THE NATURE OF INTERCRYSTALLINE INTERLAYERS

M. V. Klassen-Neklyudova and T. A. Kontorova

Introduction

I. The theory of the “amorphous” interlayer
1. Beilby’s hypothesis. 2. Initial theories of the “amorphous” interlayer. 3. Rosenhain’s work. 4. Jeffries’s experiments. 5. Gradual rejection of the theory of “amorphous cement.”

II. The theory of the “transition” zone
6. Gough’s ideas. 7. The “pseudo-molecule” hypothesis. 8. Hunt’s considerations. 9. Hargreaves and Hills’s “transition zone.” 10. The “phase” theory. 11. Tammann’s ideas.

III. Experimental data on certain properties of intercrystalline interlayers
12. Isolation of the intercrystalline interlayer. 13. Detection of grain boundaries by etching. 14. Data on the density of the intercrystalline interlayer. 15. Diffusion of foreign substances along interlayers. 16. Fracture of material along intercrystalline interlayers. 17. On the character of plastic deformation in the intercrystalline interlayer. 19. Study of the intercrystalline interlayer by the method of electron diffraction. 20. An attempt to calculate the spatial extent of the intercrystalline interlayer.

Conclusion.

Introduction

The metals with which one has to deal in everyday practice are, as is known, an aggregate of differently oriented crystalline grains.

Under normal conditions the fracture of a polycrystalline material, as a rule, occurs by rupture through the crystalline grains.

It is known from practice, however, that under certain special conditions the picture changes—fracture acquires an “intercrystalline” character, proceeding no longer through the grains but between them.

Thus, for example, the cause of intercrystalline fracture of technical metals in a whole number of cases is the presence in them of certain impurities (phenomena of cold shortness and red shortness). Fracture of a material along grain boundaries is very often caused by the penetration into the metal of oxygen, ammonia, and certain other gases. It is also observed under the action of seawater

and when certain metals come into contact with mercury. The dangerous effect exerted by solders on many metals and alloys is well known, in particular on steel and brass; in this case, too, destruction proceeds along the grain boundaries. A similar character of destruction is observed in the spontaneous cracking of brass articles—in so-called “season cracking.” Intercrystalline destruction also often occurs during the operation of metallic parts at high temperatures. There are, furthermore, a number of indications that processes taking place at grain boundaries play a very substantial role in so-called “creep”—the plastic flow of metals observed in parts of heat-power installations operating at high pressures and high temperatures.

In connection with all these phenomena, which lead to the premature destruction of metals, the study of the structure and physical properties of the regions where grains are in contact with one another is of extraordinary interest. In what follows we shall call these regions intercrystalline layers.

Despite the very large number of experimental works devoted to the study of the polycrystalline state, the question of the structure and properties of the intercrystalline layer is still, at the present time, far from its final resolution.

The first ideas about the state of a metal in the region of grain boundaries date from the end of the nineteenth century. In the works of Quincke¹ (1868), Brillouin² (1898), as well as Osmond³ (1889) and Sirs⁴ (1908), one first encounters the assertion that the properties of the intercrystalline layer differ from the properties of the crystalline grain.

The development of ideas about the structure of intercrystalline layers may be divided into two stages.

1. Early theories assume that the bond between crystalline grains is effected by means of a certain cementing layer belonging to a new phase. Most authors regard this layer as amorphous.

2. Subsequently, alongside the development of conceptions of the layer as a substantially new phase, there arise conceptions of the presence between grains of a certain intermediate (“transition”) zone, whose structure is entirely dependent on the orientation of the grains surrounding it.

In the first and second chapters of the present article we set forth, in historical sequence, the principal points of view on the structure of intercrystalline layers.

The third chapter is devoted to consideration of experimental data that make it possible to draw certain conclusions about the physical properties of the layers.

CHAPTER I. THEORIES OF THE “AMORPHOUS” LAYER

§ 1. Beilby’s Hypothesis

The hypothesis of the possible “amorphous” state of metals was first formulated by Beilby⁵ (1911) as a result of the study-

...of the structure of polished metal surfaces. According to Beilby, in the process of polishing a metal, a film several hundred molecules thick is formed on its surface, possessing “the mobility of a liquid state.” Upon completion of the polishing process, this film solidifies in an “amorphous,” “glass-like” state.

Beilby gives the following interpretation of the terms “amorphous” and “glass-like.” “Amorphous means non-crystalline in the full sense of the word; in this state the order and orientation characteristic of crystals are absent.” Beilby adds the term “glass-like” in order to mark the difference between the state under consideration and the colloidal state, and to emphasize its similarity to the glass-like form of silicates, assumed by them upon solidification from the melt.

The formation of analogous amorphous layers, in Beilby’s opinion, also takes place within the metal along the slip traces arising in the process of deformation of the material. “These layers,” writes Beilby, “retain their mobility only for a very short period; then they solidify..., forming a cementing material along all slip surfaces.”

§ 2. First theories of the “amorphous” interlayer

The term “amorphous” as applied to the intercrystalline interlayer was first used by Osmond (1896). According to the latter’s hypothesis: “Between two grains there exists an amorphous shell, the average thickness of which is of the same order as the dimensions of the ‘crystalline molecules,’ by the formation of which the crystallization of metals from the melt is accomplished...” In Osmond’s own works, however, this hypothesis did not receive further development.

Conceptions of a non-crystalline structure of the interlayer are also found in Sirs⁴ (1908). In his work devoted to the study of elastic after-effect in metals, there is the assertion that, in the space between grains, particles are distributed with relatively low density; they do not belong, moreover, to any one of the grains (“dangle” between them). These particles are found “in liquid or semi-liquid conditions,” in consequence of which the interlayer must possess great viscosity.

Bengough⁶ (1912) was one of the first to use Beilby’s hypothesis on the possible existence of “amorphous” metals in considering the question of the nature of the intercrystalline interlayer. Discussing the possible type of structure of the interlayer, Bengough relies on the experimental fact, discovered shortly before by a number of other investigators, that at room temperatures the fracture of metals and alloys “tends to pass through the metallic grains rather than between them.”

This circumstance, indicating the high strength of the interlayer in comparison with the grains, and also the easier etchability of the interlayer, leads Bengough to the hypothesis that the individual grains of a polycrystal are connected with one another by “some substance,

“...whose strength is greater than that of the grains themselves.” At the same time, Bengough unconditionally transfers to the intercrystalline interlayer the ideas of Beilby set forth above, developed by Beilby himself only for polished metal surfaces and traces of slip in deformed material: “The substance of the interlayer is nothing other than Beilby’s amorphous substance, situated in a thin, more or less continuous layer around the crystals. Its presence has so far been clearly established only in strongly deformed metals...”

The presence of this amorphous substance at the grain boundary, according to Bengough, may be due to several causes. First of all, its formation may result from the counteraction exerted by grains growing toward one another upon particles of liquid melt enclosed between them; owing to this action the particles of melt cannot attach themselves to the lattice of any of the grains. Secondly, its formation, in Bengough’s opinion, may be caused by the presence in the metal of compressive stresses. Thirdly, the increased concentration of impurities remaining between the grains in the liquid phase hinders the crystallization process, thereby promoting the formation of amorphous material.

Bengough’s further ideas concerning the properties of the intercrystalline interlayer are based on a study of the dependence of the mechanical properties of a number of metals and alloys on temperature. In this connection Bengough is the first to determine the strength and elongation both of certain pure metals (copper and aluminum) and of a number of alloys (Cu—Ni, various types of brass, Muntz metal) over a temperature range from room temperature up to the melting points. In analogous work by previous investigators the experimental temperature usually did not exceed 350°; Rosenhain carried out the corresponding measurements up to temperatures of the order of 450—500°.

Analyzing the curves of the dependence of material strength on temperature, Bengough comes to the conclusion that for each of the metals, at a certain definite temperature, a sharp break in the curve is observed. Bengough calls the temperature corresponding to the point of inflection the “recuperation temperature.” It is noteworthy in that, at temperatures lying above it, the fall in the strength of the specimen with increasing temperature proceeds more slowly than at temperatures lying below it. The corresponding curve of the dependence of copper strength on temperature is given in Fig. 1. An analogous curve was obtained for aluminum. For copper the recuperation temperature is 650°, for aluminum—395°.

As the author himself notes, this curve ought to be represented differently—so that there would be a smooth transition from one part of the curve to the other. Bengough, however, deliberately extrapolates both portions of the curve up to the point of their intersection in order to emphasize the different, in his opinion, nature of the processes taking place in the metal under investigation below and above the “recuperation point.” He notes, moreover, that the recuperation temperature represents

by itself a “mechanical” critical point, having nothing in common with the critical points of phase transformations.

Trying to explain the change in the course of the curve at the recovery temperature, Bengough arrives at the hypothesis that above this temperature “the amorphous material cementing the crystalline surfaces is no longer capable of existing even instantaneously. Beginning with this temperature, the rupture will thus have an intercrystalline character.” Bengough, however, gives no more detailed explanations for the presence of a rectilinear segment of the curve; it becomes completely incomprehensible why, in such a case, in the absence of an intercrystalline interlayer the polycrystal does not fall apart spontaneously into separate grains, without the action of external forces.

Fig. 1.
Cu. Temperature, °C. Recovery temperature. Strength in kg/mm².

Defining the recovery temperature as the temperature above which a metal cannot be in the amorphous state, Bengough comes to the conclusion that at high temperatures the amorphous metal formed as a result of deformation in individual grains along slip planes must instantly undergo recrystallization. Owing to this, “hot working” of metals is not accompanied by strengthening.

“Cold working,” according to Bengough’s definition, is “working of a material at temperatures lying below the recovery temperature; it leads to the formation of a significant amount of amorphous substance.” Bengough notes that the numerical data he obtained for the recovery temperature of various metals pertain to quite definite experimental conditions; in actual fact, the position of the recovery point depends on the rate of deformation of the specimen.

In conclusion he writes: “Beilby’s unstable glassy amorphous material plays a considerably more essential role in determining the mechanical properties of metals and alloys than could hitherto have been suspected... Without it all metals would be soft, plastic, viscous bodies, resembling resin or perhaps tin...”

Irrespective of the correctness of Bengough’s views set forth above on the nature of the intercrystalline interlayer, his work is of considerable interest in that it was the first to carry out a systematic study of the mechanical properties of a metal at high temperatures, and also established the presence of a certain critical temperature (“recovery temperature”) at which a change occurs in the character of fracture of polycrystals.

Absolute values of this temperature, however, are in fact not determined, since they depend on the rate of deformation, and the latter did not remain constant in Bengough’s experiments.

§ 3. Rosenhain’s Works

Before Rosenhain’s works it was customary to believe that the cohesive forces between the grains of a polycrystal are smaller than the cohesive forces within the grains themselves; intercrystalline boundaries were accordingly regarded as “surfaces of weakness.”

