LATENT PHOTOGRAPHIC IMAGE

P. V. Meiklyar

PART I

1

The change produced by light in a photographic layer under ordinary exposures can be detected only after the action of a developer on such a layer. For this reason this change is called the latent photographic image.

A photographic emulsion is an aggregate of fine silver halide crystals suspended in gelatin. These small crystals often have a plate-like form. The area of the projection of one crystallite onto the surface of the photographic layer is on average \(0.5\text{–}1.0\,\mu^2\) for high-sensitivity photographic layers and \(0.1\text{–}0.3\,\mu^2\) for low-sensitivity layers. The area of individual crystals reaches several square microns. Per square centimeter of photographic layer there are from \(10^9\) to \(10^{12}\) crystals, and they are arranged through the thickness of the layer in many rows (up to 40–50).

The crystals of technically manufactured high-sensitivity photographic layers consist of silver bromide with a small addition of silver iodide (about 3%). In low-sensitivity layers, used chiefly for obtaining a positive image, the crystals often consist of a mixture of silver bromide and silver chloride, and sometimes only of silver chloride.

The crystalline ionic lattice of silver halide is cubic. The lattice constant for silver bromide is \(2.88\,\text{Å}\), and for silver chloride \(2.77\,\text{Å}\). The binding energy of the crystal lattice is \(202\ \text{kcal/mol}\) for silver bromide and \(206\ \text{kcal/mol}\) for silver chloride. The refractive index of silver bromide is high—2.5 (for \(\lambda = 550\,\text{m}\mu\)). The dielectric constant of silver bromide for static fields is close to 13.

Silver chloride is completely transparent in the visible region of the spectrum and, beginning to absorb light at \(400\,\text{m}\mu\), is characterized by very strong absorption in the ultraviolet region of the spectrum with maxi-

mum at approximately 250 mµ. Silver bromide crystals have a yellowish color. Silver bromide begins to absorb light at 500 mµ and also has a considerable absorption coefficient in the ultraviolet region of the spectrum.

When AgBr and AgCl crystals are irradiated with ultraviolet rays, they become colored, i.e., an additional absorption band appears in the visible region of the spectrum. In 1928 T. P. Kravets¹ expressed the idea that in these crystals, under the action of light, the smallest colloidal particles of metallic silver are formed. In doing so, T. P. Kravets proceeded from the analogy between the photochemical processes occurring in alkali-halide and in silver-halide crystals, and indicated that the color of the colored crystals has the same nature as that of colloidal suspensions of metals, i.e., is determined by the scattering of light by these particles.

At the present time the fact of the formation, under the action of light, of the smallest particles of silver in silver-halide crystals is considered established. This is evidenced by the following experimental facts.

1) Savostyanova² and, simultaneously, Gillett and Pohl³ observed, upon illumination of a silver-halide crystal, the appearance of a new absorption band. This band is situated in the visible region of the spectrum, with a maximum at 520–550 mµ for silver chloride and 670–690 mµ for silver bromide. Savostyanova calculated, by the formulas of Rayleigh–Mie optics for turbid media, the absorption of the Ag–AgBr system and obtained good agreement between the experimentally observed and the calculated absorption curves.

2) It is known that, when free metal is formed in a salt, the dielectric constant of the salt changes. In this case the dielectric constant of the impurity present in the salt can be found if the amount of the impurity can be determined. A study of the change in dielectric constant upon illumination of a silver chloride crystal was carried out by Faik and Schaum⁴, the amount of impurity being determined by titration. For the dielectric constant of the impurity they obtained a value of the order of 1000, which corresponds to a metal.

3) Koch and Vogler⁵ carried out an X-ray study of silver bromide by the Debye–Scherrer method. On the X-ray photographs of crystals after illumination, rings appeared corresponding to the lattice of free silver. On the X-ray photographs of layers fixed after illumination, rings were also visible that are characteristic of silver. Trillat and Mérigoux⁶ obtained analogous results for electron diffraction.

4) Koch and Kraiz⁷ undertook a study of the change in weight of a silver bromide crystal subjected to illumination. If one assumes that silver is formed in the illuminated crystal, then bromine must be liberated. Koch and Kraiz suspended crystals of silver brom-

silver of average diameter \((0.4—2.5)\cdot 10^{-4}\) cm between the horizontal plates of a capacitor, and by Millikan’s method they were able to detect a gradual decrease in the weight of the crystals when they were illuminated.

5) If silver halide absorbs a very large quantity of light, considerably greater than that which is necessary for the formation of a photographic image, then a large quantity of silver is liberated. Weigert, as well as many others, determined this quantity of silver by microchemical analysis. It was shown that, with an increase in the quantity of light falling on the photographic layer, the quantity of silver formed also increases. It was also established that the quantum yield, calculated with respect to the quantity of absorbed energy, is close to unity.

6) Toporits and Savostyanova were able, with the aid of an ultramicroscope, to observe visually in AgBr the formation of a new phase. On subsequent illumination of such a colored crystal with red light, it could be noticed that these ultramicroscopic centers scatter and disappear.

7) The latent photographic image can be destroyed by a number of oxidizing agents, such as chromic acid, potassium persulfate, or halogen. These substances oxidize metallic silver.

8) Dankov noticed that, when all bromine ions are removed from the crystal lattice of silver bromide, the remaining silver ions form the crystal lattice of metallic silver. True, for this a change in the lattice constant in one direction is required.

It must be said that all the facts cited, except item 7, refer only to those cases when the quantity of light incident on the crystals of silver halide is considerably greater than that which is necessary to create the latent image. If we wish to regard the latent image also as consisting of the smallest particles of silver, then we must make a certain extrapolation. However, there are no data that would indicate the illegitimacy of such an extrapolation.

A somewhat different supposition was made by Schwartz and Urbach. In the preparation of a photographic emulsion, an electric double layer is formed on the surface of the crystals. Schwartz and Urbach proposed that this double layer hinders the development of the emulsion crystal. Under the action of light on a grain, this double layer is disrupted at individual points, which leads to the developability of the crystal. However, at the present time it is known that centers of the latent image are formed not only on the surface of emulsion crystals, but also within them, which is not very understandable from this point of view. Apparently, this double layer can influence only the kinetics of development, and specifically the induction period.

2

The question of how silver particles are formed upon illumination of silver halide still cannot be considered fully clarified.

The absorption of light by a silver halide crystal is effected by halide ions. This follows from the analogy between the absorption of light by silver-halide and alkali-halide crystals. Thus, comparing the absorption bands of all the bromides of the alkali metals, one may note that their maxima are always situated in approximately the same places. Even a splitting of the first peak of the absorption bands of bromides and iodides is observed, corresponding to the doublet splitting in the absorption spectrum of the halogen atoms. Unfortunately, the absorption bands of silver halide crystals are strongly broadened, and such sharply expressed peaks cannot be observed (except for AgJ). However, the long-wavelength boundary of the absorption bands, just as in alkali-halide crystals, shifts, in going from chlorine to bromine and then to iodine, toward longer wavelengths.

At first the simplest assumption was made^13: that upon absorption of a quantum of light the electron of a bromine ion passes to a neighboring silver ion, with the formation of silver and bromine atoms. The bromine atoms diffuse through the crystal and, upon emerging at its surface, depart. Since it came to be regarded as proven that the centers of the latent image are colloidal particles of silver, it became necessary to make the additional assumption that these silver atoms gather together, forming groups of at least several atoms. In doing so, investigators proceeded from the analogy with photochemical processes occurring in alkali-halide crystals. Thus, it is known that an alkali-halide crystal can be colored, and moreover by a wide variety of methods (the action of X-rays, ultraviolet rays, the introduction of electrons from outside, heating the crystal in the vapor of an alkali metal). The yellow coloration of an alkali-halide crystal appearing under such conditions was attributed to the absorption of light by atoms of the alkali metal formed in the crystal. Upon heating such a crystal, the yellow coloration changes to blue, which apparently corresponds to the formation of the smallest particles of the metal. Recently, however, analysis of all the phenomena observed in alkali-halide crystals has led investigators to the conclusion that the yellow coloration is caused by absorption of light not by metal atoms, but by electrons located at sites where halide ions are absent^14. For this reason it does not seem possible to make full use of the analogies between the photochemical processes occurring in alkali-halide and silver-halide crystals, since in the latter the ionic conductivity is determined only by silver ions, and all halide ions remain in their own places (see § 4). There are many other

reasons for doubting that the formation of the centers of the latent image passes through an atomic phase. Let us list the chief ones.

