STORED ENERGY IN ALKALI-HALIDE CRYSTALS

A. A. VOROB'EV, E. K. ZAVADOVSKAYA, E. M. GOLOVCHANSKII,
A. V. KUZ'MINA, A. P. AR'YANOV, V. G. VAKHROMEEV

The article presents the results of investigations of changes in stored energy over a wide range of irradiation doses in alkali-halide crystals, the influence of crystal treatment, and also the irradiation conditions on the magnitude and kinetics of accumulation of stored energy. Studies have been carried out on changes in microhardness and stored energy as a function of annealing time at various temperatures.

The activation energy of the process of defect annealing in the temperature interval 100–200°C has been found; it agrees well with literature data.

It has been established that the principal contribution to stored energy in alkali-halide crystals and their solid solutions is made by electron–hole color centers.

In the paper are described the results of investigation concerning the change of storage energy in alkali—halides in the wide range of irradiation dose, the influence of crystal treatment and irradiation conditions on the value and kinetics of accumulation of storage energy. The research has been carried out on the change of microhardness and storage energy with the annealing time at different temperatures.

The activation euergy of defects annealing process in determined in the temperature range 100—200°C, which is consistent with the data of other workers.

At is established that the main contribution to storage energy in alkali—halides and their solid solvents is due to electron — hole colour centers.

Stored energy in alkali-halide crystals is small. Its maximum value in NaCl is about 10% of the heat of dissolution of this compound in water. Therefore the measurement of stored energy presents great difficulties. To measure the energy stored in defects, the defects must be destroyed. This is achieved either by heating the irradiated specimen to high temperatures, or by complete destruction of the crystal lattice when the irradiated specimen enters into a chemical reaction with some substance (dissolution, exchange reactions, etc.).

In accordance with the above, all methods used to measure stored energy may be divided [1] into:

1. Calorimetric methods using annealing of specimens. These include: a) isothermal annealing, in which energy is released at constant temperature and can be determined as a function of annealing time; b) nonisothermal annealing, in which the temperature is raised at a preselected rate, and the released energy is measured as a function of temperature.

1. Methods involving chemical reactions, in which the irradiated crystal reacts with another substance (water) in a calorimeter. The difference between the heats of dissolution of irradiated and unirradiated crystals, with allowance for the chemical correction, gives us the value of the stored energy.

The principal advantage of annealing methods is that they provide direct information on the kinetics of release of the stored energy. A drawback of the isothermal annealing method is that the heat released when the specimen is brought to the annealing temperature cannot be determined accurately. Investigation of stored energy by the dissolution method makes it possible to increase labor productivity considerably and to improve the accuracy of measurement. For this method it is necessary to select solvents for which the heats of dissolution will be small.

Essentially all studies of stored energy have been carried out using the technique proposed by Overhauser [2], although this method is not free from certain shortcomings, which include the great labor-intensiveness of the experiment at low sensitivity and low measurement accuracy (15–20%).

At high irradiation doses, the curves of stored-energy release as a function of heating temperature may be distorted owing to the effect of “catastrophic” energy release. This phenomenon is discussed in detail in [3].

It was shown earlier that the release of stored energy in NaCl and KCl crystals has two maxima. In these crystals the height of the low-temperature maximum increases with irradiation dose, while the height of the second maximum does not change noticeably with the dose of gamma irradiation. In contrast to NaCl and KCl, in LiF crystals the rate of stored-energy release has one maximum at a temperature of 230°C. The two-stage process of energy release in NaCl and KCl crystals is explained by the existence of two types of $F$ centers [4]. A change in the sign of the difference between the heats of dissolution of irradiated and unirradiated NaCl and KJ crystals was observed. This phenomenon was explained by the fact that, with increasing irradiation dose, the magnitude of the chemical correction changes [4]. In crystals with a higher lattice energy the value of the stored energy is greater. The main contribution to the stored energy in NaCl and KCl crystals is made by $F$ centers, whereas in KBr and KJ crystals the main contribution to the stored energy is made by defects that are complex complexes not determined by the optical method.

