CHANGE IN THE CRYSTAL LATTICE PERIOD OF KCl—KBr SOLID SOLUTIONS AS A FUNCTION OF TEMPERATURE, THE ACTION OF IONIZING RADIATION, AND STORAGE TIME

V. E. AVERICHEVA, V. N. SUSLOVA

The crystal-lattice period is one of the characteristics reflecting the structure of a solid and changing as a function of various physical actions on a crystal, for example mechanical, thermal, and radiation effects. The lattice period of crystals increases with increasing temperature; however, the thermal motion of atoms in a crystal cannot be reduced solely to thermal vibrations and the thermal expansion associated with them [1]. At high temperatures evaporation becomes intense, and disturbances of the regular structure of a real crystal arise in the form of mobile vacancies, the number of which increases with rising temperature. Vacancies may coagulate, forming microvoids. The formation of microvoids leads to an increase in the macroscopic volume of the body, but should not change the average interatomic distance. The change in the lattice period with rising temperature reflects to a greater extent the thermal expansion of the crystal, which prepares the conditions under which the regular arrangement of atoms becomes unstable. Using the example of a three-atom model, Ya. I. Frenkel [1] showed that the regular arrangement of atoms exists only when the interatomic distance does not exceed a certain value. As the interatomic distance approaches this limiting value, and when it is exceeded, the position of an atom at the midpoint between two neighboring atoms becomes unstable. Thermal expansion facilitates and accelerates the elimination of long-range order in the crystal; when the melting temperature is reached, the long-range order in the arrangement of atoms is destroyed, and the substance passes into the liquid state.

For studying the process of transition of a solid into the liquid state, it is of interest to investigate the phenomenon of thermal expansion and the change in the crystal-lattice period at temperatures close to the melting temperature. However, the number of works devoted to such measurements for alkali-halide compounds is small, which is evidently determined by serious experimental difficulties.

The change in the lattice period of solid solutions of alkali-halide compounds as a function of composition has been studied only for a small number of systems [2—5] and only at room temperatures.

We measured the lattice periods of solid solutions of the KCl—KBr system at high temperatures. A high-temperature chamber designed by V. G. Kuznetsov with A. A. Mochalov [6] and manufactured in the workshops of the I. S. Kurnakov Institute of General and Inorganic Chemistry, Academy of Sciences of the USSR, was used. It makes it possible to carry out X-ray diffraction of a sample at a controlled specified high temperature up to the melting temperatures of alkali-halide compounds. A sample in the form of a needle 0.5 mm thick was cleaved from a single crystal of the solid solution grown by the Kyropoulos method. X-ray diffraction was carried out on a URS-55a unit using Cu \(K\) radiation at an anode current of 12 mA and an anode voltage of 42 kV.

Fig. 1. Change in the lattice period of KCl—KBr solid solutions as a function of composition at high temperatures.

The exposure time ranged from 40 min to 1.5 h; the temperature of the sample was measured with a thermocouple with an accuracy up to \(10^\circ\). The diameter of the X-ray camera cassette was 85.95 mm. The film was arranged in the camera by an asymmetric method.

On the X-ray diffraction photographs, reflection lines corresponding to maximum Bragg angles up to \(78^\circ\) were recorded at temperatures \(t < 400^\circ\text{C}\), and up to \(50^\circ\) at \(600\)—\(700^\circ\text{C}\). At temperatures up to \(300^\circ\text{C}\), the lattice period was calculated from the lines of two doublets, \(K_{\alpha_1}\) and \(K_{\alpha_2}\). At higher temperatures the doublet lines disappeared on the X-ray diffraction photographs.

or were of such low intensity and so blurred that measurements became impossible. In such cases the period was calculated from the last clear lines of the radiograph, which considerably reduced the accuracy of measuring the lattice period. At \(t < 400^\circ\mathrm{C}\) the period was measured with an error of \(\Delta a = \pm 0.002\ \text{Å}\); at \(t > 400^\circ\mathrm{C}\) the error increased to \(\pm 0.005\ \text{Å}\), and at \(700^\circ\mathrm{C}\) reached a value of \(\pm 0.01\ \text{Å}\), i.e., amounted to 0.16%. The measurement errors are due chiefly to the broadening of the interference lines and to a decrease in their intensity, which, of course, is an inevitable consequence of thermal vibrations of the ions of the crystal lattice. The values of the lattice period of KCl, KBr, and their solid solutions at various temperatures are given in Table 1.

Table 1

Values of the lattice period of solid solutions of the KCl—KBr system
at various temperatures

The general tendency in the change of the lattice period of KCl—KBr solid solutions with temperature is as follows: at room temperature Vegard’s law is satisfied in first approximation; with increasing temperature the values of the lattice period of the solid solutions are somewhat smaller than the additive value; however, at a temperature of 600°–700°C, when the stability of the crystal lattice decreases noticeably, the lattice period of the solid solutions becomes larger than the additive value. The deviation from additivity exceeds the magnitude of the error in measuring the period. It is not possible to calculate the coefficient of thermal expansion of the crystals at high temperatures, since the error in measuring the period exceeds that (0.03%) which is permissible in determining \(\alpha\) by X-ray methods [7].