1. In the formation of silver atoms there should arise a new absorption band caused by these silver atoms. No one has succeeded in detecting such an absorption band; this may, however, indicate that these silver atoms very rapidly combine into groups. On the other hand, theoretical calculations15 show that the maximum of this absorption band should be situated at \(\lambda = 520\ \mathrm{m}\mu\) for silver chloride and at \(\lambda = 575\ \mathrm{m}\mu\) for silver bromide, i.e. in the same region in which the absorption of larger silver particles is observed. This makes the detection of such a band extremely difficult, even if it exists.

It has been possible to detect the absorption band of atomic silver introduced into the lattice of alkali-halide crystals16.

1. Bodenstein17 carried out theoretical calculations of the energy of formation of a silver atom in the crystal lattice of silver bromide, using the Born-Haber cycle. This energy proved to be equal to \(114\ \text{kcal/mol}\), which corresponds, for an elementary act, to \(\lambda = 255\ \mathrm{m}\mu\). At the same time, as was indicated above, the absorption of silver bromide extends to \(500\ \mathrm{m}\mu\). Bodenstein came to the conclusion that the missing part of the energy is supplied by the energy of condensation in the formation of metallic silver, which is an argument in favor of the formation of colloidal particles. Although the latter is perhaps correct from the point of view of the overall energy balance, yet, as Terenin18 pointed out, it is unlikely that the condensation energy released would affect the process of light absorption by the bromine ion.

2. The main argument against the view that, upon absorption of light, an electron passes from a bromine ion to a neighboring silver ion is the internal photoelectric effect19, 20, 21, observed in all silver-halide single crystals and manifested especially strongly in silver chloride. The photocurrent is practically independent of temperature down to the temperature of liquid air and decreases only upon further cooling of the crystals. The curve of the spectral distribution of the photocurrent has a somewhat different character in the works of different investigators and depends on the thickness of the crystal22. In any case, this curve lies in the region of the intrinsic absorption of silver halide, which indicates that the carriers of the photocurrent are electrons removed by light from halide ions and subsequently migrating through the crystal. Experiments have shown that the mean free path of the electron is sufficiently large and comparable with the sizes of the grains of the photographic layer (\(\sim 10^{-4}\ \mathrm{cm}\)).

Recently West and Carroll23 observed a photocurrent in illuminated crystals of the photographic layer. It was shown that the spectral curve of the photocurrent corresponds to the curve of spectral sensitivity

It was also shown that in the region of low illuminations the magnitude of the photocurrent is proportional to the illumination, while with a considerable increase in illumination it grows proportionally to its square root. The authors explained the latter result by the recombination of electrons with halide atoms.

Kirilov\(^{19}\) found that in colored AgCl and AgBr crystals there arises an additional spectral band of the photoeffect, situated in the absorption region of the color centers, i.e., of photochemically formed silver particles. It should therefore be considered that the scattering of these particles under the action of yellow or red light begins with the removal of electrons.

Tilly and Pohl\(^{3}\) observed that if light of a narrow spectral region from the absorption band of the silver particles falls on a colored crystal, then the absorption of the crystal decreases only near this spectral region. This fact, as well as comparison of the theoretical absorption curves obtained by Savost’yanova for silver particles in AgCl and AgBr with the experimentally observed absorption curves of colored crystals, indicates that when crystals are illuminated with blue and ultraviolet light, metallic particles of the most varied sizes are formed in them. The spectral absorption curve of such a crystal is the aggregate of a large number of elementary absorption curves of particles of different size. Meiklyar\(^{20}\) found that under prolonged illumination of an AgCl single crystal the maximum of the absorption curve gradually shifts toward longer wavelengths, which corresponds, according to the Mie theory, to coarsening of the particles.

3

Thus, when a silver halide crystal is illuminated, free electrons appear in it and traverse rather large distances through the crystal. The quantum yield in this process, according to LeFeld’s\(^{20}\) data, is close to unity. The electron mean free path depends on the strength of the electric field and on the presence of inhomogeneities in it. Apparently, the more imperfections there are in the crystal, the smaller the electron mean free path. From this point of view it is of interest to assess where an electron released by light can become trapped. This is important because at the place where the electron is trapped a silver particle is subsequently formed.

First, the surface of the crystal may be such a place. This indeed agrees with experimental facts. When an AgCl or AgBr single crystal is illuminated without any additions, coloration appears on its surfaces, both on the one facing the light source and on the opposite one. If the surface layer is scraped off, the coloration disappears.

Second, such places are all kinds of local disturbances of the ideal crystal lattice, cracks, etc. Toporets and

Savostyanova^9 observed that ultramicroscopic color centers are concentrated mainly along cracks in single crystals. This applies especially to the emulsion grain, where, as a result of the interaction of silver halide with gelatin, a large number of local inclusions are formed—particles of silver sulfide^25, silver^26, etc. From the work of Chibisov and co-workers^26 it follows that silver has the determining significance in this respect. These authors compared data from microanalysis of the solid phase of a photographic emulsion with the photographic properties of the latter. It turned out that the formation of centers of metallic silver during preparation of the emulsion determines its photosensitivity and its tendency to form fog. The formation of silver sulfide centers on the surface of emulsion crystals is of secondary importance. Centers of metallic silver are called sensitivity centers, in contrast to the developed centers of the latent image.

Third, such sites may be silver particles formed in the crystal under the action of the first portions of light. It was first discovered for alkali-halide crystals^27, and later for silver-halide crystals^20, that with an increase in the concentration of color centers the mean free path of the electron decreases. It is interesting to note here that color centers formed at low temperature \((-170^\circ \mathrm{C})\) do not decrease the electron mean free path, but, on the contrary, increase it. If one compares the spectral absorption curves of crystals colored at different temperatures with the curves calculated according to Mie’s theory, it turns out that at low temperature smaller silver particles are formed than at room temperature. Hence it follows that smaller silver particles increase the electron mean free path, whereas larger ones decrease it. If one also bears in mind that the observation of the photocurrent is carried out at low temperature (to reduce the dark current), then it follows that at this temperature free electrons can be trapped only on larger particles. Smaller silver particles, being charged by the first electrons, repel the subsequent ones.

Fourth, apparently there is a possibility for trapping a free electron even in an ideal crystal. Landau^28 pointed out that an electron, by acting with its electrostatic field on the surrounding lattice ions, displaces them somewhat. This leads to a change in the field acting from the ions on the electron itself, as a result of which the electron finds itself in a lower energy state and becomes trapped. This hypothesis was subsequently developed by Pekar^29, which led to interesting conclusions for alkali-halide crystals. However, it must be said that in the case of silver-halide crystals this phenomenon cannot be decisive, since both the photosensitivity of photographic layers and the electron mean free path depend strongly on the presence of impurities.

Thus, in an emulsion crystal there is a very large number of various inhomogeneities on which a free electron can become trapped. Corresponding to them is an entire set of energy levels, all these levels being situated between the conduction band and the fundamental band of the crystal and, apparently, adjoining the conduction band. An electron trapped at a level close to the conduction band can, after some time, be liberated under the influence of thermal motion. In this sense we obtain an analogy with the temporary trapping of electrons that occurs in the phosphorescence of crystals.

An electron liberated by a quantum of light can, moreover, recombine with halide atoms. This phenomenon is of importance especially when diffusion of halide atoms out of the crystal is for some reason impeded. Usually, after absorption of a light quantum by a halide ion, with the formation of a free electron and a halide atom, the latter rather rapidly diffuses to the surface of the crystal. The mechanism of this diffusion is represented as follows: the electron of a neighboring halide ion passes to the atom, which is equivalent to a transition of the atom in the opposite direction. This process is repeated many times until the halide atom reaches the surface of the crystal. It is also possible that, upon absorption of a light quantum and detachment of an electron, the halide atom leaves the node of the crystal lattice. Subsequently it migrates through the interstices until it reaches the surface of the crystal.

