On the Physical Nature of the Latent Photographic Image

M. V. Savostyanova, Leningrad

As is known, an exposed, undeveloped photographic plate is in outward appearance no different from an unexposed one; therefore the image obtained on the plate is customarily called hidden, latent. In the 100 years that have elapsed since the invention of photography, a firm conviction has arisen that the latent image is something invisible, weightless, something that cannot in any way be detected directly, and that becomes accessible to investigation only after its “development” by chemical agents. Physico-chemical and purely chemical methods, which in recent times have yielded much of value for elucidating the nature of the “visible” image, have remained powerless in elucidating the nature of the “hidden” image—the mysteriousness of which, however, does not prevent millions of amateur photographers from making daily use of it in all corners of the globe.

Almost all the numerous theories of the latent image that have succeeded one another throughout the history of photography may be assigned to one of two main groups: some of them assume that, under the action of light, certain chemical changes occur in the halide salt; this includes the so-called subhalide theory of Luther and Eder, which assumed the formation of compounds of the type \(\mathrm{Ag_m Hal_n}\) (subhalides). It persisted for quite a long time, but has now been abandoned, since, despite numerous attempts, no one has yet succeeded in

to isolate these hypothetical subhalide compounds in pure form.

Other theories see the essence of the latent image in “elementary” silver, separated under the action of illumination inside or on the surface of the emulsion grains. From the point of view of these theories, the study of the properties of the latent image should be reduced to the study of the properties of this “elementary” silver, which, obviously, in its behavior must differ from massive silver. This problem has a purely physical character and represents a particular case of the more general question of the properties of metallic particles separated inside crystals as a result of a photochemical process and in some way embedded in the crystal lattice; this question, in all its breadth, has long been the subject of investigations by the Göttingen school of physicists of R. Pohl, to whom belongs the credit for the definitive clarification of the nature of the latent image. Thus here too, as often happens in science, we owe the solution of the question to investigators who were never specialists in the given problem.

The present article is devoted to the exposition of the results achieved by Pohl in this direction and constituting the content of his last work on the photochemical process in halide-silver salts.¹ This work, which contains on a few pages the entire theory of the photographic process, is one of the last links in a long series of investigations of the photochemical process in alkali-halide salts. In view of this, in our exposition we must first dwell on these salts, which have been studied most fully and comprehensively: the study of their properties will prepare the ground for clarifying the picture of the photographic process in a halide-silver emulsion.

We must at the same time make the reservation that the discussion will deal exclusively with the primary stage of the photographic process, which is the immediate consequence of the absorption of light in the photosensitive emulsion; we con-

we shall not touch at all upon those secondary processes which take place in the presence of gelatin and developer and lead to the transformation of the latent image into a visible one. A detailed exposition of all questions connected with development may be found in the article by K. V. Chibisov in the pages of this journal (“Advances in the Physical Sciences,” 1930, p. 367, issue 3).

The photochemical process in crystals of alkali-halide salts

A typical representative of the alkali-halide salts is rock salt; the fact that it is colored yellow-brown by X-rays or gamma rays has long been known. The same phenomenon is also observed in all other alkali-halide salts—thus, KBr becomes blue, KCl violet. As Smakula has recently shown,\(^2\) coloring can also be produced by the slower quanta of ultraviolet radiations absorbed by the crystals. Both of these methods of coloring, to which one may also add the rarely used method of coloring by cathode rays, are customarily called subtractive methods, although it would be more correct to give them the name photochemical. Opposed to them is the additive method, in which a colorless crystal is impregnated with vapors of the metal that is a constituent of the given salt. Thus, rock salt is colored the same yellow if it is heated in molten sodium to a temperature of 500–600° (Jijelava’s method).\(^3\) In all cases the coloring is accompanied by a change in the electrical properties of the crystals; therefore, in describing the photochemical process in these salts, we shall have to dwell on both the optical and the electrical aspects of the phenomenon.

Optical properties of crystals of alkali-halide salts

As is known, all crystalline substances very strongly absorb light in the ultraviolet part of the spectrum; in particular, the absorption spectrum of alkali-halide salts

located near 200 mμ. The absorption coefficient in this region is extremely large and reaches, at its maximum, a value of the order of \(10^5\ \mathrm{mm}^{-1}\); this circumstance caused great difficulties in the measurements, since all the light is in fact absorbed already in a thin surface layer. By using very thin crystalline layers several microns thick, Hilsh and Pohl[^1] were nevertheless able to overcome this difficulty and to measure the absorption curves for all the alkali-halide salts; a typical curve for KJ is given in the left part of Fig. 1. When the salts are colored by one of the above-mentioned methods, a second maximum appears in the visible part of the spectrum, which is what causes one or another coloration of the crystal. Thus KBr appears blue, since the red part of the spectrum is cut off, while the yellow coloration of NaCl is caused by absorption in the blue part. In Fig. 2 are given the absorption curves for the majority of the colored alkali-halide salts according to the measurements of Pohl’s collaborator, Ottmer;[^4] one of these curves (for KJ) is given, for comparison with the first maximum, in the right part of Fig. 1 (since the absorption in the visible region is almost \(10^6\) times weaker than in the ultraviolet, the scale is not preserved, and both curves are plotted to a common ordinate). In this figure

Fig. 1.

clearly sees the different character of both absorption maxima, indicating the different nature of the absorbing centers: the ultraviolet absorption bands are attributed, as is known, to vibrations within the elements themselves of the crystal lattice—these are the so-called “intrinsic” absorption bands (Eigenfärbung). In the second maximum we are evidently dealing with completely different “coloring” centers, which arise in the crystal during the coloring process. Postponing the elucidation of their nature until one of the following sections, we shall dwell on certain details of the coloring process, namely on the dependence of the degree of coloring on the duration of illumination and on the intensity of the light.

Fig. 2.

In all salts the coloring proceeds in the same way: the absorption coefficient, which numerically characterizes the degree of coloring, at first increases proportionally to the absorbed energy, but then gradually approaches a certain greatest value (the saturation state). In Fig. 3 a series of typical coloring curves is given (for rock salt colored by radium), expressing, for three different intensities, the absorption as a function of time; it is easy to see that the dependence of the absorption on the intensity is expressed by a similar curve. However

the time factor and the intensity factor turn out to be non-equivalent—this is clearly seen if one writes out (from the data of Fig. 3) the values of the absorption coefficient for different intensities, but for one and the same amount of energy \(Jt\):

(here the intensity values are given in arbitrary units, whereas the time \(t\) is expressed in days).

Fig. 3.

We see that by increasing the intensity one can achieve a greater effect than by a corresponding increase in the illumination time, but finally here too a limiting state is reached, when no illumination, however strong and prolonged, is any longer able to increase the degree of coloration; the magnitude of this limiting absorption coefficient depends to a high degree on the individual characteristics of the crystals, on the quality of the crystal lattice.

