QUANTUM THEORY AND PHOTOGRAPHY¹

J. Eggert and V. Noddack, Berlin.

I. Introduction.

Radiation and matter may enter into various mutual relationships. In this process, generally speaking, radiation changes under the influence of matter. But matter, too, may undergo physical and chemical changes. Physical changes include, for example, the heating of bodies under illumination, the emission of electrons, fluorescence, and so forth. These phenomena are the subject of photophysics. Chemical changes may manifest themselves in decompositions and other chemical processes.

Photophysics and photochemistry are comparatively young fields of research. Only quantum theory made possible a quantitative treatment of these processes, for it established the connection between the two quantities that determine the phenomenon, i.e. between the amount of radiation acting and the amount of substance that changes physically or chemically.

A special branch of photochemistry, one of great technical and scientific interest, is photography. Its interpretation on the basis of quantum theory is still at an initial stage. However, the results obtained, set out below, give hope for further advances. In any case, the possibility has arisen of a scientific systematization in a field that previously lent itself only to qualitative description (1).

II. Initial Observations.

The earliest observation bearing, albeit very remotely, on photography was described by Homberg in 1694. He observed that a bone vessel, accidentally moistened with a solution of lunar caustic (lapis), blackened in daylight. Other equally accidental observations confirmed the photosensitivity of silver salts, but only in 1777 did Scheele undertake a systematic study of the phenomenon.

¹ Naturwissenschaften 15, 57, 1927.

He illuminated silver chloride (horn silver) with spectrally decomposed sunlight and found that the action occurs in the region of short waves. This fact accords with the Grotthuss–Draper law, according to which a photochemical reaction can be caused only by absorbed rays.

III. Confirmation of the Grotthuss–Draper Law in the Case of AgCl and AgBr (2)

Figs. 1 and 2 illustrate the law in two technically important silver salts: silver bromide and silver chloride. In practical application, the salts are placed in a gelatin medium, in the form of an emulsion. The mercury spectrum (a) serves to indicate the wavelengths; b is the continuous spectrum of the nitro-lamp;¹ c is the absorption spectrum of silver chloride. For this purpose the spectrum of the nitro-lamp was photographed through a transparent plate of melted and solidified silver chloride. These three photographs were obtained on a panchromatic plate, sensiti-

Fig. 1. a — mercury spectrum on a panchromatic plate; b — continuous spectrum of a nitro-lamp; c — absorption spectrum of silver chloride; d — spectrum of a nitro-lamp on a plate with a silver-chloride emulsion; e — mercury spectrum on such a plate.

Fig. 2. Photographic action on bromide salts. a — mercury spectrum; b — spectrum of a nitro-lamp; c — spectrum of a nitro-lamp photographed through a bromide-salt plate on a panchromatic plate; d — spectrum of a nitro-lamp on a silver-bromide plate; e — mercury spectrum on a silver-bromide plate.

¹ The spectrum of the nitro-lamp was evidently photographed with a very small exposure in comparison with spectrum c; hence the paradoxical impression is produced that the spectrum which passed through the salt plate is broader than the unabsorbed one. The minimum in the green part of this spectrum is explained by the insensitivity of panchromatic plates in this region. (Translator’s note.)

is sensitive for all rays of the spectrum. The remaining two spectra from the nitrolamp (d) and from the mercury lamp e were obtained on a plate with a silver chloride emulsion. We see that the photographic action, just as the blackening of horn silver in Scheele’s experiment, takes place only in the violet part of the spectrum. Moreover, in accordance with the Grotthuss–Draper law, it is evident that the action of light (d) begins precisely at the place in the spectrum where the absorption by silver chloride becomes noticeable (2). The same is essentially true of Fig. 2, but in silver bromide the photographic action extends farther into the visible region than in silver chloride; correspondingly, the color of silver bromide is yellow, whereas silver chloride is almost colorless. It should also be noted that the photographs in Fig. 1 were obtained with a quartz spectrograph, and those in Fig. 2 with a glass one.

IV. Primary process.

Qualitative results. Just like the silver halides named, almost all other silver salts blacken under the action of the rays absorbed by them. The blackening corresponds to a residual chemical change in the substance. If the illuminated salts are subjected to the action of reagents which dissolve the unilluminated salts without residue, metallic silver remains. The interpretation of the process of photolysis of silver salts that suggests itself first of all consists in the idea that the salts, under the influence of illumination, decompose into silver and the corresponding electronegative part (an atom of chlorine, bromine, etc.).

For a long time such an explanation aroused doubts. If one extracts from an illuminated silver salt the metal that has separated out by means of such silver solvents as dilute hydrochloric acid, chromic acid, etc., it turns out that only a small fraction of the metal dissolves, while the remaining amount is retained. This strange phenomenon was explained in two ways.

The first explanation (Eder) is that, on illumination, silver compounds with a higher content of metal are formed, which resist the action of solvents. But against this speaks the impossibility of isolating stoichiometrically definite salts of such a type. Furthermore, it is unclear why such weak solvents as hyposulfite can decompose the hypothetical products of illumination into silver and the original silver salt, whereas strong reagents (dilute hydrochloric acid) do not act on these products (3).