With an increase in the intensity of the light incident on the crystal, the concentration of free electrons and, correspondingly, of halide atoms increases, which leads to an increase in the probability of their recombination. On the other hand, diffusion of halide atoms requires, albeit small, thermal activation, as a result of which the probability of recombination also increases with decreasing temperature. At low temperature one can observe the fluorescence both of photographic layers and of silver halide single crystals. Meidinger \(^{30}\) observed the fluorescence of photographic layers, the center of gravity of the spectral emission curve being located, for silver bromide layers, at \(\lambda = 550\ \mathrm{m}\mu\), and for silver chloride layers at \(\lambda = 470\ \mathrm{m}\mu\). Golub \(^{31}\) observed the fluorescence of silver halide single crystals, the maximum of the spectral emission curve being located at \(\lambda = 540\ \mathrm{m}\mu\)* for silver bromide and at \(\lambda = 480\ \mathrm{m}\mu\) for silver chloride. In addition, Golub observed phosphorescence of silver chloride single crystals with a hyperbolic law of decay. The latter precisely testifies to the recombination character of the luminescence. The relation between the wavelengths at which the luminescence of both salts is maximal points to the same thing. \(\lambda = 540\ \mathrm{m}\mu\) corresponds to the edge

* In Golub’s article, \(450\ \mathrm{m}\mu\) was erroneously printed. According to his communication, it should read \(540\ \mathrm{m}\mu\).

THE LATENT PHOTOGRAPHIC IMAGE

of the intrinsic absorption band of AgBr, and \(\lambda = 470\) mµ the same for AgCl. This should, apparently, correspond approximately to the width of the forbidden bands—\(2.3\) eV for AgBr and \(2.6\) eV for AgCl, since fluorescence is caused by the transition of electrons from the lower levels of the conduction band to the upper levels of the filled band (see Fig. 6).

At room temperature, and all the more at elevated temperature, the diffusion of bromine atoms in the crystal lattice is apparently very great. This follows, for example, from the experiments of Stasiw and Teltow \(^{32}\), who heated a photochemically colored AgBr crystal in bromine vapor and observed how, gradually, beginning from the edges of the crystal toward its middle, the coloration disappeared. Having calculated the mobility of bromine atoms, they came to the conclusion that at \(t = 20^\circ\)C it is, in order of magnitude, close to \(10^6\) lattice constants per second.

The process of recombination of an electron with a bromine atom depends on how rapidly the atoms of bromine liberated from the surface are removed. In the photographic layer this is promoted by gelatin, which is a good acceptor of bromine. Simple soaking of the photographic layer in water increases its photosensitivity*). Beginning with a solution pH equal to 8 and higher, the photosensitivity increases still more sharply \(^{32}\). Bagdasar’yan \(^{34}\) explains this by the fact that the hydroxyl ion (especially at high concentrations) gives its electron to the bromine atom liberated on the surface of the grain, converting it into a bromine ion. In this case the bromine ion does not pass into solution, but remains as an external ion of the AgBr crystal lattice. Bagdasar’yan showed that under such conditions the reaction of interaction of the bromine atom with the hydroxyl ion will be exothermic.

Thus the electron freed upon absorption of a light quantum can either be fixed at certain places in the crystal, or recombine with a bromine atom. Since experiments determining the amount of photochemically formed silver indicate that the quantum yield is close to unity, it must be assumed that at room temperature and at moderate levels of illumination recombination processes do not play an essential role. When the temperature is lowered, however, the quantum yield decreases \(^{34}\), which may be caused by recombination.

Of substantial importance for the theory of latent-image formation is the question of how many electrons can simultaneously be present at a trapping center. In fact, the first trapped electron, by its electrostatic field, will repel the next approaching electron. Gurney and Mott \(^{36}\) assumed that the electrostatic energy of the second electron in the field of the first should not be greater than the energy of its thermal motion. This is natural, since electrons in the conduction band must move with thermal—

*) Here the removal from the layer of soluble salts of alkali metals, left in the layer during its manufacture, is also of importance.

with high velocities. Gurney and Mott believed that electrons are trapped mainly on inclusions of silver or silver sulfide. These centers, as was said above, are created in the process of preparing the emulsion. If such a center is regarded as a metallic sphere in a medium with dielectric constant \(\varepsilon\), then the potential on its surface is equal to \(\dfrac{ne}{\varepsilon R}\), where \(n\) is the number of electrons sitting on it, the charge of each of which is \(e\), and \(R\) is the radius of the sphere. In other words, the condition

\[ \frac{ne^2}{\varepsilon R}<\frac{3}{2}\,kT \]

must be satisfied, or

\[ n<\frac{3}{2}\,\frac{\varepsilon R kT}{e^2}. \]

It is very difficult to estimate the quantity \(R\), i.e. the size of the sensitivity center. It can hardly be assumed that \(R=5\cdot 10^{-5}\,\text{cm}\), as Gurney and Mott assume. Using data from microchemical analysis obtained earlier by Sheppard\({}^{38}\), and assuming that silver sulfide molecules in the process of emulsion preparation are grouped into small centers according to the law of chance, Berg\({}^{37}\) calculated how many silver sulfide molecules must be present in such a center. He came to the conclusion that if the sensitivity center is a formation consisting of the maximum number of \(Ag_2S\) molecules, then the optimal amount of \(Ag_2S\) in the emulsion

\[ \left(5\cdot 10^{-4}\,\frac{\text{grams }Ag_2S}{\text{grams }AgBr}\right) \]

corresponds to sensitivity centers consisting of ten molecules. The radius of such a center is \(R=3.4\cdot 10^{-8}\,\text{cm}\). If this value of \(R\) is adopted, it follows that \(n\) must be less than unity, i.e. only one electron can be present on the given center at the same time. Even if it is assumed that each electron-trapping center consists of 1000 silver atoms or 1000 \(Ag_2S\) molecules, which corresponds to \(2\cdot 10^{-7}\,\text{cm}\), even then \(n\) is found to be less than unity\({}^{39}\)*).

One may, however, disagree with the assumption of Gurney and Mott that, when calculating the potential for such small particles, they should be regarded as conducting spheres. Rather, such a particle with an excess electron should be regarded as a point charge. In this case the second electron also will not be able to approach the particle closer than the distance at which the energy of electrostatic repulsion is equal to the kinetic energy of the electron, i.e. to the energy of thermal motion. The required distance \(l\) is found from the relation

\[ \frac{e^2}{\varepsilon l}=\frac{3}{2}\,kT \]

or

\[ l=\frac{2e^2}{3\varepsilon kT}, \]

which for room temperature gives \(l=2\cdot 10^{-7}\,\text{cm}\), i.e. approximately seven lattice constants. Thus it follows that no more than one electron can be located at the given trapping center until this electron is neutralized by a positive charge.

*) In the cited article by Berg\({}^{39}\) there is an error which increases the potentials by a factor of 15. However, the corrected values of the potentials indicate that \(n\) for 1000 atoms is less than unity.

4

According to present-day views, the neutralization of captured electrons occurs by means of interstitial silver ions. Such a mechanism was proposed by Gurney and Mott^40. Silver halide, like a number of other dielectrics, possesses dark conductivity of an ionic character. Tubandt’s experiments^41 established that AgCl, AgBr, and β-AgI in the dark are purely cationic conductors, i.e., that charge transport is due exclusively to silver ions. A scheme for the mechanism of this conductivity was proposed by Ya. I. Frenkel^42. According to this scheme, some of the ions located at the sites of the crystal lattice are capable, under the influence of thermal motion, of leaving these positions and wandering through the crystal.

These ions are called “interstitial” ions. Ionic conductivity according to this scheme is determined by the displacement, in an electric field, of interstitial ions, and also by the displacement of vacant sites—“holes”—through the transition into them of neighboring lattice ions. The theory gives the following expression for the conductivity of the crystal

\[ \sigma=\sigma_0 e^{-\frac{\left(\frac12 W_0+U\right)}{kT}}, \]

where \(W_0\) is the activation energy necessary for the transition of an ion into an interstitial state, and \(U\) is the activation energy necessary for the transition of an interstitial ion from one interstice of the lattice to a neighboring one.

Fig. 1. Ionic conductivity of silver-halide single crystals (after Lehfeldt).

Indeed, investigations of the ionic conductivity of silver-halide crystals have shown that there is always an exponential dependence of conductivity on temperature. Lehfeldt^43 found that the curve of the dependence of the logarithm of the conductivity of single crystals on temperature (more precisely, on \(1/T\)) consists of two straight lines with different slopes, passing into one another at approximately \(0^\circ\)C (Fig. 1). In Lehfeldt’s experiments the high-temperature part of the curve had a large slope and was the same for all single-crystal specimens. The low-temperature part of the curve was flatter, and its position depended on the history of the given specimen, although in every case these straight lines were parallel to one another. The same data were subsequently obtained by Koch and Wagner^44 and by Shapiro and Kolthoff^45. The conditions of the experiments of Shapiro and Kolthoff were apparently closest to the conditions in which crystals of a photographic emulsion are found, since the authors dealt with AgBr powders which had been subjected to pres-

soldering or sintering. Although the straight lines of Shapiro and Kolthoff proved to be parallel to the corresponding straight lines of other authors, the temperature range in which the high-temperature straight line passes into the low-temperature ones lay at higher temperatures, about \(80^\circ\) C. For this reason the very value of the conductivity at \(20^\circ\) C also proved to be 1–3 orders of magnitude higher than in Lehfeldt and in Koch and Wagner.

