Nature of Intercrystalline Interlayers1

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

§ 16. Fracture of a Material along Intercrystalline Interlayers

It is well known that the addition of very small amounts of certain impurities to a metal melt has a very sharp effect on the mechanical properties of the material. The presence of impurities in single crystals or in a crystalline grain usually causes an increase in resistance to shear and an increase in tensile strength. It was shown above, however, that in a crystalline aggregate the principal location of impurities is the intercrystalline interlayer. The presence of an impurity in the interlayer, in a number of cases, sharply lowers the strength of the polycrystalline material, causing intercrystalline brittleness.

As early as the end of the last century Arnold and Jefferson[^58], and also Osmond and Roberts-Austen[^59], showed that the addition of 0.1% bismuth to a gold melt causes intercrystalline brittleness in the latter.

Tammann notes that, as a result of the addition of aluminum, intercrystalline fracture is observed in brass articles. Castings of β-brass containing more than 3% aluminum usually reveal a tendency toward brittle fracture along the grain boundaries. With slow application of the load, however, fracture proceeds through the grains, and the strength of the brass has a normal value.

We also mentioned that the formation of Al₂O₃ along the grain boundaries of iron causes intercrystalline brittleness in the latter.

The brittleness of beryllium is usually explained by the presence, in the intercrystalline interlayer of this metal, of traces of oxides which it does not appear possible to remove.

It is known from practice how dangerous the presence of traces of sulfur is in various grades of steel. The sulfur compound FeS envelops the crystalline grains with a thin

film, in a whole series of cases causing intercrystalline brittleness of steel articles. In connection with this, one always tries not to allow a high sulfur content in steel (not above 0.05%).

It is generally known that phosphorus has a harmful effect on the mechanical properties of iron and steel when the latter contain a large amount of carbon. The presence of phosphorus even at ordinary temperatures causes brittleness of the material (cold shortness along dendrite boundaries). The presence of phosphorus is thereby all the more dangerous the higher the carbon content of the steel.

Equally harmful is the presence of sulfur in a copper melt. With a high sulfur content (of the order of 0.3%) the compound Cu₂S (semisulfurous copper) is formed, accumulating chiefly along grain boundaries.

Still more dangerous is the addition of bismuth impurities to copper. Bismuth, almost not dissolving in the crystalline grains of copper, forms brittle shells around them. Sometimes such shells are so thin that they cannot be noticed under the microscope. Yet even in these cases their presence causes intercrystalline fracture of the material both at ordinary and at high temperatures (cold shortness and red shortness).

The tendency toward intercrystalline destruction of copper containing bismuth can partly be eliminated by adding to it certain other impurities (for example, oxygen or arsenic), apparently capable of forming with bismuth less brittle chemical compounds. In this connection it becomes understandable why the presence of lead impurities in copper proves less dangerous than the presence of bismuth in it. Lead, like bismuth, almost does not dissolve in the grains of copper; intercrystalline shells of grains containing lead, however, at ordinary temperatures do not impart increased brittleness to the material.

In a whole series of cases the appearance of intercrystalline brittleness in metallic articles is caused by the diffusion of foreign particles along grain boundaries. Thus, for example, hydrogen and some of its compounds, diffusing along interlayers, cause intercrystalline brittleness of steel articles. Diffusion of oxygen along grain boundaries likewise causes intercrystalline brittleness of steel. The metal grains are then surrounded by oxide films.

In the preceding paragraph we already mentioned the experiments of Desch, which showed that the penetration of mercury into β-brass causes its disintegration into separate grains. In this case the destruction of the polycrystal is apparently due to dissolution of the interlayer material in the mercury.

It is known from practice that the penetration of molten

metals, in particular solders, leads to the destruction of materials along grain boundaries.

Of great interest is Miller’s work^56, devoted to studying the influence of molten tin, lead, Sn—Pb solder, and mercury on the mechanical properties of various grades of brass.

Specimens of annealed brass were subjected to tension in a vessel containing molten metal. The tensile strength, elongation, and reduction of the specimen’s cross section were determined.

Table 7 gives the test results for brass containing 70.53% copper, 29.43% zinc, 0.01% tin, 0.02% iron, and 0.01% nickel.

TABLE 7

Medium	Test temperature in °C	Test time in minutes	Strength in kg/mm²	Elongation in %	Reduction of cross section in %
Air	260	—	34.0	27.5	62.5
Tin	260	0	28.0	2.5	10.0
Tin	260	21.5	24.5	2.5	8.6
Air	220	—	34.1	28	62.7
Same	220	0	27.5	2.75	8.4
Same	220	26	24.4	2.0	10.2
Air	350	0	33.0	14.5	24.7
Lead	350	0	19.0	0.5	2.3
Lead	350	6.5	14.0	1.5	3.2
Air	15	0	36.5	38.75	68.8
Same	15	0	27.0	21.5	43.5
Same	15	27	11.5	3.0	4.5

From this table it follows that under normal conditions (in air) fracture is preceded by considerable elongation of the specimen and a sharp decrease in the dimensions of its cross section. In the presence of molten metal, the strength of brass decreases sharply. Fracture in this case is brittle in character, as is evidenced by the very slight change in the dimensions of the specimen. A microphotographic study of specimens that had undergone fracture shows that in all cases the sites of fracture are the grain boundaries, and that the molten metal penetrates into the interior of the specimen along the intercrystalline layer. In Fig. 20 a photograph is presented (magnification 700 times) illustrating the penetration of lead into brass.