Colored crystals retain their coloration in the dark for an indefinitely long time, whereas in the light, and also upon heating \((100—150^\circ)\), they become bleached more or less rapidly. This circumstance sometimes greatly complicates measurements.

coefficient of absorption, since the active radiations here too are those which are absorbed by the crystal (in the region of the second maximum). Fading is reflected in a change in the absorption curve, and this change may be of two kinds: in the first case the entire absorption curve is lowered and disappears—we have an irreversible process of discoloration; in the second case only the appearance of the absorption curve changes—the maximum is lowered and the long-wave portion is raised (Fig. 4). This change is temporary; the initial curve is restored—of course with a correction for discoloration—upon heating and under the action of long waves, i.e., of those which begin to be absorbed by the crystal in its new state (for the designation of this state, the Göttingen school has adopted the not entirely successful term “excitation”—Erregung). The quantitative relation between the two processes of discoloration and excitation is different in different crystals; excitation is most strongly expressed in natural crystals of rock salt, especially at low temperatures. At high temperatures it is not observed at all. This circumstance shows that here too, apparently, the quality of the lattice plays the primary role; imperfections of the lattice, as well as enhanced thermal motion, contribute not to the temporary but to the complete disappearance of the coloring centers.

Fig. 4.

The experimental material presented makes it possible to sketch the following schematic picture of the coloring process:

1. Absorption of energy in the region of the first ultraviolet maximum leads to the formation of coloring centers and to the appearance of the second maximum in the visible part.

2. Absorption of energy in the region of the second maximum leads: a) to bleaching of the crystal, i.e. to the complete disappearance of the coloring centers; b) to “excitation,” i.e. to a temporary transition of the coloring centers into some other state, accompanied by a rise of the long-wave (infrared) part of the curve.

3. Absorption of energy in the infrared part (in excited crystals) leads to the destruction of the “excitation” and to the restoration of the original form of the curve of the second maximum.

Quantum yield of an elementary photochemical process in a crystalline medium

A comparison of the experimental facts enumerated above shows that underlying all these phenomena is an elementary photochemical process in a crystalline medium. Thus the question of the mechanism of coloration enters into the circle of ideas of modern photochemistry, whose central point is the question of the applicability of Einstein’s law of quantum equivalence. According to this law, the absorption of one quantum of energy causes a photochemical reaction, the product of which is one center. As is known, in gaseous and liquid media, where photochemical reactions in most cases give rise to a whole series of side products, being chain reactions, this law is not fulfilled—we have reactions in which one quantum produces \(10^6\) centers (the reaction \(H_2 + Cl_2 = 2HCl\)); in other cases (the fading of dyes), conversely, the production of one center requires up to \(10^3\) quanta. It seemed probable, however, that in a crystalline medium, where exchange by reaction products is impeded, Einstein’s law is fulfilled in its pure form, and the quantum yield will be close to unity. In view of this, determination of the quantum yield in coloration, bleaching,

and excitation of salts represents a great achievement of Pohl’s school.

As is known, the quantum yield is the number of separated centers per one absorbed quantum of energy. The negligible concentration of coloring centers excludes the possibility of applying chemical methods; for determining their number the most suitable, although not ideal, method is the optical method, based on measurements of the absorption band of colored media. This method was applied by Pohl’s collaborator, Smakula;²˒⁵ we shall now turn to its exposition.

All theories of dispersion give a relation between the number of active centers \(N\) and the absorption coefficient \(K\); the simplest expression has the form:

\[ \frac{\nu Kc}{2} = N\frac{e^{2}}{m}\, \frac{hn^{2}}{(-n^{2}+n_{0}^{2})^{2}+h^{2}n^{2}} \tag{*} \]

and gives the form of the absorption curve as a function of the number of oscillations. As is easy to see, the maximum of this curve lies at \(n=n_{0}\); the corresponding value of the maximum absorption \(K_{0}\) can be obtained by substituting \(n_{0}\) for \(n\) in this equation:

\[ \frac{\nu K_{0}ch}{2} = N\frac{e^{2}}{m}. \tag{**} \]

Simple algebraic calculations show that \(h\) (the damping coefficient) gives us the width of the absorption band at the place where the absorption falls to half its maximum value (Halbwertsbreite); hence it follows that, in order to determine the number of coloring centers, it is necessary to have precise information about the absorption maximum causing the coloration—about the magnitude of the maximum absorption coefficient and about the width of the absorption band; these data are obtained by spectrophotometric measurements. All the other quantities entering into the formula have well-known constant values—thus, \(e^{2}\) and \(m\) are the known electronic constants, \(c\) is the speed of light; as for \(\nu\) (the refractive index of the medium), this quantity, as is known, varies very little, so that instead of \(\nu\) one may

be substituted its partial value for the maximum absorption \(\nu_0\). Formulas () and (*) were obtained by us from Drude’s theory; Smakula proceeded from Füchtbauer’s theory, which takes into account the influence of neighboring molecules, and therefore used a more complicated expression.

It must be noted, however, that both the one and the other formula should be applied with major limitations, to which T. P. Kravets drew attention in his time, namely:

1. The shape of the absorption bands of colored media departs very strongly from the theoretical one; in all probability, they are a superposition of many narrower bands, as a consequence of which the width of the overall absorption band can in no way characterize the damping \(h\) entering into the formula.

2. The theory on which the formula is based does not take into account the influence of other electrons present in the atom and the bonds arising from them (Koppelungen), the presence of which quantitatively changes the band (raises or lowers it).

3. The theory also does not take into account the influence of the solvent molecules, in the present case the surrounding crystal lattice. Füchtbauer’s attempt, and Smakula’s equivalent derivation, proceeding from an incorrectly applied Lorentz–Planck formula, must be recognized as insufficiently justified.

4. At the present time an even more important consideration is being advanced—the complete incompatibility of the ideas of the classical oscillation theory with modern quantum views. Unfortunately, the latter have not served for the development of a scheme necessary for considering the case of interest to us.

Nevertheless, there can be no doubt that the order of magnitude of \(N \dfrac{e^2}{m}\) will be given correctly by formula (**); one should simply not attach credence to the exact values of the quantities obtained from it.

Knowing the magnitude \(N \dfrac{e^2}{m}\), and hence also \(N\), one can have su-

judgment about the concentration of coloring centers at one or another degree of coloring, and two circumstances should be taken into account: first, we must be sure that the coloring centers are distributed uniformly throughout the entire thickness of the crystal—this is easily achieved when coloring with X-rays or gamma rays, but certain difficulties are encountered when illumination is by ultraviolet rays, which, as we have seen, are wholly absorbed already in a thin surface film. In this case one has to use such wavelengths as could penetrate through the entire thickness of the crystal. The second limitation is dictated by the fact of the dependence of the absorption coefficient—and consequently also of the concentration—on the quality of the crystal lattice; it is obvious that the properties of different salts can be compared with one another only at such exposures for which the absorption coefficient is still proportional to the exposure, and the individual peculiarities of the crystals have not yet come to the fore.

In all the work of Pohl and his collaborators both these circumstances were taken into account: in coloring the crystals they used exclusively the long-wave part of the intrinsic absorption curve of the crystals, where the absorption coefficient is still not very large; furthermore, they worked at concentrations that were still far from limiting values.

Under observance of these conditions an interesting result was obtained: at one and the same intensity of the incident light (of the order of \(10^{-18}\)—\(10^{-14}\) quanta per \(1\ \mathrm{cm}^{2}\) per sec.), all salts become colored approximately equally, the absorption coefficient at the maximum being of the order of \(10^{-1}\ \mathrm{mm}^{-1}\), which corresponds to a concentration of the order of \(10^{-7}\). The concentration values for different salts are given in Table 1.