The purpose of the present work is to investigate the change in stored energy over a wide range of irradiation doses in alkali-halide crystals, the influence of crystal treatment, and also of irradiation conditions on the magnitude and kinetics of accumulation of stored energy.

To determine the contribution of various types of defects created in the crystal to the magnitude of the stored energy, we investigated the thermal and temporal stability of defects in a strongly irradiated NaCl crystal.

Experimental procedure

To carry out work on stored energy, the cyclotron of the Scientific Research Institute of Nuclear Physics at the Tomsk Polytechnic Institute, with a proton energy of 4.5 MeV, was used as the irradiation source. Irradiation was carried out in air. To prevent luminescence of the crystals, they were wrapped in thin aluminum foil.

Let us denote by \(W\) the thermal power released in the calorimetric chamber. The release of this power will cause a deflection of the pointer of the recording instrument by an amount \(h\), i.e.,

\[ W=\kappa h . \tag{1} \]

During the dissolution process \(W\) is variable. The heat released in the calorimetric chamber, \(Q\), can be determined from the formula

\[ Q=\int_{t_1}^{t_2} W\,dt, \tag{2} \]

or

\[ Q=\int_{t_1}^{t_2} \kappa h\,dt=\kappa \int_{t_1}^{t_2} h\,dt . \]

Let us denote

\[ \int_{t_2}^{t_1} h\,dt=S; \]

then

\[ Q=\kappa S, \tag{3} \]

where

\(S\) is the area enclosed between the heat-release curve and the time axis from \(t_1\) to \(t_2\),

\(\kappa\) is the value of one \(\text{cm}^2\) of the scale of the recording instrument, in joules.

The dissolution process takes place simultaneously in both calorimetric chambers, and, because of their differential connection, the instrument measures the difference between the heats of dissolution of the irradiated and unirradiated specimens.

\[ Q_1-Q_2=\kappa(S_1-S_2)=\kappa\Delta S; \tag{4} \]

where \(Q_1\) and \(Q_2\) are the heat absorbed in the first and second calorimetric chambers, respectively,

\(\Delta S\) is the area recorded on the diagram of the recording instrument.

Calorimeters of this type have a background, which arises from nonidentity in the manufacture of the chambers. The magnitude of the background \(\Phi\) is determined by the area recorded by the instrument during simultaneous dissolution of two single crystals identical in weight and surface area. Consequently, when the irradiated crystal is dissolved in the first calorimetric element,

\[ \Delta Q_1=E+\Phi \tag{5} \]

and in the second,

\[ \Delta Q_2=E-\Phi . \tag{6} \]

Solving these equations simultaneously, we obtain

\[ E=\frac{\Delta Q_1+\Delta Q_2}{2}, \tag{7} \]

where \(E\) is the magnitude of the stored energy, without taking account of the chemical correction;

\(Q_1\) and \(Q_2\) are the difference in heat release upon dissolution of the irradiated crystal in chambers 1 and 2, respectively.

For the case in which the background is greater than the magnitude of the stored energy,

\[ E=\frac{\Delta Q_1-\Delta Q_2}{2}. \tag{8} \]

Thermodynamic State of an Irradiated Crystal

The state of a solid is described by the change in the isobaric-isothermal potential \(\Phi\), which is equal to

\[ \Phi = U + pV - TS, \tag{9} \]

where
\(U\) is the internal energy of the crystal,
\(p\) is the external pressure,
\(V\) and \(T\) are, respectively, the volume and temperature of the crystal.

Owing to defects introduced by irradiation, the isobaric potential changes by the amount

\[ \Delta \Phi = \Delta U - T\Delta S + p\Delta V. \tag{10} \]

The change in internal energy \(\Delta U\) can be determined from the expression

\[ \Delta U = \sum_j \Delta n_j E_j. \tag{11} \]

Here
\(\Delta n_j\) is the number of defects of the given type newly formed by irradiation,
\(E_j\) is the formation energy of one defect of the given type.