The most pronounced effect on the mechanical properties of brass is exerted by the penetration of mercury into it. The degree of reduc-

of the mechanical characteristics of the material depends noticeably on the duration of testing of the specimen. Under normal conditions, a decrease in the rate of deformation leads to an increase in the degree of elongation and to an increase in the transverse contraction of the specimen. From the table it is evident that in the present case an increase in the duration of testing produces the opposite effect. This is explained by the increase, with time, in the depth of penetration of the molten metal into the brass.

Fig. 20

In the preceding paragraph we have already noted that the penetration of foreign particles into the intercrystalline interlayer of a metal occurs most readily when the latter is in a stressed state.

Miller carried out special experiments which vividly illustrate the influence of internal stresses in brass on the rate of penetration into it of molten metals. Brass tubes in which internal stresses were known to be present were immersed in baths containing a 3% solution of mercury nitrate or a molten metal (Pb, Sn, Sn + Pb).

Table 8 gives the results of tests of four brass tubes; the degree of internal stresses increases from tube No. 1 to tube No. 4. Tube No. 4 was in

TABLE 8

Specimen No.	Time required for cracking	Time required for cracking
	in mercury	in molten metal
1	Does not crack	Does not crack
2	15–20 min.	Does not crack
3	Less than 1 min.	Does not crack
4	Several seconds	5–60 sec.

conditions of greatest stress. In these experiments cracking, as in all the preceding cases, took place along the grain boundaries.

Miller notes that for the penetration of molten metal into brass the presence of very considerable stresses (internal or external) is necessary. In the complete absence of stresses, destruction of brass articles upon immersion in molten metal was not observed.

Hartley^60, like Miller, studied changes in the mechanical properties of copper and brass caused by the penetration into them of molten metals (tin and certain solders). His work is of interest in that he investigated the influence of annealing on the behavior of rolled brass when it was immersed in molten metal. It turned out that annealing at 300°C for 20 min completely eliminates the tendency of brass to crack when immersed in a melt of tin. Penetration of tin into the brass in this case likewise did not occur.

In other respects, the results obtained by Hartley in testing unannealed brass in tension did not differ in principle from the results obtained by Miller.

Fracture along intercrystalline interlayers is also observed when brass and copper penetrate along the grain boundaries of mild steel. This phenomenon was first studied in detail by Duncan^61, and subsequently by Jenderson^62.

In some* cases the destruction of metallic articles takes place without any visible reasons for it (“season-cracking”). Thus, for example, as was already mentioned above, unannealed brass articles, after remaining in air for a long time, are often subject to “spontaneous” cracking. In this case the cracks always strictly follow the grain boundaries.

“Spontaneous” formation of intercrystalline cracks is also observed in articles made of steel, aluminum, lead, and copper.

The tendency of a material toward such spontaneous intercrystalline destruction can, however, be completely eliminated by preliminary annealing. Thus, Hartley indicates that after annealing rolled brass for 20 min at 300°C, cracking was not observed.

The principal factor responsible for the “spontaneous” cracking of metals along grain boundaries is at present considered to be the penetration into the intercrystalline interlayer of the metal of certain substances present in the surrounding medium (predominantly gaseous), which cause corrosion of the material along the grain boundaries. Such substances may be, for example, oxygen or ammonia vapors, which, as is known, belong to the most active corrosive agents.

In all these cases, a necessary prerequisite for the penetration of foreign substances into the intercrystalline interlayer is the presence of internal stresses in the material. The removal of the latter by preliminary annealing is a widely used practical method for protecting metallic products from “spontaneous” cracking.

In all the cases mentioned in this paragraph, the destruction of the material along intercrystalline interlayers is the result of the introduction into them of certain impurities—either added to the melt of the given metal or penetrating by diffusion along the grain boundaries; in this process the chemical composition of the interlayer changes. It is apparently accompanied either by the appearance of new chemical compounds or by the formation of eutectics, the presence of which imparts considerable brittleness to the intercrystalline interlayer.

Hartley’s work makes it possible to draw certain conclusions about the nature of the chemical compounds formed in the intercrystalline interlayer of brass when molten tin penetrates into it.

Hartley established that, as a result of prolonged holding of annealed specimens of $\alpha\beta$- or $\beta$-brass in molten tin (at $300^\circ$ C), a thin film of brittle substance forms on the surface of the brass. Analysis showed that this substance contains about 43% copper, 45% zinc, and 12% tin. In order to be able to assess the mechanical properties of such a substance, Hartley prepared a number of alloys of approximately the same composition. One of these alloys, containing 44.3% copper, 45.9% zinc, and 9.8% tin, did indeed exhibit very great brittleness. X-ray investigation showed that this alloy has a structure similar to that of $\gamma$-brass and $\delta$-tin. In this connection Hartley comes to the conclusion that on the surface of the brass there occurred the formation of a layer of a solid solution of the two intermetallic compounds $\mathrm{Cu}_5\mathrm{Zn}_8$ and $\mathrm{Cu}_4\mathrm{Sn}$. Hartley considers the formation of such a solid solution also possible along the grain boundaries of brass when tin penetrates into it. The latter, as was already mentioned above, takes place only when the brass is in a stressed state.

Destruction of the material along grain boundaries may be caused by the introduction of impurities into the intercrystalline interlayer, i.e., by a change in its chemical composition.

