strip 2–3 mm wide, encircling the crystal along the surface in a plane parallel to the plane of the specimen \(ab\), also made of aquadag. The electrode area was \(S = 2.9\ \text{cm}^2\).

Fig. 2. View of the specimen in longitudinal (a) and transverse (b) sections. \(D\)—diameter of the specimen; \(d\)—thickness of the specimen; \(ab\)—the actual specimen being tested; \(v\)—guard ring of aquadag encircling the specimen around the perimeter of the transverse section; P—field electrode; I—measuring electrode (both electrodes of aquadag); T—thermocouple inside the specimen; \(R_g\)—beam of X-rays. The overall size of the specimen is approximately \(25 \times 25 \times 40\) mm.

The temperature of the specimen was measured with a differential thermocouple, one end of which was inserted into the body of the specimen placed in an electric furnace.

The source of X-rays consisted of X-ray units URS—70 up to 70 kV and RUP—2 up to 200 kV. The window of the X-ray tube was covered with a lead plate 1.5 cm thick, with an aperture for the exit of the rays about 6 mm in diameter. The beam of X-rays emerging from this aperture was interrupted by means of a relay with a lead shutter 1.5 cm thick. The source of the voltage applied to the specimen was a rectifier with electronic stabilization up to 2.5 kV. The temperature dependence of the electrical conductivity of NaCl was determined under irradiation and without irradiation.

In order to eliminate the influence of photocurrents, the specimen was protected from visible light.

Results of measurements and their analysis

Figs. 3 and 4 show the dependences of the logarithm of the electrical conductivity on the reciprocal absolute temperature for NaCl. The conditions under which these curves were obtained are given in Table 1. All measurements were carried out at steady-state current.

The curves of Fig. 3, as well as those of Fig. 4 \(A\), \(A_1\), and \(A_2\), were taken at an electric-field intensity \(E = 20.9\ \text{kV/cm}\), during heating; curves \(B\) and \(B_1\)—in a field \(E = 41.8\ \text{kV/cm}\), during cooling. Curves \(A\) and \(B\) were obtained in the absence of X-ray irradiation, i.e., they are the ordinary curves of the temperature dependence of the conductivity of ionic crystals known in the literature [1,2,3]. The electrical conductivity without irradiation for alkali-halide crystals, as is known, is due to ions [14, 15, 16, 17]; therefore curves \(A\) and \(B\) represent the temperature dependence of the ionic conductivity of NaCl, which obeys the law [14, 15, 16, 17, etc.]

\[ \sigma_i = A_i e^{-\frac{W_i}{kT}}. \tag{1} \]

The curves of Fig. 3 \(A_1\), \(A_2\), \(B_1\) were obtained under irradiation with X-rays at 70 kV, 10 mA (\(A_1\)) and 20 mA (\(A_2\)), and at 200 kV, 15 mA (\(B_1\)).

Comparison of curves \(A_1\), \(A_2\), and \(B_1\) under irradiation with curves \(A\) and \(B\) without irradiation clearly shows that X-rays considerably increase the conductivity \(\sigma\) of NaCl at temperatures close to room temperature; for example, at \(t = +17^\circ\mathrm{C}\) the conductivity increases by approximately a factor of 3000 during irradiation at a tube voltage of 70 kV and a current through the tube of 20 mA.

Fig. 3. Electrical conductivity of a NaCl single crystal as a function of temperature under irradiation with X-rays. \(A\)—without irradiation at \(E = 20.9\ \mathrm{kV/cm}\); \(A_1\) and \(A_2\)—under irradiation with X-rays at 70 kV with tube current 10 mA (\(A_1\)) and 20 mA (\(A_2\)) at \(E = 20.9\ \mathrm{kV/cm}\), without filter. \(B\)—without irradiation at \(E = 41.8\ \mathrm{kV/cm}\); \(B_1\)—under irradiation at 200 kV, 15 mA, at \(E = 41.8\ \mathrm{kV/cm}\), filter 0.7 mm Cu + 3 mm Al. \(175^\circ\mathrm{C}\) and \(119^\circ\mathrm{C}\) are the temperatures above which the influence of X-rays is imperceptible. The curves designated by the letter \(A\) were recorded while the sample was being heated; the curves designated by \(B\), while the temperature was being lowered. The lowest point of curve \(A\) (\(\odot\)) is the result of several measurements before the beginning of the experiment.

As the temperature rises, the increase in conductivity under irradiation decreases and at a certain temperature (\(119^\circ\mathrm{C}\) and \(175^\circ\mathrm{C}\)) disappears completely. At higher temperatures the conductivity under irradiation and without irradiation is practically the same.