An increase in the defectiveness of the crystal leads to a change in the entropy of the crystal by the amount

\[ \Delta S = \Delta S_1 + \Delta S_2 + \Delta S_3, \tag{12} \]

where \(\Delta S_1\), \(\Delta S_2\), \(\Delta S_3\) are, respectively, the increase in the configurational component of the entropy; the increase in entropy associated with the change in the frequency of the proper vibrations of ions near point defects; and the increase in entropy associated with the radiation expansion of the crystal.

Substituting (11) and (12) into (10), we have

\[ \Delta \Phi = \sum_j \Delta n_j E_j - T(\Delta S_1 + \Delta S_2 + \Delta S_3) + p\Delta V. \tag{13} \]

The calculations performed showed that the term \(p\Delta V\) is small.

Contribution to Stored Energy from Various Types of Defects

Let us consider, using NaCl as an example, the contribution of various defects to the change in the isobaric potential (to the stored energy). First of all, let us determine the influence of the entropic factor on the magnitude of the stored energy. The entropy of formation of Schottky defects in NaCl is equal to \(5.35 \cdot 10^{-4}\) eV/°K per pair [5].

The effect of dislocations on the configurational and vibrational entropy is small (not more than \(10^{-4}\) eV/°K per atomic plane [6]). Recently [7], when considering the reaction \(2F \to M\), it was found that, as a result of this reaction, the entropy changes by \(2.21 \cdot 10^{-3}\) eV/degree per \(M\)-center. Thus, it may be concluded that the increase in entropy is mainly due to radiation-chemical coagulation reactions of \(F\)-centers into larger aggregates.

Let us consider the band model of NaCl. The width of the forbidden band for this crystal is \(9.6\) eV [8]. According to Mott and Gurney, the thermal activation energy of an \(F\)-center is \(1.86\) eV [9]. According to [10], the depth of the \(V\)-bands is about \(0.6\) eV. Hence, upon recombination of one \(F\)-center with a hole center, an energy of \(7.1\) eV is released. At the second stage of coloration, where Schottky defects are generated, upon formation of an \(F\)-center, according to Phelps [10], an energy of \(9.2\) eV is stored.

(room temperature). If it is assumed that the energy of defect formation does not depend on the number of defects, then \(\sum_j \Delta n_j E_j \gg T\Delta S\), and, consequently, the stored energy is determined by the number of defects and by their formation energy, i.e.,

\[ \Delta \Phi = E = \sum_j \Delta n_j E_j . \tag{14} \]

Then, through the formation of a single complex electronic center, an amount of energy is stored that is larger in magnitude than by one \(F\)-center, i.e.,

\[ E_1 < E_2 < E_3 \quad \text{etc.,} \tag{15} \]

where \(E_1, E_2, E_3\) are the energies stored by one \(F\)-, \(M\)-, and \(R\)-center, respectively, but

\[ E_1 < E_2 < 2E_1, \tag{16} \]

\[ E_2 < E_3 < 3E_1. \tag{17} \]

A vacancy aggregate consisting of \(n\) vacancies stores the energy

\[ E_n = \kappa n E_{\mathrm{v}}, \tag{18} \]

where \(\kappa\) is a coefficient smaller than unity, introducing a correction for the decrease in surface energy;

\(E_{\mathrm{v}}\) is the energy of formation of a vacancy pair;

\(n\) is the number of vacancy pairs.

It follows from expression (18) that the contribution of large vacancy aggregates to the stored energy is insignificant, since their number is considerably smaller than that of single and paired vacancies.

In [15] it was shown that, upon irradiation of alkali-halide crystals, dislocations are generated in them. We believe that, in contrast to metals, in alkali halides dislocations do not make a substantial contribution to the stored energy, since their number is considerably smaller than the number of dislocations in a metal, while the energy of formation of a dislocation in alkali-halide crystals and in noble metals is of the same order [16]. To verify this assumption, we carried out experiments on quenching NaCl crystals. We did not observe an increase in stored energy with increasing number of dislocations (Table 1).

