LATTICE DEFECTS IN SILVER BROMIDE

The question of the nature of lattice defects in silver bromide is of special interest for crystal physics in connection with the photosensitivity of this substance. The mechanism of photolysis of silver bromide crystals, which is of exceptional interest for scientific and practical photography, is determined to a considerable extent by the nature of lattice defects. The problem under consideration is usually reduced to clarifying the degree of participation of “Frenkel” defects and “Schottky” defects in the processes of conductivity and diffusion. The mobility of bromine ions is usually regarded as evidence for the presence of Schottky defects, since simple difficulties prevent the transition of bromine ions to interstitial positions. Consequently, Frenkel defects may be interstitial silver ions and vacant silver sites, while Schottky defects may be vacant bromine and silver sites.

According to the theory of Gurney and Mott, photolysis of silver bromide crystals proceeds in two principal stages—electronic and ionic. Almost every quantum of light absorbed by silver bromide transfers an electron into the conduction band of the crystal. After some time, this electron ...

...is captured by various lattice disturbances (local levels). A negatively charged disturbance attracts interstitial silver ions (Frenkel defect), which is converted into an atom of silver. Repetition of this process leads to the formation of a center consisting of several silver atoms, which is the center of the latent image or of photographic development.

The existence in silver bromide of only Frenkel defects is confirmed by a number of studies. Tubandt’s experimental data² showed that at elevated temperatures (200–300°C) molten silver bromide is a purely cationic conductor. Shapiro and Kolthoff³ found that not only molten but also freshly precipitated silver bromide, with its enormous surface favorable to the formation of Schottky defects, possesses cationic conductivity at room and higher temperatures. Precise measurements of the density and lattice constant of silver bromide⁴ showed that, when heated from 20 to 400°C, the average number of molecules or ions in the elementary cell remains the same within the limits of experimental error (1%). If Schottky defects predominated, this number should have decreased by approximately 16%.

On the other hand, studies of isotope exchange⁵–⁷ between silver and bromine ions in solution and the corresponding ions in solid silver bromide showed that the diffusion coefficients of silver and bromine ions are close in magnitude. Such a result is incompatible with the existence of Frenkel defects and with the conductivity data. This compelled some authors⁸ to reconsider the results obtained by Tubandt and others and to propose another mechanism for the formation of the latent image, based on the diffusion of Schottky defects. A new theory, which satisfactorily explained a number of photographic phenomena⁹, became fairly widespread. In particular, P. Meiklejohn¹⁰ attempted to prove experimentally the existence of F-centers in silver bromide crystals, analogous to F-centers in alkali-halide crystals.

However, the experimental grounds for the new view of the nature of the defects were clearly insufficient. In this connection the question was again reconsidered in a number of experimental studies. First of all, in new isotope-exchange experiments¹¹ at room temperature, the absence of exchange of bromine ions and rapid exchange of silver ions were demonstrated. The erroneous results of previous studies⁵–⁷ are explained by a trivial case of dissolution and recrystallization of the silver bromide suspension on which the exchange experiments were performed. According to new data, the self-diffusion coefficient of bromine ions in silver bromide at room temperature is 3–4 orders of magnitude lower than its value for silver ions.

Studies of the diffusion of bromine and silver ions in silver bromide at 300°¹² with the aid of labeled silver and bromine showed that the diffusion coefficient of bromine ions is 3–4 orders of magnitude lower than the value for silver ions. This, in the authors’ opinion, indicates an insignificantly small concentration of vacant bromine sites.

Studies of the anomalous thermal expansion of silver bromide¹³ near the melting temperature and of the molar heat capacity at elevated temperatures¹⁴ indicate, taking into account new data on the energies of formation of interstitial ions¹⁵, the predominance of Frenkel defects, whose concentration near the melting point may be estimated at ≈2%. The fairly high concentration of defects at high temperature makes it possible to investigate this region by the method of X-ray structural analysis. A very careful measurement of the lattice constant of silver bromide at high temperatures¹⁶ showed that the assumption of the existence only of Frenkel defects agrees well with the experimental data, although the possibility is not excluded that the concentration of defects

FROM CURRENT LITERATURE

according to Schottky reaches 10% of the total concentration of defects. However, according to unpublished data \(^{17}\), the interpretation of radiographs at high defect concentrations is very unreliable, so this question remains open.