Intercrystalline brittleness of a material may also arise as a result of the different influence of temperature on the strength of the grain and of the interlayer. This phenomenon was first studied in detail by Bengough and Rosenhain (see §§ 2 and 3). Let us recall that the latter showed that under normal conditions the strength of the interlayer exceeds the strength of the grain. An increase in tempera-

...temperature leads, however, to a relatively more rapid decrease in the strength of the interlayer as compared with the strength of the grain.

Several years later Jeffries introduced the concept of the “equicohesive temperature” as the temperature at which the strength of the grain becomes equal to the strength of the interlayer. At temperatures exceeding the equicohesive temperature, destruction of the material proceeds along the grain boundaries.

Attempts to determine precisely the equicohesive temperature for various metals encounter, however, a number of difficulties. As Rosenhain and Jeffries noted in their time (see § 4), the position of the equicohesive temperature depends to a large extent on the rate of deformation of the specimen. Recrystallization of the material, which may occur in the course of deformation at high temperatures, can also exert a considerable influence on it. The disintegration of grains caused by recrystallization may substantially affect the relation between the strength of the interlayer and the strength of the grain.

In Desch’s book^57 (1932), the following data are given on the equicohesive temperature of certain metals (Table 9).

TABLE 9

Metal	Equicohesive temperature in °K	Melting temperature in °K
Aluminum	673	932
Copper	923	1 356
Silver	813	1 234
Gold	833	1 336
Iron	1 118	1 800
Platinum	1 093	2 028
Tungsten	1 843	3 643

Desch notes that the equicohesive temperature usually amounts to 50–70% of the melting temperature of the metal. These figures cannot, however, be regarded as entirely reliable, since it is unknown to what rate of deformation they refer.

§ 17. On the character of plastic deformation of a grain near its boundaries

In § 16 we considered the conditions under which the fracture of metals proceeds along grain boundaries.

Under ordinary conditions, as was also shown by Rosenhain, the place of rupture of a polycrystalline material is, however, the crystalline grain. The destruction of a grain is preceded by plastic deformation, which is effected...

as is known, by shear transformation. We shall not dwell here on the mechanism of this phenomenon—this does not fall within the scope of our review.

How, then, does the presence of an intercrystalline interlayer affect the mechanical properties of metals?

At the present time it may be regarded as firmly established that the strength of a polycrystalline specimen considerably exceeds the strength of a single crystal of the same substance; moreover, under ordinary conditions, the strength of a polycrystal increases noticeably as the grain size decreases.

The relatively higher strength of a polycrystalline material is usually considered a consequence of the circumstance that in a polycrystal each of the grains, being surrounded by neighbors, is thereby deprived of the possibility of freely changing its shape.

The process of shear transformation taking place within a grain must be impeded at its boundaries. This effect is customarily called the “blocking” of shears.

Carpenter and Elam^63, studying the deformation of aluminum specimens consisting of several very large grains, were among the first to come to the conclusion that the middle of a grain is deformed in the normal manner, whereas along the grain boundaries the formation of shears is not observed. In the regions where grains adjoin one another, the reduction in the transverse dimensions of the specimen is, in this case, considerably smaller than in portions of the specimen that do not contain grain boundaries.

Gough^14 describes the following experiment.

An aluminum specimen consisting of three large grains was subjected to torsion. Microscopic examination showed that, in portions of grains remote from the boundary, the slip traces do not differ in any way from the slip traces observed in single crystals.

If the orientations of neighboring grains differ little from one another, then the slip traces extend right up to the boundary itself, which indicates the absence of blocking of shears (in this case, revealing the grain boundaries by etching proves difficult).

In the case where the orientations of two neighboring grains are sharply different, the greater part of the slip traces does not reach the grain boundary, becoming arrested at some distance from it; those few slip traces that do reach the boundary change their direction in doing so.

Aston^64 (1927) subjected aluminum specimens consisting of three large crystals to tension. The principal aim here was to study the character of deformation both within the grains and in the region of their boundaries. The changes that occurred during deformation were recorded in three ways:

1) X-ray photographs were taken from different parts of the specimen (both before tension and after its completion);

2) a series of parallel light scratches, serving as reference lines, was applied to the surface of the specimen. Before and after deformation the distances between them were measured;

3) on the basis of X-ray analysis data, the displacement of the axis of the specimen relative to the crystallographic axes was studied.

The observations were made at room temperature at two stages of deformation—at elongations of 10 and 20%. In complete agreement with the experiments of Carpenter and Elam, and also with Gough’s experiments, they showed that regions of the crystal remote from boundaries deform in the usual way. At the points where grains adjoin one another, deformation is impeded: the narrowing of the cross-section of the specimen proves to be least in this region; the direction of the reference lines near the grain boundary changes somewhat, though to a considerably smaller degree than in the center of the grains.

Reference lines crossing grain boundaries, even in the case of very large deformations, do not undergo a break in passing from one grain to the adjacent one (Fig. 21). This indicates the absence of sliding of the grains with respect to one another.

Fig. 21

Analogous results were obtained on the basis of studying the character of the displacement of the axis of the specimen in its various parts. This displacement has its smallest value at the grain boundaries. Aston believes that deformation in the region of the grain boundaries does not exceed 50% of the deformation in the center of the grain.

