Minute Metal Particles Inside a Crystal Lattice

M. V. Savostyanova, Leningrad

Introduction

Over the last decade there has been broad development of a field of physics concerned with the precipitation of metal inside a crystal lattice. Examples of such phenomena may include: (a) the coloration of certain minerals (blue rock salt, violet fluorite), (b) the extensive field of photographic phenomena, and, finally, (c) the no less extensive field of complex photocathodes in the external photoelectric effect and complex emitters in secondary electron emission.

At present it may be considered established that the principal role in the processes mentioned is played not by any complex chemical compounds, but by a pure metal in the minutest, so-called colloidal, distribution; for the cases mentioned above of NaCl and CaF₂ these will be sodium and calcium; as for the silver-halide salts, in which the photographic process takes place, the carrier of the properties of the latent image has long been recognized as metallic silver, precipitated in the grains of AgBr under the action of light.

The study of the properties of such metallic crystalline sols is already of considerable and, moreover, practical interest in itself, since it makes it possible, for photographic and photoelectric phenomena, to explain and, perhaps, to alter in a direction more advantageous to us certain properties of photographic layers and photocathodes, and, for minerals, to clarify the possibilities of artificial coloration and, most importantly, of decolorizing naturally colored specimens (smoky quartz, yellow Iceland spar).

Of very great interest is the study of the mechanism of incorporation and distribution of metal in the crystal lattice in the case when the particles of the metallic element are atoms and ions; here we have all the conditions for approaching the question of the mechanism of formation of a solid phase—a process whose importance need not be demonstrated. It should be borne in mind, however, that

other processes of formation of a solid phase, such as coagulation of particles in liquid colloidal solutions or condensation of vapor on cold surfaces, cannot provide us with explanations in this direction, since the initial moments of the phenomenon elude us, whereas the process of separation of a metal within the crystal lattice can be carefully followed by means of objective physical methods.

One of such methods is the optical method, which also includes photoelectric measurements: metals distributed in the crystal lattice in ionic, atomic, and, finally, microcrystalline (colloidal) states possess optical and photoelectric properties sharply distinct for each of the phases mentioned separately.

The main tasks before us in studying the above-mentioned phases are: a) elucidating the structure and some physical properties of the particles and b) the mechanism of their formation. The optical method in some cases makes it possible to solve these questions unambiguously.

I. IONIC AND ATOMIC DISTRIBUTION OF METALS
IN THE CRYSTAL LATTICE

§ 1. Some information on ionic crystals

When an atom with a small ionization potential comes into contact with an atom with a large electron-affinity energy¹), all the conditions exist for the transfer of an electron from the first atom to the second; thus an ionic molecule is obtained, for example a molecule of an alkali-halide salt, in which the ions attract each other under the action of Coulomb forces.

Two molecules can be attracted to each other by oppositely charged ions, thereby initiating the crystal lattice. As is known, an ideal crystal may be conceived as one gigantic molecule, in which the positions of the ions are firmly fixed.

In a first approximation, ions and atoms are represented in the form of hard spheres. Then, during formation of the crystal, two oppositely charged ions will approach one another until the distance between their centers becomes equal to the sum of their radii.

The entire crystal in the ideal case is represented as an absolutely regular lattice, the nodes of which are the centers of the spheres.

Such a scheme of an ideal lattice is never realized in real crystals. Deviations from the ideal structure may

¹) Electron-affinity energy is the energy released when an atom captures the number of electrons necessary to assume the configuration of a noble-gas atom.
We give the values of the electron-affinity energy for the halides: F — 4.1; Cl — 3.75; Br — 3.55; J — 3.2 eV.

proceed along several paths. First, these will be more or less gross disturbances of the structure—ruptures between individual blocks, with dimensions from 100 to 10,000 Å, which separately have an ideal structure (see, for example, \(^{41}\), or \(^{13}\), p. 179). A scheme of a real crystal\(^{1}\) is given in Fig. 1. Second, inside the blocks themselves there may occur distortions caused by: a) thermal vibrations of the ions, b) mutual deformation of the electronic shells of the ions, c) the presence of impurities.

Consider certain physical properties of ionic crystals that are important for the further exposition, namely their electrical conductivity and polarizability. It is known that alkali-halide and silver-halide salts possess ionic conductivity, indicating the mobility of ions within the lattice. This conductivity depends noticeably on temperature and, in absolute magnitude, differs greatly for salts of different types. Thus, a conductivity \(\sigma = 10^{-9}\ \mathrm{A}/\mathrm{V}\,\mathrm{cm}\) for NaCl, KBr, etc. is attained at temperatures of the order of 300–400°, whereas for AgBr it is attained already at a temperature equal to \(0^\circ\mathrm{C}\).

Fig. 1

In 1926 A. F. Ioffe came to the conclusion that the electrical conductivity\(^{2}\) of ionic crystals is caused by ions that are dislodged during thermal vibrations from stationary positions at the lattice sites and become trapped in interstices. This point of view was developed and quantitatively substantiated by Ya. I. Frenkel; in subsequent years it underwent further development by Jost. At the same time Schottky proposed a somewhat different scheme, according to which the wandering ions mentioned above may be absent from the crystal. In Schottky’s scheme the ions can go out onto the internal or external surfaces of the crystal, while the conductivity is determined exclusively by the “holes” of both signs that remain after these ions depart. The number of holes in thermodynamic equilibrium with the lattice increases with temperature according to the exponential law \(e^{-E/kT}\). According to the calculations of Schottky, and also of Mott, such a scheme is very probable for alkali-halide salts; on the contrary, for silver-halide salts one should adopt Frenkel’s scheme. Experiment\(^{11}\) has confirmed these considerations in the part concerning silver salts\(^{3}\).

\(^{1}\) See also V. D. Kuznetsov \(^{13}\), p. 179.
\(^{2}\) A detailed exposition of modern theories of electrical conductivity may be found in the review by Seitz \(^{14}\).
\(^{3}\) See, however, Seitz’s criticism \(^{26}\).

M. V. SAVOSTYANOVA

Interaction between ions can lead to a large deviation of the ions from spherical symmetry. Such a deviation is the sharper, the more readily deformation of the electron shells occurs under the influence of the electric field, i.e. the greater the polarizability of the ion. There are a number of methods for determining this quantity1 (see, for example, Van Arkel2, p. 17; de Boer[^3], p. 40)2.

As is seen from the footnote, the polarizability of halide ions is much greater than the polarizability of alkali-metal ions. This is explained by the large radius of the halide ions and the large ionization potential of the metal ions. It is therefore customary to speak of polarizable and polarizing ions, the difference between which has, of course, only a quantitative character.

In what follows we shall be interested in the ions of heavy metals in the lattice of alkali-halide salts—Ag, Cu, Tl; unfortunately, for the latter we have no reliable quantitative data. In the footnote, only values for ions constructed identically are comparable, for example for \( \mathrm{Cl}^- \), \( \mathrm{K}^+ \), \( \mathrm{Ca}^{++} \). On the basis of crystal-chemical data one may, however, assert that ions of the side series, for example \( \mathrm{As}^+ \), \( \mathrm{Zn}^{++} \), will polarize more strongly (by an approximate estimate by \(\sim 10\) times) than analogous ions of approximately the same radius in the main series.

Let us consider the interaction of a polarizable ion with a polarizing one. Here the following two limiting cases may occur: 1) both ions are free; the consequence is an approach of the ions to a distance smaller than the sum of the radii of the free ions (HCl); in the limiting case, according to Fajans[^6], an atomic compound with two shared electrons may arise; 2) the ions are elements of a regular lattice with high symmetry (a cubic lattice of the NaCl type); generally speaking, here a decrease in the distance between ions should not occur, since each ion is surrounded by cations symmetrically on all sides; polarization therefore does not lead to the formation of dipoles. Here there may occur only a relatively weak compression of the whole lattice, which is a second-order effect. And indeed, for alkali-halide crystals the values for the lattice constant obtained experimentally are, within experimental accuracy, equal to the sums of the ionic radii.