Table 1

Change in stored energy with quenching temperature for NaCl crystals

From the foregoing it may be concluded that the main contribution to the stored energy in alkali-halide crystals is made by

electron–hole color centers. To confirm this proposition, we investigated the change in stored energy, color centers, and microhardness during isothermal and nonisothermal annealing of the crystal.

Isothermal Annealing

Isothermal annealing of defects was carried out at temperatures of 100, 150, and 200°C. Samples irradiated with a dose of \(6.75 \cdot 10^{14}\) protons/cm\(^2\), as well as unirradiated samples, were placed in a furnace. They were kept there for a specified time and then, by means of a special device, were ejected onto a cotton-wool pad. After their cooling, the stored energy was determined by the dissolution method. In Fig. 1 \((a, b)\) the dependences are presented of the change in stored energy and microhardness on annealing time at various temperatures.

Fig. 1. Dependence of stored energy \((1,a)\) and microhardness \((1,b)\) on annealing time at various temperatures

In Fig. 2 the isothermal annealing \((200^\circ\mathrm{C})\) of color centers is presented. Let us compare the dependences obtained at an annealing temperature of \(200^\circ\mathrm{C}\). During 2 min of annealing at this temperature, the microhardness of the irradiated crystal is practically equal to the microhardness of an unirradiated...

of NaCl, while a number of complex bands appear in the optical absorption spectrum; these overlap the \(F\)- and \(M\)-bands, so that it is impossible to trace the annealing of the \(F\)- and \(M\)-centers. At the same time, the stored energy decreased by 50% of its initial value. Further

Optical density
Wavelength, nm

Labels on the curves: 2 min.; 8 min.; 18 min.; 23 min.; 28 min.; 33 min.; 47 min.; 578 nm.

Fig. 2. Isothermal annealing at 200°C of color centers in NaCl irradiated with protons at a dose of \(6.75 \cdot 10^{14}\) protons/cm\(^2\)

annealing of NaCl leads to the complete destruction of the \(F\)- and \(M\)-bands and to the appearance of a band at 578 nm; in this process a large part of the stored energy is released (about 75%). After 60 minutes of annealing at a temperature of 200°C the crystals became completely decolorized. Annealing for 6 hours leads to the complete destruction of radiation defects.

Comparing the change in absorption and the release of energy at an annealing temperature of 200°C, it was concluded that energy storage in alkali-halide crystals occurs at electronic color centers.

Comparison of the annealing of defects responsible for the change in microhardness with the annealing of defects responsible for the stored energy and optical absorption permits the conclusion that the increase in microhardness is associated with defects that do not make a substantial contribution to the stored energy and are optically invisible.

Such defects may be either vacancy clusters of a definite size or hole centers.

From the obtained regularities (Fig. 1a) of the annealing of radiation defects we shall determine the activation energy and the order of the annealing reaction. The curves presented (Fig. 1a) can be described by the kinetic equation [17]

\[ \frac{dn}{d\tau}=-n^x A\exp\left(-\frac{U}{kT}\right), \tag{19} \]

where

\(n\) is the concentration of defects in the crystal;

\(\dfrac{dn}{d\tau}\) is the rate of decrease of the defects;

\(U\) is the activation energy;

\(x\) is the order of the reaction;

\(A\) is a constant containing the frequency factor.

As indicated above, the stored energy is proportional to the concentration of defects. Therefore, in equation (19) we replace \(\dfrac{dn}{d\tau}\) by the experimentally obtained decrease of the stored energy \(\dfrac{dE}{d\tau}\). After substitution, integration, and taking logarithms, we have

\[ \ln \int_{E_0}^{E}\frac{dE}{E^x} = \ln \mathrm{const} - \frac{U}{kT} + \ln \tau . \tag{20} \]

Having curves of isothermal annealing of defects at different temperatures, one can find the activation energy of the annealing process from the expression

\[ U=k\frac{\ln \tau_2/\tau_1}{1/T_2-1/T_1} = 0.862\cdot 10^{-4} \frac{\ln \tau_2/\tau_1}{1/T_2-1/T_1}. \tag{21} \]