Direct study of X-ray photographs of the specimen, taken from its different parts, did not, however, lead to any definite results. It might have been supposed that in the region of the grain boundaries, owing to the relatively smaller degree of deformation, the spots on the X-ray photograph would be more sharply outlined. It turned out, however, that in the immediate vicinity of the grain boundary the X-ray photograph acquires a more diffuse character. Aston explains this effect by the fact that the beam of X-rays (beam diameter 0.4 mm) in this case includes a region in which a change of orientation takes place.

Aston’s work also contains an indication that the presence of grain boundaries not only reduces the degree of deformation of the material, but also gives rise in the grains to slips in crystallographic directions different from the normal ones.

This can be judged from certain anomalies in the displacements of the specimen axis relative to the crystallographic axes.

Seimel[^65] (1936) notes that in specimens of coarse-crystalline aluminum the deformation near grain boundaries does not differ in any way from the deformation in single crystals; only its degree diminishes. In connection with this he comes to the conclusion that “deformation near grain boundaries does not cease, but is only impeded.”

He arrived at these conclusions on the basis of a detailed study of the topology of the surface of deformed specimens. Instead of the usual grid, consisting of thin scratches, small circles (1.5 mm in diameter) were applied to various portions of the specimen surface by means of a special device; measurements were then made of their dimensions and of the distances between them at different stages of deformation.

In the same work, the distribution of slip traces in deformed specimens was studied. It was established that, as the grain boundary is approached, the density of slip traces decreases.

All these works indicate that the process of plastic deformation taking place in the grains of a polycrystal is retarded in the region of their boundaries. As has already been noted, most authors attribute these effects to a decrease in the degree of deformation of each of the grains in the environment of its neighbors.

Indeed, it is known that in the case of a single crystal, and consequently also in the case of a crystalline grain, the degree of elongation under plastic deformation depends very sharply on the orientation of the system of slip planes in the specimen relative to the direction of action of the external force.

In a polycrystalline aggregate, grains of all possible orientations are encountered; for a given direction of the external force, some grains will as a result prove to be especially “plastic,” while others will offer greater resistance to deformation. The less plastic grains must hinder the change in shape of the grains surrounding them—“blocking” shear formation in them.

Polanyi and Schmid[^66] describe the following experiment. Two wires of single-crystal tin were brought into contact and welded together by melting over a certain portion of their length. The initial single crystals had different orientations. The bicrystal obtained in this way was subjected to tension at room temperature. It turned out that the portion of the specimen containing the fused single crystals was almost completely undeformed, whereas the unfused parts of the wires stretched in the usual way.

In addition to the blocking influence of differently oriented grains, the cause of the retardation of deformation in a polycrystalline aggregate could also be the presence in it of inter-

THE NATURE OF INTERCRYSTALLINE LAYERS

crystalline interlayer as such. On the basis of the experiments described above, however, it does not seem possible to differentiate these two factors.

From this point of view, the work of Chalmers\(^{67}\) is very interesting; he attempted to establish directly what role the intercrystalline interlayer plays in the propagation of plastic deformation in a polycrystal.

The object of study was specially grown “bicrystals” of \(\beta\)-tin. In comparison with crystals of many other metals, tin crystals have, in the present case, the advantage that slip can occur in them along a considerably larger number of crystallographic elements.

The lattice of \(\beta\)-tin belongs to the tetragonal system; at room temperature slip is observed in it on four different types of planes: \((110)\), \((100)\), \((101)\), and \((121)\); on each of these planes it may proceed in one or even several directions.

Chalmers assumes that, for any orientation of a tin single crystal relative to the direction of action of the external force, there will always be in it a plane situated favorably for slip. Owing to this, in polycrystalline tin the degree of deformation of each grain should in practice not depend on its orientation, nor on the orientations of the neighboring grains. Chalmers considers that if the degree of plastic deformation of tin bicrystals were, nevertheless, to prove dependent on the relative orientation of the grains forming the bicrystal, then this effect could be attributed entirely to the presence in it of an intercrystalline interlayer.

Bicrystalline specimens were prepared in the following manner: a seed, consisting of two tin single crystals of different orientation joined to one another, was placed in the drawn-out end of a glass tube. The tube was filled with pieces of tin, which were then melted in such a way that the seed remained in the solid state. Upon subsequent cooling of the tube, a bicrystal grew in it; the plane of separation between the two crystals composing it was parallel to the axis of the tube. The seed crystals were oriented so that the 001 axis of both components of the specimen was always perpendicular, and the 101 axis at an angle of \(45^\circ\) to the axis of the specimen (the grain boundary); from specimen to specimen only the angle \(\varphi\) between the 001 axes of the components of the bicrystal was varied.

The specimens were subjected to tensile deformation; the load corresponding to the appearance of small residual deformations of a predetermined magnitude was determined. The numerical value of this load \(p\) proved to depend on the magnitude of the angle \(\varphi\); measurements showed that \(p\) is almost directly proportional to \(\varphi\).

The greater the difference in the orientations of the grains of the bicrystal, the smaller, in this way, is the degree of deformation of the specimen as a whole.

According to Chalmers, the dependence of the mechanical properties of tin bicrystals on the mutual orientation of their components is due to differences in the structure of the intercrystalline interlayers enclosed between grains of different orientation. Chalmers regards the presence of such a dependence as direct experimental proof of the non-amorphous nature of the intercrystalline interlayer.