An exception in this respect is presented by lattices built of strongly polarizing and polarizable ions, for example AgCl, AgBr, and especially AgI. Here there occurs a very strong decrease in the distance between ions as compared with the sum of the ionic radii; thus we approach the first of

of the cases analyzed by us. In the limit there may occur an “isolation” of the electrons and a transition from ionic bonding to atomic bonding (Van Arkel, ch. VI)\(^2\). Such a case actually occurs in lattices of the zinc-blende type, ZnS, which in their properties approach the lattices of metals. The same also applies to AgJ, which, as is known, at temperatures above \(146^\circ\) crystallizes in a lattice of the NaCl type, and below \(146^\circ\)—in a lattice of the ZnS or wurtzite type\(^4\).

A few words about the absorption spectrum of crystals of the halide salts. As is known, the absorption spectrum of molecules of the halide salts in the vapor state consists of a series of broad absorption maxima in the region \(200\text{—}300\,m\mu\).

A similar picture is also found for alkali-halide crystals: the absorption spectrum—the so-called intrinsic absorption—consists of a series of more or less sharp peaks in the region around \(200\,m\mu\); for bromides and iodides the peaks are double\(^1\). At about \(100\,m\mu\) continuous absorption begins. The absorption coefficient (in the first peak) is very large and reaches values \(K\,cm^{-1}=10^6\); the value \(nx\) has the order \(1\text{—}1.5\), approaching the value \(nx\) for metallic absorption\(^ {18}\).

For crystals of bromides\(^2\) the spacings between the components of the doublet are: LiBr—0.48, NaBr—0.60, KBr—0.56, RbBr—0.50, CsBr—0.48 eV, i.e. of the order of 0.44 for Br in the free state\(^ {25,3}\).

The sharpness of the bands decreases with increasing action of polarization, which, as we saw above, increases from the fluoride salts to the iodide salts and from the salts of cesium to the salts of lithium. Correspondingly, in the silver halide salts (Fig. 2) we have still more diffuse absorption, extending also into the visible part of the spectrum. In the silver salts the absorption is almost independent of temperature. By contrast, for the alkali-halide salts such a dependence is observed (KJ in Fig. 2).

Fig. 2

\(^1\) The fact of splitting of the peaks is also encountered in gases\(^7\) and aqueous solutions\(^ {28}\); there it is attributed to the doublet structure of the ground state of the halogen atom \(({}^2P^{o}_{3/2};\ {}^2P^{o}_{1/2})\). The splittings between the doublet components in the gaseous state are as follows: Cl—0.11; Br—0.44; J—0.94 eV.

\(^2\) For chlorides the peaks have not been experimentally resolved.

\(^3\) See the note on p. 9.

§ 2. Introduction into the Crystal Lattice of Metallic Ions

There are several methods for introducing metal ions into a crystal lattice. Most simply, the metal is introduced into a single crystal of a salt by diffusion, which occurs upon sufficiently prolonged heating of the metal and salt in contact. According to Artsibyshev’s data1, the rate of penetration—the mobility of metallic ions in a given crystal—is in a number of cases equal to zero (platinum). On the other hand, some ions possess enormous mobility—of the same order as in aqueous solutions (thus, the mobility of the gold ion in KJ at \(670^\circ\) is only 1.5 times less than in water). In most cases, however, ions, penetrating into the crystal, form local destructions of the lattice with formation of the corresponding halide salts, and dendrite-like inclusions arise. Such ions include the ions of Mg, Te, Sb, Bi, Sn, Al. Conversely, the ions Cu, Au, Ag, and Ni enter the lattice quite easily, without destroying it.

Such crystals are, generally speaking, very convenient objects of investigation. It must be borne in mind, however, that we cannot regulate the concentration of the ions entering the crystal, and that in some cases (Ag) the diffusion rate is very small, which makes the investigation extremely difficult. This method of introducing ions into the lattice is inapplicable to silver salts, in which dendrites begin to form during electrolysis.

By growing crystals from the melt[^35], we can introduce foreign ions into the crystal by adding to the melt, in small quantity, a foreign metal in the form of the corresponding salt (for example, for NaCl—chloride).

At low concentration of the impurity, so-called mixed crystals are obtained from such a melt—the metal ions are regularly distributed over the lattice.

At higher concentration it is no longer possible to obtain optically good, regular crystals. By this method one can readily obtain crystals with Cu, Ag, Ni, and also with Tl, Pb at concentrations up to 0.5–1 mole %; gold enters the lattice with great difficulty[^14], giving anomalies of behavior which will be discussed below.

Crystals containing a foreign metal exhibit a strongly pronounced ability to fluoresce and phosphoresce, which is why it is customary to call them phosphors.

For what follows it is very important to know how the foreign ions are situated in the lattice. Zaur and Stasov[^23] carried out an X-ray investigation of KBr—KN and KCl—TlCl crystals at very low impurity concentration (up to 1 mole % KN and up to 20 mole % TlCl), and in both cases obtained a change in the lattice constant—a decrease in the first case (by \(0.005 \text{ Å}\) for 1.4% KN) and an increase in the second (by \(0.008 \text{ Å}\) for 9% TlCl). These results indicate that the impurities are not concentrated in separate pla-

states, but are distributed throughout the whole volume of the lattice, uniformly changing its constant, as indeed must be the case for a mixed crystal. But at the same time the cited authors discovered certain peculiarities for these systems: the change in \(d\) turns out to be almost half as small as the value required by Vegard’s law of additivity \(^{38}\). Below we shall point to a number of facts indicating a more complicated type of introduction of foreign ions of the complex; it is also very probable that hydrogen ions, having a comparatively small radius, can enter the lattice in interstices \(^{1}\) (according to Frenkel), which, of course, will affect the lattice constant more weakly. Attempts at a more careful study of the structure of such phosphors have not yet been made.

The electrical conductivity of mixed crystals (phosphors) turns out to be somewhat greater than the electrical conductivity of pure crystals (see the data of Ponomareva and Egorova) \(^{19}\).

Fig. 3. Absorption spectrum of phosphors: \(a\)—KCl \(+\) 0.016 mol.% TlCl, \(b\)—KCl \(+\) 1 mol.% CuCl, \(v\)—KCl \(+\) 0.015 mol.% PbCl\(_2\)

It is necessary to note the characteristic features of the absorption spectrum of phosphors, namely the appearance of a new absorption band in the region \(230\text{—}250\,m\mu\) (Fig. 3).

Replacement of the halide ion, in particular by hydrogen ions, also causes the appearance of a new absorption band around \(200\text{—}220\,m\mu\). This is the so-called \(U\)-band.

The hydrogen atom has one ground state, and accordingly the \(U\)-band has no doublet structure.

Absorption curves from the region of the \(U\)-band, as well as curves of “intrinsic absorption” in alkali-halide salts, exhibit a noticeable temperature dependence (Fig. 4).

§ 3. The atomic distribution and its optical properties

a) The primary photochemical process. It has been established by photochemical studies that upon absorption

\(^{1}\) See the remark by K. Wagner in the paper by Zauhr and Stasiw \(^{23}\).

of light in vapors of halide salts, the molecules decompose into their constituent parts. The decomposition energy can be calculated independently (from thermochemical data); by comparing these data with the energy values obtained optically (the quantity \(h\nu\) of the absorption maxima), one can verify assumptions about the reaction products. Thus, for example, it has been found that upon absorption of light at the first (long-wavelength—

Fig. 4. Dependence of the shape and position of the \(U\)-band on temperature

—maximum of absorption of alkali-halide molecules, two normal atoms arise—a halogen and a metal—which corresponds to the transfer of an electron from the halogen ion to the metal ion. For the salts of silver and thallium (as well as for the alkali halides in the shorter-wavelength region), we have decomposition into one normal and one excited atom.