These contradictions led to another explanation, according to which silver is initially formed, but it is absorbed by the salt in colloidal form. This theory was first proposed by Abegg, soon thereafter by Lorenz, and was then substantiated in various ways.

and became generally accepted (Abegg, Ostwald, Kogelmann, Luppo-Cramer, Valer and Krupko, Lorenz and Hige, Eggert and Noddack, Fajans and Frankenburger, Shaum and Fejk) (4).

The electronegative residue, as a reaction product, can also be detected in certain cases. Recently Schwarz (5) and especially Hartung have investigated the splitting off of bromine upon illumination of silver bromide. Hartung, by Folmer’s method (6), exposed a silvered quartz plate on a microbalance to the action of bromine vapors and then illuminated in a vacuum the layer of silver bromide that had formed. By weighing the quartz plate and the copper spiral serving for the accumulation of the bromine being split off, he was able to establish that silver bromide gradually decomposed under the action of light: ultimately 96.6% decomposed. The same result was reached by P. P. Koch and Kreiss, who observed silver-halide dust particles weighing \(10^{-13}\) g under illumination in a Millikan condenser (7).

Quantitative results (8). If one follows quantitatively the course of the illumination process in gelatin plates with silver halides by the amount of silver formed, it turns out that at first the amount of metal separated is expressed by the product: illumination intensity \(\times\) time (quantity of light). With further illumination this proportionality begins to be disturbed. The cause of such deviations from proportionality should be sought in the growth of the reverse reaction of formation of silver halide from the cleavage products. If substances capable of binding the liberated halide are added to the silver halide, the proportionality holds for a considerably longer time. Substances of this kind (acceptors) may be alkalis, nitrites, and gelatin itself. The ability of a halide to bind to an acceptor increases from iodine to chlorine. In chlorosilver gelatin the proportionality of the action to the quantity of light continues considerably longer than in bromosilver gelatin; in iodosilver gelatin proportionality has not been proved at all.

Relation to the quantum theory. For further investigation of the primary process it is important to establish the connection between the absorbed radiant energy and the amount of decomposed silver halide. Such a connection is established most clearly by the quantum theory, since the atomic structure of matter is here opposed to the atomic structure of energy, at least in the process of absorption. According to Einstein’s law, each absorbed quantum of energy corresponds to an elementary chemical reaction. According to this law, for each absorbed quantum \(h\nu\) one molecule of silver bromide must decompose, and one atom of silver must be liberated, approximately according to the equation:

\[ \mathrm{AgBr} + h\nu = \mathrm{Ag} + \mathrm{Br}. \]

J. Eggert and W. Noddack

The details of this representation will be discussed below.

To verify this consequence of the quantum theory on a silver-bromide gelatin plate, three measurements are needed:

1) It is necessary to determine the energy used, best of all in the region of strong absorption by silver bromide (cf. Fig. 2d), and to convert it into quanta.

2) It is necessary to find the absorption by the silver bromide of the photographic layer. In doing so it should be remembered that only part of the energy is absorbed in the silver bromide; the other part is absorbed by the gelatin. Fig. 3 gives an idea of the distribution of the absorbed energy. Curve I depicts the percentage absorption of the photographic layer as a function of wavelength; curve II indicates the course of the absorption by gelatin alone; the difference of the areas encompassed by the two curves is shaded; curve III, constructed from the differences of the ordinates of curves I and II, gives the true absorption by silver bromide1.

Fig. 3. I. Absorption curve of a silver-bromide gelatin plate. II. Absorption of pure gelatin in a thick layer. III. Difference of the two curves. The shaded area corresponds to the true absorption of silver bromide.

3) It is necessary to find the amount of silver formed under illumination and to express it as a number of atoms. The measurements described were made for wavelengths of 436, 405, and 365 mμ. The true absorption of silver bromide in this region proved to be approximately 10–20%, and undoubtedly each absorbed quantum corresponds to the liberation of one atom of silver.

For silver-chloride gelatin emulsions, for a wavelength of 365 mμ the same result was found. Copying emulsions containing, besides silver chloride, also other soluble silver salts reveal the same regularity.

The action of other rays (11). Under the action of other rays (besides those indicated) that are absorbed in the photographic layer, qualitatively similar results are obtained. With increasing radiant energy, the liberation of silver increases. But from the point of view of the quantum theory the results differ substantially from the preceding ones. Thus, for example, for Roentgen rays with a mean wavelength of 0.4 Å, approximately 1000 atoms are liberated for each quantum \(h\nu\).

Still more energetic radiations, for example the α-rays of radium emanation, give for each α-particle up to 50,000 silver atoms. What the “quantum yield” is in the vast intermediate region between visible light and X-rays is as yet unknown, just as we do not know how many silver atoms are formed when halide compounds are bombarded by electrons or ions.

