On the Physics of Catalytic Phenomena

Structure and Genesis of Catalysts

P. D. Dankov, Leningrad

One of the most difficult questions of heterogeneous catalysis is the question of the structure and genesis of catalyzing bodies. The mutual connection between the structure of a catalyst and its history is obvious. To each structure there corresponds a definite complex of physicochemical stages that preceded its formation and determined its forms. Every slight modification of the conditions under which a catalyst is formed may lead to a serious change in its structure and, conversely, every requirement with respect to structure can be satisfied only after a complex analysis of the conditions of formation of the catalyst. Such a profound dependence undoubtedly requires a synthesis of our knowledge concerning the structure of solids and the processes of their emergence and transition into an equilibrium state.

In the first part of the present article—before analyzing the conditions of formation of catalysts—we have preferred to give a survey of data on their structure. Using a method employed by us in practical work, we differentiate the structural aspects of catalysts and consider each of them separately. In the second part, devoted to the genesis of catalysts, we shall try to approach structure and genesis synthetically.

Structure of Catalysts

1. Atomic-Molecular Parameters

In the doctrine of catalysis, a dependence between the atomic parameters of the catalyst and the parameters of the molecules reacting on its surface seemed natural. However, the factual material in this respect is very scanty.

In 1925 O. Schmidt[^1] noted that hydrogenation catalysis on metals proceeds in those cases when the corresponding metallic ion has a radius smaller than 0.49 Å for a monovalent ion, 0.7 Å for a divalent ion, 0.86 Å for a trivalent ion, and 0.99 Å for a tetravalent ion. The statement put forward was based on experiments on the hydrogenation of ethylene on various metallic—

hydrogenation catalysts. The sizes of the ions were taken from Grimm’s data². According to O. Schmidt, the explanation of the dependence between hydrogenation and the magnitude of the ion radius consists in the fact that small ion sizes facilitate ionization of the hydrogen molecule.

In his report at the physico-chemical conference, Academician L. V. Pisarzhevsky³ expressed the idea that the hydrogenation process is directly connected with the ability of the hydrogen molecule to penetrate inside the crystal lattice of the metallic catalyst. Penetration of the hydrogen molecule into the lattice proves possible in the case of sufficiently large interionic distances. The latter are calculated as doubled differences between the radii of atoms and the corresponding ions. Table 1 below contains the indicated interionic distances cited in the report.

TABLE 1

Ions	Fe++	Fe+++	Co++	Co+++	Ni++	Ni+++	Ru++	Rh++
Interionic distances in Å	0.88	1.2	0.88	1.22	0.92	1.24	1.3	1.32

Pd++	Os++	Ir++	Pt++	Cu+	Cu++	Ag+	Au+	Pb++
1.38	1.28	1.36	1.44	0.64	1.08	0.62	0.16	0.82

Comparing the values obtained with the dimensions of the hydrogen molecule (the distance between protons is approximately 0.5 Å and between electrons—1.01 Å), the speaker notes that typical hydrogenation catalysts have interionic distances reaching 1.25–1.4 Å; the same quantities for poor catalysts (Ag, Au and Pb) prove to be less than 1 Å. At the same time, the speaker indicated that for lead peroxide and manganese peroxide, on which hydrogenation catalysis does not proceed, the interionic distances approach zero. Without entering into a discussion of the supposition put forward by Acad. Pisarzhevsky, it should be noted that the comparison he made is of broad interest.

The work of Bredig and Allolio⁴ showed that a slight change in the crystallographic parameters of platinum and palladium under deep adsorption of hydrogen (possibly—the formation of hydrides) completely destroys the catalytic activity of these metals. Similarly, upon the transition of nickel from the cubic system to

hexagonal (likewise with deep absorption of hydrogen) hydrogenation catalysis ceased.

Of particular interest is the work of Balandin,^5 who investigated the dehydrogenation of cyclohexane \((\mathrm{C}_6\mathrm{H}_{12})\) on metals. In the hypothesis proposed by Balandin, the existence is assumed of special active regions of the surface which determine the formation of a given chemical bond between two atoms adsorbed and oriented by this region. For each pair of atoms there must be corresponding active regions, and for a complex transformation a definite combination of such regions is required. In considering the phenomenon of the dehydrogenation of cyclohexane, the author uses geometrical schemes for this purpose. It is assumed in advance that the arrangement of the active centers on the surface must possess a symmetry coinciding with the symmetry of cyclohexane. For metals of the cubic system such an arrangement of atoms of active centers is realized for octahedral faces, on which, in the author’s opinion, dehydrogenation catalysis also takes place. In Fig. 1 below an octahedral face is shown, on which the metal atoms are arranged at the vertices of triangles. The position of cyclohexane is marked by heavy lines, with the carbon atoms indicated by dots. The active centers—metal atoms—are marked in the scheme by crosses \((1, 2, 3, 4, 5, 6)\), where atoms \(1, 2, 3\) hold pairs of carbon atoms, while atoms \(4, 5, 6\) attract two hydrogen atoms. In the figure the arrows indicate the direction of motion of the hydrogen atoms when they are removed from the cyclohexane molecule (dehydrogenation). On the basis of the model obtained, the author showed that partial dehydrogenation is impossible, for example the formation of cyclohexene \((\mathrm{C}_6\mathrm{H}_{10})\) or cyclohexadiene \((\mathrm{C}_6\mathrm{H}_8)\).

Fig. 1.

In exactly the same way the experimental fact was substantiated^6 that five- and seven-membered hydrogenated rings cannot catalytically lose hydrogen; the latter follows directly from the constructed model of catalysis (the absence of coincident elements of symmetry in the lattices of the catalysts and of the corresponding cyclic compound). A comparison of the data on dehydrogenation catalysis on various metals and of their geometrical characteristics convincingly indicates that only those metals are capable of catalysis which have faces with the above-noted arrangement of atoms at the vertices of triangles. The latter occurs for metals with a cubic lattice, with centered faces, and with the hexagonal lattice of the basal pinacoid. The number of active metals should decrease if one takes into account the dimensions of the lattice elements and of the cyclohexane molecule. A simple geometrical calculation shows that, at a corresponding distance of the hydrogen atom being removed from the attracting center (for example

4 of the atom in Fig. 1) or, conversely, its excessive approach leads to the impossibility of dehydrogenation catalysis. In Fig. 2 the change in the indicated distance of the hydrogen atom is shown graphically as a function of the radius of the catalyst atom. The narrow interval of distances from \(1.0\ \text{Å}\) to \(0.79\ \text{Å}\) corresponds to good dehydrogenation catalysts.

The hypothesis put forward by Balandin finds confirmation also for other six-membered cyclic compounds.

Fig. 2.

We have dwelt in considerable detail on Balandin’s hypothesis and considerations because of their clarity and concreteness, which rarely penetrate into the theory of heterogeneous catalysis. It must be noted, however, that spatial concepts in catalytic phenomena had already been expressed in general form by Berck\(^7\), Langmuir\(^8\), Adkins\(^9\), and others.

A concrete comparison of the parameters of the crystal lattice of a catalyst and its selective activity may be found in the X-ray and catalytic study by Aborn and Davidson\(^ {10}\) of the Cu—ZnO system. (Here one should also mention the most recent work of Ekkel, Zeit. Elektrochem., 39, 865, 1933, on the dependence of the lattice constant of \(\mathrm{Fe_2O_3—Al_2O_3}\) and catalytic activity.) They showed that, when the weight ratios of the components were changed, the lattice constants of copper and zinc oxide changed and passed through a maximum or a minimum. At the same time it was found that the composition of the final products of the catalytic decomposition of methyl alcohol is related to the lattice parameters of Cu and ZnO. A comparison of the curves of the change in the parameters and the yield of the corresponding products of decomposition of methyl alcohol as a function of the composition of the catalyst (Figs. 3 and 4) shows that this relationship does indeed exist. As may be seen from the figures, the yield of methyl formate \((\mathrm{HCOOCH_3})\) falls rapidly with increasing lattice constant of copper and remains almost constant in the region between the maximum and the minimum. In exactly the same way, the yield of carbon monoxide correspondingly increases as the lattice parameters of zinc oxide decrease and falls as they increase.