Expansion of the lattice, and an increase in the macroscopic volume of the crystal, may also occur as a result of the action of various ionizing radiations.

Systematic studies of the influence of ionizing radiations on the lattice period of alkali-halide compounds, and still more of their solid solutions, are necessary in connection with solving the general problem of the interaction of radiation with a solid.

The most complete studies of the influence of irradiation on the crystal-lattice parameter have been carried out on LiF crystals irradiated with neutrons [8, 9]. It was observed that, as the dose is varied in the interval \(5 \cdot 10^{16} \div 3 \cdot 10^{19}\ \dfrac{\text{neutrons}}{\text{cm}^2}\), the lattice period first increases, and then, after a dose of \(3 \cdot 10^{17}\ \dfrac{\text{neutrons}}{\text{cm}^2}\) has been reached, decreases, i.e., compression of the crystals begins.

Similar studies have scarcely been carried out on crystals of other compounds. However, in Berry’s work [10] results are given for measurements of the lattice period of KCl under the action on the crystal of soft x-radiation from a tube with a Ni anticathode. The irradiation was performed with a beam of rays whose intensity at its center was \(19\ \dfrac{\text{roentgens}}{\text{sec}}\). The change in the lattice period occurs only during the first hour of exposure to x-rays and amounts to \(\dfrac{\Delta a}{a} = 10^{-5}\). No appreciable change in the lattice dimensions was found when the exposure time to x-rays was increased from 1 to 20 hours.

In connection with studies of the influence of ionizing radiations on the structure of the surface layer of crystals of KCl—KBr solid solutions, we carried out a whole series of measurements of the lattice period of crystals of several compositions of this system subjected to the action of various types of radiation.

We observed an increase in the lattice period of pre-annealed KCl crystals after exposure to Cu \(K_{\alpha}\) x-radiation for up to 2 hours. The relative change in the period is \(\dfrac{\Delta a}{a} = 10^{-4}\) and exceeds the measurement error, which on average is \(\pm 0.0003\ \text{Å}\). The measurements were performed on a URS-55a unit in an RKE camera at room temperatures. The specimens tested were prepared in the form of plates cleaved from single crystals.

An increase in the lattice period of pre-annealed KCl crystals is also observed after they are exposed to a beam of protons with an energy of \(4.5\ \text{MeV}\) and a total dose of \(10^{16}\ \dfrac{\text{protons}}{\text{cm}^2}\) (the irradiation was carried out on the cyclotron of the Research Institute of Technical Physics). The increase in the lattice period \(\Delta a\) does not exceed \(0.001\ \text{Å}\).

A similar increase in the lattice period was not found in crystals of the equimolar KCl—KBr solid solution and KCl which had not been pre-annealed before proton irradiation.

The lattice period of unannealed crystals of the equimolar KCl—KBr solid solution, when exposed to radiation from an Ra—\(\alpha\)—Be source with a neutron activity of \(4.8 \cdot 10^6\ \dfrac{\text{neutrons}}{\text{sec}}\) and gamma radiation of \(10\ \dfrac{\text{roentgens}}{\text{min}}\) (mean energy \(E_{\gamma} = 2\ \text{MeV}\)), with a total dose of \(10^{11}\ \text{neutrons}/\text{cm}^2\), does not change.

However, the character of the interference reflection lines differs for crystals of the equimolar solid solution irradiated with the above-mentioned doses of protons and neutrons. A decrease in the intensity of the x-ray lines and their broadening was found only in solid ...

solutions subjected to the action of a proton beam. A similar effect was also found for the solid solution of composition 75 mol% KCl in KBr that we studied.

Fig. 2 shows photometric curves of $\log \dfrac{I(x)}{I_0}$ for the x-ray lines of the doublet corresponding to reflection from the (800) plane for crystals of composition 50 and 75 mol% KCl in KBr. In each graph, for comparison, curves corresponding to irradiated and nonirradiated crystals are superposed. As is seen from the graphs, the magnitude of the maximum of the relative intensity decreases noticeably and the background increases on the x-ray patterns obtained from irradiated specimens.

In the literature [11] numerous experimental facts are described indicating a change in the intensity of interference lines on x-ray patterns of deformed metals, but there is still no single interpretation of the causes producing these changes.