V. Development of the Primary Process.

History. The primary process described is applied in practice only in printing papers, in which the silver precipitated under the action of light directly gives the image. The other processes of practical photography are based on a special property of illuminated silver halide. This property consists, generally speaking, in the possibility of intensifying the primary light imprint by various means. The development of the “latent image” was discovered by Daguerre (1838). He turned the polished surface of silver plates into light-sensitive silver iodide by exposing it to iodine vapor. Even if the plate was illuminated for so short a time that no change whatever was noticeable on it, the light imprint appeared clearly if the plate was exposed to mercury vapor. In this case the process of development consists simply in the fact that metallic mercury condenses preferentially on the illuminated places. The image arising in this case is a positive.

Modern methods. The photographic layers used today require, owing to their essentially different properties, other methods of development as well. In the Maddox process (1871), silver bromide is caused to precipitate in an aqueous solution of gelatin; the resulting “emulsion,” after removal of the dissolved salts, is poured onto a glass plate, a celluloid film, or paper, on which it dries. Depending on the conditions of treatment, the silver bromide forms in the gelatin microscopic or ultra-microscopic particles, called grains.

In Fig. 4 are given microphotograms of certain types of grains1. If such layers are illuminated very little, then no changes are noticeable on the grains; but if the plate is immersed in a solution of a suitable reducing agent, the illuminated places immediately blacken, since in them the silver bromide is converted into metallic silver. Examples of such developers are pyrogallol, hydroquinone, para-aminophenol, para-oxyphenylglycine (12).

From a theoretical point of view, another method of development is of interest, one that is now almost never used in practice. It somewhat resembles Daguerre’s method and consists in the fact that silver in statu nascendi is deposited predominantly on the illuminated grains. In this method the exposed plate is immersed in a solution of a silver salt that at the same time contains a slowly reducing substance.

Fig. 4. 1500-fold magnification of undeveloped grains.

Fig. 5. 1500-fold magnification of slightly developed grains of silver bromide.

Fig. 6. 1500-fold magnification of overdeveloped grains of silver bromide.

It is remarkable that such development takes place even after fixing has already begun (“physical” development before fixation and after fixation).

Blackening and its measurement. In all methods of development, the layer acquires, through the reduction of grains, a “blackening,” the degree of which depends on the quantity of radiant energy that has acted. Using the concept of extinction of an absorbing medium introduced by Bunsen and Roscoe, Hurter and Driffield (14) proposed the following measure of blackening. Let a parallel beam of light pass through the blackened layer, its intensity being \(J_0\) at the entrance and \(J\) at the exit (\(J_0 > J\)); then the blackening \(s\) is determined by the formula:

\[ s=\log_{10}\frac{J_0}{J}. \]

For a layer that transmits one tenth of the incident light, the blackening is

\[ s=\log_{10}\frac{J_0}{0.1J_0}=1. \]

Extinction in optically homogeneous media, for example in dye solutions, corresponds to a molecularly dispersed system; photographic blackening, however, depends on grains of microscopic dimensions. Therefore it is determined not only by true absorption, but also by scattering. Investigations have shown an increase of scattering with increasing grain size, and also a dependence of the scattering on the solid angle of the cone of incident light (15).

For the practical determination of blackening, in most cases photometers are used with adjustment for equality of the illumination of the fields. The intensity of the comparison light source is changed by polarizing prisms, diaphragms, or rotating sectors. The eye, or a photocell, serves as the indicator. In precise measurements of blackening it is necessary to take into account the magnitude of the above-mentioned scattering (16).

Fig. 7. Dependence of blackening (I), number of grains (II), and quantity of silver (III) in a developed Agfa-Spezial plate.

Blackening, quantity of silver and number of grains. The blackening of a photographic layer is caused by silver grains, and therefore it is to be expected that the magnitude \(s\) is in some relation to the number of grains and to the quantity of developed silver. This relation is presented in Fig. 7. Along the abscissa are plotted the common logarithms of the exposure time \(t\), at constant intensity expressed in meter-candles \([1\ \text{NK (Hefner candle)} = 22.6 \cdot 10^{-6}\ \frac{\text{cal}}{\text{cm}^{2}\ \text{sec}}]\); the ordinates of curve I are the values of \(s\), of curve II the numbers of grains per each \(3 \cdot 10^{-6}\ \text{cm}^{2}\), and of curve III the quantity of silver in \(\gamma\) per \(\text{cm}^{2}\), multiplied by \(10^{4}\). From the figure it is seen that the ordinates of the three curves are approximately proportional, at least where blackening increases with increasing quantity of light. We shall return later to the processes connected with the decrease of blackening upon a further increase of the quantity of light (solarization) (17). Curves I and III were obtained for a normal Agfa-Spezial plate. Curve II was obtained with the same emulsion, but diluted 20-fold (to facilitate counting the grains in the region of solarization).

VI. The Blackening Curve and Its Interpretation

The form of the blackening curve. Plotting the magnitude of blackening as a function of the quantity of light, we obtain the photographic blackening curve. In Fig. 8 the quantities of light are laid off as abscissae (not logarithms), which, for a constant source, are proportional to the exposure time \(t\).