Here \(T_2\) and \(T_1\) are the temperatures at which isothermal annealing occurs, and \(\tau_1\) and \(\tau_2\) are the times over which the stored energy decreases by one and the same amount at temperatures \(T_1\) and \(T_2\), respectively. As is evident from equation (21), the activation energy does not depend on the reaction order, but for its calculation it is necessary that, in the given temperature interval, the activation energy be constant. To determine the reaction order we plot \(\ln\ln E_t/E_0\) versus \(\ln \tau\). The resulting linear dependence indicates that, in the temperature range \(100\div 200^\circ\mathrm{C}\), the annealing of radiation defects is described by a first-order equation.

The activation energy calculated from the data of isothermal annealing in the temperature range \(100\div 150^\circ\mathrm{C}\) (Table 2) is close to the activation energy of a cation vacancy, obtained experimentally in a study of the electrical conductivity of NaCl [5], and agrees well with the theoretical value of the activation energy of a cation vacancy [18].

The increase in activation energy observed by us in the temperature region \(150\div 200^\circ\mathrm{C}\) indicates that the cation vacancy in this dia-

range of temperatures is in a complex, and additional energy is required for its detachment.

Table 2

Activation energy for annealing of defects in NaCl irradiated with protons

In contrast to metals, in alkali-halide crystals it is impossible to determine, from the activation energy, the type of defects that contribute to the stored energy. Annealing of defects in these compounds is due to migration of cation vacancies (hole centers) and is accompanied both by the destruction and by the coalescence of defects into larger aggregates.

Nonisothermal annealing

A batch of NaCl crystals irradiated with a dose of \(6.75 \cdot 10^{14}\) protons/cm\(^2\) was placed in a furnace that was heated at a rate of \(1.34^\circ\) min\(^{-1}\). Upon reaching a given temperature, several crystals were removed from the furnace, and the stored energy in them was determined by the dissolution method.

Figure (3,a) shows the dependence of \(E_0/E_t\) on the annealing temperature, where \(E_0\) is the stored energy of unannealed specimens and \(E_t\) is the stored energy in specimens after annealing at the specified temperature. Annealing of radiation defects proceeds in three stages. The maxima of stored-energy release are located at temperatures of 125, 177, and 218°C. The positions of the energy-release maxima are the same in different batches of specimens. The maximum of energy release at 218°C is poorly resolved.

In addition to measuring the stored energy during nonisothermal annealing, the change in optical absorption of the specimens at different annealing temperatures was studied (Fig. 3,b). Because of the high concentration of \(F\)-centers, the maximum of the \(F\)-band was not measured up to 140°C. In this temperature region, annealing of \(F\)-centers can be characterized by the growth of \(M\) and more complex bands. Up to 150°C an increase of the \(M\)-band is observed, along with the appearance, on its long-wavelength slope, of a new band whose exact position could not be determined. In this same temperature interval, absorption in the region of 940–950 nm increases. With increasing temperature, the absorption between the \(F\)- and \(M\)-bands increases. At temperatures of 150–180°C, intense coagulation of \(F\)- and \(M\)-centers into complex centers occurs. A series of \(R\)-bands appears. Further heating of the specimens to 180°C leads to the appearance of a band at 578 nm, which is annealed without further transformation. At a temperature of 220°C the crystal becomes completely bleached.

Comparison of the change in stored energy as a function of annealing temperature with the change in the optical-absorption spectra makes it possible to explain, in the following way, the two-stage character of stored-energy release. It is known that the shape of the annealing curve of \(F\)-centers depends on the degree of imperfection of the crystal lattice [19]. The less perfect the structure of the crystal, the more complex the character of the annealing curve of \(F\)-centers. In contrast to [20], we believe that

Fig. 3. Dependence of \(\dfrac{E_t}{E_0}\) on the annealing temperature in NaCl crystals irradiated with protons at a dose of \(6.75 \cdot 10^{14}\) protons/cm\(^2\) (3, a, curve 1), and the change in the optical absorption of NaCl irradiated with protons at various annealing temperatures (3, b).

the release of energy in the region 100–160°C is caused both by partial recombination of \(F\)-centers with hole centers and by the association of \(F\)-centers into more complex centers. The release of energy in the temperature region 160–200°C is connected with the destruction of \(F\)- and \(M\)-centers, which is accompanied by the formation of a band at 578 nm. The destruction of the band at 578 nm is accompanied by the release of energy with a maximum at 218°C.