From the magnitude of the conductivity one cannot determine separately the values of \(W_0\) and \(U\). Therefore Koch and Wagner introduced small admixtures of lead and cadmium halide salts into AgCl and AgBr crystals. The introduction of these impurities considerably increases the conductivity of the crystal. Thus, the addition of \(1\%\) \(CdCl_2\) increases the conductivity of AgCl at \(200^\circ\) C by more than 100 times. Each divalent cadmium ion replaces two silver ions, as a result of which an additional constant number of vacant sites—“holes”—appears in the lattice. At high temperature these “holes” are joined by additional “holes” newly formed under the influence of thermal motion. At low temperature the number of the latter is small, while their mobility is the same as in the pure crystal. Therefore at low temperature the conductivity of the mixed crystal is proportional to \(e^{-\frac{U}{kT}}\), i.e. it depends on temperature only through the mobility. Koch and Wagner assumed that the mobility of the “holes” is approximately equal to the mobility of the interstitial silver ions, and found for \(W_0\) and \(U\) the values given in Table I.

Table I

Shapiro and Kolthoff found the following values for AgBr: \(W_0 = 0.86\) eV and \(U = 0.36\) eV. These authors believe that at low temperature the conductivity is determined by a constant number of “holes,” “frozen in” on the surface of the crystals or near imperfections, and that it is proportional to the surface area of the elementary intergrown crystallites. Recently Breckenridge\(^{46}\) determined the value of \(U\) for AgCl crystals from the magnitude of the dielectric polarization upon application of a field of sonic frequency (\(10^3\) cycles). This author also found for \(U\) the value 0.26 eV and, in addition, obtained an additional value \(U' = 0.21\) eV, which he ascribed to the work of activation for the diffusion of “holes.” From the data of Koch and Wagner one can determine the concentration of interstitial \(Ag^+\) ions and, correspondingly, of “holes” at room temperature. It turns out to be \(10^{-6}\)–\(10^{-5}\) for AgBr and \(10^{-8}\)–\(10^{-7}\) for AgCl.

Zimens\(^{47}\) measured the rate of exchange of silver ions between the photographic layer and a solution containing ions of radioactive

isotope of silver. From his data it follows that the ionic conductivity in the grains of the photographic layer must be approximately ten times greater than that found by Koch and Wagner.

Table II gives data on the ionic conductivity of silver bromide at room temperature, obtained by various authors.

Table II

Thus, all the data cited indicate that in silver-halide crystals there is appreciable ionic conductivity, the charge carriers being interstitial silver ions and “holes.” At the same time, crystals with a relatively large surface have greater conductivity.

According to the theory of Gurney and Mott, the process of formation of the latent-image center takes place as follows. Upon absorption of a quantum of light, an electron of a bromine ion is liberated; it migrates through the crystal until it becomes trapped at a sensitivity center. Under the influence of the electrostatic field that has arisen, the interstitial silver ion which at that moment is nearest is attracted; it neutralizes the electron. In this way the sensitivity center grows by one silver atom. This process is repeated several times, as a result of which a sufficiently large developable latent-image center is formed. Of essential importance for the theory of latent-image formation is an estimate of the time required for neutralization of the trapped electron. This time can readily be calculated\(^{36}\). The field created by the electron at a distance \(r\) will be \(E=\dfrac{e}{\varepsilon r^{2}}\). This field will cause motion toward the sensitivity center of the interstitial silver ions, and the total current due to these ions is \(i=4\pi r^{2}j=4\pi r^{2}\cdot\dfrac{\sigma}{2}E=\dfrac{2\pi\sigma e}{\varepsilon}\).

Here \(j\) is the current density, and \(\dfrac{\sigma}{2}\) appears as the conductivity, since only the motion of ions is to be taken into account. Hence the time required to neutralize the charge of one electron is \(t=\dfrac{\varepsilon}{2\pi\sigma}\). Taking \(\varepsilon=13\), and \(\sigma_{20^\circ\mathrm{C}}=10^{-7}\ \Omega^{-1}\ \mathrm{cm}^{-1}=9\cdot10^{4}\) abs. units, we obtain \(t_{20^\circ\mathrm{C}}=2\cdot10^{-5}\) sec. For a temperature of \(-50^\circ\mathrm{C}\) this time is already \(0.02\) sec. At the temperature of liquid air this time is apparently of the order of an hour.

The calculation presented here should be borne in mind when considering the kinetics of formation of latent-image centers at different illumination intensities of the layer and, correspondingly, at different exposure times. Thus, if light of high intensity falls on a silver bromide crystal, then a large number of free electrons are formed simultaneously in the crystal. In this case the neutralization of the first electron that has entered a trapping center may not have time to occur before the next one arrives. However, it was shown above that two electrons cannot be located simultaneously on one center. For this reason, under intense illumination of the crystal, electrons will be trapped in a large number of centers, which will lead to the formation of a larger number of smaller silver particles. This was shown experimentally by Meiklyar^24^ for single crystals of silver chloride; in that work the magnitude of the photochemically formed silver particles was estimated from the spectral curve of light absorption by these particles by comparison with similar curves calculated according to Mie’s theory. Analogous conditions for the formation of silver particles are observed at low temperature even under weak illumination, since in this case the neutralization time of a trapped electron is very long, and a large number of small particles is likewise formed. This was shown in the work of Lelle^48^.

Apparently, under intense illumination of a silver halide crystal at room temperature, when there is both a large concentration of free electrons and a sufficient concentration of interstitial positive silver ions, there is some probability of their combining with the formation of silver atoms. However, such a silver atom, in all probability, possesses negligible mobility as a consequence of its comparatively large size. In any case, at present it is impossible to judge how this silver atom may participate in the formation of the latent image.

Under intense illumination of the crystal, when a large number of free electrons is formed simultaneously, some of these electrons are trapped at comparatively “shallow”*) centers and, apparently, subsequently may be released under the influence of thermal motion. Even if these electrons are neutralized by silver ions, but the number of atoms in the center is very small, thermal dissociation of such a center is possible. For this reason, the process of formation of latent-image centers apparently continues even after illumination of the crystal has ceased.

Similarly, under very weak illumination of the crystal, when a small number of latent-image centers grows very slowly, thermal dissociation may proceed simultaneously with the growth of the centers. This is in agreement with the results of experiments carried out with photographic layers (see Part II).

*) In the energetic sense.

5

Thus, the formation of latent-image centers is reduced to the gradual growth of sensitivity centers up to such a size that the center becomes developable. Sensitivity centers are created in the course of manufacture of the photographic emulsion. During the development of the grains of the photographic layer, the ions of the developer give up their electrons to the latent-image centers. It should therefore be assumed that the electron levels of the sensitivity centers lie above the level of the electron corresponding to the developer ion, whereas the levels of the latent-image centers lie below the level of the developer ion. In other words, as the size of the silver particle increases, the electron levels must descend. This means that the work function for an electron into the conduction band of the crystal must be smaller for a smaller particle than for a larger one. It also means that, as the size of the metallic particle photochemically formed in the crystal lattice of the silver halide increases, the spectral curve of light absorption must shift into the shorter-wavelength region of the spectrum. Such a regularity was logically inferred by Berg^49, but it has not been confirmed experimentally by direct experiments.

For larger silver particles formed in the crystal after the action of a large quantity of light upon it, the opposite regularity is observed. As the amount of absorbed light increases, the spectral absorption curve of AgBr crystals corresponding to the photochemically formed silver particles shifts toward longer wavelengths^24,48. This is in accord with Mie’s theoretical absorption curves, obtained from the theory of scattering of light by small metallic particles. These theoretical curves shift toward longer wavelengths as the particle size increases. True, in the latter case the particle size is much greater than the size of the latent-image centers, and the character of absorption adopted by Mie is entirely different from the photoelectric absorption considered by Berg. However, the region of spectral absorption of the latent-image centers, obtained from studies of latent-image scattering (see Part II), coincides with the absorption region of large silver particles. It therefore remains unclear how to reconcile the hypothesis advanced by Berg with the regularities observed for large silver particles.