Since the number of centers produced is proportional to the absorption coefficient \(K\), this table can also be used for other degrees of coloring. Thus, one can calculate the limiting concentration, for example for the yellow

Table 1.

of rock salt, for which the maximum absorption coefficient attained so far has a value of about \(2\ \mathrm{mm}^{-1}\); as we see, even for the most strongly colored dark-brown NaCl crystals it does not exceed \(3 \cdot 10^{-6}\).

The determination of the number of absorbed quanta \(Q\), necessary for calculating the quantum yield \(N/Q\), presents no fundamental difficulties: the incident energy is measured by means of a thermoelement and is expressed in watts per \(\mathrm{cm}^2\) and in quanta per \(\mathrm{cm}^2\) per sec., with the loss by reflection being taken into account; knowing the absorption coefficient for the given wavelength and the thickness of the crystal, one can calculate the number of quanta absorbed in the given specimen. It should be borne in mind, however, that correct values for the quantum yield will be obtained only in the case where the number of centers produced is proportional to the number of quanta absorbed, which, as we have seen, is observed only at small concentrations. In his latest work Smakula\(^5\) took this circumstance into account; plotting, for each intensity of the incident light, the complete coloration curve (Fig. 3), he took from it only those points which still lay on the rectilinear portion of the curve. Thus he had to work at very weak

colorations—\(K_0\) did not exceed \(0.02\) mm—which could not have affected the accuracy of the results.

In a similar way, by illuminating an already colored crystal with rays from the region of the second maximum and measuring the decrease of the absorption coefficient, Smakula was able to determine the number of centers that “fell out” during bleaching, and to calculate the quantum yield for this case as well.

The values of the quantum yield for various salts, both for coloration and for bleaching, are given in Table 2. As can be seen, all the numbers are so close to unity that there can be no doubt that the deviations from this value are explained only by errors of the method.

Table 2.

Thus it must be acknowledged that in the present case we are dealing with the application of Einstein’s law in its pure form, and it may be formulated in the form of the following two propositions:

1. The absorption of one quantum in the region of the first (ultraviolet) maximum leads to the liberation of one coloring center.

1. The absorption of a single quantum in the region of the second maximum leads to the disappearance (complete or temporary) of one color center.

Electrical Properties of Crystals of Alkali-Halide Salts

Colored salts are practically insulators in the dark; when they are illuminated by rays of the visible spectrum, their electrical conductivity increases many times over, and they begin to conduct current appreciably. The change in electrical conductivity under illumination is a phenomenon inherent in many semiconductors and insulators and has long been known—it is enough to note the extensive literature devoted to the electrical conductivity of selenium. But whereas in semiconductors the primary process of the appearance of an electric current under illumination is masked by a whole series of secondary phenomena, in large crystals of good insulators, such as, for example, alkali-halide salts, the phenomenon can be resolved into separate components, and the primary process isolated in pure form. Indeed, the physical nature of the change in electrical conductivity under illumination began to be clarified only after Gudden and Pohl⁷ subjected to systematic study the process of the passage of electric current in crystals of diamond and ZnS, and then in colored salts (it should be noted that the point of departure for work in this direction was the study by Röntgen and Joffe⁸ of the electrical conductivity of yellow rock salt).

From the extensive experimental material accumulated by the Göttingen school, we single out only a few of the most thoroughly developed points that are of direct importance for clarifying the physical nature of the phenomenon; of these the most essential is the following proposition: only those radiations which are absorbed by the given crystal prove to be active radiations, producing a change in the electrical conductivity of the crystals. This circumstance, quite

...which is understandable from the energetic point of view, reveals the photoelectric essence of the phenomenon: at the basis of all the processes there evidently lies the phenomenon of the internal photoelectric effect, in which quanta of the absorbed energy tear electrons away inside the crystal. Under the action of the electric field these photoelectrons begin to move from the cathode to the anode and give a photoelectric current in the external circuit.

Without yet raising the question of where exactly inside the crystal the electrons are torn away, let us note that, in accordance with this view, we must expect the appearance of a photoelectric current upon illumination both by rays of the ultraviolet region (the “proper” absorption of crystals) and by rays of the region of the second maximum in the visible part of the spectrum. Indeed, in the majority of the substances investigated the photoelectric current has been found precisely in the region of the first maximum; besides the already mentioned diamond and ZnS, where the photocurrent was first studied in pure form, we must note the silver salts of special interest to us—AgBr and AgCl. In the halide salts of the alkali metals, in the region of the first absorption maximum, which lies in the far ultraviolet part of the spectrum and has only recently been investigated, the internal photoelectric effect has not yet been detected; but in the region of the 2nd maximum it has been studied in considerable detail by Gudden and Pohl,¹ who succeeded in resolving the phenomenon into separate phases. The first phase consists in the motion of the photoelectrons torn away by the light—this is the “negative part of the primary photoelectric current.” As the photoelectrons are carried off into the external circuit, positive charges are formed inside the crystal; the deficiency of electrons may be made up by an influx of new electrons from the cathode; thus there arises the “positive part of the primary photoelectric current,” which is sometimes superposed on the negative part and sometimes, as occurs for example in rock salt, may be separated from it. This “replacement” current arises either upon heating an unilluminated crystal or upon its illumination by long waves; this latter circumstance points to its closest connection with the phenomenon of “excitation.” The acti-

Thus, we have already seen that the excitation is destroyed by those wavelengths which begin to be absorbed by the crystal in its excited state; parallel with this there is a fall of the “substitution” current, which ceases altogether, evidently, when the deficiency of electrons has been made up. Thus proceeds, according to Gudden and Pohl, the primary photoelectric process; usually it is complicated by a whole series of secondary phenomena, which we shall not touch upon here at all. For us only the primary current is of interest (more precisely—its negative part); Gudden and Pohl established the following properties of it:

1. The strength of the primary current at first increases in direct proportion to the applied voltage, but then reaches a certain constant value (“saturation current”). The magnitude of the voltage at which this state is reached depends on the thickness of the crystal (being directly proportional to the square of its thickness), and also on the individual features of the crystal lattice. Thus, in plates of diamond or ZnS about 15 mm thick, the saturation current is observed already at a voltage of about 1,000 V/cm, whereas in rock salt it was obtained by Flechsig^10 only for very thin plates about 0.1 mm thick at voltages of the order of 50,000 V/cm.

This circumstance indicates that the electrons torn out by light are capable of passing only short distances inside the crystal, as a result of which not all of them reach the cathode. The greater the applied voltage, the greater the path length; and the greater the number of electrons that appear in the photoelectric current. Finally, the paths of the electrons become comparable with the thickness of the crystal—only then do all the electrons torn out by light reach the anode, and the current strength ceases to increase. The different behavior of diamond and NaCl crystals indicates that the magnitude of the free path of the electrons inside these crystals is different; according to Joffé’s calculations,^12 the path of an electron in a rock-salt crystal at a voltage of about 2,000 V/cm is of the order of 1/3000 mm.

1. The primary current is established instantaneously upon switching—

of illumination and likewise disappears instantly when it is discontinued, which is direct proof of its photoelectric nature. The interval of time between the beginning of illumination and the appearance of the current does not exceed (for NaCl) \(10^{-4}\) sec., i.e. it is of the same order as the inertia of the instrument.