Rosenhain and his coworkers, as a result of a systematic study of the character of fracture of polycrystals under various experimental conditions, showed, however, that under normal circumstances fracture, as a rule, proceeds not along the intercrystalline interlayer but through the grain. Fracture along the interlayer occurs only under certain special conditions. Thus, for example, in Arnold’s classic experiments (1896), the fracture of gold polycrystals along grain boundaries was produced by adding 0.1% bismuth to the gold.

On the basis of these data, Rosenhain^7 comes to the conclusion that “the intercrystalline boundaries of normal pure metals are not surfaces of weakness, but surfaces of special strength. At the same time the mechanical properties of intercrystalline boundaries differ substantially from the properties of the crystalline grain...”

In Rosenhain’s opinion, the mutual cohesion of the grains themselves cannot ensure the high strength of the intercrystalline boundary; it is necessary to assume the presence of a special “cementing medium existing between neighboring crystals.”

Proceeding from (quite incorrect, as will be shown below) ideas about the uniform character of the distribution of impurities throughout the entire mass of the polycrystal, Rosenhain asserts that, from the point of view of its chemical composition, the intercrystalline “cement” consists of the same material as the grain, differing, however, from the latter in the arrangement of the molecules in it (i.e., being in another physical state).

Referring to the works of Beilby, who assumes the possibility of the existence of metals in an amorphous state, Rosenhain, like Bengough, considers the intercrystalline cement “amorphous.” According to Rosenhain, such an “amorphous” cement must, however, be present in the polycrystal at any values of temperature.

In one of his early works^7 (1912), clarifying the concept of “amorphous cement,” Rosenhain writes: “the term ‘amorphous’ indicates opposition to ‘crystalline.’ ‘Amorphous’ therefore means the absence of a regular arrangement of particles.

In his next work^8 (1913), Rosenhain adds: “The grains of a pure metal are surrounded by an amorphous interlayer, the properties of which correspond to a liquid supercooled metal. This amorphous phase corresponds to Beilby’s amorphous interlayer... Resist-”

formation of cement is the resistance of a viscous liquid, whose properties are similar to those of glass or resin.”

Unlike Beilby, Rosengain considers it possible for an amorphous interlayer to form in the absence of external stresses. Like Osmond, Rosengain assumes that crystallization of a metal from the melt proceeds by the formation of molecular complexes (“crystalline molecules” or “bricks”), whose dimensions are large in comparison with the dimensions of ordinary molecules of the liquid melt. Each of the crystalline grains consists of such regularly arranged and closely packed “bricks.” When two grains, in the process of growth, meet one another, then in the gaps remaining between them the formation of “bricks” often proves impossible; the particles of liquid that find themselves in these gaps “therefore remain in an amorphous state.”

Of great interest is the first attempt, contained in one of the cited works, to establish the possible physical properties of the “amorphous cement.”

Proceeding from the notions that the properties of amorphous cement are identical with those of a supercooled liquid, and that the vapor pressure of the liquid phase is greater than the vapor pressure of the crystalline phase, Rosengain comes to the conclusion that, under the given experimental conditions, amorphous cement must possess an increased volatility as compared with the grain. A comparative study of the evaporation rates of coarse- and fine-grained specimens of one and the same material could lead to direct proof of the existence of amorphous cement if it turned out that the fine-grained material, characterized by a relatively large content of amorphous cement, evaporates faster than the coarse-grained material.

Experimental investigations showed that, when heated in vacuum, coarse-grained specimens of copper, silver, and zinc do in fact undergo a smaller loss in weight than fine-grained specimens of these metals. Thus, for example, fine-grained zinc specimens, other experimental conditions being equal, lose on average more than twice as much weight as coarse-grained specimens (Table 1).

Table 1

Metal	Heating temperature, °C	Ratio of weight losses of fine- and coarse-grained specimens
Zinc	335	2.25—2.37
Silver	870	1.16—1.27
Copper	1015	1.31—1.56

Rosengain further notes that if the volatility of the amorphous cement is indeed greater than the volatility of the grain, then heating a specimen in vacuum, leading to a decrease in the amount of the cementing interlayer, should cause a decrease in the cohesion between grains—the “heat brittleness” of the material. Indeed, after prolonged heating of silver specimens in vacuum, Rosengain was able to observe brittle fracture of the metal along the interlayers.

According to Rosengain, a consequence of the high volatility of the amorphous interlayer is also the formation of deep channels along grain boundaries, observed in the study of the microstructure of certain metals (especially silver) subjected to prolonged heating in vacuum.

The amorphous interlayer, in Rosengain’s opinion, must also possess increased chemical activity as compared with the crystalline grain. As confirmation, Rosengain refers to the experiments of Humphrey, who showed that heat treatment of steel in vacuum in the presence of very small amounts of oxygen leads to the destruction of the material along the grain boundaries. Rosengain considers this phenomenon a consequence of the process of oxidation of the intercrystalline cement, leading to its weakening.

In one of Rosengain’s principal works[^9] (1913), devoted to the study of the mechanical properties of steel at high temperatures, his ideas about the physical properties of the amorphous cement receive further development.

This work presents highly interesting data on the strength, degree of deformation, and character of fracture of soft grades of steel in the temperature interval from \(756—1080^\circ\). The experiments were carried out in vacuum at a constant rate of deformation. In Fig. 2 is shown

Fig. 2

the curve obtained by Rosengain for the dependence of the strength of steel on temperature. The fracture points observed on the curve correspond to the allotropic transformations of iron. At \(830^\circ\) there is a minimum of strength.

The simultaneous study of mechanical characteristics, micro-

structure and the character of fracture of specimens at different temperatures lead Rosengain to the conclusion that the behavior of the material in the region of the γ-phase (at temperatures above 900°) differs substantially from its behavior in the region of lower temperatures (500–900°).

In the latter case, just as at room temperatures, deformation proceeds by the formation of slip traces and is accompanied by a noticeable elongation of the specimen. Rupture of the specimen is preceded by the formation of a neck; the site of rupture is a crystalline grain.

At higher temperatures in the region of the γ-phase the character of deformation changes sharply; in this region there is observed a displacement of grains relative to one another so abrupt that channels form between them, clearly visible under the microscope. In this case rupture proceeds along an intercrystalline layer, and the site of rupture, according to Rosengain’s data, coincides with the grain boundaries. The grains themselves are deformed only very slightly, and the transverse dimensions of the specimen at the site of rupture do not undergo appreciable changes.

The difference in the character of fracture of the specimen at low and high temperatures becomes still more striking at very low rates of deformation. In this case slip traces within the grains are almost not observed. Rosengain notes, however, that their disappearance should not be regarded as evidence of the absence of plastic deformation within the grain; in Rosengain’s opinion it is a consequence of evaporation of part of the metal from the surface of the polished section at high temperatures in vacuum.

As the rate of deformation is increased, the difference between the appearance of fracture of specimens at low and high temperatures gradually disappears; at higher rates of deformation, rupture through the grain can also be obtained in the region of the γ-phase. These experiments testify to the sharp influence of temperature and rate of deformation on the character of rupture of specimens.

According to Rosengain, all these data can receive a satisfactory explanation from the standpoint of the hypothesis he advanced concerning the existence in a polycrystal of an “amorphous cement.”

In considering the mechanical characteristics of the polycrystalline state, Rosengain bases himself on the complete analogy he assumes between the properties of the amorphous cement and the properties of a supercooled liquid. In doing so he refers to the behavior of glasses under various experimental conditions (different temperatures and different rates of deformation). Concerning the latter he writes:

“Such substances are considerably harder and more brittle, but also stronger, than these same substances in the crystalline state... Their viscosity at ordinary temperature is very great; on the other hand, they possess the capacity for flow... With increasing temperature their viscosity decreases, at first slowly, then faster and faster...”

In accordance with this, Rosengain assumes that at ordinary temperatures the amorphous cement must possess greater hardness

and strength than the material of the crystalline grain, while an increase in temperature should lead to its gradual softening. On the other hand, Rosenghain notes, the resistance to shear within the crystalline grain should not undergo very rapid changes as the temperature rises.

On the basis of these considerations he comes to the conclusion that “up to a certain temperature we should expect to find a regularity corresponding to a decrease of internal friction in solids; then the softening of the cementing ‘liquid’ will dominate over the softening of the crystals, and, beginning with this temperature, the curve of the dependence of the strength of the material on temperature will follow the law of decreasing viscosity of the liquid with increasing temperature.”

As an illustration, Rosenghain gives the curve of the dependence of strength on temperature shown in Fig. 3. The dotted curves I and II characterize the behavior of a supercooled liquid at two different rates of deformation. The straight line AB describes the change in strength of an individual crystalline grain (Rosenghain notes in this connection that the dependence of \(P\) on \(T\) has been chosen rectilinear only for simplicity. It, of course, does not correspond to reality). At temperatures lying below point C (or, at a higher rate of deformation, below point D), the amorphous cement is stronger, and deformation proceeds through the grain. Above point C (or D) the cementing interlayer is softer than the grain, deformation proceeds predominantly in the interlayer, and the fracture gradually acquires an intercrystalline character. Points C and D on Rosenghain’s curves apparently correspond to Beilby’s “recuperation” temperature; their position is determined by the rate of deformation of the specimen. It should, however, be noted that the curves given by Rosenghain correspond neither to the experimental curves obtained by Beilby for aluminum and copper, nor to Rosenghain’s own experimental curve for iron.

Fig. 3

Rosenghain believes that if the rupture of the material is produced at temperatures lying considerably above the temperature corresponding to point D (at the given rate of deformation), then it may be expected that rupture, which under these conditions has an intercrystalline character, will not be accompanied by any noticeable deformation of the grains themselves, even in the case when they belong to an extremely plastic metal.

In order to verify these assumptions, Rosenghain investigated the type of rupture of a number of low-melting metals—lead, tin, aluminum

and bismuth at temperatures close to their melting temperatures. The test specimen was heated to a temperature lying 50° below the melting point of the corresponding material; a small constant load was then suspended from the lower end of the specimen, and the temperature was slowly raised (at a rate of 3° per 1 min.) until rupture of the specimen occurred. The load in this case was specially chosen so that the rupture “was not accompanied by deformation of the crystals.”

As in the case of mild steel, at high temperature the rupture of the specimens is not accompanied by their elongation or by a change in cross section. Study of the microphotographs shows that rupture under these conditions “follows exactly the grain boundaries.”

The temperature corresponding to the onset of “brittle intercrystalline rupture” was determined with the aid of a thermocouple fixed inside the specimen (accuracy of measurement—3–4°). The results thus obtained are given in Table 2. In the last column of the table, for comparison, the melting temperatures of the corresponding metals are indicated.