The analogy between the absorption spectra of vapors and crystals of halide compounds, on the one hand, and also the comparison of the absorption curves for the Na and K salts, which shows that the cation plays a secondary role in the absorption process, make it possible to suppose that the energy of the quantum upon absorption is expended in tearing an electron from the halogen ion. As a result of this process, neutral halogen and metal atoms are formed in the crystal (Franck[^5], Sheppard and Trivelli[^29]).

It has long been known that when alkali-halide salts are illuminated with ultraviolet light from the region of the long-wavelength “tail” (at the absorption peak the absorption is so strong that all the light is practically retained in the very surface layer), a new absorption band appears (Fig. 5), for the most part in the visible part of the spectrum, causing coloration of the crystal. Thus, NaCl acquires a yellow color, KCl a violet one, etc. The coloring centers,

…causing the appearance of coloration, were named \(F\)-centers (Farbzentren)\(^1\).

A similar band is also observed in the case of phosphors; for silver phosphors in alkali-halide salts, according to Toyortz’s data,\(^{34}\) the new band lies in the region of \(300\,m\mu\) (Fig. 6).

Fig. 5. \(F\)-bands in alkali-halide crystals

Fig. 6. \(1\)—KBr \(+ 0.02\) mol. % Ag, \(2\)—KJ \(+ 0.02\) mol. % Ag

There was every reason to suppose that the role of coloring centers is played by the neutral atoms of the metal that have formed (the absorption spectrum of neutral halogen atoms should lie in the ultraviolet region and overlap with the intrinsic absorption).

\(^1\) By analogy, the centers causing the appearance of the \(U\)-band are customarily called \(U\)-centers. In what follows we shall often use this term. We believe that, through a number of experimental investigations of the Göttingen school (see \(^{10,11,23}\)), the question of the nature of these centers (hydrogen ions) has been definitively settled.

Study of the properties of coloring \(F\)-centers has shown conclusively that electrons play an essential role in their formation: careful experiments carried out in Pohl’s laboratory in Göttingen established that, when a crystal containing \(F\)-centers is illuminated with light absorbed in the \(F\)-band, photoconductivity is observed (i.e. the appearance of free electrons), accompanied by decoloration of the crystal. Each absorbed quantum liberates one electron, while at the same time one coloring center is destroyed (in exact accordance with Einstein’s law). To test the idea of the formation of neutral atoms in the lattice, it was quite natural to calculate directly the dissociation energy.

The first attempt at such a calculation (Wolff and Herzfeld)\(^{37}\), however, gave for the first absorption peak values of \(h\nu\) that differed greatly (by about 30 percent) from the experimental ones.

We cannot here deal in greater detail with this question of the photochemistry of crystals, which lies outside the scope of the present article, and we refer the reader to the very complete review by L. M. Shamovsky\(^{39}\); we shall note only that at present there is a whole series of calculations of the energy \(h\nu\) (at the first peak or at the long-wavelength absorption limit, as Shamovsky does) with much more accurate results; thus, in Shamovsky’s recent works, agreement between \(h\nu\) (experimental) and \(h\nu\) (theoretical) is achieved to an accuracy of \(\pm 4\%\), and this not only for alkali-halide salts and their phosphors, but also for hydrides and salts of the \(CaF_2\) type.

In all these works it is assumed that, upon absorption in the first peak, an electron is transferred from a halide ion to the nearest metal ion. The role of the halide in this process is demonstrated by the above-mentioned doublet structure of the peaks; the role of the metal ion will be discussed below (§ 7).

Let us now consider the process of absorption in phosphors. According to Shamovsky’s calculations, here too the basis of the process is the transfer of an electron from a halide ion to the nearest ion of the foreign metal. Here, however, we encounter certain difficulties: as Fig. 3 shows, the absorption spectrum of phosphors is rather complicated; it consists mainly of three bands, whose relative intensity depends on temperature; these bands are single, not exhibiting the doublet structure which, according to the conception of electron transfer from a halide ion, ought to occur here as well.

A second essential difference between phosphors and alkali-halide salts consists in the fact that the former, as the name itself indicates, exhibit strong luminescence (fluorescence and phosphorescence) under the action of light from the absorption region, whereas in pure salts no luminescence could ever be observed in this process. All these facts show that the mechanism of absorption in phosphors must proceed differently than in pure salts. There is as yet no complete picture of this process; there are only a number of separate conceptions. Thus, Seitz\(^{25,27}\) assumes that

upon absorption of light in phosphors the active center is not the halide ion, as is assumed for pure salts, but the ion of the embedded metal; the act of absorption consists in the excitation of the internal electrons of this ion. In this case we may be dealing with a number of levels, which is reflected in the complex structure of the absorption bands.

However, a substantial objection to this conception is the experimental fact (unpublished data of Toporets and Ul’yanov) that colloidal (and, apparently, atomic) silver centers appear when a silver phosphor is illuminated by the light of a powerful ultraviolet spark; here, consequently, we have not ionization or excitation of the metal ion, but its reduction at the expense of a foreign electron.

Furthermore, certain indications of the nature of the absorption centers of phosphors can be obtained from a comparison of the absorption spectra of phosphors in solid and liquid media (for details see the review by Terenin[^33]). There are grounds for considering that these will be complexes of the type \((\mathrm{MHal}_n)^{m-}\). This supposition was confirmed for thallium salts by Gilsch[^33] through observation of luminescence in aqueous solutions of these salts.

Another indication of the possibility of complex formations in phosphors is the fact of a sharp change in the absorption spectrum of the phosphor \(\mathrm{KJ} + \mathrm{AgJ}\) with increasing temperature, namely at \(t \sim 148^\circ\), corresponding to the temperature of transition from the \(\alpha\)- to the \(\beta\)-modification of \(\mathrm{AgJ}\). This circumstance indicates that, at least for \(\mathrm{AgJ}\), the lattice retains its individuality even at the very small concentration with which one usually has to deal in phosphors.

Some confirmation of such a conception may be afforded, first, by observations on crystals of \(\mathrm{NaCl}\) or \(\mathrm{KCl}\) with a large amount of \(\mathrm{Ag}\)—up to 10 mole % (unpublished data of Ul’yanov); such crystals become violet and blue in light, in exactly the same way as crystals of pure silver halide.

Secondly, we have indirect data (unpublished observations of Gorokhovsky and Smirnov) concerning the spectral sensitivity of mixed emulsions: whereas for \(\mathrm{AgBr}\) and \(\mathrm{AgCl}\) emulsions we have complete additivity of spectral sensitivity, in \(\mathrm{AgJ}\) emulsions the action of the iodide salt sharply predominates.

One may imagine that, for example, in the case of silver admixed with \(\mathrm{NaCl}\), we have in the \(\mathrm{NaCl}\) lattice more or less large “islands” of \(\mathrm{AgCl}\)—the above-mentioned “complexes”—with a lattice modified in such a way that its constant is equal also to the slightly altered constant of the surrounding lattice.

b) Methods of obtaining \(F\)-centers. Coloring centers in crystals of alkali-halide salts may be obtained by a number of methods. To the first group belongs the method described above of coloration under the action of ultraviolet rays from the region of the intrinsic...

from the region of intrinsic absorption and from the region of the \(U\)-band (in this case the electrons are torn away from \(H\)-ions), as well as the long-known method of action by larger quanta of X-rays or \(\gamma\)-rays. These methods may be called photochemical or subtractive, since the electron participating in the creation of the \(F\)-center is taken from within the lattice itself.