The dependence of \(\log \sigma\) on \(\dfrac{1}{T}\) under irradiation with X-rays exhibits a bend in the temperature range \(60\text{–}120^\circ\mathrm{C}\), and at lower temperatures again tends toward a straight line, but with a considerably smaller slope.

The presence of this bend indicates a difference in the mechanism of conductivity at high and low temperatures when NaCl is irradiated with X-rays.

It is natural to suppose that under X-ray irradiation in NaCl, in addition to the ions that produce the current in the absence of irradiation (ionic current), other charge carriers arise with a considerably smaller activation energy.

than \(W_R\), than \(W_i\) in (1) (the small slope of the curve at low temperatures, Fig. 3).

In NaCl the new charge carriers in this case can evidently be only electrons, torn, at the expense of the energy of the X-ray quanta, from the orbits of Na and Cl atoms and transferred to levels close to the conduction band, from which they are transferred by thermal motion into the conduction band.

Fig. 4. Dependence of the electronic component of the conductivity of NaCl, excited by X-irradiation, on temperature. Field: for \(A\), \(A'\), and \(A''\), \(E = 20.9\ \mathrm{kV/cm}\); for \(B\) and \(B'\), \(E = 41.8\ \mathrm{kV/cm}\). X-irradiation: tube voltage for \(A'\) and \(A''\)—70 kV, for \(B'\)—200 kV, tube current: \(A'\)—10 mA, \(A''\)—20 mA, \(B'\)—15 mA. The curves are constructed from the data of the graphs in Fig. 3. At 70 kV the X-rays were unfiltered; at 200 kV the rays were filtered by a filter of 0.7 mm Cu + 3 mm Al. For comparison, curves \(A\) and \(B\) for the ionic component, transferred from Fig. 3, are given.

Consequently, under irradiation the total conductivity \(\sigma_{\mathrm{tot}}\) is composed of the ionic conductivity \(\sigma_i\) and the electronic conductivity \(\sigma_R\) added by the X-rays, that is,

\[ \sigma_{\mathrm{tot}} = \sigma_i + \sigma_R. \tag{2} \]

Knowing from experiment \(\sigma_{\mathrm{tot}}\) (curves \(A_1\), \(A_2\), and \(B_1\), Fig. 3) and \(\sigma_i\) (curves \(A\) and \(B\)), from (2) it is easy to find \(\sigma_R\).

Figure 4 presents graphs of the dependence of \(\log \sigma_R\) on \(\dfrac{1}{T}\) in the temperature range \(+90\) to \(+30^\circ\mathrm{C}\). All three graphs are straight lines with a small slope; consequently, the law of variation of \(\sigma_R\) with \(T\) is expressed by the same formula as \(\sigma_i\) in (1), namely

\[ \sigma_R = A_R e^{-\frac{W_R}{kT}}, \tag{3} \]

where \(A_R\) and \(W_R\) are considerably smaller than \(A_i\) and \(W_i\) (Table 1). The total conductivity under irradiation is expressed as

\[ \sigma_{\mathrm{tot}} = A_i e^{-\frac{W_i}{kT}} + A_R e^{-\frac{W_R}{kT}}, \tag{4} \]

where \(W_i\) and \(W_R\) are the activation energies, respectively, for the ionic and electronic components of the conductivity;

\(A_i\) and \(A_R\) are coefficients independent of, or only weakly dependent on, \(T\).

The ionic component of the conductivity \(\sigma_i\) corresponds to curves \(A\) and \(B\) in Fig. 4, and also in Fig. 3. The electronic component of the conductivity \(\sigma_R\), added by X-rays to \(\sigma_i\), corresponds to curves \(A'\), \(A''\), and \(B'\).

In sum, these two terms of (4), on a semilogarithmic scale, give the curves \(A_1, A_2\) and \(B_1\), Fig. 3.

Figs. 3 and 4 show that at low temperatures the second term of formula (4) predominates, i.e. \(\sigma_R \gg \sigma_i\); at high temperatures the first term of formula (4) predominates, i.e. \(\sigma_R \ll \sigma_i\).

At high temperatures the current caused by X-radiation, although it is considerably greater than at low temperatures, is not detected by the method indicated above, for the reason that the ionic current is many times greater than the current excited by irradiation, and the latter cannot be separated from the ionic current.

Therefore, at high temperatures no influence of X-rays on the electrical conductivity is observed.

At low temperatures, on the contrary, the ionic component of the total current, which decreases with temperature considerably more rapidly, becomes negligible in comparison with the electronic current.

The ionic current increases very rapidly with temperature, whereas the electronic current depends only weakly on \(T\); the latter argues in favor of the fact that \(\sigma_R\) is due to electrons.