From the data of Aborn and Davidson it is impossible to draw quantitative

conclusions. However, this work points to the necessity of investigations in this direction, and it must be thought that the regularities in the catalytic process on catalysts with changing lattice parameters will receive quantitative formulation.

Fig. 3. Axes: copper lattice constant \(b\), Å; \(\%\) decomposition of methanol to \(\mathrm{HCOOCH_3}\); composition scale \(\mathrm{ZnO}\) / \(\mathrm{Cu}\).

Fig. 3.

The X-ray study of such an important catalyst as iron has been carried out by various investigators. In 1928 Meyer\(^{11}\) established that iron is present in the form of \(\alpha\)-iron (cubic with centered faces). The work of Wickoff and Crittenden\(^{12}\) led to the same results and, in addition to them, showed that an iron catalyst in the presence of activating additives preserves the structure of \(\alpha\)-iron. In agreement with the works noted is the investigation of supersensitive iron catalysts by Mittasch and Kuss\(^{13}\). Finzi’s pyrophoric iron\(^{15}\) also proved to be an \(\alpha\)-modification.

Fig. 4. Axes: zinc lattice constant \(b\), Å; \(\%\) decomposition of methyl alcohol to \(\mathrm{CO}\); composition scale \(\mathrm{ZnO}\) / \(\mathrm{Cu}\).

Fig. 4.

Different data were obtained by Aizengut and Kaup\(^{14}\), who studied the Fe—N system after a sufficiently prolonged interaction of iron with ammonia. It turned out that the interaction of nitrogen and iron is so great that iron nitrides can be formed; as a result of this, lines of \(\gamma\)-iron appear in the X-ray diagrams. At the same time, of course, changes in the parameters of the catalyst occur. Obviously, the synthetic process is self-prepar-

*

paves its way by changing the parameters of the catalyst to the required value. An X-ray study of iron nitrides, carried out by Hegg¹⁶, also indicates the formation of a γ-structure in nitrogen-containing iron.

We have dwelt on the role of atomic-crystalline parameters of metallic catalysts in catalysis. This does not mean that they are important only for metals. The same can also be observed for more complex catalysts.

Thus, for example, Boudart and Velo¹⁷ established for iron oxide (Fe₂O₃) two sharply differing activities, which corresponded to two crystalline modifications of iron oxide (cubic and noncubic). In parallel with this, the magnetic properties of the oxide changed. The magnetic (cubic) modification of iron oxide was very catalytically active and possessed a large adsorption capacity; the nonmagnetic (rhombic) modification was inactive and adsorbed weakly.

In the wave-mechanical work on catalysis that appeared in 1931, Born and Weizkopf¹⁸, in their calculations, assign a place also to the atomic-molecular parameters of the catalyst and of the reacting molecules.

However, the role of atomic parameters in catalysis has not yet been sufficiently clarified. Experimental material has still not been accumulated in sufficient quantity, and, in this connection, the existing theoretical schemes suffer from one-sidedness.

Quite recently, Eckell⁷⁵ drew attention to the catalytic properties of cold-worked materials. As is known, rolled or drawn metals possess a so-called “phase structure” (i.e., orientation of crystallites), which is almost always accompanied by distortion of the parameters of the crystal lattice. In Eckell’s opinion, the change in the parameters of the crystal lattice (in comparison with the normal one) is the explanation for the high catalytic activity both of a rolled nickel plate and of a polished nickel surface.

2. Character of aggregation and degree of dispersion

As early as 1843, Mitscherlich¹⁹ attempted to characterize a catalyst by its specific surface. The latter in fact has enormous significance for a catalyst, primarily determining its effectiveness and productivity.

Massive metals (for example, those fused into an ingot) are also catalysts, but their catalytic effectiveness is negligible. This is entirely natural, since the productivity of any catalyst is proportional to its surface (provided that other physical factors do not change), and the surface of a massive body is negligibly small in comparison with the surface of the catalysts usually used. Thus, for example, 1 cm³ of a substance shaped as a cube has a surface

in 6 cm². After such a cube has been broken up into small cubes whose edges are no greater than \(10^{-6}\) cm (the most commonly used catalysts have particles of 10–15, \(10^{-6}\) cm), their total surface area increases a millionfold, i.e., the surface grows already to 60 m². A comparison of these quantities—6 cm² and 60 m²—convincingly demonstrates the validity of the experimental material which speaks of the negligible activity of massive bodies. The indicated ratios of the surface sizes of massive and subdivided bodies become less striking if we take into account the comparatively tortuous microrelief of the surface, which can increase its magnitude many times in comparison with the geometrically measured one. Thus, a platinum plate coated with electrolytic platinum has a surface 2000 times greater than the apparent one (Bouden and Rideal²⁰).*

The surface sizes of massive bodies may vary sharply from case to case. A metal plate treated with emery increased its surface 10-fold; after chemical treatment (oxidation–reduction) the surface increased 5-fold. Of essential importance for massive bodies is the degree of subdivision of the surface particles and their deformation, as was shown in the cited work of Ekkel.

Massive catalysts include the platinum gauzes used in the production of nitric acid from ammonia. Their use is explained by the high temperature and the related intensity of the process. Incidentally, it must be said that the gauzes employed are made of comparatively thin threads (for example, 0.04 mm), whose surface area for 1 cm³ will be approximately 1000 cm², i.e., almost a thousand times greater than for a solid cube.

Considering the surface of massive bodies as geometrically continuous, it should be pointed out that in practice one never deals with a crystallographically continuous surface of massive bodies. Metals usually constitute a dense aggregate of small (more often micro-) crystals, deformed in such a way that there are no gaps between them.

At present there is very little information about the nature of interparticle boundaries. It is important to note, however, that the forces binding individual crystallites to one another (at the boundaries) are considerably greater than the forces joining the elements of the lattice²¹. For a single-crystal surface there is as yet no experimental catalytic material, and, despite the importance of data on the catalytic functions of the individual lattice elements of a single crystal, this problem cannot be solved soon, owing to the difficulty of the experiment.

Passing to another type of aggregate state of cataly-

* The method used by Bouden and Rideal to determine the effective surface of plates consisted in measuring their electron potential in an atmosphere of hydrogen.

—porous, non-dense grains, we often also find very substantial bonding forces between the individual single crystals. This is expressed in the great strength of the grains. Everyone is well acquainted with the extremely strong and at the same time highly porous grains of silica gel. Modern iron catalysts for ammonia synthesis likewise consist of very strong, porous grains. X-ray analysis^12 reveals in the iron grains micro- and ultramicrocrystallites (from \(10^{-3}\) to \(10^{-6}\) cm). The nature of the bond between the crystallites, as also for metals, remains obscure for the time being. Judging from the fact that the grains of the reduced metal have approximately the same geometric volume as the grains of the initial magnetite \(\mathrm{Fe_3O_4}\), one must assume a continuous transition of magnetite into metal (during reduction). As a result of this process, the metallic atoms are displaced slightly in order to form their own lattice (body-centered cube), while the oxygen atoms, having combined with hydrogen, are removed directly from the magnetite lattice (a cube with centered faces); the vacant sites thus formed constitute a volumetric reserve for the formation of pores.

At present there is insufficient experimental material to draw a detailed structural picture of porous granular catalysts. It is to be hoped that in the future investigators will pay serious attention to this aspect of the structure of solids and thereby shed light on many obscure areas of catalysis.