The beginning of the second type of methods for coloring alkali-halide salts was laid by Rose as early as 1863. Heating crystals of rock salt and sylvine in the vapors of the corresponding alkali metal, Rose observed their coloration; later measurements of the absorption of crystals colored in this way showed their complete identity with crystals colored subtractively.

The explanation of this phenomenon seemed quite natural: it was assumed that here we were dealing with the diffusion of metallic sodium or potassium inside the crystal. Later experiments showed, however, that if diffusion of the ions of these metals does occur, it is only in the surface layer, whereas the crystals were colored throughout. But the chief objection to such an explanation was the fact that the color of the crystal was determined not by the entering metal, but by the metal of the lattice: NaCl, both in Na and in K, was colored yellow, while KCl was always colored violet, etc.

In 1932 O. Stasiw\(^{31}\) found that by applying to a crystal, for example NaBr, colored in vapors at a temperature of \(650^\circ\), a certain potential difference (of the order of \(40\ \mathrm{V/cm}\)), one can observe the propagation of the color (at a speed of the order of the electron velocity) toward the anode; the color can even be completely “driven out” of the crystal. Obviously, neutral atoms cannot move in the field. Stasiw suggested that the motion of the coloring centers is only apparent; what is real is the displacement of electrons, which jump under the action of the field from one center to another. This supposition fully explains the process of coloring crystals in vapors: when the crystal comes into contact with the vapors of the metal, electrons diffuse into it, for one reason or another forming at the crystal–metal-vapor boundary.

Artsybyshev\(^{1}\) combined the experiments of Rose and Stasiw into one and developed a method for more rapid coloring of crystals, accelerating the electrons penetrating into the lattice by means of an electric field.

A small pit is hollowed out on a face of the crystal, into which the metal (sodium) is placed. The pit is tightly covered with a lid—a plate of the same crystal. The object is clamped in an iron\(^{1}\) holder and placed in an electric furnace with a window for observation. A potential difference of the order of \(40\ \mathrm{V/cm}\) is applied to the crystal, with the sodium serving as the cathode; at a temperature of about \(400^\circ\), a colored cloud begins to emerge from the cathode. With varying speed, depending on the voltage, the cloud moves toward the anode.

\(^{1}\) Iron ions do not penetrate into the crystal.

For both pure crystals and phosphors, the absorption spectra of objects after coloration by any of the methods described have an identical form. This indicates the same nature of the coloring centers in all cases.

The separation of coloring centers in the cases described above is obtained as a result of introducing electrons into the crystal from outside; of course, in order to maintain electrical equilibrium, a corresponding part of the negative ions must leave the crystal. As a result, in the object (at least in certain parts of it) there is obtained a stoichiometric excess of metal1; hence it follows that the colored crystal must be lighter than the uncolored one; this has indeed been established experimentally; thus, Mollwo[^16], heating CaF$_2$ crystals in an atmosphere of calcium at temperatures of 1050 and 1150°, obtained a decrease in density (3.180—3.151 = 0.029 and 3.187—3.124 = 0.063), caused by the departure of fluorine ions.

The method of coloring a crystal by external electrons is naturally to be called additive, or electrochemical.

c) The nature of $F$-centers. Thus, $F$-centers are formed when external or internal electrons are introduced into the lattice and in some way become bound to a metal ion. This bond must be very weak, as is evidenced by the bleaching of photochemically colored crystals and by the diffusion of coloring centers—in additively colored crystals.

On the other hand, the peculiarities of the bond of an electron with an ion, say of sodium, are indicated by the large value of the ratio of the atomic radius to the ionic radius (1.9), and also by the magnitude of its polarizing ability (25·10$^{24}$). The large values of these quantities indicate that it makes no sense to assign the electron to a single ion; all the surrounding positive ions may claim it with equal right. The electron is practically bound not to one center, but to an entire group of lattice sites.

Such is the same picture of the bond of an electron with lattice sites in silver salts. Owing to the great polarizability in this case, one may with still greater justification speak of a collectivization of electrons upon the transition to atomic bonding.

Something different is found in the case of ions Ag, Cu, and especially Au, embedded in the lattice of an alkali-halide salt (phosphors). Here the atomic radius exceeds the true radius only slightly (and for Au is almost equal to it)2; the electron is more closely bound precisely to this ion of the foreign metal. The new center becomes in this case a foreign impurity, weakly bound to the rest of the lattice. In this sense

M. V. SAVOSTYANOVA

\(F\)-centers in phosphors already come quite close to the concept of neutral atoms. On the contrary, in the case of NaCl and other salts of the same type we have the right to speak only of atomic centers.

d) Properties of \(F\)-centers. From what has been said it follows that the properties of atomic centers in pure alkali-halide salts and in phosphors must differ sharply. This is confirmed by experiment. Let us consider the properties of atomic centers in somewhat greater detail.

1. Mobility of atomic centers. We have already mentioned the high mobility of the \(F\)-centers of pure alkali-halide salts in an electric field. The sharp dependence of the mobility of the centers on temperature is illustrated by the curves of Fig. 7 and may be expressed by the empirical formula

\[ v = v_0 e^{-\frac{E}{kT}} . \]

Fig. 7. Mobilities of electrons in cm/sec in a field of \(1\ \mathrm{V/cm}\)

Here \(E\) is the work of dissociation, and \(v_0\) is the limiting mobility of the electrons. The order of these quantities in various alkali-halide salts may be judged from the data of Table 1 (Pohl \(^{18}\)), obtained from the curves of Fig. 7.

In Fig. 8 the mobility curves are plotted (on a linear scale) for three groups of salts with one cation, and, with the corresponding choice of the temperature scale, the curves for salts with one

Table 1

	NaCl	NaBr	NaJ	KCl	KBr	KJ	RbCl	RbBr	RbJ
Limiting mobility \(v_0\), in \(m\cdot sec^{-1}/V\cdot m^{-1}\)	0,002	0,066	0,074	0,014	0,017	0,020	0,011	0,013	0,014
Work of thermal dissociation \(E\) . .	0,94	0,80	(0,76)	1,00	0,84	0,83	0,84	0,68	0,63

anion are brought into coincidence. From the fact that the points lie quite satisfactorily on a single curve, Pohl concludes that the degree of dissociation of the coloring centers, i.e. the exponential factor in the expression for the mobility, is practically determined only by the thermal vibrations of the lattice.

The data of Table 1 were obtained at small concentrations of coloring centers in the crystal; at large concentrations the mobility falls (which, incidentally, becomes noticeable only at lower temperatures). In the same way (decreasing the mobility), the presence in the crystal of centers of another kind also acts. Thus, according to Toporets’ data \(^{34}\), in a KCl crystal containing silver ions in an amount of \(0.05\) mole %, the mobility of \(F\)-centers at \(695^\circ\mathrm{C}\) is \(\sim 7\) times smaller than in a pure crystal.

Fig. 8

If an additively colored crystal already containing \(F\)-centers is heated to the corresponding temperature, then a gradual decoloration of the crystal from the edges can be observed, caused by the reverse diffusion of electrons out of the crystal.

Measuring the changes in the distribution of the concentration of coloring centers in a uniformly colored crystal during its heating, Stasov \(^{32}\) determined the values of the diffusion coefficient \(D\) \(^{1}\).