1. Both of the above-mentioned properties of the primary current point quite definitely to the quantum character of the process by which the primary current arises; quantitative confirmation is obtained by comparing the strength of the primary photocurrent \(i\) with the amount of absorbed energy \(Q\).

Let \(n_1\) denote the number of absorbed quanta, and \(n_2\) the number of photoelectrons that have reached the anode. Then we have:

\[ Q = n_1 h\nu, \]

\[ i = n_2 e, \]

where \(e\) is the charge of the electron.

It follows from this that

\[ \frac{i}{Q}=\frac{n_2}{n_1}\frac{e\lambda}{hc}, \tag{***} \]

in other words, the strength of the photocurrent, referred to unit of absorbed energy, increases linearly with the wavelength \(\lambda=\frac{c}{\nu}\).

In the case when all the electrons torn away by the light reach the anode (when \(i\) is the saturation current), the ratio \(\frac{n_2}{n_1}\) gives directly the number of photoelectrons per quantum of absorbed energy, i.e. the magnitude of the quantum yield for the photoelectric process. An experimental verification of these propositions was carried out by Gudden and Pohl¹¹ for diamond and Djulaj, and also by A. N. Arsen’eva¹² for yellow rock salt; in Fig. 5, according to Djulaj’s data, two curves are given, showing the spectral distribution of the photocurrent (curve \(e\)) and of the absorbed energy (curve \(a\)) for an unexcited crystal of yellow rock salt. The curves, as we see, almost coincide; the slight displacement of one curve relative to the other points to the quantum character of the phenomenon—if the values of the absorbed energy were expressed

in quanta, the agreement would apparently be complete. The very fact of the parallelism of the curves confirms the correctness of expression (3); this is still more clearly seen from Fig. 6, on which, for each wavelength, the values of \(\frac{i}{Q}\), obtained from the data of Fig. 5, are plotted. As we see, the dependence of \(\frac{i}{Q}\) on wavelength is indeed expressed by a straight line; the same result was also obtained by Gudden and Pohl. Since, unlike Joffé, they worked with saturation currents, they were able to use their data for calculating the quantum yield and obtained that the ratio \(\frac{n_2}{n_1}\) is very close to unity (0.962 for diamond and 0.935 for ZnS); this means that each absorbed quantum tears off one electron. Thus it may be formu-

Fig. 5.

Fig. 6.

realized the second part of Einstein’s law, relating to the photoelectric process in a crystalline medium; as we see, in this realm of phenomena too it is fully justified.

The Nature of Color Centers

A comparison of the photochemical and photoelectric phenomena described above leads quite naturally to that picture of the elementary photochemical process in a crystalline medium which, in schematic outline, was sketched by Fajans as early as 1921 and subsequently received its confirmation and development in the work of the Göttingen school. First of all, it appears quite clear that, in the coloration of salts by the photochemical method, there can be no question of any foreign impurities penetrating into the salt from outside during its coloration; the color centers must arise within the salt itself, from elements of the crystal lattice. Any attempts to investigate these centers by chemical methods must encounter insurmountable difficulties; indeed, as we have already seen, their concentration is extremely small \((10^{-7})\), and they themselves are so minute that they cannot be detected even with an ultramicroscope (the colored salts appear optically empty).

The process of formation of color centers from elements of the crystal lattice becomes, however, perfectly clear if we combine into one proposition both formulations of Einstein’s law relating to the photochemical and photoelectric aspects of the phenomenon: each quantum absorbed in the region of the first maximum tears off one electron and liberates one color center.

This proposition places the phenomenon of the internal photoelectric effect at the center of all the processes; the question of whence the tearing off of electrons occurs should present no difficulty: it is most natural to suppose that they will be torn from the negatively charged halide ions, containing

an excess valence electron. The detached electrons, which in an external electric field can manifest themselves as a photoelectric current, are among a large number of positive ions; as we have seen, they are able to travel only short distances inside the crystal—therefore the probability is very great that the “photoelectron” that has been torn off will be attracted more or less quickly to one of the positive metal ions and neutralize it. The fact that, in the coloration of salts, the quantum yield is equal to unity shows that, at least at the beginning of the process, all the detached electrons settle on the corresponding ions.

As a result of this process, which is accompanied by luminescence, neutral atoms of the metal and of the halide appear in the crystal. The generally accepted view that the coloration of crystals is caused by atoms of the metal, and not of the halide, is confirmed by the fact that crystals colored by the additive method, i.e. known in advance to contain only metal atoms, in all their properties, both optical and photoelectric, do not differ in any way from crystals colored photochemically.

As for the atoms of the halide, they do not reveal themselves optically—possibly because their absorption lies in the region of the “intrinsic” absorption of the crystals—and thus they fall outside our consideration; we may concentrate our attention only on the atomically dispersed metal.

As has already been mentioned, the concentration of coloring centers, i.e. metal atoms, depends to a high degree on the quality of the lattice; thus, melted or deformed crystals are colored much more strongly; the presence of foreign ions has a similar effect. At present it may be regarded as established that no artificial crystal, grown—whether from the melt or from solution—with the purest starting materials available to chemical technique, can compare in purity with natural crystals, in which, during their long growth, all impurities were probably concen-

were concentrated in separate regions. And indeed, with natural crystals it is never possible to obtain the same degree of coloration as with artificial crystals, where, even in the case of the greatest purity, there is still one foreign ion for every thirty lattice elements.

All these facts compel Pohl to put forward the supposition that a necessary condition for the atoms of the metal to be able to separate out at all inside the crystal is an imperfection of the crystal lattice; an ideal crystal could not be colored at all. There exist certain additional conditions for the stabilization of atoms within the lattice, which in each individual case cause a certain quite definite limiting concentration. What they consist in, we do not yet know.

The atoms that have separated out inside the lattice are connected with the other elements of the lattice by some forces not yet clarified, and therefore must cause a change in all its properties. The change in the optical properties is manifested in the appearance of a new absorption maximum, usually in the visible part of the spectrum; we may therefore speak of the absorption spectrum of an atomically distributed metal.

The absorption of quanta of light by neutral atoms again produces an internal photoelectric effect, but now with the atoms of the metal, which become charged (positively), i.e. are ionized, and thereby cease to be coloring centers. If the detached electron returns to the neutralized halide atom, the original state of the lattice will be restored and complete decoloration will take place; according to the views of the Pohl school, the electron may also fail to reach the halide atom and may “get stuck” somewhere in the lattice, thereby altering its internal potential—the crystal is “excited”—which is expressed in a change of the absorption curve (Fig. 4). As we already know, the initial curve can be restored by heating or by illumination with long waves; obviously, in these cases a “shaking” of the lattice occurs and the trapped electrons are released, returning to the atoms of the metal (the question of whether

which particular electrons undergo this repeated neutralization is of no significance; thus, in the case when an external voltage is applied to the crystal, the freed electrons are carried to the anode, and their place in the metal atoms is taken by new electrons, which pass from the cathode and give a “positive” current. What is most essential here is the evident connection with the phenomenon of phosphorescence (the term “excitation” is also taken from this field); indeed, as is known, a necessary prerequisite for the luminescence of crystals is the return to their places of electrons that have become trapped somewhere in the lattice.