6

It was pointed out above that if a colored silver-halide crystal is illuminated with red light, the coloration fades. Photochemical scattering of silver particles occurs. It was observed that if a colored crystal is illuminated with polarized red light, then such a crystal becomes dichroic. This phenomenon was carefully

was investigated by Cherdyntsev^50. Cherdyntsev assumed that polarized light produces oriented scattering by silver particles in accordance with the direction of the electric vector, transforming the silver particles into ellipsoids directed with their major semiaxes to one side. Such a system of particles is dichroic. Cherdyntsev applied to such a system Gans’ theory of light scattering by ellipsoidal particles and obtained good agreement between theory and experiment.

Weigert^51 observed similar phenomena in a photographic layer. This author found that if a photographic layer is first illuminated with white polarized light and then with red light, likewise polarized, the photographic image obtained is dichroic. This is clearly noticeable in the case when the amount of light in the first illumination is so large that it creates a visible image even without development. If, however, the result of the first illumination is noticeable only after development, then dichroism can be detected only in very fine-grained layers, since in ordinary layers depolarization occurs during the scattering of light by the crystals of the layer.

PART II

1

If a photographic layer is irradiated with a series of successively increasing portions of radiant energy, then after development we obtain a series of blackenings of ever increasing density. The graphical dependence of the density of blackening \(D\), obtained on the photographic layer, on the logarithm of the amount of radiant energy incident on the layer, \(\lg H\), is called the characteristic curve. A typical characteristic curve is shown in Fig. 2. The tangent of the angle of inclination of the curve to the abscissa axis at each point is called the density gradient, and for the rectilinear portion of the curve—the contrast coefficient, or, briefly, gamma \((\gamma)\).

The photosensitivity of a photographic layer \(S\) is determined by the amount of exposure necessary for some definite photographic action. For example, the photosensitivity may be taken to be the quantity reciprocal to the exposure \(H\) producing in the layer a blackening density of 0.2 above the fog density \(D_0\):

\[ S=\frac{1}{H_{D=D_0+0.2}}. \]

Naturally, the photosensitivity is different under the action of radiant fluxes of different spectral composition. Therefore it is often necessary to know the spectral photosensitivity

of the layer \(S_\lambda\), i.e. its sensitivity to monochromatic light. This quantity is defined as the reciprocal of the amount of illumination by monochromatic radiation that produces in the layer a density of blackening equal to unity above the fog,

\[ S_\lambda=\frac{1}{H_{D=D_0+1,0}}. \]

The light sensitivity of modern photographic layers varies within very wide limits.

Within a given photographic layer it is necessary to increase the amount of illumination tens, and sometimes hundreds, of times in order for the density of blackening to increase from barely noticeable to approaching the maximum. Since the density of blackening is approximately proportional to the number of developed crystals, this means that the number of quanta that must fall on an emulsion crystal in order for it to become developable varies, for different crystals, within very wide limits.

Fig. 2. Characteristic curve.

Some time ago\(^{52}\) attempts were made to explain such behavior of the photographic layer on the assumption that all emulsion crystals possess the same specific light sensitivity, i.e. taking into account only differences in the area of the cross section of the crystals perpendicular to the direction of the light flux.

If the average area of an emulsion crystal is \(a\), and the number of quanta that have fallen during the exposure on \(1\ \text{cm}^2\) of the layer is \(n\), then the probability that \(k\) quanta will fall on a grain is found from Poisson’s formula

\[ P_k=\frac{e^{-an}(an)^k}{k!}. \]

Therefore the number of crystals on which \(k\) quanta will fall is

\[ m_k=NP_k, \]

where \(N\) is the total number of crystals. If we assume that a crystal becomes developable after \(r\) or more quanta have fallen on it, then the number of developable crystals will be

\[ m=N\sum_{k=r}^{\infty}P_k = N\sum_{k=r}^{\infty}\frac{e^{-an}(an)^k}{k!}, \]

which can be written in the form

\[ \frac{m}{N}=1-e^{-an}\sum_{k=0}^{r-1}\frac{(an)^k}{k!}. \]

If \(r=1\), i.e., the incidence of a single quantum on a crystal is sufficient for it to become developable, then \(\frac{m}{N}=1-e^{-an}\). Indeed, for the action of \(\alpha\)-particles on a photographic layer this formula proves to be completely applicable, which indicates that the incidence of a single \(\alpha\)-particle on an emulsion crystal is sufficient for the latter to become developable. If, however, one constructs graphs of the dependence of \(\frac{m}{N}\) on \(an\) for different \(r\), one obtains the family of curves shown in Fig. 3. If these curves are compared with the characteristic curves, it turns out that the theoretical curves are already too steep for \(r>4\). Since it is known that, in reality, during exposure a significantly larger number of quanta falls on an emulsion crystal, it must be assumed that the initial premise is incorrect, i.e., different crystals may possess different light sensitivities. This consideration does not take into account the absorption of light in the layer, as a result of which considerably less light reaches the lower crystals of the layer than the upper ones. However, taking this factor into account also does not make it possible to fully explain the form of the characteristic curve. Webb\(^ {53}\) proposed several most probable distribution functions of crystals with respect to light sensitivity \(f(r)\), among which, in his opinion, the most probable is

\[ f(r)=\alpha e^{-k\left(\ln \frac{r}{r_0}\right)^2}, \]

where \(\alpha\) and \(r_0\) are parameters constant for the given layer. If the function \(f(r)\) is introduced into Poisson’s equation, one obtains

\[ \frac{m}{N}=\sum_{r=r_{\min}}^{r=r_{\max}} f(r)\sum_{k=r}^{\infty}\frac{e^{-an}(an)^k}{k!}, \]

or, expressing this dependence for the density of blackening,

\[ D=D_{\max}\sum_{r=r_{\min}}^{r=r_{\max}}\alpha e^{-k\left(\ln \frac{r}{r_0}\right)^2}\sum_{k=r}^{\infty}\frac{e^{-an}(an)^k}{k!}. \]

Fig. 3. Dependence of \(\frac{m}{N}\) on \(an\) for different \(r\).

LATENT PHOTOGRAPHIC IMAGE

Webb showed that, with a proper choice of the parameters \(\alpha\) and \(r_0\), this function is a fairly good analytical expression for the characteristic curve (more precisely, for the curve of the dependence of \(D\) on \(H\)).

Of course, from the fact that an emulsion crystal becomes developable after \(r\) quanta have fallen on it, it does not follow that \(r\) silver atoms are thereby formed in the crystal. First, not all \(r\) quanta are absorbed by the crystal, and second, not all absorbed quanta take part in the formation of the centers of the latent image. Webb attempted to use the old data of Sled and Toy\({}^{55}\) on the absorption of light by silver bromide in order to estimate what fraction of the quanta incident on the crystal is absorbed. For a single-layer preparation (a layer with one row of crystals) he obtained curves of the dependence

\[ \frac{m}{N} = f(\varepsilon an), \]

where \(\varepsilon\) is the coefficient of absorption of light. These curves, constructed for different wavelengths, proved to be very close to one another in the initial region, which indicated that the process of formation of the latent image after the act of absorption of light is the same for all wavelengths. Comparing the curves of the dependence of the fraction of developed grains on the amount of absorbed light with theoretical curves obtained on the basis of probability theory, Webb came to the conclusion that approximately one quarter of the quanta absorbed by a grain take part in the process of formation of the latent image.

Bagdasaryan\({}^{56}\) proposed another way of finding an analytical expression for the characteristic curve. He assumed that in each grain there is a large number of centers of photosensitivity of different sizes. Different centers of photosensitivity correspond to levels of potential energy of different depths. At shallow levels an electron cannot remain for long, and such a center of photosensitivity cannot become a center of the latent image. Centers of the latent image are formed at those centers of photosensitivity to which electron levels of the greatest depth correspond. Therefore, according to Bagdasaryan, the photosensitivity of grains is determined by the nature of the distribution of centers of photosensitivity on them. Bagdasaryan showed that, if one assumes that the number of centers of photosensitivity corresponding to a given depth of electron levels is proportional to this depth, then the fraction of developed grains \(\frac{m}{N}\) depends on the logarithm of the exposure amount \(\lg H\) according to the formula

\[ \frac{m}{N} = 1 - e^{-A(\lg H-\lg B)^2}, \]

where \(A\) and \(B\) are constants for the given layer. Bagdasaryan showed that such an expression agrees well with the experimental characteristic curves.