Between the diffusion coefficient and the values of the mobility of electrons in an electric field there must exist a close relation, similar to that which occurs in electrolysis. Bearing in mind that the motion of the electrons will be impeded by the slower motion of the positive charges, Stasov applies to our case the Nernst formula, extended by Wagner and Schottky \(^{2}\),

\[ v_-=\frac{D v_+}{v_+ + \frac{kT}{e}D}, \tag{A} \]

\(^{1}\) The expression for \(D\) in the present case has the following form:

\[ D= \frac{ \ln \frac{4}{\pi}+\ln \sin \frac{\pi x}{d}-\ln \frac{C_x}{C_0} }{ \frac{\pi^2 t}{d^2} } \]

(For the derivation, see Stasov’s paper.) Here \(C_x\) and \(C_0\) are the final and initial concentrations at the given point, and \(t\) is the diffusion time.

\(^{2}\) See note 6 in Stasov’s paper.

where \(v_+\) is the mobility of positive charges (not ions), \(D\) is the diffusion coefficient.

At higher temperatures (above \(700^\circ\)) and at low concentrations, when \(v_+\) is so large that the motion of electrons occurs freely, we have

\[ v_-=\dot D\,\frac{e}{kT} \tag{13} \]

(\(v\) is expressed in \(m\cdot sec^{-1}\) \(V\cdot m^{-1}\), \(D\) in \(m^2\cdot sec^{-1}\), \(k=1.37\cdot 10^{-23}\) \(W/sec\cdot grad^{-1}\), \(e=1.59\cdot 10^{-19}\) coulombs).

Fig. 9

Substituting the experimental values of \(D\) and \(v_-\) (some figures are given in Table 2) into formula (A), Stasov obtained \(v_+\). The dependences of \(v_+\) and \(v_-\) on temperature are shown in Fig. 9.

In conclusion we note that in silver phosphors the atomic centers of silver are apparently immobile, which is in complete agreement with the conception outlined above of the atomic bond in this case.

2. Optical properties. The absorption band \(F\), which determines the color of the crystals, is defined by the binding energy of the electron.

For pure crystals at a given temperature both the position of the maximum of the \(F\)-band in the spectrum and the width of the latter are constant and quite reproducible with different methods of coloration. The curve of the absorption coefficient as a function of frequency, at least in its upper part, can be calculated from the formulas of the classical theory of dispersion[^15].

Since the binding energy of the electron depends on the state of the lattice, it should be expected that the absorption band will also depend strongly on temperature conditions, especially in the case of “group” binding of the electron. This is indeed the case: a characteristic property of the \(F\)-band, distinguishing it from bands of other origin, is its reversible broadening and shift toward longer wavelengths with increasing temperature and its narrowing and shift in the opposite direction upon cooling.

Table 2

\(T^\circ C\)	\(D\) in \(m^2\cdot sec^{-1}\times 10^9\)	Electron mobility \(v_-\), \(m\cdot sec / V\cdot m^2\cdot 10^7\)
755	7.4	1.2
740	8.13	1.03
720	6.5	0.83
700	3.84	0.7
655	1.69	0.55
615	1.1	0.55
675	0.68	0.55
550	0.284	0.55
500	0.11	0.55
490	0.057	0.55

crystal (Fig. 10). The area under the curve, i.e. the number of coloring centers, remains unchanged.

The binding energy of the electron in the \(F\)-center has been calculated repeatedly; however, the calculations did not give sufficiently accurate results. The most suitable proved to be Mollwo’s empirical formula\({}^{17}\) for the maximum frequency of the absorption band \(F\):

\[ Vd^{2}=\mathrm{const}=5.02\cdot 10^{-1}\ \mathrm{cm}^{2}\cdot \mathrm{sec}^{-1}, \tag{C} \]

where \(d\) is the lattice constant.

In the silver halide salts, atomic centers have not yet been found; the coloration produced by light must be attributed to colloidal centers (see below). It is possible that the \(F\)-bands fall in the region of the colloidal absorption bands. This assumption is confirmed by calculations using the Mollwo formula. Substituting into formula (C), instead of \(d\), the sum of the ionic radii, Toporets\({}^{34}\) found that the values of \(\lambda_{\max}\) for the presumed \(F\)-centers do indeed lie in the middle part of the spectrum, i.e. in the same place as the colloidal centers

\[ (\mathrm{AgCl}:\lambda_{\max}=520\,\mathrm{m}\mu;\ \mathrm{AgBr}:\lambda_{\max}=575\,\mathrm{m}\mu). \]

Fig. 10. Influence of temperature on the shape of the \(F\) band

In phosphors, the position of the absorption maximum can be calculated from the values obtained for silver salts according to the modified Mollwo law. Toporets\({}^{34}\) introduced the assumption that, inside the medium, the electron binding energies change in the ratio of the dielectric constants. Then the positions of the absorption maxima in phosphors can be determined from the relation

\[ \frac{\lambda_{1\max}}{\lambda_{2\max}}=\frac{n_1^{2}}{n_2^{2}}, \]

where \(n_1\) and \(n_2\) are the refractive indices of two media corresponding to \(\lambda_{1\max}\) and \(\lambda_{2\max}\). The experimental results and the calculations according to the Mollwo–Toporets formula agree well.

It is interesting to compare the data on the difference of the quantities \(h\nu\) (at the maximum of the atomic absorption band) for pure salts and phosphors with the difference of the energies of the resonance lines of the corresponding alkali metal and silver (see Toporets\({}^{71}\), dissertation). For NaCl and NaBr, \(h\nu_{\mathrm{Ag}}-W_F=1.83\) and \(1.92\ \mathrm{eV}\), whereas the difference of the energies \(\mathrm{Ag}-\mathrm{Na}=1.68\ \mathrm{eV}\); for the potassium salts (KCl, KBr, KI) we have, respectively, \(2.13\), \(2.11\), and \(2.05\ \mathrm{eV}\), while \(\mathrm{Ag}-\mathrm{K}=2.09\ \mathrm{eV}\).

The agreement of the numerical data indicates that the valence electrons of the silver atom and of the alkali-metal atom, placed in the same lattice, experience the same perturbing action in the field of the surrounding lattice ions, although the binding energy, as indicated, is different in the two cases.

II. COLLOIDAL DISTRIBUTION OF METALS

§ 4. Optics of Colloidal Solutions of Metals

Colloidal solutions of certain metals—silver, gold, sodium—possess a bright and changeable coloration; this property, as well as the strong selective scattering of light by these solutions, has long attracted the attention of investigators.

The bright and varied colors of solutions of gold (Cassius’ purple \(^{6}\)) and silver (Carey Lea’s photochlorides \(^{5}\)), studied earlier than others, chemists attempted to explain by the presence within the solution of differently colored modifications of the metal (subhalides \(^{15}\)). These hypothetical compounds are sometimes mentioned even in contemporary literature \(^{1}\).

The true nature of these solutions had already been established by Faraday \(^{7}\), who was the first to obtain stable red, violet, and blue hydrosols of gold and to prove that their coloration is due to particles of pure gold suspended in water. Faraday’s thorough investigation, however, passed unnoticed. Almost half a century later, in 1898 and in 1900–1903, the presence of colloidal particles in such liquids was demonstrated by ultramicroscopic observations of Zsigmondy and Siedentopf \(^{37}\) (pp. 49, 62, 76). Faraday’s investigation served as the point of departure for Zsigmondy.

Faraday’s work is of great interest not only for colloid chemistry, but also for physics. Faraday posed with complete clarity the question of the optics of metals in a finely divided state and of its significance for the theory of light (the term “colloidal” was introduced by Graham only later, in 1862 \(^{2}\)).

The fundamental problem of the optics of metals in the colloidal state consists in calculating the amplitude of the wave scattered by a single particle, transferring these results to a collection of particles, and determining the influence of the physical properties of the particles on the scattered light.