This circumstance is of great theoretical interest for elucidating the photoelectric nature of phosphorescence. It is clear that all quantitative calculations are easier to carry out on large optically pure crystals, for example NaCl, than on the fine-crystalline powders of Lenard phosphors. Indeed, as has turned out, colored salts possess all the properties of typical crystalline phosphors and give luminescence both upon bleaching and upon the destruction of excitation (“Ausleuchtung”); but, unfortunately, their yield (Nutzeffekt) is extremely small, which considerably hampers investigation. As a result, the numerous works of both the Göttingen school and the school of Shibbram in Vienna¹³ still have a qualitative character and cannot contribute to a complete clarification of the picture. In view of this, we too shall have to confine ourselves to what has been set forth above, especially since, in the silver salts of special interest to us, neither excitation nor, so far as we know, luminescence has yet been observed.

Such, in general outline, is the picture of the elementary photochemical process, embracing into a single whole such seemingly heterogeneous phenomena as the internal photoeffect, absorption of light, and phosphorescence. Many facts from the extensive experimental material accumulated by the Göttingen school find in it their natural explanation, but much still remains subject to further investigation. It should be noted that the chain of work of the Göttingen school, encompassing the entire complex of the phenomena listed above,

of investigations, is not only far from completion but, on the contrary, is entering its most fruitful phase of quantitative interpretation of the experimental material. Calculations of the quantum yield, as we have seen, have done very much to confirm the schematic picture; next in line is the accounting of those forces which act within the lattice and cause one or another distribution of the neutralized metal atoms. It is to be hoped that work being carried out in this direction will clarify the existing ambiguities and make it possible to determine the nature of the photochemical process in all its details.

Colloidal distribution of the metal

As a result of the elementary photochemical process in a crystalline medium there appear, as we have seen, neutral atoms of the metal. Atomic dispersion, however, is not the only possible mode of distribution of the metal inside the crystal; a priori one may assume the possibility of the formation of coarser complexes, up to colloidal particles with an entirely different absorption spectrum. Indeed, long before yellow rock salt, a naturally colored blue rock salt was known, which is usually encountered in potassium deposits in the form of separate crystals up to \(100\ \mathrm{cm}^3\) in volume, colored very unevenly dark blue, and sometimes also violet. This coloration has long been a puzzle for mineralogists, since it was established by sufficiently precise chemical methods that it cannot be attributed to any impurities or contaminations. However, already Siedentopf,\(^{16}\) the first to apply the method of additive coloration, observed that crystals of rock salt impregnated with sodium exhibit, in addition to yellow, also blue and violet coloration, very strongly reminiscent of the coloration of natural salt. Later Pohl\(^{15}\) showed that similar colors, although less bright, can also be obtained photochemically, by appropriate treatment of yellow salt. Thus, compressed

yellow salt turns blue in the light, and upon subsequent heating acquires a violet hue. The same violet color can also be obtained without any deformation by simultaneous heating and illumination of the crystal (apparently what is essential in this case is the combined action of both factors, each of which, taken separately, causes decoloration). These facts have long already led to the thought that in all these cases we have one and the same cause of coloration, and the circumstance that blue and violet salts exhibit, under lateral illumination, the Tyndall effect, while additively colored blue salt opalesces very strongly, indicated that here, in all probability, we are dealing with colloidally distributed sodium.

The next task was a quantitative verification of this supposition, and this was carried out by the author of the present article. In this case the conditions were more favorable than in the coloration by atomically distributed metal,—whereas there we do not have, even now, any data for precomputing the course of the absorption curve, here there is available the theory of the optics of colloidally distributed metals, fully developed by T. Mie16 and Maxwell-Garnett.17 This theory makes it possible, knowing the optical constants of the metal and of the solvent, to calculate the course of the absorption and scattering curves of colloidal systems. Mie developed this theory as applied to colloidal solutions of gold in water, which, as is known, are distinguished by a bright and variable coloration (red, purple, and blue colloidal gold); his results were brilliantly confirmed by Steubing,18 the absorption curves measured by the latter fully coinciding with the curves calculated by Mie.

This circumstance suggested to us the idea of applying Mie’s calculations to the system Na·NaCl.19 We obtained, for particles of equal size, a series of absorption curves, and, on the other hand, we checked spectrophotometrically the absorption curves of differently colored specimens of rock salt, using both natural and artificially …

artificially (by various methods) colored crystals. The theoretical absorption curves are shown in Fig. 7; it turns out that the position and width of the absorption curve depend quite strongly on the diameter of the particles. Looking at the figure, one may say in advance that the largest particles, which give absorption in the red part of the spectrum, will cause a blue coloration of the crystal, the medium-sized particles—a violet coloration,

Fig. 7.

and the smallest—a red coloration. Indeed, all these shades could be observed experimentally; especially bright colors are obtained when additively colored crystals are heated. Here it is possible, by selecting suitable conditions of heating and especially of cooling, to obtain repeatedly on one and the same crystal first a red, then a blue, and finally a yellow coloration; evidently, we are dealing now with the enlargement of particles, now with their disintegration into smaller complexes, down to fragmentation into individual atoms.

We have a similar phenomenon also in naturally colored blue salt, which on heating to \(200^\circ\) becomes violet, and at a higher temperature (above \(360^\circ\)) acquires a red shade. The absorption of differently colored crystals of rock salt was meas-

measured on a König–Martens spectrophotometer. In Fig. 8 the curves are given for naturally colored salt; they refer to different specimens, and therefore the absorption coefficients are given in arbitrary units. Curves III and IV refer to heated crystals, while curves I and II give absorption measurements in unheated blue specimens, in which, generally speaking, all intermediate positions of the absorption maximum from 650 to 620 mμ could be observed.

Fig. 8.

As is seen from a comparison of the theoretical and experimental curves (Figs. 7 and 8), a great similarity is observed between them. Both sets cover the same spectral region; in both cases a continuous displacement of the absorption maximum toward shorter waves is observed with a gradual decrease of the curves (the similarity is disturbed only by the fact that in the experimental curves a subsidiary maximum is observed at 525 mμ, not predicted by Mie theory in its simplest form). The most extreme position of the maximum (toward the short-wave side) was obtained for additively colored salt at 550 mμ, while the maximum of the theoretical curve for the smallest sodium particles, according to the calculations, lies at 555–540 mμ. This agreement of the theoretical and experimental results not only con-

confirms the hypothesis of the colloidal nature of the coloration of rock salt, but also makes it possible to judge the diameter of the particles that produce one coloration or another; the approximate data are as follows:

The circumstance that infinitely small colloidal particles possess a very sharply expressed absorption might lead to the quite natural thought that here we are already approaching an atomic distribution of sodium, which may be regarded as a limiting case of the colloidal one. This supposition, however, is based on a misunderstanding: Mie’s theory is applicable only to sufficiently massive particles, whose optical constants do not yet differ from the optical constants of the continuous metal. Thus those “infinitely small” particles of which we spoke above must consist of at least hundreds of individual atoms. The optical properties of particles which, in their dimensions, occupy an intermediate position between the aforementioned colloidal particles and individual atoms, and which produce a yellow coloration, cannot be calculated by Mie’s theory; at present we also have no other theoretical means for precomputing the absorption maxima corresponding to them. On the basis of experimental data, however, we may assert that, in optical respect, there is no continuous transition between individual atoms embedded in the crystal and “infinitely small” colloidal complexes consisting of hundreds and thousands of atoms; never, under any conditions, has it yet been possible to detect absorption in the spectral region from 550 mμ (red salt) to 462 mμ (yellow salt). This is especially sharply noticeable in

additively colored crystals, where very often the “red” and “yellow” maxima coexist, but without any intermediate transitions.