2

When an exposed layer is immersed in a developer, the latter reacts, in any case at the beginning of development, only with the surface of the emulsion crystals. If the developer does not contain substances in which silver bromide dissolves, or contains few of them, then the question of whether a given crystal will be developed is decided by whether there are latent-image centers on the surface of the crystal. This is the case for the majority of developers used.

Hodgson[^57] immersed exposed single-layer preparations of emulsion crystals in a developer until the first traces of blackening appeared, and then examined them under a microscope. He found that development of a crystal begins at separate points on it. Svedberg[^58], having carried out an analogous experiment, obtained images of partially developed crystals in such a way that the dimensions of all these images were the same. If the centers from which development begins were distributed uniformly through the depth of the crystal, then in the image of the crystals there would be relatively more of them in the central part than at the edges of the image. In actuality, the number of development centers proved to be relatively large at the edges of the images of the crystals. From this Svedberg concluded that development begins at separate points on the surface of the crystals. In other words, the developable centers of the latent image are usually located on the surface of the crystals. The same conclusion may be reached on the basis of Chibisov’s data[^59].

However, latent-image centers are also formed inside the crystals of the photographic layer. They have little influence on the development process if the developer does not contain solvents of silver bromide, which make these centers accessible to the action of the developer, but in some cases they may be of decisive importance. The addition of a number of substances to the developer makes it possible to develop these “deep” latent-image centers. Much work has been undertaken in this direction,[^60] and at the present time the following methods are used to distinguish surface and deep latent images[^61]:

1. A developer containing no solvents of silver bromide and therefore interacting only with latent-image centers located on the surface. Such a developer is often a glycine developer, without sulfite.

2. A bleaching bath that oxidizes latent-image centers located on the surface. For this purpose oxidizing agents are used, in particular a dilute solution of chromic acid (1%).

3. A developer containing solvents of silver halide. After removal of the latent-image centers located on the surface with the aid of a bleaching solution, it is possible with this developer to develop the “deep” centers. As solvents

of silver halide, hypo in weak concentration (1%) and others is used. Another method of developing “deep” centers is physical development after fixation.

Recently, a large number of studies on the distribution of latent-image centers in a crystal have been carried out by Otto and co-workers^62. These authors distinguish three types of spatial distribution of centers: (a) on the surface, (b) immediately near the surface (no farther than a distance equal to 10 lattice constants), and (c) in the depth of the emulsion crystal. In the authors’ opinion, latent-image centers situated in the depth of the grains usually take part in the development process only when a very large quantity of light, corresponding to solarization, falls on the grain. Investigations have shown^61 that, with increasing illumination of the layer, the relative number of latent-image centers formed in the depth of the emulsion crystal increases. The same occurs when the temperature of the photographic layer is lowered. This is easy to understand on the basis of photochemical investigations (see Part I, § 4). Both with increasing illumination and with decreasing temperature, a larger number of smaller latent-image centers is formed in the depth of the crystal, whereas under weak illumination and at high temperature a small number of large centers is formed, chiefly on the surface.

3

Both the general photosensitivity of the photographic layer and its spectral sensitivity depend on the temperature at which the layer is exposed. With decreasing temperature, the photosensitivity of the layer in the region of the intrinsic absorption of AgBr decreases down to the lowest temperatures. According to Barteneva and Gorokhovsky^63, lowering the temperature from \(+20^\circ\) to \(-60^\circ\text{C}\) leads to an approximately twofold decrease in the photosensitivity of the layer. According to Berg and Mendelson^64, at the temperature of liquid air the photosensitivity of the layer amounts to about 7% of its value at room temperature, and at the temperature of liquid hydrogen—about 4%. With decreasing temperature the gamma of the layer decreases. According to Meidinger^35, lowering the temperature also decreases the amount of photochemically formed silver. According to the same author, the dependence of photosensitivity on temperature is markedly different for photographic layers with different sizes of emulsion crystal. Thus, for coarse-grained layers this dependence is considerably smaller than for fine-grained ones. In addition, as Webb^65 established, the dependence of the layer’s photosensitivity on temperature is different at different levels of illumination. Under intense illumination of the layer, photosensitivity decreases monotonically with decreasing temperature, whereas under weak

with a decrease in the temperature of exposure the photosensitivity at first increases approximately down to a temperature of \(-60^\circ\mathrm{C}\), and then also decreases.

Above we considered (Part I, § 4) the conditions for the formation of latent-image centers at low temperature. In view of the fact that neutralization of the trapped electrons is impeded, a large number of small latent-image centers is formed. At low temperature the diffusion of bromine atoms out of the crystal is also impeded. Therefore at low temperature fluorescence is observed, caused by the recombination of electrons with bromine atoms. This is also manifested in a decrease in the photosensitivity of the layers.

The neutralization of trapped electrons with the formation of latent-image centers apparently occurs only upon heating of the photographic layer, since upon heating interstitial silver ions are liberated, capable of producing neutralization. However, as was indicated above, in a given trapping center there can be only one electron. Since a latent-image center consists of several silver atoms, it should be assumed that upon heating electrons are also liberated from “shallow” (in the energetic sense) centers, which then pass to the latent-image center. Such an assumption is confirmed, on the one hand, by the work of Webb and Evans\(^{66}\), and on the other, by Berg\(^{67}\). Webb and Evans compared the result of continuous exposure of a photographic layer at the temperature of liquid air with the result of intermittent exposure, when in the intervals between the individual exposures the layer was heated to room temperature (neutralization). In both cases the amount of exposure was the same. It turned out that the more interruptions were made in the exposure, accompanied by heating, the greater was the photographic action of the light. Berg exposed a photographic layer at the temperature of liquid air first to blue light and then to mixed radiation consisting of blue and red light. In this case at first the small blackening densities increased and the large ones decreased (see Part II, 5), and then, with further prolonged exposure, all blackening densities began gradually to increase. Berg explained this result by saying that red light liberates electrons from the more “shallow” trapping centers, transferring them to the deeper photosensitivity centers. The depth of location of the “shallow” centers, according to Berg’s estimate, is less than \(0.8\ \mathrm{eV}\), and that of the “deep” ones is \(1\text{--}2\ \mathrm{eV}\) (see Part II, 5).

In accordance with the fact that at low temperature a larger number of shallower latent-image centers is formed, Berg, Merridge, and Stevens\(^{61}\) showed that at low temperature relatively more “deep” latent-image centers are formed.

LATENT PHOTOGRAPHIC IMAGE

4

In photochemistry there is a known reciprocity law, or the Bunsen–Roscoe law. This law asserts that the result of photochemical action depends only on the quantity of incident light, i.e. on the product of the light intensity \((E)\) and the exposure time \((t)\), independently of the numerical values of \(E\) and \(t\) separately. This law, introduced for gaseous photochemical reactions, proved to be invalid for the photographic layer. There exists a certain optimal exposure time and, correspondingly, an optimal magnitude of illumination, at which the photosensitivity is maximal. For larger and smaller exposure times and, correspondingly, smaller and larger values of illumination, the photosensitivity of the photographic layer is less than optimal. Therefore, if one plots a curve of the dependence of the logarithm of the quantity of illumination necessary to obtain some photographic effect (for example, \(D = 1\)) on the exposure time, the curve will have the form shown in Fig. 4. In accordance with the two branches of this curve, one speaks of deviations from the reciprocity law at small and large exposure times.

Fig. 4. Curve expressing deviations from the reciprocity law.

With a decrease in exposure time below the optimum, accompanied by a simultaneous increase in illumination, the number of electrons liberated by light during the given interval of time increases. Therefore neutralization of the electrons fixed at the centers of photosensitivity does not have time to occur, and a larger number of smaller centers is formed (Part I, 4), and moreover to a greater extent in the depth of the crystal (Part II, 2). Under these conditions there are formed not only developable centers of the latent image, but also non-developable centers, which Berg^39 proposed to call subcenters. The existence of these subcenters follows from the form of the initial portion of the curve of the dependence of the blackening density \(D\) on the exposure time \(t\) (not \(\lg t\))^68. If there were no subcenters, then the slope of this part of the curve to the abscissa axis would not increase with increasing \(t\). In reality (Fig. 5, curve \(a\)), at a high level of illumination the slope of the curve at first gradually increases. This means that in the initial stages of illumination of the crystals, the products of the photochemical reaction accumulate and facilitate the formation of latent-image centers in the subsequent stages of illumination. In fact, at

in this portion of the curve the sum of the blackening densities obtained with two independent exposures is less than the blackening density obtained with a single total exposure. The existence of these non-developable subcenters is also confirmed by the fact that preliminary intense illumination of the photographic layer increases its light sensitivity to the subsequent action of weak radiation. With such an order of double illumination of the layer, the resulting blackening density is always greater than with the reverse order,^69 especially in the region of small blackening densities.^70

Fig. 5. Dependence of the blackening density on the time of illumination at high illuminance (a) and low illuminance (b).