Fig. 8. Blackening curve as a function of exposure time.

In Fig. 9 (and also in Fig. 7, curve I) the same function is represented, but \(\log_{10} t\) is laid off as abscissae. This latter method of representing blackening curves is more convenient and is more often used when there is a large variation in time.

The rise of the curve begins only at a definite value of the quantity of light, which is called the “threshold.” Below the threshold, the blackening of exposed and unexposed places is the same and is called the “veil.” Starting from the threshold, the rise at first follows a curve convex toward the abscissa axis, then along a rectilinear portion; farther on the curve becomes concave.

It is noteworthy that, after passing a certain maximum value of blackening, the curve begins to descend with further increase in the quantity of light. This phenomenon is called solarization.

Fig. 9. Blackening curve of Fig. 8 as a function of the decimal logarithm of the exposure time.

The blackening curve and sensitivity. The somewhat controversial concept of photographic sensitivity corresponds to the fact that different types of emulsion, under identical exposure and development, exhibit different blackening.

The measure of sensitivity is often taken to be threshold sensitivity. To determine it, for example, the sensitometric method of Scheiner is used. The plates being compared in this method are subjected to identical illumination from a standard source, while the exposure time is varied in steps. Threshold sensitivity is the step of exposure time (expressed by an arbitrary number),

at which the blackening just begins to differ from the general fog (Scheiner degree). Such a characteristic of sensitivity would be sufficient if the blackening curves of all types of emulsions ran parallel; then the ratio of the sensitivities of all sorts of plates would be constant for any blackenings. In reality, the blackening curves of different types of emulsions may show different steepness.

Thus, for example, one often encounters the case represented in Figure 10, where a layer with a low threshold sensitivity has a steep blackening curve (curve II), intersecting the flatter curve of another layer with a greater threshold sensitivity (curve I); for strong illuminations the ratio of the sensitivities here becomes reversed. At the quantity of light \(P\) the sensitivities of both sorts of plates become identical. Thus, for a complete description of the sensitivity of a plate of a given sort, it is always necessary to consider the entire blackening curve. The sensitometric system of Hurter and Driffield, into the discussion of which we shall not enter here, seeks to take this circumstance into account. In more recent times the sensitometry of photographic layers has developed especially thanks to the work of Goldberg (18).

Fig. 10. Two types of blackening curves.

The blackening curve and the kind of acting rays. One may obtain a blackening curve also from X-rays. In its general appearance its form is similar to the blackening curve from visible light.

Fig. 11. Schematic blackening curves for identical emulsions for light (1) and for X-rays (2).

On close examination of the curves, however, [[unclear: part of the line is obscured]] in the figure, a point with identical blackening \((s = 0.5)\) on both curves corresponds also to the same exposure time \(t = 60\). If, starting from this point, one follows the course of both curves in the region of shorter exposure times, a characteristic difference between the curves is revealed. The steep curve for visible light shows a clear “sag,” whereas the X-ray curve proceeds in this region more nearly rectilinearly. Further,

if one disregards the general veil, then, as the dotted lines show, the light curve intersects the abscissa axis far from zero, whereas the X-ray curve tends to pass through the origin (19).

Fig. 12. Dependence of the blackening curve on development time (each curve indicates the time of blackening in minutes).

In a logarithmic representation these differences between the two curves appear less clearly, since their characteristic features are compressed at the beginning. The blackening curve for $\alpha$-rays is almost the same as for X-rays.

The blackening curve and the conditions of development. The form of the blackening curves for all kinds of rays depends on the development time. The nature of the dependence is clear from Fig. 12, which presents the light blackening curves for various development times (1, 2, 3, 4, 5 minutes in metol-hydroquinone). Especially characteristic is the increase in steepness with increasing time. This increase in steepness is accompanied by an increase in the density of the veil, and the steepness tends toward a certain limit (“overdevelopment”), which depends on the development conditions (concentration, composition, temperature of the developer).

The blackening curve and the structure of the layer. If one follows the increase in blackening for a definite quantity of light under a microscope, it is easy to see that the blackening depends on two circumstances. First, the number of reduced grains increases with time; second, the degree of reduction of each grain increases. This can be seen in Figs. 5 and 6. In Fig. 5 the undeveloped grains of Fig. 4 were photographed during reduction, and in Fig. 6—after complete transformation into silver.

Figs. 13 and 14 show how development of the photographic layer advances inward. These are microphotograms of film layers cut, after different development times, by a microtome into thin plates perpendicular to the surface (the photographs were taken by Schweinitz). From the photographs it is evident that development reaches the end of the layer only after some time (thickness $30\ \mu$). This slow advance is explained partly by swelling phenomena in the gelatin, and partly by the weakening of the developer as it penetrates inward.

Finally, the form of the blackening curve is determined by the following three quantities, determined by the structure of the layer: 1) the size of the grains, 2) their number, 3) their condition. These three quantities are, to a large extent, regulated by the method of preparing the emulsion. In this connection one must distinguish the precipitation of the silver salt and the subsequent ripen-

Development. Without entering into these complex, partly unexplained processes, we shall mention only some of their most important features.