Powdered catalysts likewise consist of grains, only of very small dimensions. Metallic powders are formed mainly by the reduction of powdered oxides or gels. They can also be formed from compact initial bodies in those cases where the bond between the crystallites that arise is insignificant, especially when there is a large difference in the volume of the starting substance and the final product. For catalysis it is a very essential circumstance that powders hinder the diffusion of reagents to the inner layers; therefore, during the process a large amount of catalyst remains inactive, as a “dead mass.” Powdered catalysts differ outwardly from one another in color when passing from powders of one dispersity to another. The most dispersed powders have the blackest coloration; the larger the powder particles, the lighter they are in color. Powders also are built of crystallites whose crystallographic parameters do not differ from those of massive bodies. Powders readily change their dispersity when the temperature is raised and during an intensive catalytic process.

Thin-layer catalysts on supports possess high dispersity and stability. Such catalysts are most often used in practice. They may arise by various routes. The most common is the chemical route, when a substance uniformly distributed over the surfac-

... the starting product (for example, a metal oxide), depending on the nature of the support, is chemically transformed (reduced) into a thin layer of catalyst. Thin layers can be obtained electrolytically, if the support conducts electricity. When granular carriers are immersed in the molten substance of the catalyst, they can become covered with a not too thick layer of solidified catalyst. Decomposition of a gaseous compound with liberation of the catalyst on the surface can also lead to the formation of thin layers. Finally, condensation of catalyst vapors on a cold surface gives a very pure catalyst in the form of extremely thin layers. The study of the structure of thin layers on supports has so far been poorly organized.

Up to now we do not know in what manner the thin layer and the support are connected with one another, which sites of the support are preferentially occupied by the catalyst, how the thin layers are oriented, and so forth.

Examples of thin-layer catalysts may be platinum on asbestos, quartz, magnesium pyrophosphate, etc. (an oxidation–reduction catalyst), then nickel on various supports (a hydrogenation catalyst), vanadium oxide on chromium oxide (an oxidation catalyst), platinum or nickel on carbon, and so on. Typical supports in various cases prove to be asbestos, carbon, silica gel, kieselguhr, and others. The study of the structure of thin-layer catalysts on supports involves a number of difficulties which, in most cases, have not allowed the question to be clarified.

Up to now the nature of the distribution of the catalyst on the support is insufficiently known: whether it is arranged in the form of the thinnest film or forms accumulations in separate regions of the carrier, leaving part of the surface uncovered. Here, optical-microscopic investigations are probably necessary. The thickness of the catalyst layer on the support may be very important. Here, there is probably a certain optimum. The work of Holmes et al.^22^ shows quite convincingly that, in the case of platinum on asbestos (and also on silica gel), there is a limit to the amount of platinum (deposited on a constant amount of asbestos surface) beyond which there is no increase in catalytic activity. Recalculation of Holmes’s data shows that an optimum already occurs at a layer thickness of 30–40 mμ. Further increase in the thickness of the platinum layer does not increase the activity of the catalyst. The results of an investigation in vacuum of condensed nickel^23^ show that the maximum activity occurs at a layer thickness of 15–20 mμ.

No less important a circumstance is, as shown in Thomson’s work^24^, the crystalline form in which thin layers on supports are obtained. It turns out that the character of the support is significantly reflected in the structure of the crystallites forming the thin layer.

Platinum black deposited on quartz has a normal...

crystallographic structure and possesses normal catalytic properties. On the contrary, platinum black deposited on copper has an abnormal crystal lattice and does not exhibit catalytic activity. For platinum on asbestos, which, as is known, has high activity, a normal lattice was not found.

The study of thin layers of metals obtained by condensing their vapors on a cold surface indicates an orientation of the deposited particles in one of the directions parallel to the surfaces of the substrate[^25]. This fact, still unexplained, probably plays an essential role in the activity of the catalyst.

One may approach the explanation of the orientation of crystallites on the surface in the following way. On the surface of the substrate there act forces directed tangentially to it. Metal atoms arriving at the surface initially possess comparatively high mobility and are easily oriented in the direction of the surface forces of the substrate. The crystallization that then proceeds is all the time under the influence of the orienting surface forces.

Apparently, such layers lie on the substrate not as a continuous film; the layers close to the surface of the substrate participate in the catalytic process just as do the uppermost ones[^23]. Perhaps the latter circumstance serves as an indication of the porosity of very thin ($10^{-6}$ cm) layers of metals. In numerous studies on the electrical conductivity of thin layers, their discontinuous structure is often assumed up to a certain thickness of the deposit (20—50 m$\mu$), whereas in other investigations the continuity of considerably thinner deposits is assumed[^26].

A special place is occupied by catalysts dispersed in a liquid in the form of the finest particles—these are colloidal catalysts and suspensions[^27]. The known colloidal solutions of platinum, palladium, nickel, etc., are excellent catalysts for hydrogenation processes, especially in liquid systems. Numerous studies in colloid chemistry provide well-known ideas about the state of colloidal particles in solutions. Already after the first works of Zsigmondy and Siedentopf with colloidal solutions of gold, no one any longer has any doubt that colloidal particles have a crystalline structure. However, the form and magnitude of the bonding of the individual crystals (which form the particles) with one another, as also for massive metals, remains unknown to us. The relatively low stability of colloidal systems indicates the presence of forces between the particles, but their nature still remains obscure. In colloidal catalysts used in practical cases there is always present the so-called “protective substance,” which prevents coagulation of the particles. According to modern conceptions, the “protective substance” envelops the catalyst particles and gives it the properties of so-called “lyophilic” particles. Along with this, the surface and

the thickness of a colloidal particle may be, in one way or another, filled with solvent molecules, which constitute the medium for the colloidal particles of the catalyst.

The attention of many investigators who have dealt with the structure of catalysts has often been concentrated on the question of the degree of dispersity of the catalyst particles.

As has already been noted earlier, real catalysts are bodies of a high degree of dispersity. The porous grains, powders, thin-layer and colloidal catalysts indicated by us are used in practice because the particles composing them have very small linear dimensions, within the limits from \(10^{-3}\) cm to \(10^{-7}\) cm.

Just as in colloidal solutions, especially in the case of lyophobic sols, primary and secondary particles are distinguished, for powders we have the same relationships. The primary particles here turn out to be the smallest single crystals of the substance, the dimensions of which may vary from tens of ångströms to several microns. These crystallites, when the temperature is raised, are capable of growing larger at the expense of smaller neighbors. Secondary particles are aggregates of primary particles bound to one another by interfacial forces and arranged randomly with respect to one another. Their size varies within the limits from fractions of a micron to several microns and depends, obviously, on those impurities (interlayers) that accompany the given powder. At the same time it also depends on the method of preparation of the given powder. As we saw above, secondary particles can reach microscopic dimensions (grains), whereas the primary particles forming these grains may remain within the limits of hundreds of ångströms.

The dimensions of secondary particles are easily determined either by microscopic observations or by mechanical methods. In the latter cases elutriation or centrifugation may be used. Application of Stokes’ law makes it possible to calculate the size of the particles. It is likewise possible to determine particle sizes by an optical method (degree of light scattering), illuminating a powder suspended in some liquid.

The dimensions of secondary particles can also be determined approximately by measuring the total internal surface of the powder. The value calculated from the internal surface will approximately characterize the linear dimensions of the secondary particles.

In addition, knowledge of the surface of a powder is of independent interest, since the activity of a catalyst has until now been associated with its dimensions. Determination of the internal surface of a powder may be carried out by various methods. Schmidt\(^1\), and after him Schwab\(^ {28}\), determined the magnitude of the surface by comparing the rates of dissolution of powders in acids. It was assumed thereby that the rate of dissolution is proportional to the surface. A refinement of the method for determining particle sizes by dissolu-

...was performed by Roller,^29 who showed that in some cases it leads to erroneous results.