Table 2

Metal	Temperature of brittle intercrystalline rupture in °C	Melting temperature in °C
Tin	223	232
Bismuth	261	268
Lead	323	327
Aluminum	637	657

Rosengain notes that all these data indicate that the theory of “amorphous cement” correctly predicted the behavior of metals at high temperatures.

Despite the fact that the temperature of brittle rupture in all cases lies very close to the melting temperature, Rosengain considers that melting of the metal nevertheless does not occur here, since otherwise the fracture would not have such sharply delineated contours.

The above-mentioned work of Rosengain is also of interest from the standpoint of studying phase transformations in iron. Rosengain definitely establishes the formation of the γ-phase at a temperature of the order of 900°, while, however, casting doubt on the existence of a transition from β-iron to α-iron.

On the curve characterizing the dependence of the strength of iron on temperature, in the region of the γ-transformation a sharp jump is observed. In contrast to Bengough, Rosengain asserts that phase transformations in metals must always be accompanied by a sharp change in the mechanical properties of the material. The latter, in Rosengain’s opinion,

is due to a change in the relative role of the grain and the interlayer upon passing through the transformation point; moreover, “if the amorphous cement is regarded as a supercooled liquid, then it should not be affected by allotropic transformations... The allotropic modification affects only the crystalline grain, without changing the properties of the amorphous cement....”

In Rosenhain’s opinion, as a result of the allotropic transformation the grains of the metal become harder and stronger. The cementing material, however, becomes relatively softer than the grain. For this reason, in iron or mild steel the transition from one type of deformation and fracture to another (at the deformation rates occurring in the present investigation) is very abrupt at temperatures of the order of 900°.

Later,^[10] (1919) Rosenhain notes that the physical properties of the thin amorphous films enveloping the crystalline grains are responsible for the mechanical properties of the polycrystal not only in the case described above, of intercrystalline fracture at high temperatures, but also under a whole series of other circumstances.

At ordinary temperatures the cause of intercrystalline brittleness may, for example, be the addition to the metal of small amounts of certain impurities. According to Rosenhain, this fact is easily explained on the assumption that the amorphous interlayer, like liquids, possesses a greater capacity than the crystalline lattice of the grain for dissolving foreign impurities.

Thus he abandons his original view—shown by a vast amount of experimental material to be false—of a uniform distribution of impurities between the interlayer and the grain. In the cases mentioned, the presence of impurities in the interlayer, in Rosenhain’s opinion, causes a lowering of its strength.

From this same point of view, the interlayer must be the location of all gases dissolved in the metal. As confirmation Rosenhain cites the experiments of Andrew and Holt, devoted to the study of the absorption of hydrogen by palladium.

These experiments showed that deformed palladium—that is, palladium containing, according to Rosenhain, a relatively larger amount of “amorphous metal”—dissolves a considerably larger amount of hydrogen than annealed material.

Rosenhain^[11] also considers the intercrystalline interlayer responsible for the phenomenon of “spontaneous cracking”—the so-called “season cracking” of certain metallic articles, chiefly brass ones, observed at ordinary temperatures, and also for the destruction of materials as a result of the very prolonged action upon them of small externally applied stresses (the latter phenomenon is now commonly called creep of metals, or “creep”).

In doing so, Rosenhain operates with the following experimental facts.

1. Brass articles, which in the course of their manufacture have undergone deformation, after the lapse of a certain interval of time, sometimes extending to several years, undergo spontaneous cracking.

2. In the lead sheaths of electric cables, cracks are found after many years of service.

3. Parts of boilers made of mild steel, after a certain time in operation, suddenly fail.

A comparative study of microphotographs of the failed parts, carried out by Rosenhain, showed that in all these cases the rupture clearly follows the boundaries of the crystalline grains (Fig. 4).

Fig. 4

Rosenhain gives one and the same interpretation to all these phenomena, attributing them to the capacity of the amorphous cement for viscous flow. The latter, in his opinion, must occur predominantly at high temperatures; nevertheless, the amorphous cement possesses sufficient mobility to flow perceptibly also at ordinary temperatures under the prolonged action of comparatively small stresses, both external and internal. Rosenhain notes that internal stresses in the material must inevitably be present in the first of the cases mentioned above; in the remaining cases, however, viscous flow of the interlayer arises as the result of the action of external conditions on the material.

In order to explain the circumstance that such intercrystalline failure of metals is not observed systematically, Rosenhain assumes that under ordinary conditions the viscous flow of the amorphous interlayer is hindered by the irregularity of the outlines of the boundaries of the crystalline grains. All these phenomena can, in his opinion, take place only when, as a result of preceding deformation, the grain boundaries have acquired more or less regular, smooth outlines.

Rosenhain was one of the first to note both the very possibility of the occurrence of intercrystalline failure of metals at ordinary temperatures and its particular danger.

The nature of “season cracking” and “creep,” however, as we shall see below, is entirely different. At the present time, the phenomenon of “season cracking” is usually understood to mean brittle spontaneous failure of a material resulting from the simultaneous action of internal stresses and corrosive factors. The role of the latter was not noted by Rosenhain.

§ 4. Jeffries’ Experiments

The hypothesis of “amorphous cement” became widespread among metallurgists, chiefly of the English school. Among its adherents one should include Jeffries, Archer, Desch, Humphrey, and many others. Their views, in essence, differ in no way from the ideas developed by Rosenhain.

Jeffries’ works ^12 (1917–1919), however, are of some interest from the point of view of the new experimental material contained in them. In particular, they present the results of studying the mechanical properties of copper, tungsten, and Armco iron in the temperature interval from the temperature of liquid air up to 900–1000°, i.e., they cover a region of considerably lower temperatures than in the experiments of Bengough and Rosenhain.

In Figs. 5 and 6 we give, by way of example, the curves obtained by Jeffries for the dependence of the strength of annealed Armco iron and copper on temperature.

Fig. 5

Like Rosenhain, Jeffries interprets the temperature corresponding to the onset of intercrystalline fracture as the temperature at which the strength of the amorphous cement is equal to the strength of the grain, applying to it the term “equicohesive” temperature. At the present time this term is generally accepted.

In analyzing the results he obtained, Jeffries uses a schematic representation of the relative behavior of the strength of the amorphous and crystalline phases at various temperatures (Fig. 7).

In Jeffries’ works, special attention is devoted to studying the influence of grain size on the mechanical properties of the material.

By comparing data on the strength of fine- and coarse-grained specimens, Jeffries showed that at low temperatures fine-grained material is stronger, while at high temperatures it is less strong than coarse-grained material.

These results Jeffries explains by the relatively large content of the amorphous phase in the fine-grained material.

He notes, however, that for each metal there exists a certain definite temperature at which a change in grain size has no effect on the strength of the material. This can occur only in the case when the strength of the grain and of the interlayer is the same.

Fig. 6

Jeffries identifies this temperature, accordingly, with the above-mentioned “equicohesive” temperature.

Fig. 7

Of considerable interest also is the phenomenon observed by Jeffries of intercrystalline fracture of Armco iron in the region of the temperature of liquid air. Jeffries attributes the destruction of the material along intercrystalline interlayers at low temperatures to the difference in the coefficients of contraction of the amorphous and crystalline phases at different temperatures.

§ 5. Gradual abandonment of the theory of
“amorphous cement”

Rosenhain’s ideas on the nature of the intercrystalline interlayer, formulated by him for the first time in 1912, insofar as this...

one may judge from his subsequent works, up to 1925 they did not undergo any substantial changes. Later, as a result of the accumulation of experimental data on the mechanical properties of single crystals, Rosengain somewhat modifies the earlier concept of “amorphous cement.”

Referring to an X-ray study of deformed single crystals, which showed that under deformation the elementary cells of the crystal lattice undergo only very slight elastic changes, Rosengain[^13] asserts that in a polycrystal the transition from one grain to another must be effected by means of “a layer of irregularly arranged atoms.” Unlike amorphous cement, such a layer must possess a certain definite structure.

The transition from a grain of one orientation to a grain of another orientation, in Rosengain’s opinion, could be accomplished in only one of the following two ways: 1) either by means of a gradual bending of the crystal lattice; 2) or through an intermediate layer of irregularly, or “amorphously,” distributed atoms.

In the first case, in the intermediate zone, during the transition from one lattice cell to another, there must occur a gradual distortion of them.

The data of X-ray analysis, however, exclude the possibility of sharp residual changes in the lattice parameter. The radius of curvature of such a “bent lattice” would have to be very large, i.e., the transition zone itself, in the case of certain mutual orientations of the grains, would be very broad.

Rosengain notes that in the case of fine-grained metals, even in the presence of the maximum possible elastic distortions of the cells, the width of the interlayer would be of the same order as the dimensions of the grains themselves.

Experimental data indicate, however, that the thickness of the interlayer is usually very small even in comparison with the finest grains, which compels Rosengain to reject the first model of the transition zone, based on the idea of a gradual distortion of the lattice.

Adopting the second possible model of the transition zone, he assumes that its difference from a regular crystal lattice consists in the fact that “in the layer of irregularly arranged atoms, the latter will be situated at the most diverse distances from one another, up to such distances at which they practically cease to be bound to one another. Such a structure is very similar to the structure attributed to glass, although its origin is quite different.”

Rosengain further notes that at low temperatures such a layer will exhibit both viscous and elastic properties, while at high temperatures it will behave as a viscous medium, similar to glass.

CHAPTER II. THEORIES OF THE “TRANSITION” ZONE

§ 6. Gough’s Conceptions

Gough’s conceptions^14 of the structure of an intercrystalline interlayer are based on the consideration that the transition from the orientation of any given grain to the orientations of the grains adjacent to it cannot take place by means of a gradual change of the constant lattice in the intermediate zone between the grains, since the latter is apparently very narrow.

Taking into account the sharp difference in the orientations of adjacent grains, Gough assumes that in this narrow zone there must be distortions exceeding those permissible in a normal crystalline lattice.

According to Gough, the intercrystalline zone is occupied by a large number of very small crystallites (crystalline fragments), the orientations of neighboring crystallites differing only slightly from one another. Their distribution in this zone is such that the required change of orientation in passing from grain to grain is achieved “by summing these small changes.”

An interlayer possessing such a structure, in Gough’s opinion, should at ordinary temperatures be stronger than the crystalline grain. Owing to the presence of lattice distortions between two neighboring crystallites, the interlayer must, however, be especially sharply susceptible to the action of temperature. Gough notes, for example, that the process of recrystallization should begin precisely at the grain boundaries. As confirmation he refers to Carpenter’s experimental data.

§ 7. The “Pseudo-Molecule” Hypothesis

The next step on the path of abandoning the theory of amorphous cement in its original form belongs to Dunn^15 (1927 and 1936).