The concentration of the solutions determines to a considerable degree the number and size of the grains. In dilute solutions many small grains appear (Lippmann emulsions); in concentrated solutions few grains arise, but they are large. It is far from immaterial whether a solution of $\mathrm{AgNO_3}$ is poured into a solution of $\mathrm{KBr}$, or whether the mixing takes place in the reverse order. The kind of gelatin, the temperature of mixing, etc., are important. The latter factors especially determine the condition of the grains, namely the properties of their surface.

Fig. 13 and 14. Advancement of the developer into the depth of the layer as the duration of development increases (500-fold magnification).

It should be noted that the size of the grains and their condition for the same emulsion are not uniform; they fluctuate within wide limits around some mean value (20).

Blackening and ripening curve. Bennett (1878) discovered that the sensitivity of a silver-bromide emulsion increases if, after its preparation, it is heated for some time at $50^\circ$. This process is called ripening. The changes in the grains that occur in this process may take place for four reasons.

1. In the presence of solvents for silver bromide ($\mathrm{Br'}$ or $\mathrm{NH_3}$), large crystals may grow at the expense of small ones. This was first pointed out by W. Ostwald.

2. In the presence of reducing substances (originating from the gelatin), traces of silver may appear chemically on the surface of the grains. This was first pointed out by Lüppo-Cramer.

3. Sulfurous organic substances contained in the gelatin may, during ripening, form on the surface of the $\mathrm{AgBr}$ crystals

sulfurous silver or other sparingly soluble sulfur compounds. The possibility of this has been indicated, among others, by Sheppard (21).

1. During ripening, a change in their ionic charge may occur on the surface of the crystals. In the normal state, the grains of a layer suitable for photographic purposes are covered with bromine ions (22).

Theoretical interpretation of the blackening curves.
The interpretation of the curves for α-rays is especially simple. Each incident α-particle records its path in the photographic layer as a chain of developed grains, as is seen in Figs. 15 and 16. In such a chain, depending on the size of the grains, there are from 4 to 15 silver grains. Thus the blackening of the plate is proportional to the number of arriving α-particles, at least if this number is small in comparison with the number of emulsion grains (per \(1\ \mathrm{cm}^2\)). If the number of α-particles is so large that many of them strike the same grain, then the blackening lags behind the amount of radiation, proportionality is violated, because the second α-particle that has struck the same previously affected grain will no longer reveal its action during development. Owing to the simplicity of such a process, it is not difficult to express the blackening \(s\) as a function of the amount of radiation. The blackening \(s\), obtained with an exposure of \(t\) seconds from a constant source of radiation, approximately obeys the following equation:

\[ s=s_0(1-e^{-kt}), \]

where \(k\) is a constant, \(s_0\) is the maximum blackening that can be obtained in the given layer (23).

The action of X-rays in general obeys the same law. From the point of view of the quantum theory, the quantities of energy participating in the elementary processes under the action of α-rays and X-rays are sufficient for each affected grain to be capable of being completely developed. This will become clear if one recalls that each α-particle liberates 50,000 atoms of silver, while an X-ray quantum liberates approximately 1000 silver atoms. In the first case the liberated silver is located in 5–15 grains; in the case of X-rays the distribution has not been measured precisely, but undoubtedly the precipitated silver is concentrated in a few grains, probably in one.

Visible light acts quite differently. Here the silver atoms appear in the grains irregularly, singly and independently of one another. The developer wets only the surface of the grain; therefore the reduction process is catalyzed by only one silver atom on the surface of the crystal. Consequently, one may expect that only a few of the liberated silver atoms will be effective. In the case of α-rays, a large number of silver atoms are formed both at the place

at the entry of the α-particle into the grain, and at its exit; therefore development occurs more strongly here, and the same may be expected under the action of X-rays.

Indeed, it was shown that near the threshold approximately 300 absorbed quanta of blue light give one developed grain. On the other hand, the ratio of the number of AgBr molecules situated on the surface of the grain to the number of molecules inside the grain is also approximately equal to \(\frac{1}{300}\) (24). With increasing blackening, the ratio

\[ \frac{\text{number of grains}}{\text{number of absorbed quanta}}, \]

which at the threshold was \(\frac{1}{300}\), changes. Consequently, besides the ratio

\[ \frac{\text{number of molecules on the surface of the grain}}{\text{number of molecules inside the grain}}, \]

which depends on the form and size of the grain, some other property of the grains also has an influence.

Fig. 15, 16. Developed silver bromide layer (300- and 1500-fold magnification), on which α-rays acted. Each α-particle corresponds to a chain of 5–15 silver bromide grains.

Such a second property of the grains is, possibly, their ability to form, under the action of light, special centers that facilitate, to a greater or lesser degree, the process of development. For α-rays and X-rays, in contrast to visible light, this second property of the grains is of no significance.