§ 18. On deformation in the intercrystalline interlayer

In the preceding section it was shown that the process of shear formation occurring in grains is impeded at their boundaries. On the other hand, as we have seen, the fracture of polycrystalline materials along interlayers is usually not accompanied by any noticeable change in the shape of the specimen. It is of interest to clarify the question of whether residual deformation along grain boundaries is possible at all. Some indications of the presence of deformation in the intercrystalline interlayer, as well as some information on the character of such deformation, can be obtained on the basis of experimental data on the creep, or so-called “creep,” of metals.

Creep is commonly understood to mean one of the varieties of plastic deformation of materials, the characteristic feature of which is that it occurs under stresses lying considerably below the yield point of the material, and at an extremely low rate. The relative elongations of a material under creep usually do not exceed 0–4% per hour, i.e., 1% per year.

This phenomenon was first discovered in heat-power installations operating on superheated steam (450–500°C) under conditions of high pressures (130–230 atm). In steel, creep was first discovered at temperatures of the order of 500–600°C; at the present time there are indications of creep in steel also at lower temperatures (400°C and below). In the case of lead and tin, clearly pronounced creep can be observed already at room temperatures. At present it may be considered that the possibility of detecting creep is wholly determined by the accuracy of the method for measuring small deformations.

In addition to the small rates of deformation, the phenomenon of creep is characterized by a whole series of features that substantially distinguish this variety of plastic deformation from residual deformation occurring under ordinary experimental conditions.

Thus, for example:

1. The usual mechanical characteristics (temporary resistance and yield point) are not a criterion of cri-

CREEP RESISTANCE of the material. Materials that are relatively stronger at normal temperatures and normal testing rates, in a whole series of cases, reveal an increased tendency toward creep.

1. As is known, preceding mechanical treatment increases the strength, the elastic limit, and the yield point of a material (the so-called phenomenon of work hardening). In the broad practice of boiler-turbine construction it is known, however, that cold-worked (deformed in the cold state) materials show a reduced resistance to creep.

2. Not all impurities that under ordinary conditions cause an increase in the mechanical characteristics of a material at the same time increase the material’s resistance to creep. Thus, for example, the presence of carbon and nickel, which increases the strength of steel, does not increase its creep resistance. The resistance of steel to creep increases, nevertheless, when steel is alloyed with molybdenum, vanadium, chromium, and tungsten.

3. It is well known that a reduction in grain size usually leads to an increase in the strength of a material. Fine-grained material, however, possesses less creep resistance than coarse-grained material.

4. Hot working of metals, which under ordinary conditions lowers their mechanical properties, increases the creep resistance of the material. This effect may be attributed to grain coarsening as a consequence of recrystallization during heating.

These experimental facts contradict our notions of the course of plastic deformation in crystalline grains (single crystals). They are also inconsistent with the behavior of polycrystals at normal temperatures and ordinary testing rates. Under normal experimental conditions, the fracture of polycrystalline materials, as has already been mentioned more than once, is preceded by a noticeable change in the shape of the specimen and in the dimensions of its cross section; plastic deformation proceeds here by means of slip in the crystalline grains.

The substantially different behavior of materials under creep compels us to suppose that in this case a very significant role belongs to the intercrystalline layer.

Without setting ourselves the aim of giving here an exhaustive survey of the phenomenon of creep in metals, we shall dwell only on the consideration of several individual works which testify that a whole series of specific features of this phenomenon can be fully attributed to processes occurring in the layer.

Hanson and Wheeler^32 (1931) were among the first to carry out systematic experiments on the study of the character of the deformation of metals under the very prolonged action (up to 575 days) of small loads. They investigated the change in the microstructure of polished surfaces of specimens subjected to tensile—

… under the action of a periodically increasing load. The experiments were carried out at room temperature and at a temperature of \(250^\circ\mathrm{C}\). Aluminum was chosen as the object of investigation, having the advantage that its surface retains its polish even at high temperatures.

Hanson and Wheeler distinguish three stages of deformation in creep.

At the initial stage of stretching, plastic flow of the material takes place through the formation of slips within the grains. In tests of crystalline aggregates at \(250^\circ\mathrm{C}\), the slips within the grains are so fine that they remain invisible under the microscope. At the same time there occurs “a slight displacement at the grain boundaries.” The degree of elongation at this stage of deformation is very small (of the order of \(3\text{—}4\%\)). Stretching is accompanied by hardening and by an insignificant decrease in the density of the material. In the primary stage of deformation the rate of flow gradually decreases as a result of hardening of the material.

In the second stage of deformation the rate of flow is extremely small. If the test is carried out at \(250^\circ\mathrm{C}\), then a noticeable decrease in the density of the material is observed (see § 14). Metallographic investigation indicates the gradual formation of cracks observed along grain boundaries or in their vicinity. At room temperature the second stage of deformation proceeds somewhat differently, being effected entirely by slip within the grains; in this case there are no indications of destruction of the material along grain boundaries; no noticeable changes in density are observed either.

The third period of stretching in all cases is characterized by a sharp increase in the degree of elongation and in the rate of deformation, up to the destruction of the material. At \(250^\circ\mathrm{C}\), deformation is accompanied by the appearance of a large number of cracks along the grain boundaries; the fracture is intercrystalline in character. At room temperature, however, deformation proceeds by slip formation in the grains; rupture of the material is preceded by the formation of a neck.

We thus have here a definite indication of the presence of deformation (though a very slight one) along the grain boundaries.