In one of his early works, entitled “Properties of the So-Called Amorphous Metal,” he discusses the possibility of the formation of an amorphous layer along slip traces in a deformed metal. Comparing the physical properties of deformed metals with the corresponding properties of metals in the undeformed state, he comes to the conclusion that the conception of an amorphous layer as a supercooled liquid leads to a number of contradictions with experimental data.

Thus, for example, according to Hill^16, a deformed metal possesses an increased heat capacity. It is known, however, Dunn notes, that the heat capacity of metals in the liquid state is less than the heat capacity of solid metals. Further, a deformed metal possesses a negative thermoelectromotive force relative to an undeformed metal, whereas it is known that, in the case of all metals (with the exception of bismuth), the thermoelectromotive force is the same for both the liquid and the solid state.

These facts lead Dean to assert that the “amorphous layer,” if it is present at all, need not possess the properties of a supercooled liquid. In Dean’s opinion, the properties of such an “amorphous” layer, formed at the boundary of slip traces in the process of plastic deformation, can be explained more satisfactorily on the basis of the following ideas.

When two parts of a single crystal are displaced relative to one another, special conditions arise at the boundary of the slip traces: the distances between neighboring atoms exceed the normal value of the lattice constant.

Considering the possible behavior of electrons under these conditions, Dean1 notes that a solid metal is characterized by the presence of free electrons belonging to the whole metal as a whole, whereas in the gas phase each electron belongs to a quite definite atom. If, however, the distance between atoms is greater than the lattice constant but less than the normal interatomic distances in a gas, then: “individual atoms will show a tendency to appropriate electrons... as a result, there will be a forced formation of molecules (or electric dipoles, according to Dean’s later terminology)...”

The observed changes in the physical properties of metals during plastic deformation—such as hardening, an increase in heat capacity, and the appearance of a negative thermoelectromotive force—are explained by Dean by the presence of such “pseudo-molecules” along the slip traces. An increase in the number of pseudo-molecules or dipoles in the process of plastic deformation causes an increase in resistance to shear; further, since it is connected with a decrease in the number of free electrons, it must be accompanied by a decrease in electrical conductivity and by the appearance of a negative thermoelectromotive force.

Dean assumes that analogous conditions also occur at the boundary between two crystalline grains, and that here, too, neighboring atoms are separated from one another by distances exceeding the normal lattice constant.

In this case they likewise form “pseudo-molecules,” to whose existence the intercrystalline interlayer owes “its special properties.”

In one of his later works Dean2 attempts to give direct experimental proof of the existence of such “pseudo-molecules” on the surface of a metal. For this purpose he uses experimental data on the dependence of the electrical resistance of metallic powders on frequency.

It has been established that the electrical resistance of powdered antimony has a sharply expressed minimum at a frequency of 50 kHz. Dean notes that this frequency may be interpreted as being in resonance with the natural frequency of oscillation of electric dipoles whose length is of the order of interatomic distances.

According to Dean, the surface of a metal is covered with electric dipoles, fixed at one end and capable of oscillating under the action of thermal motion.

Inside the metal (for example, along slip planes), such dipoles or pseudo-molecules must be fixed at both ends.

§ 8. Hunt’s Considerations

Hunt3 (1932) attempts to construct a theory of the structure of intercrystalline interlayers, starting from ideas about the processes that take place in the production of metals by electrolytic deposition. Basing himself on the fact that a polycrystal obtained in this way, under certain experimental conditions, is practically in no way different from a polycrystal of the same material obtained by cooling a melt, Hunt makes the following assertion: “there are no grounds for considering that the interlayers of electrolytic metals differ from the interlayers of metal formed during the solidification of a melt.”

In this connection he refers to the experiments of Huntington (1905) and Blum and Rawdon (1923), which showed that if the surface of the cathode is first carefully etched (in order to remove from it traces of polishing), then in the layer of the same metal deposited on it electrolytically, the grains represent a direct continuation of the already existing grains of the cathode material.

In this case the process of deposition of the metal from the electrolyte is not accompanied by the appearance of new centers of crystallization; only further growth of the grains of the substrate takes place. According to Hunt, between the two parts of the aggregate of crystals obtained in this way no difference whatsoever is found. This gives him reason to consider that the character of the distribution of particles in the intercrystalline interlayer of cast and electrolytic metals must be, in the main, one and the same.

Discussing the hypothesis of the “amorphous cement” of Bengough and Rosenhain, Hunt comes to the conclusion that it is untenable when applied to the intercrystalline interlayer of polycrystals obtained by electrolytic deposition.

“It is difficult to imagine,” he writes, “the creation of amorphous material during the slow and ordered process of electrodeposition, when the depositing ions have a sufficient amount of time to occupy equilibrium positions.”

Hunt proposes the following mechanism for the formation of electrolytic metals. Metallic ions diffuse through the electrolyte to the cathode and are deposited on its surface. As a preliminary stage in the formation of the lattice, an adsorbed layer of metallic ions is created on the cathode surface. According to Hunt, crystal growth is accomplished in a discontinuous manner; it proceeds in layers or two-dimensional lattices. The loss by the ions of their charges occurs simultaneously with the process of formation of the crystalline lattice.

Impurities present in the electrolyte—foreign cations, molecules, and colloidal particles—will influence the process of crystallization by entering the layer adsorbed on the surface of the cathode. They will not be incorporated into the crystal lattice. Hunt regards them as “remaining in the adsorbed state or in the form of molecules oscillating between positions of minimum potential energy in two neighboring lattices.”

The intercrystalline interlayer must, accordingly, contain various kinds of foreign inclusions. In this respect Hunt’s views are close to Tammann’s conceptions, according to which the interlayer in cast metals consists exclusively of impurities.

Hunt illustrates his ideas on the mechanism of the electrolytic deposition of metals with the schematic diagram shown in Fig. 8.

[Metal ions]   [Foreign cations]   [Molecules]   [Colloids]
      ↓               ↓                 ↓             ↓
                 D i f f u s i o n
                 A d s o r p t i o n
      ↓               ↓                 ↓             ↓
[Lattice formation] [Lattice distortion] [Inclusion] [Inclusion]

Fig. 8

In the case of chemically pure metals the intercrystalline interlayer would have to be a “layer of oriented metallic ions, resembling in all respects an adsorbed layer binding two differently oriented lattices.”

Passing to consideration of the structure of metals obtained by the ordinary method of crystallization from a melt, Hunt, on the basis of the considerations set forth at the very beginning of the present paragraph, assumes that in this case too the intercrystalline interlayer consists of an oriented layer of ions oscillating between equilibrium positions corresponding to two neighboring lattices.

Hunt notes, however, the following (from our point of view quite essential) difference in the behavior of cast and electrolytic metals: in the case of metals obtained from a melt, recrystallization is observed only upon heating a previously de-

of the formed material; electrolytic metals, however, undergo recrystallization upon heating even without prior strain hardening.

Hunt’s hypothesis deserves some attention in view of the fact that it is the only attempt to construct a theory of the structure of the intercrystalline interlayer on the basis of ideas about the mechanism of the processes accompanying the electrolytic deposition of metals.

Fig. 9

Fig. 10

§ 9. Hargreaves and Hill’s “Transition Zone”

In contrast to the authors of the “amorphous cement” theories, Hargreaves and Hill \(^{20}\) consider that the intercrystalline interlayer possesses a completely definite structure. They assume that, in the space between the crystalline grains, the atoms are arranged in a quite definite manner, each of them occupying some equilibrium position. For a given relative orientation of two grains and a given position of the boundary, there corresponds a certain unambiguous mode of distribution of the atoms, characterized by the smallest possible value of the potential energy under these conditions. Hargreaves and Hill call an intercrystalline interlayer of such a structure a “transition zone.”

As a possible model for the formation of such a zone, they consider the case in which two lattices of a simple cubic system border one another, the boundary of one of them being a face of the cube. In doing so, they investigate such mutual orientations of two cubic lattices in which some atoms would belong to both lattices simultaneously. One such possibility is the case in which every fifth atom of the boundary is common. The angle between the crystalline grains, as follows from Fig. 9, is in this case \(36^\circ 50'\).

Hargreaves and Hill believe that in a real intercrystalline interlayer the atoms corresponding to the coincidence points of the lattices of two neighboring grains should not be too far removed from their normal equilibrium positions. The intermediate atoms, however, are not

may remain in the initial equilibrium positions; they must rearrange, and in doing so a new distribution will be established, repeated every 5 atoms.

As an illustration, Hargreaves and Hill give the scheme of the final distribution of atoms in the transition zone shown in Fig. 10.

The angles of mutual orientation of two neighboring grains, at which they possess common atoms, are determined by the formula:

\[ \theta^{0}=\arccos \frac{2n}{n^{2}+1}, \tag{1} \]

where \(n\) is any odd number.

Hargreaves and Hill assume that, for intermediate mutual orientations of the grains, the distribution of atoms in the interlayer will be intermediate with respect to the distributions corresponding to two neighboring values of the angles determined by formula (1).

Hargreaves and Hill consider these ideas on the structure of the transition zone to be valid also in the case of other types of lattice, and also when the lattice constants of two neighboring grains differ from one another (eutectics). They note that in the latter case the transition zone must be located predominantly in the lattice of the softer metal.

Since the intercrystalline interlayer is characterized by a definite structure, it must also possess a definite limit of elasticity.

Hargreaves and Hill believe that as soon as the latter is exceeded, then, as a result of plastic flow, the middle of the interlayer passes into an amorphous state. The thickness of the amorphous part of the interlayer is then the greater, the greater the degree of plastic deformation of the material. They place beyond any doubt the very possibility of the existence of an amorphous phase of a metal, as well as Beilby’s ideas on the emergence of such a phase in the process of deformation of metals.

The properties of such an amorphous medium Hargreaves and Hill fully identify with the properties of Rosenhain’s “amorphous cement,” regarding it as similar to a viscous supercooled liquid.

On both sides of the amorphous layer, however, there remain transition zones of the structure described above, gradually penetrating into the corresponding crystalline grain. As a result of their presence, the intercrystalline interlayer of Hargreaves and Hill must possess properties different from those of the purely amorphous interlayer of Bengough and Rosenhain.

The authors note that: 1) since the transition zone possesses a definite structure, it must be affected by allotropic transformations; 2) in the process of annealing, the transition zones located on both sides of the amorphous layer may coalesce with one another at the expense of this layer, which should lead to the gradual restoration of the “normal” transition zone, corresponding to an undeformed-

...mized state. As soon as such restoration has taken place, “the presence of residual stresses in the grains will lead to migration of the boundary. Grain growth will proceed by the transition zone creeping over.” The boundary must move in the direction of growth; in this process, an unstressed lattice will be formed at the expense of the stressed lattice.

