Relationship of the Stability of $F$-Centers and Dislocation Density to the Lattice Energy of Alkali-Halide Crystals

E. K. ZAVADOVSKAYA, I. Ya. MELIK-GAIKAZIAN, I. B. BERMAN

A number of authors [1, 2, 3] have investigated the stability of centers for various alkali-halide crystals.

Kasler, Pringsheim, and Yuster [3] investigated the stability of $F$-centers produced by X-rays in NaCl, KCl, and KBr crystals at a temperature of $-185^\circ$C.

Attention is drawn to the sharp dependence of the stability of $F$ centers on the energy of the crystal lattice. As the lattice energy increases, the number of $F$-centers that decay $\left(\dfrac{\Delta n}{n}\right)$ during heating of the crystal from $-185^\circ$C to $20^\circ$C decreases (Fig. 1).

Fig. 1. Dependence of the stability of $F$-centers on the energy of the crystal lattice. (Along the ordinate axis—the percentage of decayed $F$-centers $\left(\dfrac{\Delta n}{n}\right)$ during heating of crystals from $-185^\circ$C to $20^\circ$C according to the data of Kasler, Pringsheim, and Yuster.)

The physical reason for this relation is not obvious, since it is known that the formation and decay of $F$-centers are electronic processes, whereas the lattice energy is a thermodynamic characteristic of the crystal, associated with the interaction of the ions composing an alkali-halide crystal. The explanation of the observed dependence probably consists in the following.

Many authors [4, 5, 6], on the basis of studying the kinetics of the decay of $F$-centers, have come to the conclusion that in alkali-halide crystals there exist two types of $F$-centers—“hard,” stable color centers surrounded by an undistorted crystal lattice and therefore located in a symmetric electric field, and so-called “soft” $F$-centers, located in an asymmetric field because of the presence of geometrical distortions of the latt—

Fig. 2. Patterns of selective etching of crystals: a) NaCl, b) KCl, c) KBr (symmetrical pyramidal pits correspond to the emergence points of edge dislocations; nonsymmetrical pits, to screw dislocations).

…dislocations, and therefore unstable. Dislocations in alkali-halide crystals can be revealed by the method of selective etching.

As a result of a statistical study of selective-etching patterns (Fig. 2a, b, c), we determined the dislocation density in NaCl, KCl, and KBr crystals grown from the melt under the same temperature regime. There is reason to expect that this quantity will be inversely dependent on the lattice energy, since one of the causes of dislocation formation is the presence of mechanical stresses due to the inhomogeneity of the thermal field surrounding the crystal growing from the melt. Apparently, in crystals with small bonding forces, lattice distortions arise to a greater extent, other conditions being equal. The experiment confirmed this assumption. Figure 3 shows the dependence of the dislocation density \(N\) on the crystal-lattice energy.

Fig. 3. Dependence of the dislocation density \((N)\) in crystals of alkali-halide compounds on the lattice energy.

It is evident that, with increasing lattice energy, the dislocation density in the crystal decreases.

Thus, the cause of the connection between the stability of \(F\)-centers and the lattice energy is revealed: the stability of \(F\)-centers decreases with increasing dislocation density, while the dislocation density decreases with increasing bonding forces between the particles composing the crystal.

REFERENCES

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4. Przibram, Wien. Ber. 135, 202, 1926.
5. J. Oberly, Phys. Rev. 84, 1257, 1951.
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