Kinetics of the accumulation of stored energy and the change in microhardness in alkali-halide crystals

The change in stored energy as a function of the irradiation dose in NaCl, KCl, KBr, and KI crystals, as well as in solid solutions of the KCl—KBr system, was studied by the dissolution method.

Figure 4 shows the dependence of the change in stored energy in NaCl, KCl, KBr, and KI crystals on the absorbed energy, curves 1, 2, 3, and 4, respectively. The change in stored energy with the dose of proton irradiation depends strongly on the composition of the crystal. Thus, for KCl and KBr crystals two stages are observed in the accumulation of stored energy: a rapid increase in stored energy up to an absorbed energy of \(12 \cdot 10^3\) J/g, and then a slow increase at higher irradiation doses. In KI crystals, after a dose of \(12 \cdot 10^3\) J/g, saturation of the stored energy is observed. In contrast to “pure” crystals, for solid solutions of the KCl—KBr system, in the interval of irradiation doses the dependence between the stored energy and the absorbed energy is linear (Fig. 5). Along with the study of stored energy, an investigation of microhardness was carried out in the work. For NaCl, KCl, KBr, and KI crystals the microhardness changes with the proton-irradiation dose according to a curve with saturation. Figure 6 gives the dependence of the relative hardening of solid solutions of the KCl—KBr system of different compositions on the proton-irradiation dose. At an absorbed dose of \(2 \cdot 10^{23}\) eV/cm\(^3\), the maximum hardening of all compositions of the solid solutions is observed. A further increase in the irradiation dose leads to a decrease in the microhardness of the solid solutions.

Fig. 4. Dependence of the stored energy in NaCl, KCl, KBr, and KI crystals (curves 1, 2, 3, and 4, respectively) on the absorption of energy after irradiation by protons.

The complex dependence of the accumulation of stored energy in NaCl prompted us to investigate this phenomenon in sodium chloride crystals in greater detail. First of all, it is necessary to verify whether the decrease in the accumulation of energy is caused by temporal annealing of defects both at the moment of irradiation and during the period of the experiment (1.5–2 days).

The dependence of the change in stored energy on the storage time in the dark at a temperature of 24–26°C for NaCl crystals is given in Table 3. During the first three days of storage, the stored energy does not

is released. Then its slow decrease is observed to a stable value of \(4.3\ \mathrm{J/g}\). Apparently, the decrease in the stored energy after a dose of \(16 \cdot 10^3\ \mathrm{J/g}\) is not associated with temporal annealing of defects at the moment of irradiation.

Fig. 5. Dependence of the stored energy in solid solutions of the KCl—KBr system on the absorbed energy after proton irradiation.
Curve 1 — 90 mol% KCl — 10 mol% KBr;
curve 2 — 75 mol% KCl — 25 mol% KBr;
curve 3 — 50 mol% KCl — 50 mol% KBr;
curve 4 — 25 mol% KCl — 75 mol% KBr;
curve 5 — 10 mol% KCl — 90 mol% KBr.

The influence of the intensity of proton irradiation on the kinetics of accumulation of stored energy in NaCl was investigated (Fig. 7, curve 1). Characteristic features are observed in the accumulation of energy:

a) the magnitude of the stored energy in the investigated interval of proton-irradiation intensity is determined only by the absorbed energy;

b) at all irradiation intensities, a maximum appears at the same absorbed energy; a change in intensity by more than a factor of 6 affects neither the position nor the magnitude of the maximum (Fig. 7, a);

c) the minimum value of the stored energy is observed at the same absorbed energy;

d) after the decrease in the stored energy, a tendency for its value to increase is again observed.