The substantial participation of the interlayer in the phenomenon of creep is also indicated by the formation of cracks along grain boundaries and by the decrease in the density of the material, which, as we already know, is not observed in the deformation of single crystals.

Hanffstengel and Hanemann\(^{68}\) (1938) carried out very thorough investigations, the aim of which was to study the nature of creep on the example of pure lead.

In contrast to steel and many other metals, in the case of lead distinctly expressed creep can be observed already at room temperature.

Creep of lead specimens was studied during their deformation by tension under the prolonged action of a suspended load. Particular attention was paid to the accurate measurement of the relative elongations of the specimens; the latter was carried out with an accuracy of \(10^{-1}\%\) per hour, i.e. \(1\%\) per year. The elongation was determined by means of a specially designed Martens-type mirror apparatus.

Experience showed that temperature fluctuations of the surrounding medium have a very sharp influence on the rate of flow of the material during creep. In this connection all experiments were conducted in a thermostat at a temperature of \(25^\circ\text{C}\); the temperature fluctuations did not exceed \(\pm 0.3^\circ\).

The first series of experiments was concerned with the study of the creep rate at various values of load and temperature in lead specimens with different grain sizes.

Figure 22 gives curves of the dependence of the creep rate on the magnitude of the applied stress for coarse-grained and fine-grained lead (at a constant experimental temperature). They indicate that at small values of stress the flow rate is very small; moreover, in the fine-grained material creep is expressed more sharply than in the coarse-grained material.

At a certain value of the stress the curves intersect, and at the same time the slope of the curves changes sharply—the flow rate begins to increase noticeably with increasing load. In this region the behavior of coarse- and fine-grained specimens proves to be the reverse: the fine-grained material creeps more slowly than the coarse-grained material. A similar course of the curves was observed by Zauervald in steel \({}^{69}\) (1933).

Hanfstengel and Hanemann suppose that the point of inflection of the curves corresponds to an essential change in the very mechanism of creep.

At small values of stress, “creep is concentrated chiefly along the grain boundaries.” The greater tendency of the fine-grained material to creep is in this case due to the greater total extent of the intercrystalline interlayer in comparison with the coarse-grained material.

The authors of the cited work distinguish two principal types of deformation of a polycrystalline material:

1. Deformation by means of “Platzwechsel”—transposition, exchange of places by atoms. By this they apparently mean phenomena based on processes of the diffusion type.

According to the authors, by means of “Platzwechsel” there take place: 1) recovery of the material, 2) recrystallization, 3) the creep of the material along grain boundaries described above.

In the last case, owing to the presence of an external force, diffusion must acquire a directed character; in general, go-

speaking, to deformation of this type one may apply the term viscous flow.

1. Hanfstengel and Hanemann note that “Platzwechsel” plasticity differs essentially from the second possible type of deformation, which occurs in crystalline grains by sliding along certain crystallographic planes.

The point of inflection on the curves in Fig. 22 corresponds, in their opinion, to the transition from deformation by the exchange of places by atoms in the intercrystalline interlayer to deformation by shear formation in crystalline grains.

From this point of view, the change noted above in the character of the dependence of the rate of flow on grain size becomes understandable.

In the case where plastic deformation proceeds through the grains (above the point of inflection, see Fig. 22), in fine-grained material shear formation is hindered to a greater degree (the coefficient of hardening is higher) than in coarse-grained material. Accordingly, fine-grained lead possesses a lower creep, as compared with coarse-grained lead.

Fig. 22

Fig. 23

In the present work curves are also given for the dependence of the rate of flow of coarse- and fine-grained lead on the temperature of the experiment (under constant load). As follows from Fig. 23, they have exactly the same character as in the preceding case.

At first glance the impression may arise that in the region of low temperatures the dominant role is played by deformation along grain boundaries, whereas at high temperatures it is deformation within the grain, which contradicts all the preceding considerations.

In considering these curves, however, one should not forget that along the ordinate axis the variable rate of deformation is plotted. In the region of low temperatures and small rates, the dominant role must indeed be played by deformation along grain boundaries (i.e., deformation of fine-grained ma

THE NATURE OF INTERCRYSTALLINE LAYERS

material). At high temperatures and high rates of deformation, creep takes place by sliding within the grains (a coarse-grained material as a result becomes less brittle).

To substantiate the considerations set forth above concerning the difference in the creep mechanism above and below the inflection point, Hanffstengel and Hanemann analyze the behavior of coarse- and fine-grained lead during unloading of specimens and the accompanying recovery of the material.

For this purpose, a specimen was loaded with a constant load, kept under load until a constant creep rate was established (for several days), then unloaded and, after a definite period of time, loaded again. At loads lying below the inflection point, unloading was not accompanied by recovery—the specimen’s being in the unloaded state for 24 hours did not lead to softening of the material. The instantaneous change in the length of the specimen upon unloading and repeated loading proved in this case to be the same.

The authors of the cited work regard this result as further proof that “under these loads creep is not effected by translation. It can only be the result of a diffusion process at the grain boundaries.”

Analysis of the curves of the dependence of the elongation of the specimen on time shows, however, that under these conditions there also occurs (though a very slight) plastic deformation by shear formation.

At loads lying above the inflection point, the deformation of the material is accompanied by strain hardening, which is removed during recovery after unloading.

Figure 24 gives curves of the dependence of the elongation of a specimen on time under primary and repeated loads, taken after different recovery times.

