Refractive Index of Single Crystals of Solid Solutions of Alkali-Halide Salts and Its Change during Their Aging

A. N. KISLINA

(Presented by Professor Doctor A. A. Vorob'ev)

The influence of a substance on the propagation of light in it is due to the interaction of light with the atoms and molecules of which the substance is composed. An incident electromagnetic wave, propagating in a dielectric, causes forced oscillations of its particles.

In the general case, the amplitude and phase of the forced oscillations of the particles of a dielectric are determined by the relation between the frequency of oscillation of the incident wave and the frequency of their natural oscillations in the dielectric [1].

The magnitude of the refractive index of electromagnetic waves in a dielectric is connected with the excitation of oscillations of its particles and, consequently, with the energy of their binding in the lattice. The passage of visible light through a crystal causes oscillations of electrons. The refractive index of light characterizes the binding energy of electrons in the crystal. As the binding energy of electrons in the crystal increases, their forced oscillations decrease and the refractive index decreases. It is known that the electronic component of the dielectric coefficient, \(\varepsilon_{\mathrm{e}} = n^2\), is related to polarizability by Drude’s formula:

\[ \varepsilon = 4\pi n_k \alpha \tag{1} \]

or by the Lorentz–Lorenz formula:

\[ \frac{\varepsilon - 1}{\varepsilon + 2} = \frac{4}{3}\pi n_k \alpha \tag{2}, \]

where \(n_k\) is the number of molecules or the number of ion pairs per unit volume.

Formulas (1) and (2) are applicable to nonpolar substances, liquids, and ionic crystals. The change in the square of the refractive coefficient and in the dielectric coefficient is determined by the product of the number of ion pairs \(n_k\) per unit volume and the polarizability \(\alpha\).

The quantity

\[ n_k = \frac{N\rho}{2(A_1 + A_2)} \tag{3}, \]

where \(N = 6.06 \cdot 10^{23}\), \(\rho\) is the specific gravity, and \(A_1\) and \(A_2\) are the atomic weights of the components entering into the compound.

According to experimental data, the refractive index of crystals of alkali-halide salts decreases with increasing lattice energy [2].

It is of interest to verify this regularity for solid solutions of alkali-halide salts.

In addition, the dependence of the refractive index on the chemical composition of a substance can be used for identifying the properties of materials.

Formula (2) is transformed into a formula of the form:

\[ \frac{n^2 - 1}{n^2 + 2}\cdot \frac{1}{\delta} = \operatorname{const} (4), \]

where \(\delta\) is the density of the substance.

The quantity \(\dfrac{n^2 - 1}{n^2 + 2}\) is called the refraction of a substance.

Molecular refraction is the product of the refraction of a compound substance \(R\) and the molecular weight \(M\). It is considered [3] that, in the case of single crystals of solid solutions of alkali-halide salts, the molecular refractions should add additively from the refractions of the individual components.

Consequently, the molecular refraction can be calculated from atomic constants.

The deviations that arise in this case are explained by features of the structure of the substance.

Owing to interaction between the atoms in a molecule, intramolecular polarization occurs, generally differing depending on the chemical composition of the substance. Intramolecular polarization increases with the packing density in the compound.

It is known that, with increasing field strength, the displacement of charges becomes smaller than corresponds to the elastic-bond coefficient for polarizability in weak fields. Similarly, the polarization of ions in a compound under the action of an incident electromagnetic wave becomes weaker as a result of intramolecular polarization.

Thus, intramolecular polarization reduces molecular refraction. Consequently, in an additive calculation of molecular refraction, the influence is not taken into account of: a) intramolecular polarization and b) intermolecular polarization, which, as a rule, is weaker than the former.

In crystals of alkali-halide compounds, deformation of the electronic orbits of ions takes place.

Refraction measures the displacement of electron shells, that is, the electronic polarizability in ions or molecules. The force field of a neighboring ion can change the electronic polarizability. Fajans showed in 1923 that, in ionic compounds, owing to the influence of the fields of neighboring ions, the refraction of a molecule is usually not equal to the sum of the refractions of the ions forming this compound, and differs from it by the amount: \(\Delta R = R_A + R_K - R_M\). The magnitude of the deviation may be positive, negative, or equal to zero.

Consequently, molecular refractions make it possible to control the percentage content of components in solid solutions of alkali-halide salts only approximately.

To determine the refractive index of single crystals of solid solutions, we used the immersion method [4]. The single crystal under investigation was ground into a powder and sifted through sieve No. 100. The absolute error in determining the refractive index of crystals was \(0.0015\)—\(0.002\), which corresponds to a relative error of about \(0.1\%\).

The refractive index was determined for single crystals of KCl, KBr,

KI, NaCl, NaBr, NaI, RbCl and solid solutions of the systems: KCl—KBr, KBr—NaBr, KCl—RbCl, KI—KCl, KCl—NaCl and NaCl—AgCl.

The refractive index of single crystals of solid solutions of the KCl—KBr and KBr—NaBr systems was determined for freshly grown specimens and for specimens that had undergone natural aging. In the remaining cases the refractive indices were measured on freshly grown single crystals.