\(^{1}\) From the point of view of the conception of \(F\)-centers developed above, the latter could be regarded as subhalides with the formula \(\mathrm{MHal}_{6}\).

\(^{2}\) In his Bakerian lecture of 1857 Faraday says: “The undulatory theory, if it were perfect, could explain any physical manifestation of light; since this is not so, one may, conversely, make use of these manifestations for the development and extension of the theory, if it is correct, or for its correction and replacement by a more perfect one, if it is incorrect... Light is connected with matter which it encounters on its path, and matter in turn exerts an influence upon it—light is reflected, deflected, transmitted, refracted, absorbed, etc., by particles of very small dimensions. Considering the whole probability that by means of experiment it would be possible to obtain directly appreciable results by introducing into the path of a ray particles that exert a great action on light and at the same time are very small in comparison with the wavelength, I began to seek such particles among metals”...

The history of the optics of colloidally distributed metals proves to be most closely connected with the history of the development of the optics of turbid media, of which the atmosphere is a typical representative. In one of Rayleigh’s first works on the optics of turbid media (1871), the famous law of scattering (inverse proportionality to the fourth power of the wavelength) (known as Rayleigh’s law) is established.

The physical properties of the particles enter into the expressions for the amplitudes of the wave, first, through the particle radius \(\rho\), and, second, through the quantities \(\varepsilon\) and \(\sigma\)—the dielectric constant and the conductivity.

If one sets \(\varepsilon = 0\) and \(\sigma = \infty\), i.e. regards the metal as an absolute conductor, then all metals in colloidal dispersion should behave identically in optical respects. This clearly does not correspond to reality and even contradicts qualitative observations. It is known, however, that metals in a rapidly varying periodic electric field, such as the field of a light wave, cannot be regarded as absolute conductors; this circumstance was first taken into account, in application to the present case, by Maxwell-Garnett\({}^{19}\), who, instead of the expression \(\varepsilon - i\sigma T\), used the formula \(n - in\chi\), where \(n\) and \(n\chi\) are the refractive and absorption indices of the metal.

Maxwell-Garnett dealt with the simplest case of minute spherical particles; working formulae for the case of spherical particles of different diameters were given by Mie\({}^{20}\), and for ellipsoidal (minute) particles by Gans\({}^{8}\).

These general expressions contain in full all the variety of optical properties of colloidal solutions—in dependence both on the sizes of the particles and on the optical properties of the substance of the particles. If in the expression \(n - in\chi\) one sets \(n\chi = 0\), then the corresponding formula will be applicable to dielectrics (Rayleigh’s case). Thus Rayleigh’s famous formula, explaining the blue color of the sky and, in general, of colloidal dielectrics, is a special case of the more general Rayleigh–Mie formulae.

The principal results of the optics of colloidal solutions of metals are as follows.

Colloidal solutions scatter and absorb light. Both phenomena depend on a number of factors:

derived by him on the basis of elementary considerations of the dimensionality of the quantities entering into the expression for the ratio of the scattered and incident waves.

The subsequent history of this question reduces to the analytic derivation both of this law and of a more general dependence, on the basis of diffraction theory. The main content of the works in this field, covering the period from 1871 (almost a century-long period), consisted in solving the problem of the action of light first on a single isolated particle located in a light field, and then on a medium with a large number of particles suspended in it.

Through the work of a whole series of major physicists and mathematicians, among whom one may name Poisson\({}^{23}\), Stokes\({}^{32}\), Kirchhoff\({}^{12}\), Rayleigh\({}^{25}\), Lamb\({}^{14}\), J. J. Thomson\({}^{33,34}\), Love\({}^{16}\), and finally Debye\({}^{4}\), Abraham\({}^{1}\), Sommerfeld\({}^{30,31}\), Ignatowski\({}^{10}\), Gans\({}^{9}\), Mie\({}^{20}\), Wenzel\({}^{21}\), this problem—representing, from the mathematical point of view, the solution of a wave equation with allowance for boundary conditions—was solved completely for particles of spherical form, and partially for ellipsoidal form.

The results of the works of all the above-mentioned scholars, which have now already begun to enter textbooks (for example, Born\({}^{3}\), Optics, §§ 70, 71; Frenkel\({}^{36}\), Electrodynamics, Part II, p. 538), consist in the calculation of the field of the secondary (scattered) wave.

α) Optical constants of the substance of the particles. In dielectrics we have a smooth course of scattering with wavelength (usually a rise toward shorter waves); in metals, owing to the distinctive and abrupt change of the constants and \(n\chi\), selective scattering and absorption are observed, which in a number of cases, though not always, gives a vivid coloration of the solution in scattered and transmitted light.

β) Size of the particles. As the particle size increases, absorption gradually decreases. Scattering for the smallest particles \((2\rho < 5\,m\mu)\) is practically equal to zero. As the particle diameter increases, scattering grows up to a certain limit and, with further increase, decreases again.

Fig. 11. Absorption Na—ether

Fig. 12. Scattering Na—ether

This dependence is clearly visible in Figs. 11 (absorption) and 12 (scattering), which refer to the Na—ether system (according to the calculations of O. F. Mashirova-Pavlova\(^{18}\)).

The sharp decrease of scattering for the smallest particles is an extremely important circumstance in the experimental study of colloids by their optical properties; indeed, the use of the ultramicroscope is based on the scattering of light by particles; if the field of the ultramicroscope remains optically empty, then from this one still cannot conclude that the object under investigation actually contains no colloidal particles.

The intensity of the scattered light depends on the angle between the incident ray and the direction of observation. This circumstance is important

one must bear this in mind in ultramicroscopic observations, since for not very small particles almost all the light is scattered in one direction (the Mie effect; see Born³, p. 392).

One should also dwell on the polarization of the light scattered by the particles; since the degree of polarization depends also on the wavelength, very complex relations are obtained, which determine the apparent polychroism of the particles (see Born³, p. 398).

To illustrate what has been said above, let us examine somewhat more closely the absorption color of light by colloidal solutions.

The author²⁸ calculated the course of the absorption curves for a series of metals (Ag, Al, Au, Ba, Be, Bi, C, Ca, Co, Cr, Cs, Cu, Fe, Hg, J, K, Mg, Mn, Na, Ni, Pt, Rb, Sb, Se, Sn, Sr, Tl, Zn) at the finest subdivision (diameter \(2\rho \ll 10\,m\mu\)) in a medium with refractive index \(\sim 1.5\) (NaCl). In Fig. 13 the results are given for some of these metals.

Fig. 13

All the substances investigated, with the exception of Tl, exhibit more or less sharply expressed maxima at the finest subdivision. Both in appearance and in their position in the spectrum they are extremely diverse. The course of the absorption curves is determined by the values of the optical constants of the metal, the solvent, and the size of the colloidal particles.

According to the absolute values of the optical constants of absorbing bodies and according to their spectral course, all the metals investigated can be divided into 3 groups:

\(\alpha)\) \(n\) (the refractive index) is small (\(0.2\)—\(0.5\)) and considerably (by a factor of 5) smaller than the absorption index \(n\chi\) (Mg, Ca, Sr, Ba, Al, Na, K, Ag).

\(\beta)\) \(n\) is of the same order as \(n\chi\) (the majority of metals).

\(\gamma)\) \(n\) is greater than \(n\chi\) (nonmetals C, J, Se, Te, fuchsin).

For cases β) and γ) we have very broad and flat absorption maxima, covering mainly the ultraviolet part and only partly extending into the visible part, where they descend toward the red part of the spectrum more or less gently. Therefore, in these cases one cannot expect bright colors of colloidal solutions. Indeed, as is known, a bright coloration of a substance in transmitted light is observed only in those cases when the absorption curves of this substance lie in the visible region and extinguish a portion of the spectrum corresponding to one color. Here, however, one may assume only all shades from brown to red. Thus, copper sols should have a bright-red coloration, since the absorption curve descends very steeply at \(590\,m\mu\); in the opposite case, when the curve runs almost parallel to the axis of abscissae, the color of the solution should be black-brown (Mn, Fe, Co, Cr).