Colloidal coloration has so far been studied only in rock salt; there is every reason to expect that in other alkali-halide salts the colloidal distribution of the metal will be observed on a par with the atomic one. As the author’s preliminary investigations have shown, visible coloring can be expected only for sodium salts; calculation shows that for potassium, whose optical constants have a value different from those for sodium, the entire system of absorption curves is shifted into the infrared region. Indeed, in KCl and KBr impregnated with potassium, absorption maxima around 700–800 mμ could be found.

The photochemical process in silver salts

The silver halide salts, as is known, are in their structure very close to the alkali-halide salts just discussed; X-ray analysis has shown that silver chloride and silver bromide, both in pure form and in emulsion grains, have the structure of a space cubic lattice of the NaCl type, with constant \(=5.78\ \text{Å}\) (the constant of NaCl is \(5.629\ \text{Å}\)).

Therefore there is every reason to suppose that all phenomena which accompany the absorption of light quanta in the crystal lattice, and which also constitute the essence of the photographic process in its primary stage, will proceed in the silver halide salts in exactly the same way as in the alkali-halide salts.

The idea that the latent image in a photographic plate and the yellow coloration of rock salt are essentially one and the same phenomenon was emphasized as early as 1896 by Goldstein, and then, in a more developed form, was expressed in 1921 by Sheppard and Trivelli \(^{20}\) and, independently of them, by Fajans \(^{21}\) (the above schematic picture of the photo-

chemical process was sketched by him precisely for silver salts). But at that time there were as yet no experimental data that could confirm its correctness; the chief difficulty lay in the fact that investigators working with prepared photographic emulsions had to take into account a whole series of secondary processes, which occur in gelatin and completely mask the primary process. The only correct path, and the one that led to the desired results, was the transition from emulsions to separate crystals of silver chloride and bromide. In contrast to the halide salts of the alkali metals, in which good crystals are obtained only with great difficulty, by many hours of slow cooling (for example, Kirpichev),²² the preparation of crystals of silver chloride and bromide presents no difficulty. These crystals are distinguished by their plasticity, as a result of which even rapid cooling does not cause strong cracking; they can be cut, bent, and rolled into a tube; finally, since the melting point is comparatively low—about 400°—films of any thickness, down to a few microns, can be obtained by melting the salt between quartz or glass plates.

Optical properties of the silver halide salts

Pohl and Hilsch, extending to silver salts their optical investigations of colored salts, measured the curve of “proper” absorption in very thin films of silver bromide and chloride. These curves are given in the left part of Fig. 1; in its upper part, for comparison, the curve for KJ is given. We see that in both cases the curve has the same character and represents a very complex band; the difference consists in the fact that in silver salts the separate maxima are barely distinguishable even at low temperature (−186°). For silver bromide the absorption extends into the visible part of the spectrum,

which causes the lemon-yellow coloration of the crystals; this also explains the sensitivity of silver-bromide plates to the blue rays of the spectrum. As in the alkali-halide salts, the absorption coefficient is very large and at its maximum reaches values of the order of \(10^6\ \mathrm{mm}^{-1}\). For silver bromide, appreciable absorption is observed even at \(475\,m\mu\) \((K = 1.17\ \mathrm{mm}^{-1})\); already at \(400\,m\mu\) almost all the energy—99%—is absorbed in a layer about \(2\mu\) thick.

The thickness of the active layer of a silver-bromide emulsion is of the order of \(2.5\mu\); thus the wavelength region around \(400\,m\mu\) is the limiting one at which the rays of light penetrate through the entire thickness of the photosensitive layer; at smaller wavelengths only the surface film is active.

Internal Photoeffect

The change in the electrical conductivity of silver salts upon illumination was discovered already by Arrhenius\(^{23}\) and studied by Koblenz;\(^{24}\) the photoelectric nature of the phenomenon was, however, called into question: the current was observed only in a narrow region of the spectrum, around \(460\,m\mu\), whereas the ultraviolet rays, the most active in the photographic sense, produced no effect. The most detailed investigations of this phenomenon have been carried out only very recently, on the one hand, by Toy\(^{25}\) in the physical department of the British Photographic Research Association, and on the other—by E. A. Kirillov at the Odessa Physical Institute. Using films several microns thick, Toy proved that the discrepancy between the absorption and photocurrent curves, observed by Koblenz and other investigators, is only apparent, since it is caused by the sharp increase of absorption in the ultraviolet region; in the case when absorption occurs throughout the whole thickness of the film, a complete parallelism of the two curves is observed, which fully confirms the quantum character of the phenomenon. By varying the intensity of the incident light (the blue mercury line 4358), Toy, in collab-

in collaboration with Garrison[^27] found that the strength of the photocurrent is exactly proportional to the amount of incident energy; unfortunately, the authors did not convert this to absorbed energy, and therefore could not calculate the quantum yield. Carrying out further investigations of the photocurrent, Toy and Garrison showed, by means of a very ingenious method, that the photocurrent in silver bromide films arises and ceases instantaneously when the illumination is switched on and off. In Fig. 9 a cinematographic record is presented of the deflection of a galvanometer connected into the circuit of the crystal; the vertical stripes are time marks, each interval corresponding to 0.01 sec. The illumination in this case lasted 0.08 sec., and the inertia of the shutter was 0.001 sec. In this figure it is quite clearly seen that the time of rise and disappearance of the current does not exceed 0.005 sec.; taking into account the inertia of the shutter and of the galvanometer, it must be recognized that here too, as in the external photoeffect, the detachment of the electron occurs simultaneously with the beginning of illumination. A similar picture is also observed for exposures down to 0.0005 sec.; this circumstance is of great interest for elucidating the nature of the photographic process, since here we enter the region of normal photographic exposures.

Fig. 9.

Liberation of halide

The internal photoeffect, i.e. the detachment of an electron from a halide atom, is the primary stage of the photochemical process; as a result of it, as we have seen, neutral ... must be liberated inside the crystal lattice.

halide atoms, and then the metal. In setting forth the processes occurring in the salts of the alkali metals, we did not touch at all upon the halide atoms, since optically they do not manifest themselves, and no other experiments with these salts had been carried out.