During aging the single crystals were kept in a desiccator. The refractive index of KCl—KBr solid solutions was determined on single crystals after different periods of storage. For KBr—NaBr solid solutions, determination of the refractive index was carried out on the same specimens. For this purpose, cubes approximately \(7 \times 7 \times 7\) mm in size were cleaved from KBr—NaBr crystals of various concentrations; during aging, small pieces were broken off from these cubes, ground into powder, and the refractive indices were measured. During aging, the surfaces of single crystals of KBr—NaBr solid solutions became covered with a white enamel-like layer. Therefore, before the refractive index was measured, the upper layer of the crystal was removed.

Single crystals of the KCl—KBr system, both fresh and those that had undergone aging, were transparent. Single crystals of solid solutions of the KCl—RbCl and NaCl—AgCl systems were also transparent. Single crystals of the KI—KCl and KCl—NaCl systems were transparent only for solid solutions containing up to 10 mole % of the second component; crystals of other concentrations had an enamel-like structure.

The results of the measurements are presented as graphs of the dependence of the refractive index of single crystals of solid solutions on chemical composition.

Fig. 1. Relationship of the refractive index with chemical composition for single crystals of the KCl—KBr system.
\(x\)—fresh specimens,
\(o\)—after 1 year of storage,
\(\triangle\)—after 3 years of storage.

For freshly grown single crystals of solid solutions, the dependence of the refractive index on chemical composition has positive (KCl—KBr system, Fig. 1) or negative (KBr—NaBr system, Fig. 2) nonadditivity.

During natural aging of the crystals, the “refractive index—chemical composition” curves become smoothed, approaching the straight line of additivity. The latter evidently characterizes the approach of the state of the solid solution to equilibrium during aging. This assumption is also confirmed by the fact that for fresh single crystals we have several refractive-index values, whereas for aged ones there is only one (Fig. 1).

The change in the refractive index of single crystals of the KBr—NaBr system during their aging occurs rather quickly, since after only two weeks of storage of specimens in a desiccator the curve of the dependence of the refractive index on chemical composition had become significantly smoothed. The latter is explained by the great instability of this system. After three weeks of storage of KBr—NaBr specimens of various concentrations, the refractive indices of the deep transparent

layers are close to the refractive index of KBr (Fig. 2). Whereas the refractive index of the white enamel-like layer proved to be 1.608, that is, closer to the refractive index of NaBr (1.631).

From the refractive indices we calculated the molecular refractions of the solid solutions KCl—KBr, KBr—NaBr and plotted the dependence of molecular refraction on chemical composition.

Fig. 2. Relationship between refractive index and chemical composition for single crystals of the KBr—NaBr system.
x — fresh samples,
o — after storage for 14–15 days,
△ — after storage for 20–22 days.

Figure 3 shows the dependence of molecular refraction on chemical composition for KCl—KBr single crystals of different storage times, and Fig. 4—for KBr—NaBr single crystals, fresh and after two weeks of storage.

Fig. 3. Check of the percentage ratio of KCl—KBr components by molecular refraction.
x — fresh crystals,
o — crystals stored before measurement for one year.

For single crystals of solid solutions KCl—KBr stored for one and three years, this dependence proved to be linear. An error in the refractive index of 0.002 corresponds to an error in the percentage ratio of the components of the solid solution of 2–3%.

Consequently, by molecular refraction one can monitor the chemical composition, in our case with an accuracy of up to 97–98%. A linear dependence of molecular refraction on chemical composition was obtained earlier by Hippel [5] for KCl—KBr crystals annealed for twelve hours at a temperature close to the melting point.

Fig. 4. Monitoring the percentage ratio of the components KBr—NaBr by molecular refraction.
x — fresh crystals,
o — crystals stored for two weeks before measurement.

In good agreement with our results, the dependences of the refractive index of solid solutions of alkali-halide salts (fresh and having undergone an aging stage) on chemical composition include the dependence of the refractive index of piperine alloys with arsenic and antimony iodides on composition (Fig. 5).

Fig. 5. Dependence of the refractive index of piperine alloys with arsenic and antimony iodides on composition.

The solid line shows the dependence for fresh alloys (measured by Larsen), and the dashed line that for alloys that had lain for several years (measured at the Institute of Applied Mineralogy in Moscow) [6].

Fig. 6 shows the dependence of the refractive index of single crystals of solid solutions KCl—RbCl on chemical composition.

The refractive indices of KCl and RbCl single crystals differ very little; therefore, the difference in the refractive indices of single crystals of solid solutions of individual concentrations lies within the limits of measurement error, although the refractive indices of most solid solutions of the KCl—RbCl system lie above the additivity line.