Hargreaves and Hill suppose that, in addition, recrystallization may occur in the amorphous layer itself through the formation in it of new grains. They regard the first mechanism of recrystallization—through boundary migration—as the most probable, referring in this connection to the experiments of Carpenter and Elam.

One of the principal advantages of their theory, in comparison with the theories of Rosenhain and Gough, Hargreaves and Hill consider to be the fact that it provides a mechanism for the displacement of grain boundaries, whereas from the point of view of the latter this remains an open question.

They themselves note, however, that all their arguments concerning the nature of recrystallization in polycrystals are based on the idea that, during mechanical working of the material, the lattice of the grain remains more or less unaffected.

This, as we know, does not correspond to reality.

§ 10. Theory of the “ω-phase”

One of the modern theories of the structure of the intercrystalline interlayer, belonging to Meier[^21], is based on experimental data concerning the change in the parameter of the crystal lattice as a result of mechanical working of the material.

Studying X-ray photographs of rolled copper, Wood[^22], by comparative photometry of the Debye lines, established that mechanical working leads to distortion, namely, to an increase in the lattice constant of the material. Wood considers that this distortion is distributed nonuniformly throughout the volume of the crystal lattice: for \(\frac{15}{16}\) of the material the ratio of the change in the lattice constant to its initial value is

\[ \frac{\delta d}{d} = 2.8 \cdot 10^{-4}, \]

while for the remaining part of the material,

\[ \frac{\delta d}{d} = 16.7 \cdot 10^{-4}. \]

On the basis of these data, which testify to the physical inhomogeneity of deformed metals, Meier considers that the latter can be explained in the simplest way if we assume that, as a result of deformation, part of the metal along the slip planes passes into a new phase.

To this phase he gives the special name “ω-phase.”

Discussing the possible properties of the ω-phase, Maier notes that if the atoms belonging to this phase were at greater distances from one another than in the normal lattice (as Ding assumes), then it would have a density lower than that of the ordinary material. The formation of a less dense phase—the ω-phase—in a deformed material should, however, have caused elastic compression of the main part of the lattice, which was unaffected by the deformation.

According to Wood’s data, however, the crystal lattice as a result of deformation proves to be stretched, not compressed. In connection with this, Maier comes to the conclusion that “the atoms in the ω-phase are packed more densely than in the normal lattice.”

The appearance of the denser ω-phase is compensated by stretching of the main mass of the metal, which is indeed established by X-ray photography; it is precisely this that accounts for the decrease in the density of the material as a whole that usually accompanies the mechanical working of articles.

These conceptions of the structure of slip traces in a deformed metal are also applied by Maier without qualification to the intercrystalline interlayer of polycrystals.

According to Maier: “a polycrystalline aggregate consists of two phases, one of which is a lattice whose distortions do not exceed the limit of elasticity, while the second is an intercrystalline phase with a denser packing of atoms.”

Maier notes that his views differ substantially from those of Beilby and other adherents of the theory of “amorphous cement”: the “amorphous cement” should have a density lower than that of the normal crystalline lattice.

Considering the possible causes of the appearance of the ω-phase at grain boundaries, as well as along slip planes, Maier introduces the hypothesis of “idemsorption.” By “idemsorption” he means “adsorption on a crystalline surface of a layer of atoms or molecules of the same kind as the lattice. This layer possesses a lesser degree of crystallographic symmetry than the normal lattice.”

Thus Maier conceives the ω-phase as an adsorbed layer possessing increased density. He notes, however, that only part of the ω-phase can be in the adsorbed state, since “the capacity of a given aggregate of crystals for adsorption must in a certain way be limited.”

Maier’s theory, as he himself notes, is closest to the views of Ding set forth above.

§ 11. Tammann’s Conceptions

Breaking the historical sequence of the exposition, we shall now dwell on Tammann’s conceptions[^23] of the nature of the intercrystalline interlayer. They stand somewhat apart from the other hypotheses in the sense that their author entirely does not con—

is occupied with consideration of the general question of the character of the distribution of particles at the boundary of two grains. His views are more justified, all the less so, by a considerably more consistent analysis of the very extensive experimental material on the properties of the polycrystalline state than are the views of most other investigators.

Tammann considers the formation in metals of a new phase in general, and, in particular, of an amorphous phase, to be very improbable, thus being an opponent of the theory of “amorphous cement.”

On the basis of experimental data, however, he comes to the conclusion that in technical metals the grains are separated by an “intermediate substance” (“Zwischensubstanz”), present in the form of a “very thin nonmetallic film.” He succeeded in isolating this film directly from polycrystalline specimens of certain metals (Cd, Zn, Fe, Wo, Cu, Pb) by dissolving them in specially selected chemical reagents. We shall dwell on a detailed consideration of these experiments in the following chapter. Here we shall note only that in this process the metal grains were dissolved, after which there remained an intercrystalline skeleton, the shape of whose cells corresponded exactly to the shape of the dissolved grains.

The film remaining after dissolution, in turn, as Tammann showed, can be dissolved by certain other reagents (thus, for example, in the case of cadmium—partly by hydrochloric acid, partly by hydrofluoric acid). This indicates that the intercrystalline film consists of nonmetallic impurities; its solubility in hydrochloric acid indicates the presence in it of oxides, and its solubility in hydrofluoric acid—the presence of silicates.

During crystallization of the metal, the impurities inevitably present in the melt are distributed in the following manner: part of the impurities, chiefly metallic ones, dissolves inside the grain; such impurities as, for example, oxides, silicates, sulfides, phosphides, carbides, and nitrides, which dissolve poorly in the crystalline grain, are, according to Tammann’s ideas, driven out to the grain boundaries, forming the above-mentioned “intercrystalline substance.”

The films obtained by Tammann were transparent. From this he concludes that, for the metals he investigated, the upper limit of the film thickness is 1,000 atomic layers.

The intercrystalline film separates the grains and hinders their growth; in technical metals, owing to its presence, merely raising the temperature without preceding deformation cannot lead to recrystallization of the material. According to Tammann, recrystallization of a metal can take place only in the case when, as a result of partial ruptures of the impurity film, the grains come into direct contact with one another. The latter can practically be accomplished by deforming the metal by rolling, milling, etc.

“During deformation the shell of intercrystalline substance surrounding the crystallites is torn; the latter come into direct—”

direct contact. At the places of their contact, displacement of the boundaries begins or new grains arise. The fewer such places of crystallization, the larger the “grain” will be.

These ideas of Tammann were confirmed as a result of a detailed study of films remaining after the dissolution of deformed and undeformed metals.

The intercrystalline skeleton, isolated from polycrystals obtained by cooling a melt or from an aggregate that had undergone crystallization, represents, as was already noted above, a continuous network. The intercrystalline film obtained by Tammann as a result of dissolving a plate of rolled metal, however, no longer possesses the original cellular structure. The entire interlayer is torn, and its pieces are oriented in the direction of rolling.

Thus, according to Tammann, two crystalline grains brought into direct contact with one another cannot be in equilibrium; they corrode one another, combining into a single grain.

It follows from this that the purer the melt, the larger must be the grains of the metal obtained from it, which is confirmed experimentally. “If it were possible completely to remove impurities,” writes Tammann, “then it would be possible to obtain metal single crystals of any size.”

From this one may draw the natural conclusion that absolutely pure metals in general could not exist in the form of polycrystals. In practice, all metals, even the so-called “chemically pure” ones, nevertheless contain some amount of impurities. The fraction of the latter is usually not less than \(10^{-6}\). Tammann assumes that a monoatomic interlayer of impurities is already capable of preventing the corrosion of grains by one another.

CHAPTER III. EXPERIMENTAL DATA ON CERTAIN PROPERTIES OF INTERCRYSTALLINE INTERLAYERS

§ 12. Isolation of the intercrystalline interlayer

Over the last decades, a number of investigators have attempted to provide direct experimental proof of the existence of an intercrystalline interlayer by isolating it from a polycrystalline aggregate by the method of dissolving the grains. Successful systematic investigations in this direction, as was already mentioned above, belong to Tammann.

The distinctive feature of the latter’s method consists in the use of transparent solvents, which makes it possible to observe all the changes taking place in the process of dissolution, and also in the selection of such solvents whose action, as far as possible, would not be accompanied by the release of gas bubbles capable of destroying the thin intercrystalline film. To reduce the rate of formation of gas bubbles, the crucible with the solution is immersed in ice.

In one of Tammann’s first works,^24 the following experiments are described. A cadmium plate (Kahlbaum), 0.1–0.2 mm thick, was dissolved in a 50% solution of ammonium nitrate ($\mathrm{NH_4NO_3}$). During dissolution, under the microscope it was possible to observe directly the gradual eating away of the grains. After several seconds from the beginning of dissolution, only the thinnest film remained at the bottom of the glass dish; careful investigations showed that it possessed a clearly expressed reticulate structure.

When a cadmium plate was dissolved in a weaker solution of $\mathrm{NH_4NO_3}$ (25%), it was possible completely to avoid the formation of gas bubbles; the film remaining in this case adhered tightly to the bottom of the crucible, which made it possible to pour off the solution from it and wash it with water. By treating the remaining film with various reagents, it was possible to obtain some information about its chemical composition.

It turned out that the greater part of the film dissolves in hydrochloric acid, while its residue is soluble in hydrofluoric acid. As was already noted above (§ 11), this indicates the presence in the film of oxides and silicates.

If the cadmium is purified by distillation in vacuum, then the film remaining after its dissolution proves to be considerably thinner than in the preceding case. In mass it amounts to only 0.05 of the total quantity of distilled cadmium.

After a second distillation, as a result of dissolution, separate threads and scraps of film remain; sometimes they are so thin that they become invisible, and their presence can be judged only by the sudden retardation of the motion of air bubbles. A continuous network possessing a honeycomb-like structure is no longer obtained in this case. Thus, distillation of cadmium leads to a considerable decrease in the relative proportion of interlayer material.

When zinc is dissolved in $\mathrm{NH_4NO_3}$, the interlayer film proves to be concealed by a precipitate of zinc oxide hydrate formed in the process of dissolution. As a result of adding several drops of a saturated ammonia solution, this precipitate dissolves, and the honeycomb-like network of the interlayer is revealed.

In one of Tammann’s subsequent works,^25 with collaborators, a study was made of the character of the distribution of impurities of lead, bismuth, tin, and antimony in polycrystals of cadmium and copper.

For this purpose, various, quite definite quantities of impurities were added to the liquid melt of the metal. After solidification of the metal, thin plates were prepared from it by rolling; the interlayer film, obtained by the above-described method of dissolving the grains, was studied under the microscope (at 30-fold magnification).

As a result of dissolution in a 50% solution of $\mathrm{NH_4NO_3}$ of cadmium plates to whose melt bismuth, lead, tin, and antimony had respectively been added in amounts of 0.1, 0.005, and 0.002%, scraps of film remained in the form of separate dark bands. With a further decrease in the amount of impurities (0.010%), in most cases it was not possible to isolate the film. When the plates were heated,

of cadmium, the presence of the film could, however, be detected even when the metal contained 0.01% tin.