In the silver halide salts the matter is somewhat different: here we have a number of observations on which it is worth dwelling. First of all, we must note the experiments of P. P. Koch and Kreiss,^28 who weighed the smallest grains of silver chloride and bromide in a very ingenious way, using the well-known Millikan condenser, and found that under intense illumination they can lose up to 25% of their weight. A similar result was also obtained by Hartung,^29 who weighed thin films of silver halide salts on ordinary microbalances. What is interesting in his results is that the weight is restored if the film is placed in an atmosphere of the halide, which undoubtedly indicates the liberation of chlorine or bromine atoms. Indeed, Fogel^30 had already shown by a very simple experiment that, upon illumination of silver bromide, bromine is liberated; this circumstance has found confirmation in a number of experiments by various authors, who employed the most diverse methods of investigation. Among the most recent experiments in this direction one should dwell on the experiments of Vanzelov and Sheppard,^31 who studied the appearance of a potential difference at the electrodes of so-called Becquerel photoelements. This phenomenon was discovered by Becquerel as early as 1868. He immersed in an electrolyte containing iodine ions two completely identical silver electrodes coated with a layer of silver iodide, and found that, when one of them was illuminated, a potential difference appeared between them. Vanzelov and Sheppard replaced the silver iodide by silver bromide and discovered an interesting fact: upon illumination of one of the electrodes, at first (after \(1/600\) sec.) the electrode becomes negatively charged, but after a short time (within 1 sec.) it changes sign to the opposite one. The authors explain this phenomenon by the external photoelectric effect in the surface layer of silver bromide: illu-

excited electrons have so much energy that they can overcome the contact potential difference, emerge outside, pass to the silver electrode, and charge it negatively. In the surface layer of the crystal there remain unchanged silver ions and neutralized bromine atoms, which after a certain time also reach the electrode, recombine with silver atoms, taking from them the missing valence electron, and thereby produce a positive charge. Vanselow and Sheppard confirm this picture by two vivid experiments: they surround the illuminated electrode with a substance that absorbs bromine, and find that in this case the positive charge disappears. Further, they add bromine to the electrolyte near one of the electrodes; diffusing through the layer of silver bromide, the bromine reaches the silver electrode and charges it positively—the potential difference in this case is observed without any illumination. The negative phase of the phenomenon is then absent, while the magnitude of the positive charge varies depending on the concentration of bromine in the solution.

All these experiments quite clearly indicate that, upon illumination of halide salts, a free halogen is liberated. In the primary stage of the photographic process, halogen atoms play only a secondary role, manifesting themselves chiefly in the subsequent stages of the process, which proceed in the presence of gelatin and other “bromine acceptors”; but for clarifying the general picture of the photochemical process, the very fact of their liberation is of great significance: it confirms our conception that the quanta of absorbed light tear electrons precisely from the halogen ions (true, in the experiments of Vanselow and Sheppard we are dealing not with the internal photoelectric effect, but with the external one; nevertheless, since both these phenomena are caused by the same cause, we may consider that these results confirm the correctness of our picture).

M. V. SAVOSTIANOVA

Atomic distribution of silver and the nature of the latent image

Thus, according to what has been set forth above, the absorption of light in silver chloride and silver bromide entails the appearance, within the crystals, of neutral silver atoms. We thus arrive at a completely natural conception of the nature of the latent image: it is formed by atomically dispersed silver, separated out in the illuminated places of the photographic plate.

The study of the properties of the photographic image is thus reduced to the study of the properties of atomically dispersed silver; here, in the first place, one should set the study of its spectrum (the second absorption maximum), which may be called the spectrum of the latent image. In view of this, the very first optical investigations carried out on individual crystals of silver salts by Hilsh and Pohl, as well as by the author of the present article (32), were undertaken with the aim of finding and measuring this maximum. Indeed, it turned out that lemon-yellow crystals of silver bromide turn green in the light, which indicates the appearance of absorption in the red part of the spectrum. A similar phenomenon was also found for crystals of silver chloride, which, from being colorless, become violet, and also for thallium chloride. The absorption curves of exposed crystals of AgBr and AgCl (the second maximum), measured by Hilsh and Pohl, are given in the right-hand part of Fig. 1 (p. 454); as we see, they have the same character as the absorption curves of colored alkali-halide salts (the upper part of Fig. 1). The similarity extends also to the very process of coloration: here too the concentration of separated atoms increases out of proportion to the number of absorbed quanta, reaching a certain limiting value.

Pursuing further the analogy with the alkali-halide salts, one should expect that in exposed crystals, upon absorption of light from the region of the second maximum, a photoelectric current will be detected. Indeed—

Indeed, Kirillov,^26 who investigated the electrical conductivity of fine-grained layers of silver bromide and silver chloride, found that, upon illumination of these salts in the visible part of the spectrum, a second maximum of the photocurrent appears. A similar result was also obtained by Mazaki,^33 who worked with thin films of silver bromide. According to the data of the authors mentioned, the position of the second maximum of the photocurrent does not coincide with the position of the second maximum of absorption; thus, according to Hilsch and Pohl, for silver bromide the absorption maximum lies at 690 mμ, whereas the photocurrent maximum was found by Mazaki at 520 mμ, and by Kirillov at 572 mμ. A similar discrepancy—550 mμ for absorption and 510 mμ for the photocurrent—is also observed for AgCl. Apparently, however, this disagreement is only apparent, and may be explained by the fact that precisely in this region of the spectrum we have a superposition of the absorption curves and, consequently, of the photocurrent curves of the first and second maxima. In this case, from purely geometrical considerations, the weak second maximum must be shifted toward the stronger first maximum, i.e., toward shorter waves. By subtracting the action of the second maximum, one can isolate the phenomenon, as was done by Hilsch and Pohl in measurements of absorption; one should, however, take into account the fact that the silver halide salts are not perfect insulators, but apparently also possess ionic conductivity. This circumstance gives rise to a number of complicating effects, one of which (the negative photoeffect) has been investigated in detail by Kirillov;^34 we shall not touch upon them here; let us only note that they, in turn, may strongly mask the weak photoeffect from atomically distributed silver and make its study difficult.

All these data speak in favor of the atomic theory of the latent image just set forth; quantitative confirmation is obtained by calculating the concentration and the quantum yield both in individual crystals and in the finished emulsion. In this calculation one must bear in mind the same precautions-

by the difficulty in selecting the coloring wavelength and duration of illumination, which we have already encountered when comparing the properties of different crystals (see above, p. 461). All these circumstances were taken into account by Hilsh and Pohl, who, using the Smakula method, determined the concentration and quantum yield in colored crystals of silver chloride and silver bromide. They found that, for an absorption coefficient of \(0.017\ \mathrm{mm}^{-1}\), the concentration of silver atoms is \(0.5 \cdot 10^{-7}\), while the quantum yield has the value \(0.4\) for \(\mathrm{AgCl}\) and \(0.33\) for \(\mathrm{AgBr}\), i.e. it is very close to unity. These experiments are interesting not only because they give numbers of the same order as those obtained under the same conditions for alkali-halide salts; their chief significance lies in the fact that, for the first time, the calculation is made in the region of normal photographic exposure; the corresponding concentration is obtained by Hilsh and Pohl as follows. One square centimeter of a layer of bromosilver emulsion, about \(20\ \mu\) thick, contains about \(1.6\ \mathrm{mg}\) of silver bromide, which, if uniformly distributed, would give a layer \(2.5\ \mu\) thick, with a total number of molecules \(5 \cdot 10^{18}\). With the intensity of the incident light of the order of \(2 \cdot 10^{13}\) quanta per \(\mathrm{cm}^{2}\) per sec, illumination with wavelength \(400\ \mathrm{m}\mu\) gives, on ordinary bromosilver plates, a normally developable latent image already in \(1/50\) sec.; assuming that all the incident energy is wholly absorbed in the grains of the emulsion (which is not quite true, since part of the energy is lost in the gelatin), we find that during this time \(4 \cdot 10^{11}\) quanta are absorbed in \(1\ \mathrm{cm}^{2}\) of the layer. Taking the quantum yield to be unity, we obtain for the concentration the value

\[ \frac{4 \cdot 10^{11}}{5 \cdot 10^{18}} \sim 10^{-7}. \]

