X-RAY STUDY OF SINGLE CRYSTALS OF SOLID SOLUTIONS OF ALKALI-HALIDE SALTS

A. N. KISLINA

(Presented by the Scientific Seminar on Dielectrics)

A solid solution corresponds to the case in which atoms or groups of atoms of each of the components—the solute—are “introduced” into the lattice of the other component—the solvent. On the radiograph one observes lines corresponding to the structure of the solvent, distorted by the introduction of the solute atoms. Distortions in a solid solution arise because the ions of the solvent and of the dissolved element do not coincide in size. This distortion will be nonuniform, since the foreign ion deforms the lattice more strongly at short distances and more weakly at greater distances. As a result, in some part of the volume the lattice constant retains its former value; in some regions an increase is possible, and in others a corresponding decrease of the lattice constant. X-ray methods measure a certain mean value of the lattice constant, which is then taken as the lattice constant of the solid solution.

It is considered that the change in the dimensions of the unit cell in substitutional solid solutions is directly proportional to the number of dissolved atoms. This empirical additivity rule, known as Vegard’s law [1], represents only a first approximation. Deviations are observed that have a positive sign when the lattice constant of the solid solution exceeds the value corresponding to the linear law, and deviations that have a negative sign when the lattice constant of the solid solution is less than the value corresponding to the linear law.

N. N. Sirota [2, 3] shows that the lattice parameters of two-component systems of solid solutions will deviate from the additivity rule, and by an amount increasing with the greater heat of their formation.

B. Ya. Pines [4, 5] draws attention to the considerable deviation of the lattice constants, for certain systems of solid solutions, from Vegard’s law.

Durham and Hawkins [6] calculated the value of the lattice constant of solid solutions of the systems potassium chloride—potassium bromide, rubidium bromide—rubidium chloride, rubidium chloride—potassium chloride, and rubidium bromide—potassium bromide at a temperature of 25°C. They assumed that the ions are not at a constant distance from the nearest neighbor, but occupy a position corresponding to the minimum of the potential energy relative to one another.

E. K. Zavadovskaya [7] compared the values of the interionic distances obtained by these authors with the corresponding values calculated by her according to the additivity rule. The discrepancies in the values of the interionic distances calculated by these two methods are insignificant.

Calculations by other authors, using more or less complicated initial assumptions, also lead to results that differ little from those obtained by the simple additivity rule. In calculating the lattice constant of a solid solution by the additivity rule, the important phenomenon of ion displacement is not taken into account.

The actual equilibrium position of the ions in the lattice of a solid solution does not coincide with the corresponding positions in the ideal lattice; the ions are somewhat displaced relative to the equilibrium position.

When interaction of the components is taken into account, the lattice constant of a solid solution may vary with concentration according to a more complicated law than the additivity rule.

We carried out an X-ray study of single crystals of solid solutions with substituted halogen of the systems potassium chloride—potassium bromide, sodium chloride—sodium bromide, potassium iodide—potassium chloride, and of single crystals of solid solutions with substituted metal of the systems potassium iodide—sodium iodide, potassium bromide—sodium bromide, and potassium chloride—rubidium chloride.

The X-ray photographs were taken in a Debye camera on polycrystalline cylindrical specimens prepared by grinding single crystals into powder and filling a celluloid pouch with the powder. The celluloid pouch protected the specimen from the action of moisture in the surrounding air during the taking of X-ray photographs. The diameter of the specimens was 0.6–0.8 mm.

The effective radius of the cassette, with a film thickness of 0.25 mm, was \(28.69 \pm 0.02\) mm.

As the source of X-rays, an X-ray unit of the URS-70 K1 type was used, equipped with a BSV X-ray tube with a copper anode. The current through the tube reached 8–10 milliamperes at a voltage of 40 kV. The exposure time was about 4 hours. Usually 10–15 pairs of symmetrical lines appeared on the X-ray photographs.

The single crystals studied, both of pure salts and of solid solutions, were not subjected to annealing. This was not done because solid solutions of alkali-halide salts, as is known, are very unstable and readily decompose during storage or heating. Consequently, during annealing there is a danger of changing the phase state of the solid solution.