With an increase of the illumination time above the optimum, the light sensitivity of the layer, as was said above, also decreases. Webb^69 suggested that in this case the centers of the latent image are formed so slowly that they have time partially to dissipate under the influence of thermal motion. In any case (Part I, 4), a small number of large centers of the latent image is formed. Under these conditions subcenters are formed in a considerably smaller number, and the dependence of \(D\) on \(t\) at a low level of illuminance has the form of curve b in Fig. 5, i.e. it has no portion with an increasing slope to the abscissa axis.

Thus, the processes that reduce the light sensitivity of the layer at a high level of illuminance take place at the end of its illumination, and at a low level of illuminance—at the beginning. This corresponds to the fact that, if one wishes to eliminate the decrease in light sensitivity determined by very intense and short-term illumination of the layer, it is necessary to apply subsequent weak prolonged illumination; conversely, if one wishes to eliminate the decrease in light sensitivity caused by very weak and prolonged illumination, it is necessary to apply preliminary intense and short-term illumination of the layer.

All this was shown in the work of Burton and Berg.^68 These authors also showed that, during prolonged storage of the photographic layer, small subcenters dissipate, partly supplementing the larger subcenters up to a developable size, as a result of which the blackening density of the layer increases. Raising the temperature accelerates this process.^71

The fact that, after the formation of subcenters in the grain, the sensitivity of the grain to subsequent action of weak light increases is explained as follows. Since stable centers for electron trapping already exist in the grain, subsequent thermal dissipation of the centers of the latent image in the course of their formation will not occur.

The magnitude of deviations from the reciprocity law depends on the temperature \(^{65}\). When the temperature is lowered, the entire wing of the curve \(\lg H = f(\lg t)\), corresponding to short exposure times, shifts toward longer exposure times. The value of the optimum exposure time is displaced in the same direction. This is easy to understand, since a decrease in temperature entails a decrease in the mobility of interstitial silver ions, as a result of which neutralization of the trapped electrons occurs more slowly. At long exposure times, as the temperature is lowered, the probability of dissipation of the slowly growing center decreases. For this reason the photosensitivity first increases. With a further lowering of the temperature, the optimum exposure time is shifted so far into the region of large times that practically all times are “short,” i.e. become less than the optimum. Then the photosensitivity of the layer, at any exposure time, decreases with decreasing temperature. At the temperature of liquid air, when thermal motion is practically absent, the curve of the dependence of \(\lg H\) on \(\lg t\) for a given blackening density \(D\) is a straight line parallel to the abscissa axis, i.e. the reciprocity law is obeyed.

Of particular interest is the deviation from the reciprocity law at very short exposure times. Berg \(^{72}\) found that at \(t = 20^\circ\mathrm{C}\), beginning with times close to \(10^{-5}\) sec. and less, the reciprocity law is obeyed. This can be explained if it is assumed that this time corresponds precisely to the time of neutralization of a trapped electron by an interstitial silver ion. If one uses the estimate of this time given above (Part I, 4), which gives \(t = 2 \cdot 10^{-5}\) sec.,*) then good agreement between experiment and theory is obtained. This agreement supports the hypothesis that in a given trapping center there can be only one excess electron. Indeed, if the number of excess electrons that can be present in a trapping center were \(n\), then the corresponding time would be \(t = \dfrac{\varepsilon}{2\pi\sigma n}\) (see Part I, 4), which would reduce by a factor of \(n\) the time from which the reciprocity law ceases to be obeyed. Since the center of the latent image

*) Berg estimated this time as \(2 \cdot 10^{-4}\) sec., since he used the then-available data on the ionic conductivity of silver bromide single crystals obtained by Koch and Wagner (see Part I, 4).

must consist at least of several silver atoms, it should be assumed that the growth of the center of the latent image to the developable size occurs after the completion of such short exposures (see Part I, §§ 3 and 4). Berg also showed that, with decreasing temperature, the time starting from which the reciprocity law is no longer fulfilled shifts toward longer times, and by just as much as the theory requires.

Webb^73 showed that the deviations from the reciprocity law are the same for all wavelengths of the acting radiation. This means that, beginning from the moment of liberation of the electron by the absorbed quantum of light, all subsequent processes of formation of the latent image proceed in the same way for all wavelengths. Subsequently these data were confirmed in the works of Bernanose^74 and of Biltz and Webb^75.

Deviations from the reciprocity law depend on the conditions of development. This is natural, since the larger centers of the latent image, formed under weak and prolonged illumination, must develop more rapidly than the smaller centers of the latent image formed under brief, intense illumination. This is confirmed by the fact that the optimum exposure time becomes shorter as the development time is increased^76, and the deviation from the reciprocity law itself increases with development time in the region of longer exposure times and decreases in the region of shorter exposure times^77.

5

It was already pointed out above (Part I, § 1) that when red or yellow light falls on a colored crystal of silver halide, its absorption, caused by silver particles, decreases. Photochemical resorption of these particles takes place. The same phenomenon is also observed for the latent image. If a previously exposed photographic layer is acted upon by red light, then the density of blackening after development proves to be less than without the additional action of the red light. This phenomenon is called the Herschel effect. Investigations have shown^78,^79 that the spectral region of the Herschel effect approximately corresponds to the absorption band of photochemically colored single crystals of silver halide. The long-wavelength boundary of the spectral region of the Herschel effect extends into the infrared region of the spectrum beyond \(\lambda = 1000\) mμ. From this, the conclusion was once drawn^36 that the work function of an electron from a latent-image center (metallic silver) into the conduction band of silver bromide is \(1\ \mathrm{eV}\). Since the red boundary of the external photoeffect from a silver particle in vacuum is known to be \(4.6\ \mathrm{eV}\), this makes it possible to draw the scheme shown in Fig. 6. In this

scheme the assumption is made that the electronic levels of the centers of the latent image are the same as those of massive metal, which has not been proved by anyone.

The position of the maximum of the spectral curve of scattering of the latent image, as Gorokhovskii and Shestakov^78 showed, depends on many factors. With an increase in the optical density corresponding to the preliminary exposure, and with a decrease in the photosensitivity of the photographic layer, the maximum of this curve shifts into the short-wavelength region of the spectrum. Gorokhovskii and Shestakov expressed the idea that light of any wavelength can both form and scatter the latent image. Meiklyar^80 confirmed this consideration by quantitative calculations. Indeed, the curve of spectral sensitivity of any photographic layer extends rather far into the red and infrared regions of the spectrum. This part of the curve is determined by the absorption of light by disturbances of the crystal lattice of the emulsion grains. After the action of blue light, additional absorption arises in this region of the spectrum, caused by the centers of the latent image. Depending on which of the absorption coefficients caused by these two processes is larger, the centers of the latent image, under the influence of radiation of the given spectral composition, grow or are scattered. A large optical density corresponds to a large number of centers of the latent image. In this case the absorption by the centers of the latent image may be greater than the absorption by the emulsion crystals themselves. Such a latent image is scattered until both absorption coefficients become equal. Indeed, for any wavelength of yellow and red light there is its own value of the optical density at which the action of light of the given wavelength leads to a decrease of greater densities and an increase of smaller ones. On passing to shorter waves the photosensitivity of the layer increases, and therefore the indicated optical density acquires a larger value. The very process of scattering of the latent image apparently has a photoelectric character with subsequent thermal decomposition. It has already been indicated above (part I, § 2) that in a colored crystal of silver halide there arises an additional spectral region of the internal photoeffect, corresponding to the absorption band of silver particles. Therefore, when light is absorbed by a silver particle, there occurs—

Fig. 6. Electronic levels in a silver bromide crystal.

results, apparently, in the release of an electron from this particle. Subsequently, under the influence of thermal motion, the silver ion is removed[^40], as a result of which the silver particle becomes smaller by one atom. This point of view is supported by Webb’s experiments[^66] on the study of the Herschel effect at the temperature of liquid air. This author found that a latent image formed at room temperature is not bleached by red light at the temperature of liquid air (−186° C). At this temperature only the release of an electron is possible, while thermal processes do not occur. On the other hand, if the latent image is formed at the temperature of liquid air, then red light can bleach it at this same temperature, since the process of formation of the latent image at −186° C is limited to the first electronic phase (see Part I, § 4). However, if a layer exposed at the temperature of liquid air is heated, the latent image is fully formed, and upon secondary cooling of this layer to −186° C red light can no longer exert a bleaching action.