According to Tammann, when cadmium is heated to a temperature lying above the melting temperature of the cadmium–impurity eutectic, the latter “envelops” the grains and, after they have dissolved, remains in the form of particles larger than in the preceding case. In this case Tammann apparently did not observe a continuous network of film.

Tammann notes that this method is very sensitive for detecting the presence of small amounts of various impurities in polycrystals.

Polycrystals of copper were also subjected to an analogous investigation. As a result of dissolving a plate of pure rolled copper in a dilute (7.5%) solution of ammonium persulfate, only a few (10–20) very small grains of undissolved material remained. If 1% antimony was added to the copper melt, then after dissolution of the plate, heated to 950° (the melting temperature of the copper–antimony eutectic is 650°), an intact skin of interlayer remained. With an antimony content of 0.1%, dissolution produced only fragments of a network. When the amount of antimony was reduced to 0.01%, the precipitate remaining after dissolution could no longer be distinguished from the precipitate obtained in the case of pure copper.

When bismuth was added in amounts of 1 and 0.1%, it was not possible to obtain a continuous network of interlayer.

With a content of 0.1% lead, after dissolution there remains a white film consisting of PbSO₄.

When electrolytic iron²⁶ is dissolved in a 15% solution of ammonium persulfate, a barely noticeable precipitate remains in the form of 15–20 gray grains. If, however, electrolytic iron is remelted in a quartz tube, then after its dissolution a continuous light-gray network of interlayer is obtained. In Tammann’s opinion, its appearance is due to the penetration into the metal of silicates from the walls of the tube.

In the case of iron, the formation of a continuous network of interlayer is observed at a significantly lower impurity content than in the experiments described above with cadmium and copper. Thus, for example, it occurs already in the presence of 0.1% FeS, or 0.1% Sn, or 0.1% Sb; the inclusions of FeS, Sb, or Sn are in this case oriented in the direction of rolling, as is shown in Fig. 11.

Using this method, Tammann was able to detect in iron the presence of 0.002% FeS, 0.05–0.02% Al, 0.05% Sb, 0.02% Sn, and 0.001% silicates.

Especially interesting results are obtained when aluminum is added to iron. After dissolution of an iron plate containing 0.1% Al, there remains a gray network containing separate fibers of alumina oriented in the direction of rolling. If the plate is heated to 1050°, then the film remaining after its dissolution proves to have broken up into separate regions, connected

with transparent interlayers between one another (Fig. 12). The latter consist of Al₂O₃, formed as a result of the oxidation of aluminum originally dissolved in the grains of the metal.

It is known that iron obtained by aluminothermy cannot be subjected to cold working; during forging such iron crumbles, revealing an intercrystalline fracture.

Fig. 11          Fig. 12

This fact becomes understandable in connection with the structure described above of the intercrystalline interlayer in iron containing aluminum impurities. Already in his work of 1922, Tammann noted that the brittleness of iron in this case is due not to the content of metallic aluminum in it, but to the presence of Al₂O₃. The latter partly forms an intercrystalline shell separating the Fe grains, and partly is contained inside the grains in the form of small corundum crystals. The experiments of Tammann described above, confirming the validity of these considerations, were carried out by him considerably later (in 1928).

In the case of various grades of lead²⁷ containing small amounts of metallic impurities, it was also possible to isolate an intercrystalline film.

Redistribution of impurities during heating. We have already mentioned that, in experiments with cadmium, copper, and iron, preliminary heating of the specimens leads to an increase in the relative fraction of the intercrystalline substance. Tammann believes that if a specimen is heated to a temperature exceeding the melting temperature of the eutectics contained in it and formed by impurities, then the liquid eutectic spreads around the grains along their boundaries, forming a more or less continuous (and under certain conditions, solid) film of the intercrystalline interlayer.

In this connection, heating of deformed specimens leads to the restoration of the interlayer ruptured during the process of deformation; the capacity of the material for recrystallization then disappears as a consequence of the elimination of direct contact between the grains.

The influence of heating on the character of the distribution of impurities between the grain and the interlayer was studied by Tammann \(^{28}\) in the case of cadmium containing \(0.1\%\) Sn, and also cadmium containing \(0.1\%\) Pb. The melting point of the Cd—Sn eutectic is \(170^\circ\), that of the Cd—Pb eutectic \(250^\circ\).

When Cd \(+ 0.1\%\) Sn is heated to \(150^\circ\), in the network of the interlayer remaining after dissolution, particles of Sn (black dots) are encountered both inside the Cd grains and at the boundaries of the latter. When heated to \(165^\circ\) and above, the Sn grains almost completely leave the Cd grains, concentrating at their boundaries.

In the case of Cd \(+ 0.1\%\) Pb, when the temperature is raised above \(250^\circ\), a gradual redistribution of the impurity is likewise observed.

Tammann also observed the “envelopment” of grains by liquid eutectics in the case of Fe \(+ 0.1\%\) FeS, Fe \(+ 0.1\%\) Sb, and Fe \(+ 0.1\%\) Sn when the specimens were heated to the corresponding temperatures.

The structure of the intercrystalline film is also strongly affected by the rate of cooling of the melt. In the case of rapid cooling of metals, Tammann did not succeed in obtaining a continuous intercrystalline film; with slow cooling of the melt, the intercrystalline film remaining after dissolution constituted a continuous network.

Kuchelnigg’s experiments. Tammann’s investigations were continued by Kuchelnigg \(^{29}\). The latter, dissolving pure tin foil in a \(10\%\) solution of ferric chloride, obtained as a residue a yellowish-white film of intercrystalline substance possessing a network structure. As a solvent for tin it also proved possible to use a saturated solution of pink salt \((\mathrm{SnCl}_4 2\mathrm{NH}_4\mathrm{Cl})\) in alcohol; dissolution in the latter, however, proceeds considerably more slowly.

The isolated film dissolves in hydrochloric acid and does not dissolve in nitric acid. A solution of the film in hydrochloric acid gave a positive reaction for the presence of atoms, as well as ions, of Sn.

Taking into account the good solubility of most metals in ferric chloride, Kuchelnigg notes that foreign metals can hardly be present in the remaining film; in his opinion, it consists mainly of nonmetallic compounds containing tin.

Kuchelnigg further determined the percentage content of intercrystalline substance in tin foil. For this purpose, \(10\) g of foil was dissolved in \(600\ \mathrm{cm}^3\) of a \(10\%\) solution of ferric chloride. The solution was filtered in a porcelain crucible through a porcelain filter. After thorough washing of the precipitate, the crucible with the filter was ignited until loss in weight ceased. Weighing showed that the weight of the residue was \(1.76\) mg, i.e., \(0.0176\%\) of the initial material.

Kuchelnigg himself notes, however, that this experiment was carried out insufficiently carefully; the precipitate apparently contained traces of iron that had entered it from the solvent.

§ 13. Revealing grain boundaries by etching

If the polished surface of a metallic specimen is slightly moistened with an acid solution or with some other etching composition, then after a few seconds a network with a regular cellular structure is clearly delineated under the microscope. The black lines forming the contours of the individual cells correspond in this case to the boundaries of the crystalline grains. In Fig. 13 there is shown a microphotograph of the surface of specimen Al, subjected to etching (magnification 150 times)¹.

Fig. 13

Etching the surface of a metal with acids, as well as with certain other reagents, is one of the most widespread methods of revealing the granular structure of a metal. It makes it possible to judge the shape and the size of the grain.

The fact that the contours of the grains become visible indicates the nonuniform character of the scattering of light by separate portions of the etched surface. From this one may conclude that, during etching, dissolution of different portions of the surface of the polycrystal takes place at unequal rates.

For understanding the nature of the polycrystalline state, it is of very substantial interest to clarify the question of precisely which of the elements of the polycrystal—the intercrystalline interlayer or the crystalline grain—is characterized by the greater solubility.

The picture observed under the microscope is as if grooves had formed on the smooth polished surface of the metal, following the contours of the crystalline grains. On this basis one might conclude that the substance of the interlayer dissolves more rapidly than the crystalline grain.

Hatfield³⁰ carried out special experiments to determine the relative susceptibility of the grain and the interlayer to etching. The polished surfaces of specimens of welded iron were etched with a weak solution (2%) of nitric acid. Microscopic examination showed that the grain boundaries were very sharply outlined; the crystalline grains were dissolved in this case, however, at different levels, forming terraces. Fig. 14 gives a microphotograph of a section of a specimen perpendicular to the plane—

¹ In the middle of the microphotograph of a specimen subjected to stretching, an intercrystalline crack is visible, arising as a result of “overburning” of the material during heat treatment.

ness of the etched section. The stepped character of the surface relief is clearly visible on it.

Analogous results were also obtained when an iron specimen was etched for seven days with weak solutions (0.02% and 0.5%) of sulfuric acid.

Fig. 14

On the basis of a microscopic study of transverse sections, Hatfield comes to the conclusion that at the places where grains adjoin one another there are no depressions whatsoever. He regards the data he obtained as evidence for the absence of preferential dissolution of the material of the intercrystalline interlayer; he attributes the effect of revealing grain boundaries during etching entirely to the dissolution, to different depths, of grains having different orientations, leading to the formation of steps on the surface of the section.

Etching the surface of brass with weak solutions of ammonium persulfate (0.02 and 0.5%) for seven days, and also of silver with a 10% solution of chromic acid, led to analogous results. In the case of silver, the disposition of the grains at different levels appears especially sharply.

Figure 15 shows a greatly enlarged (500×) microphotograph of the boundary between two silver grains. One might think that the entire dark band corresponds to a more sharply etched intercrystalline interlayer. According to Hatfield, however, the true boundary of the grains in this case should be considered the line \(CD\), while the dark region is, in his opinion, merely the shadow from the projection of crystals \(B\) above crystal \(A\).

Fig. 15

A similar explanation of the origin of the dark contours of grain boundaries observed in microphotographs is at present very widespread among metallographers. From this point of view, however, that widely known fact remains completely unexplained: in the process of etchi-

...first of all, the grain boundaries are usually revealed, while the structural characteristics of the grain itself are detected considerably later.

In addition, when etching with weakly concentrated solutions, only the external outlines of the grains become visible, while the grain itself remains colorless. The appearance of different shades of the grains, caused by the unequal solubility of individual crystal faces, is observed only when significantly more concentrated etchants are used.

These facts, which underlie modern methods of treating metallographic polished sections, undoubtedly indicate a more rapid dissolution of the material along the intercrystalline interlayer.

Comparatively recently (1937), McCarty^31 carried out a microscopic study of the surfaces of steel specimens etched with a one-percent solution of nitric acid in alcohol for various intervals of time.