A “center,” or nucleus, is usually understood as a small quantity of substance that makes possible the development of a heterogeneous reaction. In our case such a center is a small quantity of silver, by virtue of which the process of reduction of a silver bromide grain becomes possible. The concept of a “center” is not associated with any definite notion of the quantity of substance.

For $\alpha$-rays, which, as has been said, produce thousands of silver atoms in each grain, the center must be very large, as also for X-rays. For light rays, as if on the basis of the preceding, the center may under certain circumstances (with small quantities of light) even be a single atom. If, however, one recalls that even unexposed grains can be slightly reduced (fog), i.e., undoubtedly have centers, then it will become clear that a single silver atom arising under the action of light serves only to complete an already almost formed center. The silver that existed even before exposure arose, probably (as was said above), during ripening. From this point of view the ability of a grain to develop is determined by the presence of a center of “critical size.” This critical size of the center, composed of “ripening silver” and “light silver,” is reached the more easily, the greater the number of quanta falling upon the grain (25). For $\alpha$-rays and X-rays the critical size of the grains is reached, in any case, independently of the quantity of “ripening silver.”

This circumstance explains why the blackening curve for light rays differs from the curve for $\alpha$-rays and X-rays (cf. Fig. 11). For a clearer explanation of this fact, let us temporarily assume that all grains contain one and the same amount of “ripening silver,” so large that an insignificant addition of photolytic silver is sufficient to obtain the critical size. If such a layer is exposed, then it is clear that the blackening curve should resemble the curve for $\alpha$-rays and X-rays (an exponential curve). But the curve for visible light differs from such a curve; consequently, our assumption of a uniform distribution of ripening silver among the grains is incorrect. Such a conclusion is quite understandable, for one must expect that in the process of ripening the silver is distributed among the grains nonuniformly, according to a law analogous to Maxwell’s distribution function. A certain small number of grains may develop even without exposure (fog). A small number of grains already responds to 1 quantum $h\nu$. Two quanta, according to Maxwell’s function, will make capable of development a number of grains more than twice exceeding the preceding number. This “advance of proportionality,” characteristic of the superposition of different exponential curves with different quanta—1, 2, 3, etc.—is manifested in the blackening curve for visible light.

The assumption of the existence of some quantity of “ripening silver” on the grains even before exposure also explains why, under favorable circumstances, a grain may become developable even under the action of only one quantum $h\nu$. This will occur in the case when one silver atom, liberated upon absorption

one quantum, supplements the amount of “ripening silver” to the critical value. Conversely, under the most unfavorable circumstances (as experience shows) even thousands of quanta may be insufficient to make the grain developable. Such unfavorable circumstances may arise owing to a deficiency of ripening silver, or else because the silver atoms are liberated inside the grain (26).

Up to now, for heuristic reasons, in interpreting the reciprocity law failure we have resorted to the ripening process in order to explain the presence of silver before exposure. But other aspects of the ripening process also agree with our views. For example, the enlargement of grains during ripening is accompanied by an increase in the total absorption of the given grain; consequently the probability that the grain will be developed increases. The separation of sulfur compounds on the surface of the silver acts, one must suppose, in the same way as the separation of silver on the surface during ripening.

Above we pointed out yet another aspect of the ripening process: the displacement of the adsorption equilibrium of bromine ions between the grain surface and the solution. This process is still little known. As stated above, the grains of a normal photographic emulsion are covered with bromine ions. This excess of bromine is connected with the method of preparing the emulsion. In factory production, a solution of silver nitrate is always poured into an excess gelatin solution of potassium bromide. If one proceeds in the opposite way, the fog in emulsions proves so considerable that the plates are unusable. Pouring silver nitrate into a normal photographic emulsion in order to remove the excess of bromine ions, we find a quite definite lower limit, below which the addition of nitrate proves ineffective. If the limit is passed, then the layer begins to fog more and more, and, finally, the reducibility of the grains becomes so great that the action of light can almost not be distinguished against the background of the general dense fog that arises on development (27). It is natural to connect the limiting concentration of silver ions with the number of bromine ions present on the surface of the grains from the time of their formation. If it is assumed that silver bromide becomes developable (i.e., the layer begins to fog) as soon as the adsorbed bromine ions are removed from the grains, then it turns out that the bromine ions cover the grain with a 6–10-fold layer. This amount of bromine ions, determined from the fog on development, varies depending on the methods of preparing the layer. It has the value indicated above for normal photographic plates; it is considerably greater in fine-grained layers, for example, in Lippmann emulsions. It may seem surprising that each grain of a normal photographic layer is enveloped by a thickness of bromine ions many times exceeding the dimensions of atoms, but it should

one should remember that a considerable fraction of bromine ions is also contained in the gelatin. The high electric charge of AgBr particles is also demonstrated by measurements of the ionic charges of colloidal particles of silver halide salts. Such measurements (28), made with substantially smaller particles (without a binding medium), revealed similar relations: particles precipitated with a tenfold excess of bromine or silver ions and containing \(10^7\) molecules of silver bromide possess, for example, charges corresponding to the adsorption of \(3 \cdot 10^5\) bromine or silver ions, which corresponds to a monolayer ionic shell of the grain.