In case α), as consideration of the curves shows, the absorption maxima, first, are distinguished by their narrowness and absolute magnitude (for example Na) and, second, lie predominantly in the visible part of the spectrum. Here one may therefore expect bright and varied coloration.

The first place in this respect is occupied by sodium; the reason for this is the negligibly small (\(n < 0.05\)) refractive index.

Fig. 14

Fig. 15

The metal following sodium, potassium, which has a refractive index almost twice as large, gives a maximum situated at the boundary of the red and infrared parts of the spectrum; therefore here one cannot expect a variety of colors for subjective reasons. Probably colloidal lithium gives still brighter colors. In third place in sharpness of the maxima, and consequently in brightness

In order of coloration stands silver. Next come Ca and, finally, gold, with absorption extending widely into the far ultraviolet region.

The influence of the refractive index of the solvent is manifested in the fact that, with increasing \(n\), the absorption bands shift toward longer wavelengths; this circumstance is illustrated by Fig. 14 for silver and Fig. 15 for sodium.

With an increase in particle diameter, the absorption curves, as indicated above, in most cases shift toward longer wavelengths (Fig. 16), as a result of which a change in coloration may be expected. Most sensitive in this respect are those colloidal systems which possess high absorption maxima (Ag, Na). Least sensitive, as analysis of the formulas shows, are Cu and Au; here, up to diameters of the order of \(40\,m\mu\), the absorption maximum is almost not displaced in the spectrum (see Mie\(^{20}\), Fig. 25), and consequently the coloration remains unchanged. The seemingly abrupt change in the coloration of gold sols with further change in particle diameter is due chiefly to the fact that the maximum lies in the middle part of the spectrum, where the eye has the greatest sensitivity to changes in hue.

Fig. 16. Absorption curves of the system Ag—H\(_2\)O according to the calculations of A. Ashcheulov

§ 5. Determination of the nature of the coloring centers, and also of the size and shape of colloidal particles

a. Determination of the colloidal nature of the solution.
As we saw in the preceding paragraph, colloidal solutions of metals are more or less sharply colored. In some cases (Na, Ag) the absorption bands have the same shape as the atomic ones (\(F\)-bands), while sometimes, as we have already mentioned, in AgCl and AgBr sols they are located in the same region of the spectrum as the atomic ones. Therefore, for example, when working with colored crystals it is necessary first of all to establish the nature of the coloring centers (mineralogists very often have to deal with problems of this kind\(^1\)).

\(^1\) The urgency of this question is evidenced by the numerous reports and discussions at the conference on the colors of minerals, held in January 1938 at the Lomonosov Institute of the Academy of Sciences of the USSR. See the Proceedings of the conference, as well as the book by A. E. Fersman\(^{35}\).

Here there may be a number of possibilities.

1. The coloration may be caused by foreign colored ions incorporated into the lattice (for example Cu, Co, and many others). Such salts possess a definite absorption spectrum, but at present they have still scarcely been studied. Despite the prevalence of this case in the mineral kingdom, we shall not concern ourselves with it here, since it lies outside the scope of the present article, which deals with particles of pure metals.

2. The coloration may be due to intrinsic absorption falling within the visible part of the spectrum (AgBr).

3. Coloring centers of an atomic type may be involved (in all probability, such is the nature of the coloration of smoky quartz).

4. Colloidal particles may be involved (blue rock salt).

Let us see what optical measurements can give us in determining the nature of the centers in one case or another.

If the colloidal particles are sufficiently large, then the nature of the coloration caused by them can be determined by direct ultramicroscopic observations. This method, however, is not always sufficient, since, as has been pointed out, particles with a diameter up to \(5\,m\mu\) scatter almost no light, and such solutions appear optically empty.

Optical measurements, though more indirect, can give us indications on this question even in the case of the smallest particles. Thus, if, in measuring the absorption of light in a whole series of specimens of a colored substance, we obtain not one but an entire series of absorption or scattering curves, then already from this fact—indicating different particle diameters in each individual case—we may suppose the presence of colloidal rather than atomic coloration. Agreement of the entire system of curves with the theoretical ones should serve as a further confirmation of this supposition.

Let us illustrate what has been said by examples from the field of colored crystals that interests us in this article.

Alkali-halide salts. A typical example is naturally colored rock salt, which occurs in nature predominantly near potassium deposits in the form of dark-blue or violet pieces with a volume up to \(100\,\text{cm}^2\). Upon heating, the blue coloration passes into violet and reddish. It has long been suggested that here we are dealing not with any impurities, but with metallic sodium in colloidal distribution. Ultramicroscopic observations, carried out already by Siedentopf \(^{29}\), did in fact show the presence of a very large number of densely situated ultramicrons, colored in a color additional to the color of the crystal in transmitted light (brick-red for blue specimens, green for violet ones). A similar picture is observed in NaCl crystals colored additively (see below).

Despite the sufficient persuasiveness of direct ultramicroscopic observations, a number of mineralogists expressed doubts that here we are dealing only with sodium— na-

tion of it could not be detected by chemical methods. Therefore it seemed of interest to resort to a study of the optical properties of the colored rock salt, which was done by the author.

The absorption curves of the Na—NaCl system, calculated by the author3 from the Rayleigh—Mie formulas, are given in Fig. 17; Fig. 18 gives experimental absorption curves for a number of samples of naturally colored rock salt.

These two systems of curves coincide completely in their position in the spectrum and in the general character of the curves: as we have seen, these two factors for sodium are very characteristic and distinguish it among a number of other metals, which in most cases have broad maxima in the ultraviolet region of the spectrum. It is especially interesting that, besides the general form of the curve, its details are also reproduced; namely, the curve shows a second maximum for large particles, caused by the action of the second partial scattered wave and noticeable only in sodium because of the exceptional narrowness and sharpness of the absorption curves.

These data are sufficient to prove the colloidal nature of the coloration of rock salt.

Phosphors. We have already mentioned that, when external electrons are introduced into a phosphor containing silver ions, besides the atomic absorption band, a second band also appears, and the crystal is colored yellow. Under such treatment copper phosphor gives a bright-red coloration, nickel phosphor a brown one, and gold phosphor crimson and blue. Only in the last case does qualitative observation give indications of the colloidal nature of the coloring centers: in the first two, the field of the ultramicroscope remained optically empty even under the strongest illumination; if for silver and remarka-

Fig. 17. Absorption curves of the Na—NaCl system, calculated according to the Rayleigh—Mie theory

Fig. 18. Absorption curves for naturally colored salt (in relative units)

there was some change of hue upon heating, and also upon transition from crystal to crystal, whereas for copper the color remained unchanged.

The absorption curves were measured and compared with the theoretical ones for colloidal copper (Artsibyshev and Toporets²), nickel (Pogodaev²⁴), and silver. A cursory glance at these curves (Figs. 19 and 20) shows that here we do in fact have colloidal particles. The character of the curves is reproduced quite accurately: a sharp peak against the background of a broad absorption region for copper, and narrow maxima for silver. There is agreement with theory also in details, namely in the dependence on the refractive index of the medium. According to the theory (Fig. 14), the absorption curves of the Ag—AgCl system should be shifted toward longer wavelengths in comparison, for example, with the Ag—NaCl system; this is also observed experimentally (Fig. 20).

