SCALE FACTOR IN THE PROCESS OF RADIATION COLORATION OF FILAMENTARY ALKALI-HALIDE CRYSTALS

S. U. GOL'DENBERG

(Presented by the scientific seminar of the Laboratory of Radiation Spectroscopy)

In studying a number of physical properties of filamentary crystals (FC)—strength [1, 2], plasticity [3], dislocation structure [4, 5], microhardness [6], magnetic properties [7]—a dependence of these properties on the geometrical dimensions of the specimens (scale effect) was established. Thus, with decreasing diameter, the strength of FC increases, the degree of their structural perfection increases (the number decreases and the geometry of the arrangement of dislocations in the crystal is simplified), etc. Our investigations of the radiation properties of filamentary alkali-halide crystals show that the scale effect also occurs in the process of radiation coloration of these specimens; however, the manifestation of the scale factor depends both on the kind of color centers being studied and on the origin of the FC.

In this work the kinetics of accumulation of \(F\)- and \(M\)-centers was investigated in NaCl and KCl FC of different origin—grown from solutions and from the gas phase, and in cleavage whiskers. Growth of specimens from solution was carried out by evaporation of a saturated solution through a collodion film (the Amelincks method [8]); from the gas phase, by a procedure developed by us [9]. Cleavage whiskers were rolled out from massive single crystals of NaCl and KCl grown from the melt by the Kyropoulos method, and from rock salt. The specimens were irradiated at room temperature with X-rays (Cu, 12 mA, 45 kV). Absorption spectra were measured at the time of action of the X-radiation on a microspectrophotometric setup created by us [10], which made it possible to photometer both microspecimens and microlayers of massive crystals. The smallest diameter of the specimens investigated by us was \(20\ \mu\text{m}\). The concentration of color centers was calculated by the Smakula–Dexter formula; in calculating the concentration of \(F\)-centers, the absorption coefficient at the maximum of the \(F\)-band was corrected according to [11] by the formula

\[ K_{F_{\text{corr}}}=K_F-0.65\,K_M . \tag{1} \]

Formula (1) takes into account the absorption of \(M\)-centers in the region of the \(F\)-band.

In Fig. 1,a the accumulation curves of \(F\)-centers in NaCl FC of different diameters grown from solution are presented; for comparison, the kinetic curve is given for a near-surface microlayer of rock salt. It is seen that under isodose irradiation many more \(F\)-centers are generated in FC than in a macrospecimen, and the concentration of \(F\)-cent—

increases as the whisker diameter decreases. At the same time, in whiskers of different diameter and in the macrocrystal, approximately the same number of \(M\)-centers is generated (Fig. 1, b). Similar regularities are ob—

Fig. 1. Accumulation of \(F\)-centers (a) and \(M\)-centers (b) in NaCl grown from solution: 1 — whiskers of diameter 26 \(\mu\)m, 2 — whiskers of diameter 29 \(\mu\)m, 3 — whiskers of diameter 52 \(\mu\)m, 4 — whiskers of diameter 108 \(\mu\)m, 5 — near-surface microflow layer of rock salt.

… and to the process of accumulation of \(F\)- and \(M\)-centers in NaCl cleavage whiskers. Of particular interest is the fact that the accumulation curves for \(F\)- and \(M\)-centers in a cleavage whisker split off from a solution-grown NaCl crystal—rock salt—coincide with the kinetic curves obtained for an NaCl single-crystal whisker of the same diameter grown from solution. These specimens differ sharply in the content of dislocations in them: in a cleavage whisker, owing to dislocation loops formed during the cleavage process, the dislocation density is so high that the outlets of individual dislocations cannot be detected by the selective etching method; grown whiskers are characterized by a much higher degree of structural perfection [4, 5]. This fact convincingly supports the conclusion made by us in [12] that dislocations do not play a decisive role in the process of radiation coloration of alkali-halide crystals at room temperature.

The scale effect characteristic of the process of accumulation of \(F\)-centers in single-crystal whiskers grown from solution, and in cleavage whiskers, is especially clearly manifested in KCl specimens. In these specimens the accumulation curve for \(F\)-centers has a sharply expressed linear segment, the slope of which can be determined by processing the experimental results by the least-squares method. This yields the value of the parameter \(A_2\), which characterizes the rate of accumulation of \(F\)-centers in the linear stage according to the equation of Mitchell et al. [13]. The dependence of this parameter on the diameter of KCl whiskers is shown in Fig. 2. It is seen that, with decreasing geometrical dimensions, the rate of accumulation of \(F\)-centers in the linear stage increases. Moreover,

Fig. 2. Dependence of the rate of accumulation of \(F\)-centers in the linear stage \((A_2)\) on the diameter of KCl single-crystal whiskers: ○ — KCl single-crystal whiskers grown from solution; △ — KCl cleavage whiskers; — — — level of the value of \(A_2\) for the near-surface micro-layer of a KCl single crystal.

the wide range of diameters of the specimens investigated by us \((20\text{–}260\ \mu\text{m})\) made it possible to obtain a comparatively smooth transition from the value of \(A_2\) characteristic of the thinnest single-crystal whisker to the value of this parameter characteristic of a massive crystal.