Fig. 24

The measure of the degree of softening in this case may be the initial elongation of the specimen at the moment the load is applied. The longer the duration of recovery, the greater the initial elongation under repeated loading; the primary elongation, however, is not reached even after recovery for 800 hours.

These experiments confirm the ideas of Hanffstengel and Hanemann concerning the presence of deformation in the grains in the region of high stresses.

From the point of view of elucidating the mechanism of creep, considerable interest is also presented by the study carried out in this work of the influence of preliminary cold working of the material (work hardening) on the creep of coarse- and fine-grained lead at various temperatures.

The specimens were rolled and immediately subjected to the action of the load. Below the recrystallization threshold, at stresses lying below the bend point, in the case of fine-grained lead preliminary work hardening increases the rate of creep (see Fig. 25). Sliding deformation under these loads

Fig. 25

Fig. 26

does not occur; the authors attribute this increase in the creep rate to the removal of strengthening caused by work hardening. Creep of preliminarily work-hardened materials, as a rule, is accompanied by additional elongation of the specimens due to the recovery process.

Under the same experimental conditions (the recrystallization threshold is not reached, the load lies below the bend point, the specimen has been preliminarily work-hardened), creep in coarse-grained lead is expressed very weakly: the load proves insufficient to cause sliding in the grains. The small observed elongation of the specimens in this case is entirely due to the process of recovery of the material from work hardening.

At loads lying above the bend point, work hardening still causes an increase in the creep rate of fine-grained lead. This result may seem paradoxical, since at high loads creep proceeds by way of shear formation in the grains and should be accompanied by strengthening. The authors of the cited work likewise explain the increase in creep by elongation of the material as a result of recovery from work hardening.

Preliminary work hardening causes a decrease in the creep rate only in a single case—when testing coarse-

of coarse-grained lead under loads lying above the inflection point on the curve in Fig. 26. Hanfstengel and Hanemann explain this behavior of coarse-grained lead by the fact that in this case the creep of the material proceeds almost entirely at the expense of translation in the grains and is accompanied by hardening, which hinders further flow. The recovery process, capable of leading to elongation of the material, in this case plays no essential role, owing to the relatively small amount of hardening during cold-working of coarse-grained lead.

If the experimental conditions are such that recrystallization of the material under load takes place, then the creep rate increases markedly on account of the softening of the grains in the process of recrystallization.

Returning to the main theme of our review, one may say that all these experimental facts on the creep of metals undoubtedly testify to the possibility of plastic deformation along the intercrystalline layer.

Creep apparently represents a complex phenomenon, proceeding both by deformation along the intercrystalline layer and by slip within the grains. The process of slip in the crystalline grains is at the same time superposed by the phenomenon of softening as a result of recovery and recrystallization.

Under some experimental conditions deformation along the grains plays the dominant role; under others, deformation along the intercrystalline layers does. As for the mechanism of deformation along the layers, Hanfstengel and Hanemann’s conception of its diffusional nature, it seems to us, corresponds fully to reality (see the conclusion).

§ 19. Study of the Intercrystalline Layer by the Method of Electron Diffraction

The separation of the intercrystalline layer in the form of a thin film makes it possible to study its structure by means of the electron-diffraction method. The first attempt at electronographic analysis of an intercrystalline film was undertaken, however, only comparatively recently (in 1937) by a group of American physicists—Morgan, Steckler, and Miller^70. The principal aim of their investigation was to clarify the question of the presence in the layer separating the grains of any compounds possessing a crystalline structure, and also to determine the chemical composition of the latter.

The object of study was transformer and electrolytic iron. The separation of the layer was carried out by Tammann’s method. The surfaces of the iron plates (measuring \(4 \times 6 \times 0.2\) mm) were carefully cleaned, polished, and degreased. The plates were immersed in a 12% solution of persulfuric-

ammonium persulfate \((\mathrm{NH}_4)_2\mathrm{S}_2\mathrm{O}_2\), in which they remained until the metallic grains had completely dissolved (about 16 hours). To prevent rapid evolution of gas bubbles, the crucible with the solution was cooled externally with ice.

a) Experiments with transformer iron.
The first series of experiments concerned transformer iron with a high silicon content.

As a result of dissolving the specimens, a brownish film remained. Microscopic examination showed that this film was very heterogeneous; it contained large inclusions of black color. Owing to the unsuitability of such a heterogeneous film for electron-diffraction analysis, the authors subsequently subjected the starting material to recrystallization. As a result, a considerably more homogeneous film was obtained, containing a smaller number of black inclusions. After completion of the dissolution process, the film was washed with distilled water and dried. During drying, however, the film swelled up greatly, became very thick and friable, and also changed its color (turned gray). It was not possible to obtain electron-diffraction patterns from such films; only a general blackening of the photographic plate was observed.

The electron-diffraction patterns were taken in a transmitted beam; the authors believe that the cause of the unsuccessful results of these experiments was the excessively great thickness of the intercrystalline film interlayer. It was not possible, however, to obtain an intercrystalline film of smaller thickness in the case of transformer iron.

b) Experiments with electrolytic iron.
All subsequent experiments were carried out with electrolytic iron. The chemical composition of the latter, and also, for comparison, the chemical composition of transformer iron, are given in Table 10.