The electronic component \(\sigma_R\) increases approximately proportionally to the intensity \(J\) of the X-radiation. This is seen from the fact that when the current of the X-ray tube is increased from 10 to 20 ma, i.e. by a factor of 2 (the intensity of the X-rays is proportional to the tube current), the curve \(A'\) rises to the position \(A''\) (Fig. 4), i.e. \(\sigma_R\) increases by a factor of 1.9. In this case the activation energy \(W_R\) (the slope of the curve) does not change within the limits of measurement error (Table 1).

The linear dependence of \(\sigma_R\) and the independence of \(W_R\) from the irradiation intensity can be explained in the following way.

From the theory of the electrical conductivity of crystals it is known that the electrical conductivity (without irradiation) is expressed [14] by the formula

\[ \sigma=\frac{n_0\delta^2 q^2 \nu}{6kT}\cdot e^{-\frac{W}{kT}}, \tag{5} \]

where
\(n_0\) — concentration of charge carriers,
\(\delta\) — mean free path of the particles,
\(q\) — magnitude of the particle charge,
\(\nu\) — frequency of oscillation of the particles,
\(W\) — activation energy of the particle,
\(k\) and \(T\) — Boltzmann’s constant and absolute temperature.

An increase in the intensity of irradiation at unchanged hardness (wavelength \(\lambda\)) cannot change any of the quantities in (5), except \(n_0\)—the concentration of charge carriers, in our case electrons. The concentration \(n_0\) is proportional to the irradiation intensity \(J\)

\[ n_0=aJ, \tag{6} \]

where \(a\) is a proportionality coefficient depending on the substance.

Hence also

\[ A_R\sim J, \tag{7} \]

since, from comparison of (3) with (5),

\[ A_R=\frac{n_0\delta^2 q^2 \nu}{6kT}. \tag{8} \]

Consequently, for \(T=\mathrm{const}\) and \(\lambda=\mathrm{const}\),

\[ \sigma_R=CJ, \tag{9} \]

Table 1

where \(C\) is a proportionality coefficient equal to

\[ C=\frac{a\delta^{2}q^{2}\nu}{6kT}\,e^{-\frac{W}{kT}} . \tag{10} \]

The activation energy of the electrons \(W_R\) (as well as the levels at which the electrons are fixed) upon ionization of atoms by an X-ray quantum

\[ h\nu = h\frac{c}{\lambda} \]

must, other conditions being equal, depend only on the energy of the quantum \(h\nu\), and consequently on the wavelength \(\lambda\) of the X-radiation, i.e.,

\[ W_R=f(\lambda). \tag{11} \]

Table 1 gives the activation-energy values calculated from the slope of the curves for low temperatures \((+90 \div +30^\circ\mathrm{C})\) for the ionic and electronic components of the conductivity under irradiation, and also gives the values of the coefficients \(A\). Knowing these, according to (4), one can write, to illustrate the equations of the curves \(A_1\), \(A_2\), and \(B_1\) (Fig. 3), the dependence of conductivity on temperature under the action of X-radiation for natural single crystals of rock salt (Table 2).

Table 2

Changing the intensity \(J\) of irradiation does not change, within the limits of measurement error, the activation energy \(W_R\) of the electronic component of the conductivity (\(A'\) and \(A''\) in Fig. 4 are parallel). A decrease in the hardness of the X-rays from \(200\) to \(70\ \mathrm{kV}\), i.e., by a factor of \(2.85\), with a simultaneous decrease of the field strength by a factor of 2, decreases the activation energy from \(0.11\) to \(0.038\ \mathrm{eV}\) (average result), i.e., by a factor of \(2.9\). It may be supposed that this decrease in \(W_R\) is caused only by the change in the hardness (i.e., the wavelength \(\lambda\)) of the X-rays.

Conclusions

1. X-rays at low temperatures increase the electrical conductivity of natural single crystals of NaCl by 2–3 orders of magnitude. The relative increase in conductivity decreases with increasing temperature and with decreasing intensity of the X-rays.

1. The additional conductivity produced in NaCl by X-rays (electronic conductivity), as a function of temperature, obeys an exponential law, and its activation energy is considerably smaller than that for ionic conductivity.

2. The total conductivity of NaCl under X-ray irradiation, as a function of temperature, is expressed by a two-term exponential formula.

3. The activation energy of the electronic component of the conductivity does not depend on the intensity of the X-rays. The pre-exponential coefficient for electronic conductivity is proportional to the intensity of the X-rays.

In conclusion, I express my gratitude to A. A. Vorob’ev for valuable discussions and advice, and also to V. A. Sokolov for reading the article.

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Tomsk Polytechnic Institute