Here it should be mentioned that the first attempt to determine the concentration and quantum yield in an emulsion belongs to Eggert and Noddack,\({}^{35}\) who used a direct chemical method for calculating these quantities: by fixing an exposed but undeveloped plate they removed the undecomposed silver bromide and then determined by titration the quantity

of the liberated undecomposed silver. They found thereby that, at exposures of the order of \(10^{16}\) quanta per \(1\ \mathrm{cm}^2\) of the layer of a silver-bromide emulsion, up to \(0.2\cdot 10^{16}\) atoms are liberated. Eggert and Noddack believe that, owing to losses in the gelatin (through absorption and scattering), only about \(20\%\) of the energy is absorbed in the active layer—and hence values of the quantum yield are obtained that are very close to unity. These results were subjected to sharp criticism by Weyert, \({}^{36}\) whose objections concerned both the fundamental* and the technical side of the work: he believes that in fact the losses in the gelatin are much smaller, so that actually up to \(80\%\) of the incident energy is absorbed in the active layer.

Against the results of Eggert and Noddack, however, one may advance an even more serious objection, concerning those limitations in calculating concentrations of which we have already spoken above. If the first condition, concerning the choice of a wavelength suitable for the thickness of the given crystal, may be considered fulfilled—Eggert and Noddack used such wavelengths (\(365\ \mathrm{m}\mu\), \(405\ \mathrm{m}\mu\), and \(465\ \mathrm{m}\mu\)), where the absorption is not yet very large—this cannot be said of the second limitation; indeed, the concentration in their experiments was of the order of

\[ \frac{2\cdot 10^{15}}{5\cdot 10^8}=4\cdot 10^{-4}, \]

i.e. it exceeded by almost a thousand times the concentration of a normal photographic image—which, as we have seen, is indicated by Polya’s school as optimal for quantitative counts.

The experiments of Hilsh and Polya were carried out by these authors precisely at the optimal concentration (\(10^{-7}\)); this circumstance makes it possible to transfer to the photographic plate all the results obtained in the Göttingen school

* Weyert believes that the photochemical reaction in a crystalline medium is a complex reaction in which, along with the light-absorbing elements, all neighboring elements also take part (the micellar theory); therefore the quantum yield in a crystalline medium should not, in principle, be equal to unity.

for individual crystals; indeed, many of the phenomena that we encountered above find their reflection also in ordinary photographic practice.

Here, in the first place, one should mention the fact of the bleaching of colored salts when they are illuminated by rays absorbed in the region of the second maximum; this phenomenon is also observed in silver salts, and silver bromide is bleached when illuminated by red and infrared rays (Fig. 1). But precisely these rays produce, in silver-bromide plates, their devualization—the so-called Herschel effect. The nature of this phenomenon, which since Herschel’s time has attracted the attention of leading photographic specialists, remained unexplained to this day; now it receives its natural explanation.

Further, as we have already seen, the concentration of liberated atoms increases not in proportion to the number of absorbed quanta—in other words, we are dealing with an inequality of the factors of time and intensity. We likewise encounter this circumstance in photographic practice in the form of the well-known Schwarzschild expression or the more complicated Kron formula.

As in alkali-halide salts, so also in silver-halide salts, the limiting concentration of atoms depends on the quality of the crystal lattice; on the other hand, it is quite obvious that the sensitivity of plates, which is a function of a whole series of complex circumstances, must among other things also depend on that quantity of atoms which, under given conditions, can be liberated inside the grains. We recall that, in the opinion of Pohl and Smakula, in an ideal crystal the atoms could not be liberated at all; one cannot fail to compare this opinion with the recently expressed view of Trivelli,^37 according to which “a pure silver-halide salt possesses no photosensitivity.” Trivelli attaches great importance to the internal stresses arising in the grains of the emulsion during their crystallization; it should, however,

ON THE PHYSICAL NATURE OF THE LATENT PHOTOGRAPHIC IMAGE

one must also bear in mind another circumstance: as was indicated, the photographic process takes place predominantly in the very surface layer of the crystalline grains, which is precisely the layer most subject to external influences. It follows from this that ions adsorbed by the grains of the emulsion can have a very strong effect on the limiting concentration, and consequently on the sensitivity of the plates—this circumstance is widely made use of in photographic technique, as is known, among other things in the sensitization and desensitization of plates.

Finally, the visible blackening of plates that occurs at very large exposures is most naturally ascribed to the appearance of colloidal silver. The possibility of colloidal coloration of silver halide salts was shown as early as 1915 by Lorentz and Hiege1; they used both an additive method, fusing the salts with molten silver, and a photochemical method, subjecting the salt crystals to very intense illumination. In both cases they observed under the ultramicroscope the Tyndall cone characteristic of colloids, consisting of shining particles; silver bromide thereby acquired a brown coloration. Experiments carried out by the author of the present article confirm these observations and indicate the exceptional ease with which colloidal particles are formed in crystals of silver bromide; very often the atomic and colloidal phases are formed simultaneously. The application of Mie’s theory here too provides a reliable method for separating the two phases from one another; the absorption spectrum of the system Ag—AgBr or Ag—AgCl can be calculated even more accurately than in the case of rock salt, since for the optical constants of silver we have more reliable data than for sodium or potassium. Preliminary measurements show that here too we have satisfactory agreement with experiment; the different shades of colloidally colored silver bromide crystals—from dark brown to reddish—are fully explained by the absorption curves calculated according to Mie’s theory.

M. V. SAVOSTYANOVA

Conclusion

All the facts set forth above make it possible to regard the primary stage of the photographic process as a special case of the photochemical process in halide salts; on the other hand, we may extend to all phenomena in colored salts the terms of photographic practice that are familiar to us, and treat, for example, yellow rock salt as a salt that has been exposed and not developed. The difference between a latent image in a photographic plate and in a piece of yellow rock salt consists only in the different thickness of the active layer, owing to which in the latter case we see a sharp change in coloration, whereas in the former case the silver atoms, as it were, do not reveal themselves at all. But in a layer only \(2.5\,\mu\) thick no paint could give any noticeable coloration at such a dilution as corresponds to the concentration of the latent image. If we prepared an emulsion with an active-layer thickness not of \(2.5\,\mu\), but of \(2.5\,\mathrm{mm}\), and, by a correspondingly increased exposure, produced in it a latent image of the same concentration, \(10^{-7}\), then we would notice the darkening of the plate in the illuminated places and could see how the photographic image—now it is time to cease calling it hidden or latent—forms before our eyes.

The outline presented here of the primary action of light on the lattice of halide salts, containing no internal contradictions, may readily serve, as we have seen, to explain the most intricate and enigmatic phenomena of photographic practice. In any case, it has already shown its applicability as a fruitful working hypothesis and, for the first time, has made it possible to treat the formation of the latent image as a physical phenomenon amenable to investigation, and not as a riddle surrounded by an almost mystical mystery.

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1. Lorentz and Hiege. ↩