If the surface of the polished section is slightly etched with this composition, no difference is found between the two components of the steel—ferrite and cementite—while the grain boundaries are revealed quite clearly. With a longer action of the etchant, the ferrite grains acquire a darker coloration than the cementite grains.

McCarty also presents microphotographs characterizing the structure of spheroidized cementite. The grain boundaries become visible as early as 10 sec. after the beginning of etching, whereas the difference between ferrite and cementite is detected only after 30 sec.

In Fig. 16 we present a series of microphotographs obtained by McCarty during the etching of low-carbon steel. Photograph

Fig. 16

No. 1 was taken 10 sec. after the beginning of etching, No. 2—after 30 sec., No. 3 after 1 min. and 30 sec. (magnification 1000 times). Photograph No. 2 shows that more prolonged etching leads to a widening of the dark lines along the grain boundaries. McCarty notes that with further etching the middle portions of the dark contours of some grains begin to become light as a result of complete dissolution of the interlayer down to the surface of the grain lying beneath it. The formation of such light spots may be observed in photograph No. 3, where a difference in the orientations of individual grains already begins to be revealed.

The diagram given in Fig. 17 illustrates the process of gradual

1st stage    2nd stage
Etching  interlayer

Fig. 17

etching of the boundary of two grains, as a result of which the underlying grain is exposed (after McCarty). McCarty’s experiments once again testify to the preferential solubility of the intercrystalline interlayer.

The effects observed by Hatfield, associated with the formation of a stepped relief on the etched surface, must undoubtedly also occur at a certain (later) stage of etching.

The question of whether the increased solubility of the intercrystalline interlayer is due to its special structure, different from the structure of the grain, or to the presence in it of foreign impurities, however, remains open.

§ 14. Data on the density of the intercrystalline interlayer

The authors of various theories of the intercrystalline interlayer usually assert first of all that the density of the interlayer differs from the density of the crystalline grain. At the same time, supporters of the “amorphous cement” hypothesis believe that the interlayer must possess a density reduced in relation to that of the grain. According to Meyer, the intercrystalline interlayer, on the contrary, represents an “ω-phase” denser than the grain.

A direct answer to this question could be obtained by comparing the densities of mono- and polycrystalline specimens of one and the same material.

According to the data of Hanson and Wheeler[^32], the density of polycrystalline aluminum is 2.7091, the density of aluminum single crystals—2.7087. The accuracy of the density measurements in this work

did not exceed, however, 0.001, which does not entitle us to draw any definite conclusions on the basis of these figures.

In the work of Sachs and Shoji[^33] the following data are given on the density of single crystals and polycrystals of brass (with a content of 91% Cu by weight) (Table 3):

Table 3

Material	State	Density
Single crystal	Solidified from the melt (porous)	8.8042±0.0014
»	Compressed by 70% (pores closed)	8.8154±0.0014
»	Compressed, annealed for 2 hours at 600°	8.8154±0.0014
Polycrystal	Annealed for 2 hours at 500°	8.7918±0.0008

A considerably more accurate determination of the density of single-crystalline and polycrystalline specimens was recently carried out by Meyer for copper. The density of a single crystal of copper was found to be 8.95285. For comparison Meyer measured the density of two polycrystalline copper specimens prepared in the following way: the copper was melted in a graphite crucible in a vacuum of \(10^{-3}\) mm, then the temperature of the melt was slowly raised to 1150°, maintained for 1 hour, and lowered over 3 hours to 1050°. One of the specimens solidified in vacuum, the other—in a helium atmosphere (under a pressure of 4 kg). The density of the first specimen was found to be 8.94153, of the second—8.94331.

Meyer[^21] further studied the influence of various kinds of mechanical treatment on the density of copper polycrystals. In doing so he showed that, depending on the type of deformation and the annealing conditions, either a decrease or an increase in the density of the specimen may occur. In all cases, however, the density of the single crystal is considerably higher than the density of the polycrystalline specimens. In Fig. 18 a curve is given for the dependence of the density of the material on the degree of reduction of the transverse dimensions of the specimen. The upper straight line corresponds to the density of the single crystal.

The data cited here are, of course, not sufficient to draw final conclusions about the relation between the densities of polycrystals and single crystals.

Unfortunately, however, we have not been able to find such works in which measurements of the density of single-crystalline and polycrystalline specimens of one and the same material were made.

The thoroughness of Meyer’s experiments, however, leaves no doubt.

Mayer’s data, as well as the analogous results of Sachs and Shoji, may nevertheless apparently be regarded as indicating that the presence of an intercrystalline interlayer, characteristic of the polycrystalline state, causes a lowering of the density of an aggregate of crystals in comparison with the density of a crystalline grain (a single crystal).

Fig. 18

Labels in the figure: “Density in g per cm³ at 20°C”; “Deformation”; “Single crystal”; “Vacuum + helium”; “Vacuum”; \(880^\circ\mathrm{C}\), \(970^\circ\mathrm{C}\), \(995^\circ\mathrm{C}\), \(1035^\circ\mathrm{C}\).

It is also of interest to compare data on the behavior of the density of polycrystals and single crystals during mechanical treatment of the material.

Sachs and Shoji established that, when previously annealed aluminum single crystals are stretched up to the formation of a neck (elongation from 6% to 27%), no change in the density of the specimens takes place.

Gough[^14] describes the following experiment. Polycrystalline and single-crystalline aluminum specimens were subjected to fatigue testing under the action of an alternating load. Both before and after the test, careful measurements were made of the density of each of the specimens (with an accuracy of \(1/3000\)). They showed that the density of aluminum single-crystal specimens remains unchanged, whereas in polycrystalline specimens there is a decrease in density lying within the limits of \(0.037\)—\(0.1\%\) of the density of the material in the undeformed state.

Gough, Hanson, and Wright[^34] found no change in density in aluminum single crystals subjected to fatigue tests.

In the case of brass, however, the results prove to be to some extent uncertain.

According to the initial data of Sachs and Shoji, compression of brass single crystals, previously annealed for 2 hours at \(700^\circ\), is accompanied by an increase in density of the order of \(0.13\%\). The authors attribute this effect to the closing of pores present in the initial material.

In one of their later works, Sachs and Masima[^35] established that stretching brass single crystals is accompanied by a decrease in density of the order of \(0.06\%\). In compression tests of fine-grained brass specimens, however, there was a decrease in density of the order of \(0.05\%\).

The lowering of the density of polycrystalline materials as a result of most types of mechanical treatment may be considered

firmly established fact. This phenomenon was discovered as early as 1861 by O’Neill^36 in the forging of copper sheets and, somewhat later, by Spring^36 (1891) in wires, as a result of measuring their density before and after annealing. Subsequently this effect was repeatedly observed by a number of investigators; the maximum decrease in density as a result of mechanical working is of the order of 0.2%.

Hanson and Wheeler^32, studying creep in single crystals and polycrystals of aluminum, obtained a number of interesting data on the character of the density changes accompanying this phenomenon. Aluminum specimens were subjected to prolonged action (up to 570 days) of small tensile forces at various temperatures. Rupture of the material in this case occurred at stresses significantly lower than the strength of the material under normal conditions.

In polycrystalline specimens fractured as a result of such slow tests, a considerable decrease in density is observed; moreover, it is expressed the more sharply the lower the rate of testing and the higher the temperature of the experiment.

The behavior of single-crystal specimens under analogous conditions proves, however, to be essentially different. In the case of aluminum single crystals subjected to slow tension at room temperature, a change in density is likewise observed; it is, however, so insignificant that, in the opinion of Hanson and Wheeler, it may be attributed to measurement error. Testing of single crystals at a higher temperature (250°) is accompanied, nevertheless, by some lowering of the density. The results of the density measurements are given in Table 4.

Table 4

Material	Test temperature in °C	Duration of test	Density
Single crystal	18	—	2.7087
»	18	256 days	2.7084
»	18	Rapid test	2.7082
»	250	Rapid test	2.7078
»	250	33 days	2.7026
Polycrystal	18	—	2.7091
»	18	570 days	2.7059
»	18	3 minutes	2.7012
»	250	Rapid test	2.7023
»	250	Slow test	2.6800

O’Neill^37 (1924) studied the influence of cold working on the density of polycrystals and single crystals of iron. The object of the investigation was Armco iron (with a content of 0.03% C, 0.01% Si, 0.02% Mg, 0.023% S, 0.008% P, and 0.03% Cu). After anneal-

The specimens were subjected to tension up to rupture. Measurements of density were made for various sections of the specimen along its length. It was established that, as a result of deformation, the density of the polycrystalline material decreases, and this decrease is different in different sections of the specimen. The minimum density corresponded to the region where the neck was formed, i.e., the region subjected to the greatest deformation.

The density measurements were made with an accuracy of 0.0003 g. The density of the initial material was 7.8580; the density of the specimen in the region of the neck was 7.7927.

In compression tests of single crystals of silicon iron (1.81% Si, <0.01% C, 0.008% S, 0.01% P), there was in fact no change in density. The density of the initial material was 7.752; the density after 80% compression was 7.754. At 26% compression a minimum density of 7.747 was observed (the density here was 0.07% less than the initial value).

Unfortunately, no conclusions regarding the relationship between the density of single crystals and polycrystals of iron can be drawn from the data of this work, owing to the difference in the chemical composition of the single-crystal and polycrystalline specimens.

Summing up, one may say that the density of aluminum single crystals in tension, fatigue, and creep tests (according to the data of 4 different studies), as well as the density of $\alpha$-iron under compression, remains practically constant.

The changes in density observed in the case of brass single crystals are not indicative, in view of the nonuniform structure of alloy single crystals.

This gave Gow, Hanson, and certain other investigators grounds to believe that the intercrystalline interlayer alone is responsible for the change in the density of polycrystalline materials as a result of mechanical working.

Thus Gow writes: “the decrease in the density of a metallic specimen in fatigue tests is an effect concentrated near the grain boundaries, or caused by their presence. Where such boundaries do not exist, no change in density occurs.”

It may be assumed, however, that plastic deformation of single crystals is also accompanied by a decrease in the density of the material. This decrease must be local in character, occurring only in the so-called slip traces; the changes in density of the specimen as a whole are then apparently so small that they lie within the limits of experimental error.

§ 15. Diffusion of Foreign Substances along Interlayers

The experiments on the separation of the intercrystalline film, described in the preceding section, testify with sufficient clarity that the intercrystalline interlayer of real polycrystals is the site of a preferential concentration of impurities.

If foreign substances are added to the melt of a given metal, then, upon cooling of the melt, the molecules of these substances enter only to an insignificant degree into the crystal lattice of the grains, accumulating mainly at the boundaries of the latter4.