These facts argue in favor of the view that bromine ions adsorbed on the surface of grains must play a major role in the normal photographic process. They must exert a certain retarding action, which is necessary for the photographic process so that unexposed grains are practically not reduced by the developer. In agreement with this is, for example, the long-known fact that the addition of potassium bromide to the developer decreases the rate of the reduction process.

It is natural to suppose that upon exposure the charge of the grains changes. We know that light, as well as Röntgen rays and \(\alpha\)-rays, upon being absorbed by silver bromide liberate metallic silver. What role this silver, which joins the “centers” during development, plays is still unknown. The simplest assumption, on the basis of what has been said above, is that a center located on the surface of a grain weakens the portion of the shell of bromine ions lying over it, or even removes it altogether. In this way the penetration of the developer to the grain would be facilitated.

At the basis of the ideas set forth lies one assumption, which has not yet been mentioned, but which must have fundamental significance in the photographic process. In formulating the primary process, we assumed that upon absorption of each quantum \(h\nu\) the molecule of silver bromide decomposes according to the equation:

\[ \mathrm{AgBr} + h\nu = \mathrm{Ag} + \mathrm{Br}. \]

This view, however, must be somewhat qualified, for it proceeds from the assumption that we are dealing with molecules of silver bromide. In reality this is not at all so. The grains are crystals with the structure of heteropolar inorganic salts; in other words, the grains are ionic lattices built of silver and bromine ions. Taking this into account, and also the fact that the final products of photolysis are Ag and Br atoms, we conclude that the basic light process consists in an electronic reaction. The connection between the photochemical change of AgBr and the photoelectric effect has long been pointed out. Recently Fajans and Franken-

burger (29) substantiated the assumption that the primary photochemical process in the illumination of silver bromide (in contrast to the earlier interpretation) must consist in the transfer of an electron from the bromine ion to the silver ion. The process can be expressed most simply as follows:

\[ \mathrm{Br}^{-}+h\nu=\mathrm{Br}+\ominus \]

\[ \ominus+\mathrm{Ag}^{+}=\mathrm{Ag} \]

The final products of the reaction here are atoms of bromine and silver for each absorbed quantum \(h\nu\)¹). In this interpretation, however, we obtain an explanation of the following remarkable fact. When examined under a microscope, a silver-bromide grain proves to have

Figs. 17, 18, 19. Direct blackening (without development) of silver-bromide grains with increasing exposure (2000-fold magnification).

not blackened uniformly, as would be expected according to the laws of probability; the deposition of silver in the crystals occurs at separate, quite definite places. In Figs. 17, 18, 19 (taken from Mankenberg’s dissertation), which show at 2000-fold magnification the same crystals at different exposures, the indicated effect is quite clear (30). The explanation of this phenomenon is that the electrons liberated upon illumination are by no means

¹) The mechanism of the decomposition of silver bromide in the gaseous state has recently been elucidated in the work of Franck and Kuhn. Cf. on the mechanism of the photochemical decomposition of molecules in general the preceding article by E. V. Shpolsky. —Ed.

must react with silver ions located near the place of their occurrence; on the contrary, they evidently have a tendency above all to transform into atoms those silver ions which are situated in the vicinity of silver already formed. This process, having some similarity to coagulation in colloid chemistry, must inevitably have an effect in the formation and growth of “centers.” Otherwise it would be impossible to understand why a given quantum, or in any case a few quanta, act precisely near an already formed center (regardless of what substance this center may consist of).

Fig. 20.                    Fig. 21.

Comparison of two microphotographs (1000-fold magnification) of developed grains with the same total blackening. Fig. 20 corresponds to the normal region of the blackening curve; Fig. 21—to the region of solarization.

Coagulation of silver in a grain must also be of significance in other photographic processes. Here we shall touch only on solarization.

As has already been said, the blackening curve has a maximum, and the descending branch of the curve corresponds to solarization. From Fig. 7 it is clear that a decrease in blackening corresponds to a decrease in the developing silver, while the number of grains remains almost unchanged. Thus solarization is determined by a decrease in the capacity of the grains for development. This is manifested in the fact that the grains are not developed as a whole, but only fragmentarily. This can be noticed to some extent when comparing Figs. 20 and 21. Fig. 20 corresponds to the ascending branch of the blackening curve, Fig. 21—to the region of solarization. Both photographs were obtained with the same emulsion and in total give the same blackening. This circumstance is established exactly only by counting the grains (cf. Fig. 7, curve II).

The reduced capacity of the grains for development in the region of solarization is evidently hidden in a change of the active “centers.”