A similar study \(^{18}\), in which the packing density of pure silver bromide at \(25^\circ\) was determined, proceeding from the known changes in the lattice constant and density, showed that the maximum possible concentration of vacant sites at \(25^\circ\) is \(7 \cdot 10^{-5}\), i.e., it is too small for Schottky defects to be able to participate in ionic conductivity or diffusion. To clarify the nature and mobility of defects at various temperatures, a detailed investigation \(^{19}\) was carried out on the effect of pressure, temperature, and the concentration of \(\mathrm{CdBr_2}\) on the electrical conductivity of silver bromide. This work showed that below \(300^\circ\mathrm{C}\) the observed increase in volume due to the formation of 1 mole of defects \((\Delta V = 16\ \mathrm{cm^3/mole})\) indicates a significant predominance of Frenkel defects, since the minimum increase in volume upon the formation of 1 mole of Schottky defects is \(29\ \mathrm{cm^3/mole}\) (the molar volume of AgBr). The increase in volume upon formation of Frenkel defects is explained by the fact that both the formation of a vacant silver site and the formation of an interstitial silver ion require an increase in the distance between ions near the defect. Experiments at temperatures from 300 to \(406^\circ\mathrm{C}\) showed that the concentration of Schottky defects increases with temperature in this interval, reaching 2.4% at \(406^\circ\mathrm{C}\). The concentration of Frenkel defects at \(406^\circ\) is equal to 0.15%. Despite this, experiments by the same author show that at \(406^\circ\mathrm{C}\) silver bromide is a purely cationic conductor. This, according to the author, is explained by the low mobility of vacant bromine sites compared with vacant silver sites and interstitial silver ions. However, such conclusions meet with the following objection. If vacant bromine sites have very low mobility, then upon rapid heating of an AgBr crystal to, for example, \(406^\circ\), the concentration of these sites, and consequently also of vacant silver sites (which are formed in an equivalent amount), will not immediately reach the equilibrium state, and the electrical conductivity will increase with time, which is not consistent with all known experimental data. Zeitz \(^{17}\) considers that the concentration of Schottky defects near the melting point is about 0.1% and that they play the principal role in the formation of entanglements (dislocations). Considering the experimental data, Zeitz concludes that the concentration of Frenkel defects near the melting point reaches about 1%.

The works cited allow one to assert that at all temperatures up to the melting point the processes of conductivity and diffusion are determined by Frenkel defects. A small admixture of Schottky defects is entirely permissible at all temperatures, especially near the melting point.

A. Kh.

CITED LITERATURE

1. N. Mott and R. Gurney, Electronic Processes in Ionic Crystals, IL, 1950.
2. C. Tubandt, Hand. d. Exper. Phys., 12, 1 (1932).
3. J. Shapiro, I. Kolthoff, J. Chem. Phys., 15, 41 (1947).
4. C. Wagner, J. Beyer, Zeits. phys. Chem., 32, 113 (1936).
5. A. Länger, J. Chem. Phys., 10, 321 (1942); 11, 11 (1943).
6. A. Polesitskii, DAN SSSR, 24, 668 (1939).

1. J. Kolthoff, O’Brien, J. Amer. Chem. Soc., 61, 3409, 3414 (1939).
2. J. Mitchell, Phil. Mag. 40, 249, 667 (1949); collection “Chemistry of Photographic Processes,” Izd. Inostr. Lit., 1951.
3. J. Mitchell, report in the collection Fundamental Mechanism of Photographic Sensitivity, Lond., 1951.
4. P. Meiklyar, E. Lutseyko, DAN SSSR, 73, 63 (1950).
5. K. Zimen, report in the collection Fundamental Mechanism of Photographic Sensitivity, Lond., 1951.
6. A. Murin and Yu. Taush, DAN SSSR, 80, 4 (1951).
7. A. Lawson, Phys. Rev., 78, 185 (1950).
8. R. Christy, A. Lawson, J. Chem. Phys., 19, 517 (1951).
9. J. Teltow, Ann. d. Physik., 5, 63 (1949).
10. Ch. R. Berry, Phys. Rev., 82, 422 (1951).
11. F. Seitz, Rev. Mod. Phys., 23, 328 (1951), reference 6.
12. H. Keith, J. Mitchell, Phil. Mag., 42, 1331 (1951).
13. S. Kurnick, J. Chem. Phys., 20, 218 (1952).