In calculating the lattice constant, we took into account all the lines of the X-ray photograph, with allowance for the weight of each measurement, according to the method for processing results of measurements made with different accuracy. The correction to the lattice constant was made only for the thickness of the specimen. The total error in calculating the lattice constant was also determined with allowance for the weight of the errors of the individual measurements.

The result of the measurements is presented in the form of graphs of the dependence of the lattice constant on the chemical composition of single crystals of solid solutions of various systems (Figs. 1–6).

For single crystals of solid solutions of the systems potassium chloride—potassium bromide (Fig. 1), potassium chloride—rubidium chloride (Fig. 2), sodium chloride—sodium bromide (Fig. 3), potassium iodide—potassium chloride (Fig. 4), it may be considered that, within the errors of our measurements, the additivity law is fulfilled. The deviation from the additivity law of one point in the case of the potassium chloride—potassium bromide system and of one point in the case of the potassium iodide—potassium chloride system is most likely explained by a deviation of the concentration of the grown-

Fig. 1. Dependence of the lattice constant on the chemical composition of single crystals of solid solutions KCl—KBr

Fig. 2. Dependence of the lattice constant on the chemical composition of single crystals of solid solutions KCl—RbCl

Fig. 3. Dependence of the lattice constant on the chemical composition of single crystals of solid solutions NaCl—NaBr

Fig. 4. Dependence of the lattice constant on the chemical composition of single crystals of solid solutions KCl—KJ.

Fig. 5. Dependence of the lattice constant on the composition of single crystals of solid solutions KJ—NaJ.

Fig. 6. Dependence of the lattice constant of single crystals of solid solutions KBr—NaBr on chemical composition.

of the crystal on the concentration of the salt mixture before growth. For solid solutions of the potassium iodide—sodium iodide system (Fig. 5), there is a positive nonadditivity in the dependence of the lattice constant on chemical composition, while for the potassium bromide—sodium bromide system (Fig. 6) the deviation from the rule of additivity has both a positive and a negative sign.

The lines in the X-ray photographs of solid solutions of the systems potassium chloride—potassium bromide, potassium chloride—rubidium chloride, sodium chloride—sodium bromide, and of solid solutions containing up to 20 mol % sodium iodide in potassium iodide, up to 20 mol % potassium chloride in potassium iodide, up to 10 mol % potassium iodide in potassium chloride, and up to 30 mol % sodium bromide in potassium bromide, were sufficiently sharp; whereas for the remaining solid solutions they were diffuse. The latter characterizes either a nonequilibrium state of the crystals of these solid solutions or the onset of decomposition. The appearance of lines corresponding to pure potassium iodide in the solid solution 60 mol % potassium iodide—40 mol % potassium chloride, along with lines corresponding to the solid solution, is explained by the decomposition process. It is evident that, upon decomposition of solid solutions, the heavier component separates into a phase more rapidly.

In Fig. 4, for a single crystal of the solid solution 60 mol % KI and 40 mol % KCl, two values of the lattice constant are plotted. In Fig. 5, for a crystal of the equimolar solid solution potassium iodide—sodium iodide, two values of the lattice constant are likewise plotted, for the X-ray photograph reveals a decomposed solid solution.

A linear dependence of the lattice constant on the chemical composition of single crystals of solid solutions potassium chloride—potassium bromide and potassium chloride—rubidium chloride was obtained earlier by Missner [8].

REFERENCES

1. Vegard, L., Zs. f. Physik, 5, 17, 1921.
2. Sirota, N. N., DAN SSSR, vol. 56, no. 6, 607, 1947.
3. Sirota, N. N., ISFKhA, 21, 90–100, 1952.
4. Pines, B. Ya., ZhETF, 11, 147–158, 1941.
5. Pines, B. Ya., Lectures on Structural Analysis, ONTI, DNTVU Publ., 1940.
6. Durham, G. S., Hawkins, J. A., Zow. Chem. Phys., 19, 149, 1951.
7. Zavadskaia, E. K., Proceedings of Tomsk Polytechnic Institute, vol. 77, 1953.
8. Missner, G., Pick, H., Zs. f. Phys., Bd. 134, 576, 1953.