Paneth,^30 and also Hahn,^31 measured the surface by adsorption of a radioactive substance and subsequent determination (by the electrometric method) of the quantity of adsorbed radioactive molecules, the number of which was taken as proportional to the surface of the powder. Numerous determinations of surfaces were based on measurements of adsorption on powders.^32

Dunn^33 and Constable^34 determined the surface of a powder from the thickness of an oxide layer obtained by introducing into a vessel with the powder a known quantity of oxygen. The thickness of the film was determined from the coefficient of refraction of the film from the temper colors (according to Newton’s equation for the rings named after him).

For determining the sizes of primary particles, in all cases it is necessary to use the X-ray method, which makes it possible—for a definite range of sizes—to calculate the magnitude of the particle from the width of the Debye lines by the Debye–Scherrer formula

\[ B = 2\sqrt{\frac{\ln c^{2}}{\pi}\cdot\frac{\lambda}{D}\cdot\frac{1}{\cos \frac{\Theta}{2}}} + b, \]

where \(\lambda\) is the wavelength of the X-rays, \(D\) is the linear dimensions of the crystallite, \(\Theta\) is the diffraction angle, and \(b\) is a constant depending on the dimensions of the camera.

For larger particles, the method developed by Czochralski^35 proves applicable. This method consists in illuminating the specimen with a narrow beam of “white” X-rays, and recording the diffraction pattern on a flat photographic plate; moreover, the number of Laue spots on it proves to be approximately proportional to the number of crystals falling within the field of the beam of rays.

Very important data on the dispersion of a catalytic powder are given in the work of Taylor, Kistiakowsky, and Perry,^36 who determined the particle sizes of platinum powders by various methods and measured their activity. It was found that the sizes of crystallites measured by X-ray analysis proved to be many times smaller than the values obtained in mechanical (elutriation and centrifugation) and microscopic studies. Thus, for two samples of platinum powder, from the width of the X-ray lines the order of magnitude of the crystallite sizes was determined to be 30 Å, whereas microscopically (and also by calculations according to Stokes’ formula from elutriation and centrifugation experiments) the measured particle size was of the order of 10,000 Å. Here the necessity is especially clearly seen of distinguishing two types of dispersion of powders: 1) dispersion characterizing the sizes of primary particles, crystallographically homogeneous in structure, and 2) dispersion of secondary particles, representing a disordered aggregate of primary ones. Measurement of the activity of two preparations of platinum powders having approximately identical sizes of secon-

particular particles (10,000 Å), showed that the preparation whose primary-particle sizes were of the order of 30 Å proved to be substantially more active, whereas the particle sizes of the other preparation differed little from the magnitude of the secondary formations.

The importance we have noted of the magnitude of the catalyst surface, as the surface of contact with the reactants, is determined by its degree of dispersion. At the same time, the number of the so-called “active sites” of the catalyst is also determined by the degree of dispersion. In the works of Taylor 37, Schwab 38, Stransky 39, and others, the doctrine of “active sites” received broad development, and active sites were often localized at the corners and edges of crystallites. The difficulties of establishing the role of crystalline edges and corners in heterogeneous catalysis have not made it possible to solve the problem completely, although a considerable number of works have been devoted to the question under consideration.

In colloid chemistry one can find a simple calculation of the total surface of a dispersed substance. There it is indicated that the sum of the surfaces of cubes \((S)\), obtained by crushing one cube with edge length \(l\) into \(n^3\) parts, will be equal to:

\[ S = 6\left(\frac{l}{n}\right)^2 n^3 = 6ln, \tag{1} \]

i.e., it is directly proportional to the dispersion \((n)\). It is easy to find that the sum of the perimeters of the edges \((p)\) of the same cubes changes differently 40; it will be equal to:

\[ P = 12\left(\frac{l}{n}\right)n^3 = 12ln^2, \tag{2} \]

i.e., the total perimeter of the edges of cubes obtained by dispersing a cube with edge length \(l\) into \(n^3\) parts is proportional to the square of the dispersion \((n^2)\).

It is still simpler to find that the total number of trihedral angles is proportional to the cube of the dispersion \((n^3)\).

Taking the noted relationships into account and making parallel measurements of the dispersion and activity of catalysts, it would be possible to establish which elements of the crystal lattice play the decisive role in the catalytic process, since, with a uniform distribution of “active points,” the activity of the catalyst would be proportional to the surface (i.e., to the dispersion); with a nonuniform distribution of them, the activity would be proportional either to the total length of the edges (i.e., to the square of the dispersion) or to the number of trihedral angles (i.e., to the cube of the dispersion).

In the problem posed, special difficulties are encountered, connected with the existence of primary and secondary particles. It is necessary to consider two kinds of dispersion, depending on the size of the monocrystals, on the one hand, and on the magnitude of their aggregates, on the other. We as yet have no data for recognizing the predominant significance of one of the kinds of dispersion in the phenomena of catalysis. In all probability, they are互相

complement each other. If the size of the secondary particle affects primarily the total surface of the catalyst, then the magnitude of the primary particle is reflected chiefly in the number of active elements of this surface. It seems to us that the sizes of the primary particles play the predominant role, as was also shown in the work of Taylor, Kistiakowsky, and others.^36

The first data on the dependence of activity on dispersity may be found in O. Schmidt,^1 who worked with nickel catalysts. Dispersity was determined by comparing the rates of dissolution of nickel powders in acid, and activity from the hydrogenation reaction of ethylene ($\mathrm{C_2H_4 + H_2 = C_2H_6}$). A simple proportionality was established between activity and dispersity (surface). Similar results were obtained by the Italian chemist Levi,^41 who investigated a platinum catalyst for the oxidation of sulfurous gas. In this case the dispersity was determined already by an X-ray method, by comparing the width of the interference bands, i.e., in this case data were obtained for the size of the primary particles (single crystallites).

Fig. 5.

In the field of catalysis at the solid—liquid boundary, one may note the work of Lottermoser,^42 who studied the relationship between the particle sizes of metallic tungsten and the rate constant of the decomposition of hydrogen peroxide. The author dealt with coarse suspensions, the particles of which reached $0.13$ mm in cross section. It is difficult to say what type of particles was used for the experiment. However, from the diagram (Fig. 5) it is evident that the reaction rate increases not in proportion to the square of the particle cross section, but more slowly. From this it may be concluded that in Lottermoser’s experiment some complicating circumstances were superimposed on the phenomenon, probably connected with the formation of $\mathrm{WO_3}$ during the reaction, since in the simplest case the reaction rate should have been proportional to the surface of the catalyst, i.e., to the square of the cross section of the particles.

Rather confused relationships are found in the work of Christiansen and Huffman ^43, who investigated the reaction between vapors of methyl alcohol and water \((\mathrm{CH_3OH} + \mathrm{H_2O} \to \mathrm{CO_2} + 3\mathrm{H_2})\) on copper diluted with various amounts of magnesium oxide. In the authors’ opinion, the copper thereby obtained had different dispersities, depending on the amount of magnesium oxide added. A decrease in the amount of copper in the mixture caused an increase in the activity of the preparation up to a certain limit, after which a fall in activity was observed. The authors assume that one possible reason for the observed course of activity may be the lowered activity of highly dispersed copper.

An X-ray and microscopic study of certain metal oxides was carried out by Bredig ^44 and others, who found a parallelism between particle sizes and the activity of the preparations.

In the work of Clark, Asberg, and Wick ^45 we already find a decrease in catalyst activity with increasing dispersion. The investigators determined, by the X-ray method, the dispersity of nickel preparations obtained by various methods (reduction by organic substances, hydrogen, sodium hypophosphite, etc.). The activity of such preparations was studied in the work of Adkins and Lazier ^46.

Fig. 6.