It is assumed [11] that the change in the intensity of interference lines may be caused by the presence of static displacements, i.e., by displacement of the centers of thermal vibrations of the atom, while the magnitude of the amplitude of their vibrations about these centers is preserved. On the other hand, the same effect in the change of the intensity of interference lines will also be obtained in the case where static distortions are absent, and only the characteristic temperature $\Theta$ and the strength of the interatomic bonds have changed. This means that, at a given unchanged temperature of the substance, the frequency spectrum of elastic vibrations has changed, while the centers of vibrations retain their position. In both cases the mean value of the lattice parameter in deformed specimens does not change in comparison with undeformed specimens.

Fig. 2. Photometric curves of the relative intensity of x-ray lines corresponding to nonirradiated ($\triangle$) and irradiated ($\circ$) crystals.

Based on this explanation, we can evidently say that deformation and irradiation with protons must produce identical residual changes in the crystal, which in turn lead to identical diffraction effects in the reflection of x rays from deformed crystals and crystals irradiated with protons.

A similar conclusion was made by E. V. Kolontsova [12] on the basis of an analysis of diffuse maxima in the scattering of x rays by deformed crystals of LiF and crystals irradiated with neutrons (at a dose of $10^{18}\ \dfrac{\text{neutrons}}{\text{cm}^2}$).

We can qualitatively trace the change in the integral intensities of the corresponding interference lines, recorded in our experiments on X-ray diffraction patterns from irradiated and unirradiated solid solutions of the same composition. Let us denote the ratio

Fig. 3. Dependence of the ratio \(\dfrac{S_{\mathrm{irr}}}{S_{\mathrm{unirr}}}\) on the composition of the KCl—KBr solid solution.

\[ \frac{\int I_{\mathrm{irr}}(x)\,dx}{\int I_{\mathrm{unirr}}(x)\,dx} = \frac{S_{\mathrm{irr}}}{S_{\mathrm{unirr}}}, \]

where \(S_{\mathrm{irr}}\) and \(S_{\mathrm{unirr}}\) are the areas bounded by the abscissa axis and the intensity curve for the irradiated and unirradiated specimens, respectively.

Fig. 4. Dependence of the change in lattice period \(\Delta a\) on the composition of the KCl—KBr solid solution.

The magnitude of this ratio makes it possible, to some extent, to form an idea of the degree of distortion of the surface of a crystal irradiated with protons. The change in the ratio

\[ \frac{S_{\mathrm{irr}}}{S_{\mathrm{unirr}}} \]

as a function of chemical composition is shown in Fig. 3; from it we see that the strongest lattice distortions, which cause diffuse scattering of X-rays, are observed when a proton beam acts on the equimolar solid solution.

A noticeable change in the lattice period of KCl—KBr solid solutions occurs with the storage time of the specimens after they have been cleaved from single crystals. In all the specimens studied, after 1.5–2 months of storage at room temperature, a decrease of the period from \(a_0\) (the lattice period in the surface layer of a freshly cleaved specimen) to \(a\) was observed. During this interval of time the period approaches the steady-

to the newly established value. The decrease in the lattice constant \(\Delta a = a_0 - a\) varies with the composition of the solid solution, increasing with the content of KBr in KCl (Fig. 4).

Conclusions

1. An increase in the lattice period of annealed KCl crystals after irradiation with protons and X-rays has been observed. In unannealed KCl crystals, no change in the period is observed under the same conditions.

2. A weakening of the intensity of interference lines is observed on radiographs of proton-irradiated crystals of KCl—KBr solid solutions in comparison with unirradiated ones (especially at the equimolar composition), which indicates a change in the structure of the surface layer under the influence of irradiation.

3. A noticeable change in the lattice period of KCl—KBr solid solutions occurs with the storage time of the samples after they have been split from single crystals; this is apparently caused by deformation of the surface layer of the sample during cleavage and by the subsequent return of the system to an equilibrium state.

References

1. Ya. I. Frenkel. Introduction to the Theory of Metals. GIFML, 1958.

2. E. T. Teatum and Smith. Journal of Physical Chemistry. Vol. 61, 1957.

3. A. N. Kislina. Proceedings of SFTI, issue 35, 1956.

4. A. N. Kislina. Izv. TPI, 91, 1956.

5. M. S. Ivankina. Candidate’s dissertation, Tomsk, 1959.

6. V. G. Kuznetsov. Zh. N. Kh., 1, No. 7, 1956.

7. V. V. Zubenko, M. M. Umanskii. Crystallography, 1, issue 4, 1956.

8. Meyer, Perrio, Zhigon, Tournari. Materials of the International Conference on the Peaceful Uses of Atomic Energy. Geneva, vol. 7, Moscow, GNTI of Chemical Literature, 1958, p. 786.

9. R. E. Smolman and B. M. Willis. Philos. Mag., 2, 1018, 1957.

10. C. R. Berry. Phys. Rev., Vol. 98, 4, 1955, pp. 934–936.

11. G. F. Kosolapov. Radiography. 1962.

12. E. V. Kolontsova. The Action of Nuclear Radiations on Materials. Publishing House of the Academy of Sciences of the USSR, 1962.