At the same time, one must not think of a decrease in the number of centers, since in the region of solarization the quantity of silver deposited increases with the duration of illumination. Rather, one may suppose a growth of the grain, i.e., a change connected with an increase in its mass. This change is accompanied by a decrease in the catalytic capacity during development. From this point of view, solarization is a consequence of coagulation of the center on the grain, accompanied by a decrease of the effective surface of the center (31). Objections have repeatedly been raised against such a view. Opponents defend the following point of view: the occurrence of solarization is explained by a decrease in the quantity of silver as a result of recombination of silver with the bromine that has split off. Such a view, however, can explain only part of the observed facts (32). The theory of coagulation explains, besides solarization, other facts as well in the photographic process. These include, for example, the Abney–Schwarzschild effect and the desensitization discovered by Lüppo-Cramer. With respect to these phenomena, which are still in a stage of lively development, we confine ourselves to referring to the special literature (33).

Looking once more at the totality of the phenomena described, we may assert that the quantum theory has introduced here, as in other processes connected with the action of radiant energy, a considerable order. But there is no doubt that, following the primary quantum process in the silver halides (as in most other photochemical reactions), a number of secondary processes appear, and these give the whole field its characteristic imprint.

LITERATURE

1. Sheppard und Mees. Der photographische Prozess. S. 213. Halle a. d. S.; Knapp 1920.

2. Eggert und Noddack ZS. f. Phys. 20, 299, 1923; 21, 264, 1924; 31, 922, 1925.

3. l. c. (1).

4. Feick und Schaum ZS. f. wiss. Phot. 23, 389, 1925, see also (2).

5. Schwarz und Stock Ber. d. d. chem. Ges. 54, 2111, 1921.

6. Hartung Journ. of the Am. chem. soc. 125, 2198, 1924. Volmer Diss. Leipzig (1910).

7. Koch und Kreiss ZS. f. Phys. 32, 84, 1925.

8, 9. l. c. (2).

1. Weigert ZS. Phys. Chemie 99, 499, 1921; ZS. f. Phys. 18, 232, 1923; ZS. f. Phys. 34, 914, 1925; Eggert und Noddack ZS. f. Phys. 20, 299, 1923; 21, 264, 1924; 31, 925, 1925; 34, 918, 1925.

2. Nernst und Noddack. Sitzb. d. preuss. Ak. d. Wiss. 1923 S. 110.

3. Cf., for example, the review by Meidinger, ZS. f. Phys. Chemie 114, 89, 1925.

1. E. Mankenberg, Dissertation. Dresden 1925.

2. The photographic researches of F. Hurter and Vero C. Driffield, The Royal Photographic Society of Great Britain, 120.

3. Eggert und Archenhold. ZS. f. phys. Chem. 110, 498, 1924.

4. Koch. Ann. d. Phys. (4) 39, 705, 1912; Ornstein. Report at the Physics Congress in Bonn, September 1923; Dorgelo. ZS. f. Phys. 31, 827, 1925.

5. Scheffers. ZS. f. Phys. 20, 109, 1924.

6. E. Goldberg. Der Aufbau des photographischen Bildes. Halle a. d. S. Knapp 1922; cf. review by F. Weigert, Naturwissenschaften 10, 861, 1922.

7. Friedrich und Koch. Ann. d. Phys. 45, 399, 1914; Glocker und Traub. Phys. ZS. 22, 345, 1921; Bothe. ZS. f. Phys. 8, 243, 1922; Bouwers. ZS. f. Phys. 13, 374, 1923.

8. Wightman, Trivelli und Scheppard. Trans. of Faraday Soc. 19, November 1923.

9. Scheppard. Phot. Ind. 38, 1032, 1925.

10. Fajans und Frankenburger. ZS. f. Elektrochemie 28, 499, 1922.

11. The Svedberg and Anderson. Phot. Journ. 61, 1921; The Svedberg. Phot. Journ. 62, 310, 1922; also Meidinger loc. cit. (12).

12. Eggert und Noddack. Sitzb. d. preuss. Ak. d. Wiss. 1921. S. 631.

13. Scheppard, Trivelli and Loveland. J. Franklin Inst. 200, 51, 1925.

14. l. c. (12).

15. Cf. the dissertation of A. Strehlow, Berlin, 1926.

16. Eder. Handbuch der Photographie, latest edition. Cf. also (22).

17. Trivelli and Scheppard. Journ. of Phys. Chem. 24, 1568, 1925.

18. l. c. (17); Arens. ZS. f. Phys. Chemie 114, 337, 1925.

19. Eder. ZS. f. wiss. Phot. 23, 377, 1925.

20. Eggert. ZS. f. Elektrochemie 32, 500, 1926.

A summary of the literature data may be found in the following articles and books.

Eggert und Noddack. Verh. d. d. Phys. Ges. III. Reihe 5, 29, 1924.

Dorgelo. ZS. f. Phys. 31, 827, 1925.

Lorenz und Eitel. Pyrosol., Leipzig; Akad. Verlagsgesellschaft, 1926.

Meidinger. Die Bronsilberplatte. Handbuch d. Phys. Optik.

Eder—cf. (29). Article by Eggert and Noddack.

Technical details may be found in the monograph: Fr. Wentzel. Die photographisch-chemische Industrie. Leipzig. Th. Steinkopff, 1926.

1. Taken from the dissertation of E. Manksenberg (13), carried out in the institute of Prof. R. Luther in Dresden. ↩↩