The striking result obtained by Clark and others can to some extent be explained by unaccounted-for features of the aggregation of crystallites. It is possible that the size of the crystalline aggregates increased together with the decrease in the dimensions of the primary crystallites measured by the X-ray method.

A systematic investigation of the question of the influence of dispersion on activity was carried out by Schwab and Rudolph ^28. The object of the investigation was also nickel, which in all cases was obtained by reduction of nickel oxide with hydrogen. The dispersity of the catalyst was varied by changing the reduction temperature. It was measured, as in O. Schmidt’s work, by comparing the rates of dissolution of the powders in hydrochloric acid. The data obtained by Schwab and Rudolph decisively indicate that the catalytic activity increases far from proportionally with dispersity. The results of Schwab and Rudolph’s work are well characterized by the diagram in Fig. 6.

As is evident from the figure, the activity curve \((b)\) rises very steeply already from the very beginning. If the activity \((a)\) is expressed as a function of the surface \((S)\) (dispersity),

\[ a = kS^m, \]

then we find that the magnitude of the exponent \((m)\) will lie within the limits \(2 < m < 3\).

Based on Schwab’s data, we too may conclude that in the activity of a catalyst the predominant role is played partly by the edges and partly by the corners of crystallites. It should nevertheless be noted that the investigators’ conclusions are based on only four preparations—experiments; the method they used for determining particle size may contain sources of error, as Roller has recently shown.^29

At the same time, the dissolution method does not give definite results either for the magnitude of primary particles or for secondary particles, providing only a general summary picture.

Moreover, the catalytic reaction was carried out in a liquid (condensed) system, work with which also often leads to errors. It seems to us that the important problem concerning the significance of dispersion, posed before researchers of catalysis, has not yet been sufficiently solved and awaits its earliest and thorough development.

In the study of catalysts containing minimal additions of an “activator” (promoter), their high dispersion is found, which reaches a high degree under the influence of these additions.

It has long been known that powders of pure substances possess a significantly smaller specific surface than contaminated powders. This was shown in 1899 by Baxter^47 in the study of hydrogen absorption by metals obtained from oxides of varying degrees of purity. He also showed that some impurities produce the opposite effect—a decrease in surface (for example, cobalt bromide added to the original cobalt oxide), or do not affect the degree of dispersion (sodium bromide added to the original cobalt oxide).

In the work noted by us of Wijkoff and Crittenden^12 it was shown that crystals of iron obtained from a pure oxide are significantly larger than crystals arising from an oxide containing \(K_2O\) and \(Al_2O_3\).

The adsorption experiments of Taylor and Russell^48 and the investigation of the activity by Medsforth^49 for a pure nickel catalyst and one “promoted” with thoria showed that a 20% change in the adsorption capacity of nickel leads to a 10-fold increase in activity.

Turning to the structural language, it can be established that the addition of thoria increases the surface of nickel powder by 1.2 times and the number of active sites by 10 times.

If by active sites we take corners, then, considering their number proportional to the cube of the dispersion, or, what is the same, to the cube of the surface, this gives an increase in activity only by a factor of 1.7:

\[ \frac{a_2}{a_1}=\frac{k(1.2)^3}{k(1)^3}=1.7. \]

It would seem that for the case considered it is necessary to accept not quantitative changes in the catalyst, but qualitative ones.

However, there are considerations, so far as we know not yet introduced in the literature, which leave open the possibility of applying quantitative measures when comparing changes in a catalyst in the presence of foreign substances and changes in its activity.

Very simple geometrical constructions show that the perimeter of the edges of crystallites (and likewise the number of angles), with negligible changes in their dimensions, may increase very greatly because of irregularities of growth. Thus, for example, if cubic recesses are made on the surface of the original cube in a checkerboard pattern (as shown in Fig. 7), then the surface under such a change of the cube increases twofold independently of the number of recesses along the length of the cube edge, whereas the perimeter of the edges grows in proportion to this number, namely:

$$ P = 6l(n + 2)^*, $$

where \(l\) is the edge length and \(n\) is the doubled number of recesses along the edge length of the original cube.

Fig. 7.

Considering the case discussed by Taylor and Russell (ni-

* The calculation of the change in the magnitude of the surface and of the perimeter was carried out as follows.

If \(m\) is the linear dimension of a recess, then along the edge length the number of these recesses will be \(l/2m\). On one face their number will be \(\left(\dfrac{l}{2m}\right)^2\), and for all faces it is equal to

$$ 6\left(\frac{l}{2m}\right)^2 - 6\frac{l}{2m} = \frac{3l}{m}\left(\frac{l}{2m} - 1\right). $$

For sufficiently small values of \(m\) (in comparison with \(l\)), the unit may be neglected in comparison with \(\dfrac{l}{2m}\). Then the number of recesses \((N)\) will be expressed by the formula:

$$ N = \frac{3}{2}\left(\frac{l}{m}\right)^2 . \tag{1} $$

The surface dimensions for a crystal with recesses are found in the following way: each recess is associated in the general case with the disappearance of a surface \(m^2\) and the appearance of a new surface \(= 5m^2\), i.e., an increase by \(4m^2\). For the entire surface of the cube, the increment of surface \((\Delta S)\) is determined by formula (2):

$$ \Delta S = \frac{3}{2}\left(\frac{l}{m}\right)^2 \cdot 4m^2 = 6l^2 . \tag{2} $$

The surface of the original cube, as is known, is equal to \(6l^2\), i.e., for any number of recesses (if it is sufficiently large) the surface of the cube increases twofold and will be equal to \(12l^2\).

The perimeter of the edges of the altered cube is also determined quite simply. In the general case, with the appearance of a recess, new edges are formed with a total length,

kel and thorium oxide), we find that as little as 19% of the nickel crystals, owing to growth irregularities in the presence of thorium oxide, need form indentations of the type analyzed for the total surface of the crystals to increase by a factor of 1.2. If we take a portion of crystals with surface \(=0.18 S\) and subject them to the above-mentioned change, we obtain \(=0.38 S\); adding to this the unchanged remainder \(0.82 S\), we obtain \(1.20 S\). In order that the number of active sites (the perimeter of edges) of the entire catalyst should increase 10-fold, it is necessary that the activity of the 19% of crystals taken by us increase 50-fold, with the number of indentations determined from the relation:

\[ \frac{6l(n+2)}{12l}=50, \]

whence \(n=23\), or the number of indentations is \(\sim 11\) along the length of the edge of each crystallite. (The linear dimensions of an indentation \(=\frac{l}{n}=\frac{l}{23}\).)

Fig. 8.

In reality, of course, there is no such regularity in the distribution of convolutions (indentations) in the crystals, although the simplified method of calculation used by us probably leads to results corresponding to reality. In any case, facts which seemed to require a qualitative explanation find a quantitative answer.

When passing into the region of high dispersion of the catalyst, we find a phenomenon that contradicts the foregoing. A far-reaching increase in the degree of dispersion may lead to a decrease in the activity of the catalyst.

In colloid chemistry the existence of the so-called “region of maximum colloidality” has long been pointed out. Considering the intensity of various properties as a function of the degree of dispersion \((n)\), one can find such a region of dispersion in which these properties reach their maximum expression (Fig. 8). Thus, for example, the color of many colloidal solutions is strongest for true colloidal particle sizes \((10^{-6}—10^{-7}\ \text{cm})\), whereas coarse suspensions \((10^{-3}—10^{-4})\) and molecular-ato—

equal to \(3m\). For all faces the increase in the perimeter of edges \((\Delta P)\) is expressed by the formula:

\[ \Delta P=\frac{3}{2}\left(\frac{l}{m}\right)^2\,4m=6\frac{l^2}{m}, \tag{3} \]

putting \(n=\frac{l}{m}\), where \(n\) is twice the number of indentations, we obtain for the magnitude of the full perimeter of edges \((P_2)\):

\[ P_2=6ln+12l=6l(n+2). \tag{3a} \]

mary solutions, on the contrary, are weakly colored. The same may be said of viscosity and other properties.