In contrast to the above

Table 3

Change in stored energy with storage time of NaCl crystals

when the irradiation temperature is raised to 70–80°C, the kinetics of stored-energy accumulation in NaCl depends on the irradiation intensity (Fig. 7, curves 2, 6). In addition, just as at room temperatures, a maximum is observed in the magnitude of the stored energy, but at a considerably larger irradiation dose and at a smaller value of the stored energy.

Fig. 6. Dependence of the relative strengthening of solid solutions of the KCl—KBr system of various compositions on the dose of proton irradiation

a) the stored energy in doped crystals at large irradiation doses is considerably smaller than in pure crystals;

Investigation of the influence of calcium impurity on the character of energy accumulation in NaCl made it possible to draw the following conclusions:

b) the rate of accumulation of stored energy at small irradiation doses increases with increasing \(Ca^{++}\) content (Fig. 7, curves 3, 4).

c) in impurity crystals the maximum in the kinetics of energy accumulation is considerably smaller and is shifted toward the region of smaller doses;

d) after an absorbed energy of about \(16\cdot 10^3\) J/g, a tendency toward saturation of the stored energy is observed (Fig. 7, curves 3, 4).

We have shown that, under identical irradiation conditions (intensity \(1.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h), both the magnitude and the character of the accumulation

Fig. 7. Effect of the prehistory and intensity of proton irradiation on the kinetics of accumulation of stored energy in NaCl.

Curve 1 — NaCl grown from the melt, irradiation temperature \(30^\circ\)C.

—△—△—△— — intensity \(1.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h;
—○—○—○— — intensity \(3.0\cdot 10^{14}\) protons/\(\text{cm}^2\) h;
—×—×—×— — intensity \(4.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h;

curve 2 — NaCl grown from the melt, irradiation temperature \(80^\circ\)C, intensity \(4.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h;

curve 3 — NaCl grown from the melt with an admixture of 0.1 mol.% CaCl\(_2\), irradiation temperature \(30^\circ\)C, intensity \(1.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h;

curve 4 — NaCl grown from the melt with an admixture of 1.0 mol.% CaCl\(_2\), irradiation temperature \(30^\circ\)C, intensity \(1.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h;

curve 5 — rock salt, irradiation temperature \(30^\circ\)C, intensity \(1.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h;

curve 6 — NaCl grown from the melt, irradiation temperature \(80^\circ\)C, intensity \(1.5\cdot 10^{14}\) protons/\(\text{cm}^2\) h.

The impurity content is given for the charge.

energies in NaCl depend on the origin of the crystal (Fig. 7, curves 1, 5).

Discussion of the results on the kinetics of accumulation of stored energy

In the experiments discussed earlier on the annealing of radiation defects in a heavily irradiated NaCl crystal, we came to the conclusion that the main contribution to the stored energy of alkali-halide crystals is made by electron–hole centers.

It is known that at small irradiation doses the number of \(F\)-centers is significantly greater than the number of \(M\)-centers; under these irradiation conditions the change in stored energy will reproduce the kinetics of accumulation of \(F\)-centers. This case occurs at the first stage of energy accumulation in crystals of NaCl, KCl, KBr, and KI, as well as in solid solutions of the KCl—KBr system.

With increasing irradiation dose, the number of \(F\)-centers increases and the probability of their combining into aggregate centers rises. In this case, complex color centers (\(M\)-, \(R\)-, \(N\)-, etc. centers) make a noticeable contribution to the stored energy, but the rate of energy accumulation decreases, since \(E_1 < E_2 < E_3\), etc. The contribution of complex color centers to the stored energy can be judged from the plotted dependence \(E = f(n_F)\) for NaCl (Fig. 8). The deviation of this dependence from a straight line indicates

Fig. 8. Dependence of stored energy on the concentration of \(F\)-centers in NaCl crystals irradiated with protons

that at doses above 300 J/g it is necessary to take into account the contribution to the stored energy of complex centers ($M$-centers).