Of great interest should also be the study of the nature of the distribution of foreign substances when they penetrate into metals that are in the solid state. In particular, clarification of the question of the conditions under which foreign particles diffuse predominantly through the grains and under which through the interlayers should enable us to draw certain conclusions about the nature of the difference between the structures of the grain and the interlayer.

From this point of view it would be interesting, first of all, to compare data on the diffusion rates of various substances in polycrystals and single crystals of one and the same metal. These data, unfortunately, are not very numerous.

Geiss and Van Liempt[^38] showed that carbon, iron, and molybdenum practically do not diffuse into single crystals of tungsten, whereas under the same experimental conditions the diffusion of these substances in pressed tungsten powder takes place comparatively readily.

Zwikker[^39] found that the rate of diffusion of carbon in fine-grained tungsten is 4 times greater than the rate of its diffusion in single crystals of tungsten.

Van Liempt[^40] mentions that, at one and the same experimental temperature, the diffusion coefficient of molybdenum in polycrystalline tungsten considerably exceeds the diffusion coefficient of molybdenum in single crystals of tungsten. Thus, for example, in the case of fine-grained tungsten specimens (average grain diameter \(20 \mu\)) at \(1600^\circ\) it is 10 times greater than the diffusion coefficient in single-crystalline tungsten.

Very interesting are the experiments of Hevesy[^41], devoted to the study of the phenomenon of “self-diffusion” in lead. In order to be able to follow the course of this process in time, a radioactive isotope of lead—thorium B—was chosen as the diffusing substance. The diffusion rate of thorium was measured by counting the scintillations produced by \(\alpha\)-particles. It turned out that this diffusion process takes place in polycrystalline lead (the diffusion rate being the greater, the finer the lead grains), but is practically not observed at all in single crystals of lead.

Edmunds[^54] did not observe diffusion of copper in single crystals of zinc, whereas the diffusion of copper in polycrystalline zinc proceeds at a measurable rate.

Compton and Langmuir[^42] note that the diffusion of thorium in tungsten proceeds especially rapidly along the boundaries of the crystalline grains.

Dushman and Koller ^43 showed that the rate of diffusion of thorium in tungsten depends on the grain size. From Klausing’s experiments ^44 it follows that in fine-grained tungsten specimens diffusion proceeds almost exclusively along grain boundaries.

Langmuir’s calculations ^45 showed that at 2400° K the rate of diffusion of thorium along the grain boundaries of tungsten is approximately 100 times greater than its rate of diffusion inside the grain.

Fond, Jung, and Wahlke ^46, who studied the diffusion of thorium in coarse- and fine-grained tungsten specimens, obtained very interesting results. It turned out that the diffusion coefficient decreases noticeably as the grain size increases. Table 5 gives the values of the diffusion coefficients of thorium in tungsten corresponding to different grain sizes (at a temperature of 2400° K).

Table 5

Grain radius in μ	Diffusion coefficient in cm² sec⁻¹ · 10⁹
4.0	4.1
5.3	3.2
6.3	2.2
7.3	1.3
8.6	1.0
1000	0.21
3000	0.01

An increase in grain size means a decrease in the relative extent of the boundaries of crystalline grains. On the basis of these data one may conclude that thorium diffuses mainly along the intercrystalline layers of tungsten.

Stead ^47 showed that oxidation of steel is accompanied by the diffusion of oxygen along grain boundaries.

Almost simultaneously, Hartley ^54 observed the formation of oxides along grain boundaries in specimens of steel and copper that had been subjected to stretching at high temperatures.

According to the data of Rolfe ^48, oxygen penetrates into the intercrystalline layer of copper and bronze.

Moore, Beckinsale, and Malinson ^49 observed selective penetration of ammonia along the grain boundaries of brass.

Dickenson ^50 was one of the first to observe the penetration of various solders into the intercrystalline layer.

The grain boundaries of some alloys are subject to preferential corrosion. In the corrosion of α-brass by seawater and by certain other reagents, the process of “dezincification” takes place—the removal of zinc from the alloy as a result of its dissolution. By microscopic investigation, Desch ^51 showed that the diffusion of zinc from α-brass proceeds along grain boundaries.

All these experiments seem to indicate that the diffusion of foreign substances proceeds chiefly along intercrystalline layers.

There are, however, a number of experimental facts that contradict this general conclusion. Thus, for example, Hedges showed that the diffusion coefficient of polonium in lead is the same for both polycrystalline and single-crystalline material.

Seith and Keil52 were unable to detect any substantial difference between the diffusion rates of a radioactive isotope of lead in polycrystalline and single-crystalline lead.

According to Elam’s data53, in the diffusion of zinc in copper no preferential penetration of zinc along grain boundaries is observed.

Mehl54 mentions unpublished experiments devoted to the study of the diffusion of nitrogen in $\alpha$-iron. Coarse-grained (1 grain per $1\ \mathrm{mm}^2$) and fine-grained (200 grains per $1\ \mathrm{mm}^2$) iron specimens were nitrided in ammonia for 24 hours at $525^\circ$. The depth of penetration of nitrogen could be judged from the dimensions of the nitride “needles.” In both specimens the length of these needles proved, however, to be the same, amounting to $1 \pm 0.05\ \mathrm{mm}$.

A very widespread opinion is that the diffusion of hydrogen in metals also proceeds chiefly along the boundaries of crystalline grains. For a direct verification of the correctness of these ideas, Smithells and Ransley55 measured the diffusion coefficient of hydrogen in single crystals and polycrystals of iron.

Table 6 gives the numerical values of the diffusion coefficient measured at different experimental temperatures. The polycrystalline specimen had a fine-grained structure (100 grains per $1\ \mathrm{mm}^2$).

Table 6

Temperature in $^\circ\mathrm{K}$	Diffusion coefficient $\cdot\ (10^6)$ in a polycrystal	Diffusion coefficient $\cdot\ (10^6)$ in a single crystal
518	2.4	1.2
686	17.6	17.1
894	92.8	89.5
1052	203	205

This table indicates that in the present case the presence of intercrystalline boundaries has no substantial influence on the rate of the diffusion process.

The experimental data on the relative rate of diffusion in single crystals and polycrystals thus prove to be somewhat contradictory.

In view of the complexity of the phenomenon itself, it is difficult here, however, to expect the existence of any strict regularities. The character of the process of diffusion of foreign particles in solids is determined by a whole series of diverse factors. Thus, for example, Smithells and Ransley give experimental data indicating that

diffusion of foreign particles in metals is observed only in those cases when these particles are capable of being adsorbed on the surface of the given metal. In the case of the diffusion of gases, as a preliminary stage, there apparently takes place the adsorption of gas molecules, accompanied by their dissociation. The state of the surface of the metallic specimen must, therefore, exert a substantial influence on the rate of diffusion into the specimen.

In the case when diffusion proceeds along intercrystalline interlayers, the picture must become greatly complicated. We have already noted above that the interlayer is the place of preferential concentration of impurities. Its chemical composition may differ considerably from the chemical composition of the grains. In chemically different media the diffusion of one and the same substance proceeds, as is known, at different rates. The presence of certain impurities in the metal may, in this connection, lead to the most unexpected results in measuring diffusion rates. The process of diffusion is especially complicated in the case when the diffusing particles are capable of entering into chemical combination with impurities present in the interlayer.

The majority of experimental data nevertheless indicate that, under the same experimental conditions, the diffusion coefficient of a polycrystalline material exceeds the diffusion coefficient in single crystals of the same substance.

The easier penetration of foreign particles into the intercrystalline interlayer is apparently due to the relatively less dense packing of particles in the interlayer as compared with the grain.

A consequence of this less dense packing of particles should be a lowering of the height of the potential barrier which they must overcome in passing from one equilibrium position to a neighboring one.

As confirmation of these considerations we mention Langmuir’s calculations, which showed that, in the case of the diffusion of thorium in tungsten, the diffusion coefficient of thorium within the grain volume can be represented by the following formula:

\[ D_1 = (D_0)_1 e^{-\frac{U_1}{RT}}, \]

whereas for diffusion along grain boundaries:

\[ D_2 = (D_0)_2 e^{-\frac{U_2}{RT}}, \]

where the activation energies \(U_1\) and \(U_2\) (the heights of the potential barriers) are respectively equal to:

\[ U_1 = 120.000 \ \text{cal/g-mol}, \qquad U_2 = 90\,000 \ \text{cal/g-mol}. \]

At the present time it is customary to distinguish three types of diffusion in solids: diffusion in the volume of crystalline grains,

diffusion along grain boundaries and diffusion over the surface of the metal.

Comparing data on the diffusion rates of thorium in tungsten under various experimental conditions, Langmuir comes to the conclusion that diffusion proceeds at the greatest rate over the surface of tungsten, and at the smallest rate—inside the crystalline grain. Fig. 19 illustrates the dependence found by Langmuir of the logarithm of the diffusion coefficient on temperature for all three types of diffusion.

Fig. 19

Of considerable interest is the comparative study of the character of diffusion in deformed and undeformed specimens of one and the same material.

We have already mentioned the experiments of Andrew and Holt^54, which showed that the rate of diffusion of hydrogen in palladium increases with an increase in the degree of deformation of the palladium specimens.

Zeit and Keil established that in deformed lead diffusion proceeds at a higher rate than in specimens that had undergone recrystallization.

Molten tin, lead, and certain solders are capable of penetrating between the grains of many varieties of brass.

For this it is necessary, however, that the brass be in a state of tension. In unstressed or compressed brass specimens, as was established by Dickinson^50 and Miller^56, penetration of the molten metals does not occur.

Moore and co-workers^49 showed that mercury, as well as solutions of some of its salts, are capable of diffusing along the grain boundaries of stretched specimens of α-brass.

In the process of soldering, molten brass penetrates between the grains of mild steel, again only in the presence of tensile stresses.

The works of Desch^57, devoted to the study of the penetration of mercury into β-brass containing small admixtures of aluminum (about 3%), are very interesting. If a specimen of such brass is immersed in mercury, then after several seconds it breaks up into separate grains. The sizes and shape of the grains do not change in this process. This phenomenon is observed at room temperature.

Desch notes that this disintegration of β-brass into grains upon its immersion in mercury is apparently also connected with the presence of certain internal stresses in the material. This is evidenced by the crackling sound accompanying the disintegration of the brass, detectable with the aid of a microphone.

Especially indicative is the fact that annealing brass at 700° completely eliminates its ability to disintegrate in mercury.

The totality of these data indicates that the rate of diffusion in the deformed material exceeds the rate of diffusion in undeformed specimens, while the diffusion process itself still proceeds predominantly along interlayers.

The increased rate of diffusion in specimens that have undergone deformation may in part be due to the circumstance that, in the deformed region, the atoms possess an increased

3. 19 ↩

4. We shall not consider here those cases in which the formation of solid solutions is possible. ↩