The catalytic properties probably also obey this rule. We know that a colloidal solution of platinum, containing the finest crystallites of platinum, is an excellent catalyst; platinum suspensions are less active, and ionic platinum solutions are not active at all. As the studies of Clark and Aborn1 have shown, the region of optimum catalytic activity of platinum does indeed exist.

A sharp decrease in the catalytic activity of colloidal gold (decomposition of \(H_2O_2\)) is observed2 at microscopic sizes of gold particles (\(2—4m\mu\)).

In the experiments of Gauger3, who studied condensed nickel in a vacuum, the absence of catalytic activity can probably be explained by the high dispersion of very small amounts of nickel distributed over the large surface of the glass wool. Some experiments of Dankov4 with very thin layers of nickel led to negative results for the same reason.

Despite a number of available data, the question of a maximum of catalyst activity in a definite region of dispersion must be subjected to experimental verification.

It is difficult at present to speak of the causes for the existence of a maximum of activity. However, already from the considerations expressed in the chapter on atomic-molecular parameters, it follows that in many cases the presence of a certain number of elements of the crystal lattice is necessary for spatial catalysis to be able to proceed. Taking corners and edges as the bearers of the active properties of a catalyst, one must think that faces play a secondary, but necessary, role in catalysis. As was already noted in the work of Dóse and Kelberer5, faces, or in general surfaces free from active sites, may serve as reservoirs from which material is drawn for active sites (edges, corners) and to which newly formed molecules at first pass, if one assumes their two-dimensional motion over the surface according to Volmer6 and Kassel7.

It should be noted that the region of maximum activity corresponds to such particle sizes as are close to the critical size (\(2m\mu\)), which is the limiting size of a crystalline nucleus capable of growth.

It is interesting to note that solid catalysts were sometimes obtained in the form of extremely dispersed bodies. Levi and Gaardt8 describe platinum powders whose primary particles (X-ray method) decreased to \(48\ \text{Å}\); for other metals of the platinum group still lower values were obtained: for osmium \(17\ \text{Å}\), for iridium \(16\ \text{Å}\), for rhodium \(22\ \text{Å}\), etc.

The following table, taken from the work of Frankenburger and Mairofer9, gives a broader idea of the particle sizes of an iron catalyst (see p. 82):

TABLE 2

\(Fe/H_2\)	Edge length of individual particles, in at. max	Edge length of individual particles, in Å	Ratio of active sites to entire surface: a) corners	Ratio of active sites to entire surface: b) corners and edges	Method of preparation
1	1—4	2.6—10	\(1-\dfrac{1}{8}\)	\(1-\dfrac{1}{3}\)	Iron vapors condensed at \(-195^\circ\) to \(-150^\circ\) in the presence of ice and \(H_2\).
2—5	15—30	32—75	\(\dfrac{1}{100}-\dfrac{1}{700}\)	\(\dfrac{1}{5}-\dfrac{1}{15}\)	Iron vapors condensed at \(-100^\circ\) to \(-20^\circ\) in the presence of NaCl.
3—6	20—40	50—100	\(\dfrac{1}{300}-\dfrac{1}{1200}\)	\(\dfrac{1}{7}-\dfrac{1}{20}\)	Fe condensed at \(-195^\circ\) to \(-150^\circ\) in the presence of \(H_3\) and traces of moisture.
7—9	40—60	100—150	\(\dfrac{1}{1200}-\dfrac{1}{2500}\)	\(\dfrac{1}{20}-\dfrac{1}{30}\)	At \(-195^\circ\) to \(-150^\circ\mathrm{C}\) and with completely dry \(H_2\).
\(\sim 70\)	\(\sim 400\)	\(\sim 1000\)	—	\(\dfrac{1}{200}\)	Activated iron catalyst (\(Al_2O_3\) and aqueous iron oxide).
\(\sim 700\)	\(\sim 4000\)	\(\sim 10000\)	—	\(\dfrac{1}{2000}^{*}\)	Iron catalyst obtained by reduction of \(F_2O_3\) at \(444^\circ\mathrm{C}\).

It should, however, be noted that preparations containing crystals of minimal dimensions (from 1 to 100 Å) proved inactive as catalysts.

3. Surface structure

Obviously, the most essential element of a catalyst is its surface. In the final analysis, the properties of a catalyst are determined by its surface structure. Accordingly, we shall examine in greater detail the existing data on surface structure, touching upon the methodology of its investigation.

Until recently, our ideas about the surface both of a solid body in general and of a solid catalyst were based chiefly on theoretical and indirect experimental data. The doctrine of surface energy, the phenomena of adsorption, the optical photoelectric effect, and chemical and photochemical concepts of the strength of a solid body—in the majority of cases—served as the source of our knowledge of the structure of the surface. Microscopic observations, as the most direct ones, in the overwhelming—

* According to Almquist.

... which, in most cases, proved not to achieve the goal, owing to the particular subtlety of the structure under consideration.

The decisive factor in the study of surface structure proved to be the electronographic method, whose rapid development in recent years has led to very interesting results; we shall consider them below.

Solid catalysts, as extensive experience shows, are always in the crystalline state. Consequently, the surface of the catalyzing body is a natural plane lattice, built according to the same type as the plane lattices located in the depth of the body. The atoms lying in the surface planes are arranged just as systematically in a plane lattice as are the atoms of the internal layers. However, the surface atoms (Fig. 9) differ from the internal ones in that they lack neighbors and, as is known, they are under a very strong one-sided pressure (internal pressure) directed into the body. One would have to expect an increase in the density of the surface layers, although this is difficult to confirm experimentally. Each surface atom (or ion) must in this case experience a displacement (polarization) of its outer electron shell, the greater the closer the atom (ion) is to the surface.

Each crystal has natural surface inhomogeneities. Besides the numerous atoms sitting on the faces of the crystal,

TABLE 3*

Position	Energy liberated upon condensation of an ion
1	0.8738
2	0.2490
3	0.1806
4	0.0903
5	0.0662

Fig. 9.

we have a series of atoms located on the edges and a small number of them at the corners. In each of these cases the atoms (ions) are in different energetic states and, probably, have a somewhat distorted structure of the electronic orbits.

How different the free energy is of atoms (ions) sitting at the corners, on the edges, and on the faces of a crystal may be seen from Table 3 and Fig. 10, which contain data for the energy liberated upon the deposition of ions onto the elements of the lattice of common salt \({}^{39,58}\). In the presence in the crystal of faces having different indices, we

* The unit of energy adopted is the energy of interaction of two ions situated at the normal distance.

we shall also have to distinguish energetically atoms sitting on different faces.

In accordance with the available crystallographic classes, we must also distinguish groupings of atoms on faces. Figs. 10, 11, 12, and 13 show possible surface groupings of atoms of faces with various indices on crystals of different systems.

Fig. 10.

Fig. 11.

Fig. 12.

On the figures given, the arrangement of atoms on certain typical faces is depicted. One can imagine a very large number of planar arrangements of atoms, but we shall confine ourselves to those presented. The character of the arrangement of the surface atoms, and along with this the parameters (the distances of the atoms from one another), may be very significant even in considering reactions of simple molecules, and still more so for complex molecules. The above-mentioned work of Balandin^5 confirms what has been said, using as an example the dehydrogenation of cyclohexane on an octahedral face of the lattice of a cube with centered faces.

Fig. 13.

Fig. 14.

The homogeneity of the crystal surface may be disturbed, for example, under the influence of mechanical actions^59, which, without causing destruction of the crystal, may lead to sliding of parts of the crystal along cleavage planes (Fig. 14). In this case a well-formed crystalline surface is spoiled; there are formed

depressions and protrusions, which substantially change the magnitude of the surface. At large tangential stresses on the surface of the crystal, slip twins may arise (Fig. 15), which may also result from improper growth.