Figs. 7, 8, and 9 show the dependence of the refractive indices of single crystals of solid solutions of the systems NaCl—AgCl (Fig. 7), KCl—NaCl (Fig. 8), and KCl—KJ (Fig. 9) on chemical composition. For all three systems there is negative nonadditivity in the change of the refractive index as a function of chemical composition. The single crystals of the NaCl—AgCl system had a clearly nonuniform concent-

![Graph: Dependence of refractive index \(n\) on chemical composition for KCl—RbCl solid-solution single crystals. Vertical axis: “Refractive index”; horizontal composition scale: \(100, 80, 60, 40, 20, 0\) mol% KCl and \(0, 20, 40, 60, 80, 100\) mol% RbCl; \(n\) ranges from 1.48 to 1.52.]

Fig. 6. Dependence of the refractive index of single crystals of KCl—RbCl solid solutions on chemical composition.

![Graph: Dependence of refractive index \(n\) on chemical composition for NaCl—AgCl solid-solution single crystals. Vertical axis: “Refractive index”; horizontal axis: \(10, 20, 30, 40\) mol% AgCl; \(n\) ranges from 1.54 to 1.70.]

Fig. 7. Dependence of the refractive index of single crystals of NaCl—AgCl solid solutions on chemical composition.

![Graph: Dependence of refractive index \(n\) on chemical composition for KCl—NaCl solid-solution single crystals. Vertical axis: “Refractive index”; horizontal composition scale: \(0, 20, 40, 60, 80, 100\) mol% NaCl and \(100, 80, 60, 40, 20, 0\) mol% KCl; \(n\) ranges from 1.49 to 1.55.]

Fig. 8. Dependence of the refractive index of single crystals of KCl—NaCl solid solutions on chemical composition.

ratio over the height of the crystal. The lower part of the crystal had a green color, whereas the upper layer was transparent with a slightly greenish tint. The refractive index of the upper part of the crystal was lower than that of the lower part.

For the solid solutions KCl—NaCl and KCl—KI, in Figs. 8–9 the crosses denote the limiting values of the refractive index of single crystals of the individual concentrations.

Fig. 9. Dependence of the refractive index of single crystals of solid solutions KJ—KCl on chemical composition

A considerable scatter in the refractive indices for one and the same crystal of a KCl—NaCl and KCl—KI solid solution indicates, on the one hand, the nonequilibrium of the concentration, which is usually characteristic of solid-solution crystals grown from the melt, and, on the other hand, the decomposition of the solid solutions.

Fig. 10. Distribution of crystalline grains of an equimolar KJ—KCl solid solution by refractive index.

The decomposition of the KI—KCl solid solution of equimolar composition is well confirmed by Fig. 10, which shows the distribution of crystalline grains of the given composition by refractive index after 1.5 months of storage of the crystal in dried transformer oil.

It is seen from Fig. 10 that approximately 40% of the grains from the composition of the crystal have a refractive index corresponding to the equimolar solid solution, and 9% of the grains have a refractive index equal to the refractive index of KI. Consequently, the heavier component KI separates out in pure form during decomposition more rapidly than the lighter KCl, which we observed earlier in the X-ray study [8] of this crystal. The refractive index of the decomposing KI—KCl solid solution of equimolar composition and, in part, the refractive index of single crystals of the KCl—NaCl and KCl—KI systems were measured by us jointly with the student E. V. Beinarovich. In Table 1 we give the refractive indices measured by us

for single crystals of alkali-halide salts in the visible region of light, and the tabulated values corresponding to the sodium D line.

It is seen from Table 1 that the greater the refractive index of the crystal, the greater the differences between the refractive indices measured for the visible region of light and the tabulated \(n_D\). In this case \(n_{\text{meas.}}\), as a rule, is lower than \(n_D\).

Table 1

However, Wood and Frank [7] observed refractive indices for CsCl and CsBr in sodium light also lower by 0.0025 than indicated in the table for the same sodium light.

The lattice energy (calculated theoretically) for solid solutions of alkali-halide salts—for example, the systems KCl—KBr, KCl—KI—changes additively with change in composition, decreasing from KCl to KI and KBr; while the refractive index increases from KCl to KI and KBr with a certain positive (KCl—KBr system) or negative (KCl—KI system) nonadditivity, approaching the additive value in the course of aging.

Consequently, for crystals of solid solutions of alkali-halide salts, as for crystals of pure salts, the refractive index decreases with increasing lattice energy of the solid solution.

LITERATURE

1. Fermi E. Molecules and Crystals, G.I.I.L., 1947.
2. Vorob’ev A. A. DAN, vol. 108, 1, 1956.
3. Herzfeld K. F. Theory of the Solid State, ONTI, 107, 1936.
4. Tatarskii V. B. Crystal Optics and the Immersion Method for Determining Matter. Publishing House of Leningrad State University, 1949.
5. Hippel A. V. Electrical strength of alkali-halide crystals and the influence on it of the formation of mixed crystals and foreign impurities. Z. f. Physik, 88, 358, 1934.
6. Bakkii G. V. The Immersion Method. Publishing House of Moscow State University, 1948.
7. Wood L. I.; Frank A. I. Refractive index as a supplement to the method of X-ray analysis of crystals of solid solutions. Analyt. Chemistr. J. v. 23, 5, 695—699, 1951.
8. Kislina A. N. X-ray study of single crystals of solid solutions of alkali-halide salts (present issue).