A NOTE ON THE RELATIONSHIP BETWEEN THE F ABSORPTION BAND IN ALKALI-HALIDE CRYSTALS AND THE LATTICE ENERGY

E. K. Zavadovskaya

For the interpretation of the absorption spectra of binary heteropolar crystals, L. M. Shamovskii [1] proposed an energy equation for the elementary photochemical process in the form \(U = h\nu + I - E\), where \(h\nu\) is the long-wavelength limit of the intrinsic absorption of the crystal in the ultraviolet region, \(I\) is the ionization energy of the metal atom, and \(E\) is the electron affinity energy of the halide. The equation makes it possible, by means of optical measurements, to determine the energy of the crystal lattice. Thus a relationship between photochemical processes and lattice energy was established and experimentally confirmed satisfactorily. We have drawn attention to a possible relationship between the energy of the crystal lattice and photoelectric phenomena.

Fig. 1. Dependence between the absorption maximum corresponding to the \(F\)-band, in eV, and the lattice energy, in kcal/mole, for alkali-halide crystals.

It is known that, as a result of activation of alkali-halide crystals, color centers arise in them with a characteristic \(F\)-absorption band in the visible part of the spectrum. The properties of the \(F\)-absorption band in crystals depend on the structure of the crystal. The vibrational frequency \(\nu_{\max}\) corresponding to the maximum of the absorption band at room temperature is related to the lattice constant by the relation \(\nu_{\max} a^2 = 5.02 \cdot 10^{-5}\ \text{cm}^3/\text{sec}\) [2].

In several works it has been shown that many properties of crystals are determined unambiguously by the energy of the crystal lattice. Therefore, owing to the dependence of the position of the maximum of the \(F\)-absorption band on the crystal structure, one should also expect a dependence of this maximum on the energy of the crystal lattice [3].

Figure 1 shows the dependence, constructed by us, between the position of the maximum of the \(F\)-absorption band and the energy of the crystal lattice for crystals of alkali-halide salts.

A simple relationship was obtained between these quantities. The position of the maximum of the \(F\)-absorption band shifts when both the cation and the anion are replaced. With increasing lattice energy, the maximum of the \(F\)-absorption band also increases almost linearly.

It is known that the absorption of light corresponding to the \(F\)-band is accompanied by the transfer of electrons into the conduction band, and a photocurrent arises in the crystal.

Thus, the absorption of visible light is accompanied by the liberation of the most weakly bound electrons in colored crystals. The data presented in Fig. 1 show that the binding energy of the most weakly bound electrons in colored crystals is determined by the magnitude of the crystal-lattice energy and increases as the latter increases.

Establishing a connection between an electronic phenomenon in crystals and the physicochemical characteristic of the lattice energy is of considerable interest.

REFERENCES

1. Shamoskii, A. M. Absorption spectra of heteropolar crystals and crystal-lattice energy. GONTI, NKTP, 1938.
2. E. Mollwo. Zs. f. Phys. 85, 56, 1933.
3. Vorob’ev, A. A. and Zavadovskaya, E. K. DAN LXXXI, 3, 375, 1951.