With such deformations, although the integrity of the single crystal is not violated, it nevertheless already acquires the character of a twinned intergrowth, the surface of which may increase many times over, as may also the number of edge angles.

No less significant a factor changing the character and magnitude of the surface of a single crystal is constituted by ultramicroscopic cracks, which, as is known, play no small role in the surface conductivity of rock salt and in the strength of crystals in general (Joffe)\(^{60}\).

Fig. 15.

Fig. 16.

Passing to the polycrystalline surface, we can detect one more element of the surface that has no place in a single crystal: interlayers between crystals.

In modern metallography it is assumed that these interlayers play an essential role in the hardening of metals. The rupture of a polycrystalline body always occurs at places of a regularly constructed lattice; the interlayers are the strongest element of the polycrystal. The nature of the interlayers has not yet been sufficiently studied, although even now their amorphous structure is admitted\(^{61}\).*

Like the interlayers indicated in a polycrystal, the surface reveals amorphous properties after mechanical treatment (especially polishing). Thus, in studying surfaces one may encounter such cases where the regular arrangement of atoms

* The application of the electronogram method to the study of a polished surface sheds light on the nature of surface layers subjected to mechanical treatment. According to the work of French\(^{64}\) (Proc. Roy. Soc. (A) 140, 637, (1933)) and especially the work of Darbyshire and Dixit\(^{55}\) (Phyl. Mag. 1933), Beilby’s hypothesis on the amorphousness of metal at the surface finds support, which to some extent also illuminates the question of intercrystalline matter.

does not take place. This is confirmed by the electron-diffraction method in Thomson’s work, which will be discussed below.

Of great interest is the structure of the surface of thin layers deposited on substrates. For technically interesting cases (platinum on asbestos, vanadic acid on silica gel, etc.) no data are as yet available. Thin metal layers obtained by sublimation and condensation, chiefly on glass, have been studied in greater detail. Such layers, as Kundt had already noted,^25 prove to be anisotropic. In the work of Koper, Frommer, and Zocher^25 layers of gold, silver, platinum, and others, when optically investigated, proved to be anisotropic. By optical analysis the authors came to the conclusion that the layers are built of oriented needle-shaped crystals whose long axis is parallel to the surface. The same results were also obtained in an X-ray investigation of thin metal layers by Dembinska,^25 in which fiber X-ray diagrams were obtained. In all cases, metal layers up to \(10^{-6}\) cm (\(10m\mu\)) thick were considered.

There is no doubt that the structure of the surface layers of metallic films did not differ in any way from their internal structure.

The most important and promising data on surface structure have been obtained with the aid of the rapidly developing electron-diffraction method.

Essentially, the electron-diffraction method^62 consists in the following: a beam of electrons, homogenized with respect to velocity and direction by means of metallic diaphragms, falls on the surface under investigation and, on being reflected, is scattered in different directions. If the surface has a periodic structure, then the electrons, owing to their wave nature, are not scattered uniformly in different directions. In certain directions there occur scattering maxima, and these maxima satisfy Bragg’s condition, which, as is known, is expressed by the equation:

\[ \lambda = 2d \sin \theta/2, \tag{1} \]

where \(\lambda\) is the wavelength of the electron, calculated from the de Broglie relation:

\[ mv = \frac{h}{\lambda}\quad \text{or}\quad \lambda = \frac{h}{mv}, \tag{2} \]

where \(m\) is the mass of the electron, \(v\) its velocity, \(h\) Planck’s constant, \(d\) the distance between the planes of the surface layers, and \(\theta\) the angle at which the electrons give a scattering maximum.

In calculating the length of the electron wave it is better to proceed not from its mechanical velocity, but from the voltage. The accelerating voltage \((V)\) and the electron velocity \((v)\) are related by the equality \(\frac{1}{2}mv^2 = eV\). Therefore equation (2) is rewritten as:

\[ \lambda = \frac{h}{\sqrt{2me}}\cdot \frac{1}{\sqrt{v}}. \tag{3} \]

Calculations show that, at accelerating voltages not exceeding 200 V, the electron wavelength may be comparable with the wavelengths of soft X-rays.

At high values of the accelerating voltage (up to 40 kV) we are dealing with very short wavelengths (down to 0.06 Å).

In connection with the peculiarities of fast and slow electrons there exist two methods of electronograms.

The use of fast electrons makes it possible to obtain a photographic picture of the interference maxima of electron scattering on a polycrystalline surface.

With the aid of slow electrons one can investigate the surface of a single crystal or a surface built up of oriented crystallites.

Each of the methods mentioned has a number of advantages and disadvantages, upon which, for lack of space, we cannot dwell.

Below, in examining the results of applying the electronogram method, we shall consider certain details of the experiment.

Already the first work of Germer and Davisson ^63 shed much light on the structure of the surface of a single crystal. It turned out that it was possible to arrive at a completely clean surface of a nickel single crystal only after its careful degassing; at the same time it was established that the surface layers (from 10 to 20 Å thick) are constructed periodically in the same way as the interior.

The application of fast electrons (up to 40 kV), proposed by Thomson ^24, made it possible to investigate surfaces without those enormous precautions which were unavoidable in the experiments of Germer and Davisson, who dealt with slow electrons. However, Thomson’s method gave information about layers up to \(10^{-6}\) cm thick.

In Thomson’s investigation surfaces of various bodies were studied, the diffraction pattern being recorded already photographically.

A polished surface (of copper and gold) gave no diffraction rings in the photograph.* Deposits of gold on quartz, platinum black on zinc or aluminum scattered the electrons quite regularly, and in the photograph a system of half-rings of different radius was obtained. A typical electronogram is given in Fig. 17. It corresponds to a deposit of gold on quartz obtained by condensation of gold vapors. Calculations made on the basis of the data of electronograms of gold and platinum showed that the investigator was dealing with surfaces of pure Au and Pt.

* In the works of French ^64 and Derbysheir and Dixit ^35 there are electronograms for polished surfaces of Ag, Cu, Au, Cd, Bi, Ni, Pb, Sb, Te, Si, etc.; in all cases two strongly blurred circles were obtained, corresponding to the amorphous state of the substance.

Different results were obtained for platinum black on copper and platinum on asbestos. In the first case a cubic structure was established, corresponding to the parameters neither of gold nor of copper. In the second case, the complex aggregate structure was not identified, as was also the case for pure asbestos.

Thomson carried out several experiments with copper heated in air, then with a copper surface treated with solutions of sulfide, selenide, and telluride; further, with annealed and etched iron. As a result of these experiments the author successively established on the copper surface Cu₂O or CuO (Fig. 18) or Cu₂S (the structures Cu₂Se and Cu₂Te were not found). The surface of the iron in both cases proved to be built of Fe₂O₃ crystallites.

New information obtained about the surface of such materials as platinum black or platinized asbestos, which are typical catalysts, has not yet been mastered by scientific thought. It must be supposed that more broadly conceived experiments and deciphering of the structural picture will make it possible to draw important conclusions about the active elements of the surface. The electron-diffraction method (fast electrons) promises very much for the study of the surface of catalysts (and, in general, in all cases where we are dealing with a surface process). The formation of intermediate compounds (hydrides and compounds resulting from activated adsorption), poisoning of the catalyst, the size of surface particles, and their orientation will probably in the near future become objects of study by the electron-diffraction method.

Fig. 17.

Fig. 18.