Fig. 19. Absorption of Cu—NaCl.
1 — calculated curve, 2—4 — experimental curves

The case of alkali-halide salts colored by colloidal gold, silver, and copper is essentially no different from the case of glasses colored by these metals, since the refractive index of glass is very close to the \(n\) of salts. As the very names of these glasses show (copper and gold ruby), in the case of Cu and Au we have a bright red coloration; silver gives yellow glasses.

Fig. 20. Absorption curves of silver in various media (smallest and small particles).
1 — Ag—glass — measurements by Ashcheulov, 2 — Ag—KJ (0.05 mol% Ag) — measurements by Veidlo, 3 — Ag—AgCl (photochemical separation) — measurements by Meiklar

Silver-halide salts. The question of the nature of the centers obtained under the action of light on these salts is connected with the question of the nature of the hidden—

of the photographic image. The first experiments not with photographic emulsions, but with isolated crystalline films of silver chloride and bromide, carried out almost simultaneously by R. Pohl ^22 and by the author of the present article ^27, showed that these films, under the action of active rays (from the region of their own absorption, i.e., blue and violet), become colored: colorless AgCl becomes violet, and yellow AgBr becomes green. Measurements of the absorption band showed that, in external appearance, it has the same form as in the well-studied case of alkali-halide salts. It was natural to suppose that here too the primary photochemical act leads to the formation of atomic centers. Ultramicroscopic observation showed, however, that this is not so, that here we are dealing with colloidal silver. In this connection the following doubt was expressed: it is known that colloidal solutions of silver in water usually have yellow tones, whereas here, for AgBr, the absorption lies in the red part of the spectrum. This misunderstanding is completely resolved if one takes into account the influence of the refractive index of the salts, which for silver halide salts ($n \sim 2.3$) must be especially strong.

Comparison of the entire system of experimental and theoretical curves here also gives complete agreement.

If the colloidal nature of the coloring centers is established, then the question arises of their size and shape.

6. Size of colloidal particles. The size of particles can be determined by two methods: 1) by the position of the absorption or scattering maximum in the spectrum and 2) by polarization ratios in the scattered light. We shall dwell here only on the first method.

As is known, comparison of the course of theoretical and experimental absorption curves for determining the diameter of particles is widely used in the case of “white” sols (dielectrics). Since here, as indicated above, we have, according to Rayleigh, a uniform increase of absorption with decreasing wavelength, then for determining the course of the curve one may confine oneself to data for the absorption of two wavelengths sufficiently far removed from one another.

Metals, as indicated above, in a number of cases give sharply expressed maxima, which shift along the spectrum when the particle diameter changes. Therefore, for these metals (Na, Ag, Ca, and, for larger particles, also Au) it is more correct to judge the size of the particles precisely by the position of the maximum ^1). As an example we shall give data for the already considered colloidal solutions of silver, copper, and sodium.

As can be judged from comparison of theoretical and experimental absorption curves (Figs. 19 and 20), the particles that give

^1) Kazantsev ^11 transferred to the case of silver sols the method for measuring the size of particles of dielectrics and, working on the “tail” of the absorption curve of colloidal silver, where the change in absorption upon increasing the particles is almost imperceptible, therefore did not make use of all the possibilities of this method.

red coloration in the case of copper and yellow in the case of silver, are very small; they do not scatter light and therefore should not be visible in the ultramicroscope (this is indeed the case).

An approximate estimate of the diameter gives the following order of magnitude (Table 3). The change in coloration with increasing particle diameter is less sharply expressed for silver than for sodium.

Table 3

Na—NaCl	Na—NaCl	Na—NaCl	Ag—NaCl (or Ag—glass)	Ag—NaCl (or Ag—glass)	Ag—NaCl (or Ag—glass)
Color of crystal	Position of maximum in mμ	Particle size \(2\rho\) in mμ	Color of crystal	Position of maximum in mμ	Particle size \(2\rho\) in mμ
Red	560—575	\(<20\)	Yellow	425—435	\(<30\)
Violet	575—600	20—40	Orange	435—500	30—80
Blue	600—650	40—80	Violet-blue	500—550	80—100

c. Shape of colloidal particles. The question of the shape of colloidal particles is of extremely great importance in elucidating the mechanism of their formation, i.e., the mechanism of crystallization. Indeed, the basic formulas of the optics of colloidal metals were derived on the assumption that the particles have a spherical shape. If this condition may be considered satisfied when a crystallite of a metal crystallizing in the cubic system is in fact a cube, then it is obviously not fulfilled for metals crystallizing in the hexagonal system. But even in the case of metals of the cubic system we have a very large number of forms other than the cube, in which crystallization of a given metal can occur. Particularly often, along with the cubic form, the octahedral form is encountered (for gold the octahedral form is encountered most often). Likewise, in artificial crystallization, for example in electrocrystallization[^17], silver separates in the form of octahedra.

If one calculates the volume occupied by an octahedron with edge \(a\), and compares it with the volume of a sphere circumscribed about the octahedron and of an elongated ellipsoid inscribed in the octahedron (such a calculation was made by Krishnan[^13]), it turns out that the volume of the inscribed ellipsoid \((0.65a^3)\) is closest to the volume of the octahedron \((0.47a^3)\), whereas the volume of the circumscribed sphere \((1.50a^3)\) is almost three times greater than the volume of the octahedron. Thus, by identifying the octahedron with a sphere, we make an error in estimating its size.

Methods for determining the shape of colloidal particles are based on 1) the study of absorption, 2) the investigation of polarization со-

relations in the scattered light (depolarization). Let us dwell again on the first method.

As was indicated above, Gans⁸˒⁹ extended the Rayleigh–Mie formulas to the case of oblate and prolate ellipsoids, though only for the smallest particles. The principal result of his calculations is that, if all the particles are oriented at random, the main absorption maximum splits into two. Chernyaev³⁸ modified Gans’s formulas for the case in which all

Fig. 21. System Ag—AgCl. \(a\)—absorption curve of spherical particles; \(б, в\)—absorption curves of oblate ellipsoids with an axial ratio of 0.62, for the \(\perp\) and \(\parallel\) positions of the electric vector; \(г\)—dichroism curve \(K_\perp - K_\parallel\).

the particles are oriented identically. In this case we are dealing not with a splitting of the maximum, but with its displacement—for oblate ellipsoids toward shorter wavelengths when the electric vector is parallel to the axis (Fig. 21) (the Gans curve for a random arrangement of the axes represents the superposition of the two maxima of curves \(б\) and \(в\)). In this example we encounter typical dichroism. As a measure of dichroism one usually takes the difference \(K_\perp - K_\parallel\); this quantity, generally speaking very small, can be measured directly (with a polarimeter), which considerably increases the accuracy of the results.

(To be continued in the next issue)

Literature

I, §§ 1, 2, 3

1. S. Artsybyshev, Transactions of the Physics Institute of the Academy of Sciences of the USSR, I, issue 3, 1937.
2. Van-Arkel, Chemical Bond, ONTI, 1934.
3. De Boer, Electron Emission and Adsorption, ONTI, 1936.
4. P. Evald and S. Herrmann, Strukturbericht, Ergänz. Band zur Z. Kristallogr., II, p. 211—213.
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1. In a similar manner Mollwo[^17] obtained crystals containing an excess of halide; they exhibit not electronic but “defect” (hole) conductivity. The difference from the preceding case consists in the fact that, along with electronic diffusion, diffusion of the halide in the form of charged molecules plays a large role here. ↩↩↩

2. We give the values of several atomic radii (in Å): Na — 1.86, K — 2.29, Cu — 1.24, Ag — 1.40, Au — 1.40, Tl — 1.66, Ni — 1.21, Pb — 1.69, Cl — 1.07, Br — 1.19, I — 1.36. ↩↩↩

3. As cited in the visible source page. ↩