In studying NaCl and KCl NC grown from the gas phase, we found a substantial difference between the radiation properties of these samples and NC grown from solution. This difference is as follows:

1) the sensitivity to subtractive coloration of samples obtained from the gas phase is much lower than that of samples of the same diameter but grown from solutions. Under isodose irradiation, almost 4–5 times more \(F\)-centers are produced in solution-grown NC than in NC from the gas phase,

2) for samples obtained from the gas phase, in contrast to solution-grown NC, there is no dependence of the rate of accumulation of \(F\)-centers at the linear stage on the geometrical dimensions of the sample (Fig. 3).

In [4], by methods of selective etching and diffraction microradiography, it was shown that NaCl NC grown from the gas phase are highly perfect—dislocation-free—

Fig. 3. Dependence of the rate of accumulation of \(F\)-centers at the linear stage \((A_2)\) on the diameter of KCl NC grown from the gas phase (samples subjected to plastic deformation are denoted by asterisks)

up to cross sections of \(30 \times 100\ \mu\text{m}^2\). An analogous result was also obtained by us for KCl samples. However, the absence of dislocations in NC obtained from the gas phase is not the cause of the difference, noted above, between the radiation properties of these samples and solution-grown whiskers. Indeed, the artificial creation of dislocations in dislocation-free samples from the gas phase by their plastic deformation does not change the rate of accumulation of \(F\)-centers at the linear stage (Fig. 3; the samples subjected to plastic deformation are marked by asterisks).

The experimental results described above may be explained as follows. The fact that the accumulation of \(F\)-centers in NC occurs at a higher rate than in a bulk crystal indicates that in NC there is an additional source of \(F\)-centers in comparison with macro-samples; moreover, the contribution of this source in the case of cleavage whiskers and solution-grown NC increases as the sample diameter decreases. In view of the fact that, as the geometrical dimensions of the crystal decrease, the ratio of its surface to its volume increases, it seems possible to identify the additional source of \(F\)-centers in NC with the surface of the crystal. Indeed, in accordance with the Seitz hypothesis [14], the generation of vacancies in alkali-halide crystals under the action of ionizing radiation may occur by radiation-stimulated diffusion of vacancies from the surface of the crystal. It is clear that

the role of the surface as a source of vacancies should increase with decreasing sample size. However, if the surface were responsible for the coloration of NCs in the radiation field, then its action should have been the same in samples of different origin. It was shown above that in samples of the same diameter, grown from solution and from the gas phase, different numbers of \(F\)-centers are generated under the same dose irradiation. This fact, as well as the absence of any dependence of the rate of accumulation of \(F\)-centers on the diameter in NCs obtained from the gas phase, shows that the crystal surface cannot serve as an effective source of radiation defects, at least in samples whose linear dimensions are not less than \(20\,\mu\mathrm{m}\).

In our opinion, the quantitative difference in the kinetics of accumulation of \(F\)-centers in NCs and macro-samples is due to the fact that in NCs there are excess vacancies formed as a result of the exit of dislocations from the crystal. It is known that in crystals with a NaCl-type structure, dislocations with a Burgers vector directed along \([100]\) are unstable [15]. In addition, in NCs, whose predominant growth direction is \([100]\), axial dislocations of mixed character

\[ \left(b=\frac{a}{2}[110]\right) \]

form a stable configuration if the edge components have opposite signs and the screw components have the same sign. In the process of NC growth, dislocations of an unstable configuration can form in it; these will exhibit a tendency toward mutual annihilation and exit from the crystal. In this case an excess of vacancies is formed in the crystal. It is clear that the probability of dislocations leaving an NC should increase with decreasing diameter, i.e., with increasing ratio of the sample surface to its volume. Consequently, the degree of supersaturation of the NC with vacancies should also increase with decreasing transverse dimensions, which explains the manifestation of the size effect in the process of accumulation of \(F\)-centers in NaCl and KCl NCs grown from solution. The absence of this effect in samples obtained from the gas phase is apparently connected with the fact that whisker growth occurs at high temperatures, at which annealing is possible of those defects that are left behind by dislocations leaving the crystal. In the case of cleavage whiskers, supersaturation of the crystal with vacancies occurs due to the departure of some of the dislocation loops formed during cleavage. Excess vacancies in whiskers are apparently in large clusters, the breakup of which requires large energy expenditures; therefore these vacancies contribute to a later stage of coloration of these samples.

The high rate of accumulation of \(M\)-centers that we observed in NaCl samples (Fig. 2) is a consequence of the irreversibility of the process of coagulation of \(F\)-centers in the NaCl crystal at room temperature [16], and also of the fact that the \(F\)-centers responsible for the formation of \(M\)-centers are generated in pairs. This follows from theoretical calculations performed by D. I. Vaisburd. In [16] we showed that complexes of the type calcium ion + two cation vacancies and one anion vacancy can be responsible for the pairwise creation of \(F\)-centers. The fact that the accumulation of \(M\)-centers in NaCl NCs grown from solution, in cleavage whiskers, and in a massive NaCl crystal occurs at approximately the same rate indicates that the Ca content in these samples is the same. In NaCl NC samples grown from the gas phase, the \(M\)-band is not observed under irradiation for 10–12 hours. Apparently, in view of the more equilibrium growth conditions of these crystals, incorporation of the impurity is hindered, which leads to a higher degree of their purity.

Thus, our investigations show that a scale effect, characteristic of a number of physical properties of alkali halide crystals, is also inherent in the process of their radiation coloration; however, this effect manifests itself only in the process of accumulation of \(F\)-centers and only in specimens grown from solution and cleaved from massive crystals.

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