Thomson’s results on the study of polished metals were refined by French⁶⁴ and others.* The surface of a polished metal proved to be constructed very nonuniformly. The normal crystallites composing the body of the metal protrude onto the surface of the crystal, being cut by furrows and scratches. In

* A recently published work by Germer⁶⁵ is in contradiction with the results of French and of Darbyshire and Dixit. It must be said that Germer’s conclusions do not quite follow from his incomplete experiments.

at the bottom of these grooves there remains a multitude of deformed and partially destroyed fragments of the crystal. The diffraction pattern from normal crystals is to a large extent then obscured by diffuse rings obtained from small fragments lying in depressions of the surface. More careful experiments made it possible to differentiate diffraction from normal crystals and from small fragments. The pattern appeared especially clearly when the section was etched (for example, copper with hydrochloric acid), during which the small crystallites dissolved and were removed from the surface during washing. After this the diffraction pattern from the section corresponded only to normal surface crystals. Finch’s experiments concerned copper, silver, gold, and chromium, for which analogous results were obtained. For well-polished surfaces, as noted earlier, the differences in the diffraction pattern disappear for different metals. Two different rings are obtained, which may correspond to a completely disordered arrangement of atoms in the surface layer.

The application of the fast-electron method to the study of the surface of thin-film catalysts, with a parallel investigation of their activity, was carried out by Finch, Murison, Stuart, and Thomson^66. By cathodic sputtering they obtained platinum films, which were then tested for activity and studied electronographically. Depending on the gas in which sputtering was carried out (\(O_2, N_2, A_2\)), and on the magnitude of the cathode potential during sputtering, the films were divided into active, inactive, and those developing activity after an induction period. By electronographic analysis of the films it was possible to explain the peculiar behavior of the films in various cases. Thus, for example, it was possible to establish the presence of \(PtO_2\)* on films whose reactions were accompanied by an induction period.

Very interesting data were obtained by Finch and Quarrell^67, who studied, by the fast-electron diffraction method in vacuum, condensed layers of Al, Mg, and Zn (and their oxides). They established the fact that very thin layers can form crystalline pseudomorphs of the substrate on which they were deposited (Pt). With an increase in the thickness of the layer, the abnormality of the structure of the surface of the deposited material disappeared. It was also found that heating the surface caused an orientation of the crystals in the layer.

The method of slow-electron diffraction also proved to be substantially important. With this method we learn the structure of very thin surface layers. The significance of the method was noted by Rupp in 1929^68. Soon thereafter he published a work on the investigation of the surface of catalysts before and after adsorption of reactants (\(H_2\) and \(N_2\))^69. The investigation was carried—

* Incidentally, Bredig and Allolio^4 had already noted this in their X-ray diffraction study of thin films of platinum, palladium, and nickel.

...was carried out in an apparatus, the diagram of which is shown in Fig. 19. The fixed emitter \((B)\), crystal \((T)\), and Faraday cylinder \((H)\) could not change their position during the experiment; what was varied was the velocity of the electrons, which corresponded to a change in the electron wave. The number of electrons scattered in the direction of the Faraday cylinder was measured for each value of the electron velocity (wavelength); when the Bragg condition \((\lambda = 2d \sin \theta/2)\) was satisfied, for the given crystal lattice there was a maximum in the number of electrons scattered in the direction of the Faraday cylinder.

Fig. 19.

In Rupp’s work, curves of the type shown in Fig. 20 were obtained for a pure metal. The appearance of a new maximum corresponds to a doubling of the electron velocity.

Upon brief contact of the crystalline surface with such gases as argon and nitrogen, the curves obtained in most cases did not change their form, although in general a tendency toward broadening and lowering of the maxima is observed.

The situation was different when the surface was brought into contact with hydrogen. The principal maxima broadened and decreased; in addition, new “half” maxima appeared (Fig. 21), corresponding to an increase in the electron velocity twice smaller than for the pure metal. However, the new maxima were not as sharply expressed as the principal ones. Rupp interprets the indicated maxima as a manifestation of the periodic nature of the distribution of hydrogen atoms among the surface atoms of the metal, with the distance between the hydrogen atoms and the metal equal to half the distance between the metallic atoms; thus here the construction of a half lattice of hydrogen within the metal lattice is assumed. The figure below (Fig. 22) explains what has been said. Deep adsorption of hydrogen is accompanied by the destruc-

...by the destruction of the “gas crystal” and by damage to the surface of the metal. The proper arrangement of atoms on the surface is then no longer observed. The electron diffraction pattern corresponding to this case is given in Fig. 23. It shows that regular scattering of electrons no longer takes place. The slow-electron method suffers from a special drawback,

Fig. 21.

Fig. 22.

which to some extent diminishes its importance. The diffraction of slow electrons is affected by the magnitude of the inner potential \((E_0)^{70}\), which characterizes the given crystal and enters into the expression:

\[ \lambda = \frac{h}{\sqrt{2cm}} \cdot \frac{1}{\sqrt{v + E_0}}, \]

used for calculating the length of the electron wave.

As the investigation by Boas and Rupp\({}^{71}\), who studied passive iron, has shown, the simultaneous determination of the parameter of the crystalline lattice and of the inner potential is impossible. Therefore, for purposes of structural analysis it is necessary first to determine the inner potential by another method.

Fig. 23.

4. Structure of Mixed Catalysts*

With respect to mixed catalysts, the structural relations considered above remain valid. But along with

* The question of mixed catalysts is discussed in great detail in Mittasch’s report\({}^{72}\).

it is necessary to note the presence in them of special features connected with the presence of two or more different substances in the catalytic mass. The character of the contact between the two substances constituting the catalyst may be different, ranging from the formation of a chemical compound \((\mathrm{NiMo})\) for one of the ammonia catalysts \(^{73}\) (or a solution \(\mathrm{Cu—ZnO}\)) \(^{10}\), or simple mixtures of grains \((\mathrm{Ni—ThO_2})\) \(^{48}\). At the same time, in many cases it is difficult to determine the composition of the phases present (for example, the system \(\mathrm{Fe—Al_2O_3}\) may occur either as a simple mixture, or as a solution of \(\mathrm{Al_2O_3}\) in iron, or as the chemical compound \(\mathrm{FeAl_2O_4}\) \(^{72}\)).

Without dwelling on profound changes in the components when they come into contact with one another, let us consider a system of two substances which is a simple mixture. Here one may, on the one hand, assume that an admixture of one of the substances prevents the formation of large crystals of the other substance (an increase in dispersion); on the other hand, one must reckon with the fact that numerous facts of selective catalysis cannot be explained by a mere increase in the degree of dispersion \(^{74}\).

The specific properties of the grain boundaries of two substances somehow affect the activity of the catalyst. However, despite the abundance of data indicating the significance of phase boundaries in chemical processes, we have absolutely no information about the structure of these boundaries.

The question of the atomic-molecular and aggregate structure of mixed catalysts is one of the most difficult questions of structural analysis. But the role of these catalysts in the scientific and practical fields is so great that it is worth overcoming these difficulties.

LITERATURE

1. Schmidt O., Ztschr. phys. Chem., 118, 193, 1925.
2. Grimm, Ztschr. phys. Chem., 98, 353.
3. Писаржевский Л. В. Report at the 3rd Physico-Chemical Conference, 1928, p. 135.
4. Bredig u. Allolio, Ztschr. phys. Chem., 126, 41, 1927.
5. Баландина А. А., Ж.Р.Ф.-Х.О, chemical section, 61, 909, 1929; Ztschr. phys. Chem. (b), 3, 167, 1929.
6. Зелинский, Berich. 56, 787, 1923.
7. Burk, Jour. Phys. Chem., 30, 1134, 1926.
8. Langmuir, Новые идеи в химии, 8, 56, 1924.
9. Adkins, Jour. Amer. Chem. Soc., 45, 806, 1923.
10. Aborn and Davidson, Jour. Phys. Chem., 34, 522, 1930.
    Frölich, Davidson, Fenske, Jour. Eng. Chem., 21, 109, 1929.
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