The decrease in the stored energy in NaCl at higher irradiation doses is apparently associated both with the coagulation of $F$-centers into large aggregates and with their partial destruction.

The introduction of divalent Ca$^{++}$ impurities into a NaCl crystal at small doses of proton irradiation increases the number of $F$- and $M$-centers [21]. This work indicates that, upon further irradiation, in impurity crystals the radiation-chemical reaction $F \to M$ is suppressed. We investigated the optical absorption spectra of “pure” and impurity NaCl crystals at doses two orders of magnitude higher than in the cited work. In the impurity crystals irradiated with a dose of $6 \cdot 10^{14}$ protons/cm$^2$, not only the concentration of $M$-centers but also the concentration of $F$-centers is smaller.

Since at small irradiation doses in impurity crystals the concentration of $F$- and $M$-centers is significantly greater than in pure NaCl, this explains the increase both in the rate of accumulation and in the magnitude of the stored energy. With increasing irradiation dose, the stored energy in impurity crystals becomes smaller than in “pure” ones. This is determined by the decrease in the concentration of $F$- and $M$-centers upon introduction of Ca$^{++}$ into the NaCl crystal.

The coagulation processes of $F$-centers account for the second stage in the accumulation of stored energy in KCl, KBr, and KI. The cessation of energy accumulation in KI at large irradiation doses is associated with the dynamic equilibrium of the formation and radiation destruction of defects. At present there is not a sufficient number of experimental results that would make it possible to explain the drop in stored energy in NaCl at large irradiation doses.

In most works in which the influence of irradiation intensity on the kinetics of accumulation of color centers in alkali-halide crystals was studied, the number of $F$-centers was compared not at one and the same absorbed energy, but at one and the same irradiation time. Naturally, at different intensities over the same time the crystal receives different doses and, consequently, a different number of $F$-centers is formed in it. Under proton irradiation of NaCl, it was shown in [22] that $n_F \equiv I^{1.08}$ ($I$ is the radiation intensity), i.e., the number of $F$-centers is practically independent of the irradiation intensity.

We have shown that the magnitude of the stored energy in NaCl depends only on the irradiation dose. This is apparently connected with the fact that, in the investigated intensity interval, the accumulation of color centers in NaCl at room temperature is determined only by the absorbed energy.

When the irradiation temperature is raised, diffusion processes are accelerated, which causes more intense coagulation of defects; therefore both the rate of accumulation and the magnitude of the stored energy in NaCl at an irradiation temperature of 80°C are smaller than at room temperature. With an increase in irradiation intensity, the time during which the crystal receives one and the same dose decreases; i.e., the influence of intensity under these irradiation conditions is connected with isothermal annealing of radiation defects during irradiation at elevated temperature.

The difference between the kinetics of accumulation of stored energy in rock salt and the accumulation of energy in an artificial NaCl crystal is apparently associated both with the presence of Ca$^{++}$ impurity in the latter, which is located on blocks, and with the considerable plastic deformation of rock salt.

At large irradiation doses it is impossible to estimate quantitatively the concentration of induced defects. Measurement of the stored energy

gives us the total concentration of defects in the crystal, which can be calculated from the formula

\[ E = 0.624 \cdot 10^{-19} A \cdot n \ \text{J}/\text{cm}^{3}, \tag{22} \]

where \(A\) is the width of the forbidden band in eV,
\(n\) is the concentration of electrons localized at vacancies.

Conclusions

1. The principal contribution to the stored energy in alkali-halide crystals and their solid solutions is made by electron-hole color centers.

2. The rate of energy accumulation decreases upon the formation of \(F\)-aggregate centers.

3. At room temperature, the intensity of proton irradiation does not affect the magnitude or the rate of accumulation of stored energy in an NaCl crystal.

4. The magnitude and rate of energy accumulation in alkali-halide crystals are affected by the treatment of the crystal and by the presence and distribution of impurities in the crystal.

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