An essential question is whether the amount of silver changes under the action of red light and upon bleaching of the centers of the latent image. Tollert’s experiments[^81] established that the total amount of photolytic silver remains unchanged even after the action of red light. In the crystals there apparently occurs a redistribution of silver atoms. Debot’s hypothesis[^62] is very probable: upon incidence of red light, the centers of the latent image located on the surface of the crystal are bleached, with silver atoms passing into the interior of the crystal. Debot found that when red light falls on the layer, the centers of the latent image located inside the crystal grow.

The Herschel effect depends on the level of illumination during the preliminary exposure. Meiklyar’s experiments[^82] show that red light produces the maximum effect in the case when the preliminary illumination time corresponded to the optimum time from the standpoint of deviations from the reciprocity law (Part II, § 4). With prolonged and weak illumination of the layer, large centers of the latent image are formed which are difficult to bleach by red light. Conversely, with excessively brief and intense illumination of the layer, a large number of centers are formed in the depth of the crystal that absorb red light, and the electrons released can participate in the formation of developable centers.

6

In the region of normal exposures, the blackening density of a photographic layer increases with increasing quantity of radiant energy incident on the photographic layer. With a further considerable increase in the quantity of radiant energy, the density

the blackening reaches a maximum value, after which it decreases. This phenomenon is called solarization.

Studies have shown^83 that in the region of solarization, as the amount of illumination increases, the amount of photochemically formed silver also increases, despite the fact that after development a lower blackening density is obtained. In other words, in the region of solarization processes occur that hinder the development of the centers of the latent image. According to older theories^84, solarization was explained by a redistribution of silver between the centers of the latent image, produced by light. At present the recombination theory should be considered the most probable. During illumination of the crystals of the photographic layer, along with the formation of centers of the latent image, bromine atoms are formed which emerge onto the surface of the crystal (Part I, 3). This bromine interacts with gelatin. If a very large amount of light has acted on the emulsion crystal, then the liberated bromine interacts with the centers of the latent image formed by previous portions of light and located on the surface, converting them back into silver bromide. Thus, during solarization, the centers of the latent image located on the surface of the crystals are oxidized by bromine, while a large number of them are present inside the crystals. Since ordinary developers interact only with the surface of the crystals, such crystals are not developed. The validity of this theory is confirmed by many experiments. Ebbney^85 also observed that solarization can be considerably reduced or entirely eliminated if, before illumination, some halide acceptor—for example, sodium nitrite—is introduced into the photographic layer. The same effect is produced by bathing the illuminated layer before development in a dilute solution of hyposulfite^86. Hyposulfite dissolves the surface of the crystals and exposes the centers of the latent image situated more deeply. Solarization is the more strongly expressed, the more intense the acting light^87. This is also understandable, since more intense light creates a relatively larger number of centers of the latent image in the depth of the crystals and, consequently, a relatively larger number of bromine atoms is liberated on the surface.

Webb and Evans^87 investigated the phenomenon of solarization at various temperatures. They found that at the temperature of liquid air the phenomenon of solarization is entirely absent. All the regularities they discovered are satisfactorily explained by the theory set forth above.

7

The absorption of silver halide lies chiefly in the ultraviolet region of the spectrum. Silver bromide, in addition, absorbs violet and blue rays approximately up to \(500\,m\mu\). In accordance with this, photographic layers possess considerable spectral

with sensitivity up to approximately \(500\,m\mu\). If certain organic dyes are introduced into a photographic emulsion, the photographic layer acquires additional sensitivity to light of longer wavelengths. This phenomenon is called optical sensitization. There is a large literature concerning the chemistry of sensitizing dyes. Here only the physical side of this question will be briefly considered. The main regularities concerning optical sensitization are the following.

1. The photosensitivity of a photographic layer upon sensitization to the infrared region of the spectrum decreases as the wavelength at which the maximum of the additional sensitivity is located increases. Thus, the photosensitivity of layers sensitized to the infrared region of the spectrum is always less than the photosensitivity of layers sensitized to yellow and red light.

2. As the temperature is lowered, the photosensitivity of layers in the region of sensitization decreases more rapidly than in the region of their intrinsic sensitivity[^63].

3. Under prolonged illumination of the photographic layer, each molecule of sensitizer can participate in the formation of a large number of silver atoms[^81]. The same is observed for AgBr sols containing a dye[^94].

4. As the amount of sensitizer adsorbed on the crystals of the layer increases, the photosensitivity in the region of sensitization at first increases and then, having reached a certain maximum value, falls again. The optimum amount of sensitizer corresponds approximately to a monomolecular layer of it on the surface of the crystal, or even to a smaller filling of it[^88]. In this case, the decrease in photosensitivity cannot be explained by a filter effect.

5. Sensitization of the photographic layer is often accompanied by a decrease in its intrinsic sensitivity[^89]. This decrease also cannot be explained by a filter effect.

6. Every sensitizer is adsorbed on silver bromide, but not every dye adsorbed on silver bromide is a sensitizer.

7. Sensitization of a photographic layer by one or another dye depends on the composition of the solvent[^90].

8. One and the same dye may be both a sensitizer and a desensitizer (i.e., may decrease the photosensitivity of the layer), depending on the composition of the solvent.

9. If light whose spectral composition corresponds to the absorption of the sensitizer falls on a sensitized photographic layer, then a photocurrent is observed in the silver bromide[^23].

LATENT PHOTOGRAPHIC IMAGE

1. The distribution of the latent image over the depth of the grain is the same both in the region of the layer’s intrinsic sensitivity and in the region of sensitization[^61].

The fact that one sensitizer molecule is capable of participating in the formation of many silver atoms led most investigators to believe that the dye molecule does not change its properties after absorbing a quantum of light and transferring energy to the silver bromide.

Gurney and Mott[^40] proposed the hypothesis that, when a quantum of light is absorbed by a dye molecule, the latter gives up its electron to the silver bromide.

Subsequently, as a result of a number of processes taking place in the silver bromide, the electron from the silver bromide passes into the dye molecule, which completely restores its properties and can again take part in these processes. In this supposition it remains unclear why, for the transfer of an electron from the dye molecule into the conduction band of silver bromide, a smaller quantum of light is required than when a quantum of light is absorbed by a bromine ion of the silver-bromide lattice. Gurney and Mott assumed that the unexcited level of the dye molecule lies between the fundamental band and the conduction band of silver bromide. Subsequently Mott[^91] changed his point of view. According to measurements by Gorokhovsky and Shestakov[^78] and by Eggert and Kleinshrod[^92], the curve of the spectral sensitivity of an unsensitized photographic layer extends, though only weakly, far into the infrared region of the spectrum. Mott assumed that a quantum of light is absorbed by a sensitizing-dye molecule adsorbed on the emulsion crystal, and that this excitation energy is then transferred to bromine ions located on the surface of the grain and responsible for the absorption of light in the long-wavelength region of the spectrum. In this process the electrons are liberated from these bromine ions and pass into the conduction band of the crystal. The transfer of energy from the dye molecule to the bromine ions occurs, according to Mott’s estimate, in a time of the order of \(10^{-15}\) sec, whereas the lifetime of the excited state of the dye molecule is \(10^{-8}\) sec. Stepanov and Meiklyar[^93] proposed another scheme for the process of energy transfer from the dye molecule to silver bromide. These authors assumed that the source of the additional energy is the vibrational energy of the dye molecule.

According to this scheme, the vibrational energy of the dye molecule that has absorbed a quantum of light is added to the excitation energy of that molecule. Calculations showed that the participation of only 30 degrees of freedom of the molecule is sufficient to make up the energy deficit. The scheme made it possible to explain satisfactorily all the experimentally known regularities.

Recently, photographic layers have found ever wider application for recording ionizing particles ($\alpha$-particles, protons, mesons, etc.). The mechanism of the action of these particles on a photographic layer is not considered in the present article.

I take this opportunity to express my sincere gratitude to Prof. Yu. N. Gorokhovskii for a detailed discussion of the questions set forth in the present article and for a number of valuable suggestions.

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