Table 10

Impurity	Percentage content in electrolytic iron	Percentage content in transformer iron
Silicon	0.003	4.373
Copper	0.013	0.036
Carbon	0.015	0.018
Sulfur	0.005	0.030
Manganese	Absent	0.078
Phosphorus	"	0.008
Nitrogen	"	0.0014
Slags and oxides	0.700	Traces

When electrolytic iron is dissolved, there remains a brown soot-like film, more homogeneous and considerably

but thinner than in the case of transformer iron. This film is extremely fragile; for washing it, special precautions have to be taken, and it must be dried in alcohol vapors. In the dry state it likewise becomes friable and acquires a gray coloration, as in the case of transformer iron. Owing to its extreme fragility it cannot be mounted in the usual way at the slit of the diffraction camera: it was placed on a special support (Resoglaz).

It was possible in this way to obtain clear electron diffraction patterns consisting of a large number of sharp rings. The authors note that in most cases three broad bands due to the support are superposed on the electron diffraction pattern, which makes interpretation of the photographs more difficult.

The character of the electron diffraction patterns obtained indicates the presence in the film of substances in a crystalline state. In order to determine their chemical nature, the authors compared the electron-diffraction data they had obtained with data for a number of known crystalline substances whose presence could have been expected in the intercrystalline layer of iron. Unfortunately, the article does not give a list of the substances whose presence they attempted to establish; the authors note only that two compounds can definitely be “recognized”: iron carbide ($\mathrm{Fe_3C}$) and goethite ($\alpha\ \mathrm{FeOOH}$). At the same time, all the electron-diffraction data can be assigned both to the carbide and to the goethite, since the electron diffraction patterns of these two compounds are very close to one another. It remains unclear, however, whether only one of these substances is present in the layer, or both simultaneously. The authors note that the presence of iron carbide in the layer could have been anticipated in advance, since carbide is insoluble in ammonium persulfate, and as a result of the preceding thermal treatment of the iron specimens it should have accumulated at the grain boundaries. As for $\alpha\ \mathrm{FeOOH}$, it remains unclear whether this compound was actually contained in the interlayer of the original material, or whether it was formed as a result of some chemical reaction accompanying the dissolution of iron in $(\mathrm{NH_4})_2\mathrm{S_2O_2}$. The formation of $\alpha\ \mathrm{FeOOH}$ could, for example, be a consequence of the reaction of dissolved iron with the solvent, or the result of the combination of iron oxide with the solvent, oxygen, and water.

At the same time, a study was also carried out of the dissolution process of specimens of single-crystal iron in the same solvent. In contrast to the experiments described above with polycrystalline iron, in this case, after the dissolution process was completed, no film remained. Only a precipitate consisting of black particles separated out at the bottom of the crucible,

similar to the black inclusions observed in the interlayer of polycrystalline material.

Up to the present time this work remains the only attempt to study the structure of the intercrystalline interlayer by the method of electron diffraction.

With the aid of this method it would be possible to give a completely unambiguous answer to the question of whether the intercrystalline interlayer of real polycrystals has a purely crystalline or a purely amorphous structure. If, however, the interlayer contains both amorphous and crystalline substances at the same time, then to understand its structure from electron-diffraction data proves very difficult.

The work cited definitely indicates that in the film remaining after dissolution of the iron grains there are certain crystalline compounds. The question of the simultaneous presence in it of amorphous substances remains, however, open. One may only suppose that, if the latter are present, they are present in considerably smaller quantity than the crystalline substances, since the electron diffraction patterns obtained, as was already mentioned above, consist of sharply outlined rings.

In conclusion, we consider it necessary to note the very substantial shortcomings of Tammann’s method for isolating the intercrystalline interlayer.

The film remaining as a result of dissolution of the metal grains cannot be completely identified with the intercrystalline interlayer of the original material. Indeed, some of the substances originally contained in the interlayer might have disappeared without trace in the process of dissolution; on the contrary, as a result of chemical reactions between the substances contained in the interlayer and the solvent, new chemical compounds, not previously present, might have appeared in it. Thus, for example, in the experiments described above it would have been impossible to detect the presence of copper impurities, since the latter, along with iron, dissolve in ammonium persulfate.

Tammann’s works nevertheless constitute an extremely substantial and valuable contribution to our ideas about the structure of the polycrystalline state and make it possible to understand a whole series of phenomena connected in one way or another with the intercrystalline interlayer.

It may be hoped that comparison of the results of dissolving the same metals in different solvents, in combination with electron-diffraction and also X-ray study of the films remaining thereby, will in the future make it possible to create clearer ideas about the structure of the intercrystalline interlayer.

THE NATURE OF INTERCRYSTALLINE INTERLAYERS

§ 20. Attempts to calculate the spatial extent of the intercrystalline interlayer

The grain boundary is not a fictitious surface of separation between neighboring grains, but rather a certain region possessing spatial extent. None of the existing theories, however, contains any quantitative data on the dimensions of this region.

The first attempt to calculate the intercrystalline interlayer belongs to Kaiser ⁷¹ (1938).

Kaiser believes that even in the case of the purest metals, a definite surface and volume may be assigned to the intercrystalline interlayer, these being among its principal characteristics.

Kaiser’s calculation is based on Fedorov’s concepts of the quasigeometrical structure of a polycrystalline aggregate. According to Fedorov ⁷², a polycrystal may be considered, approximately, as a system of equilateral polyhedra densely packed in space.

Table 11 gives data on the volume \(v_0\) and surface \(S_0\) of four principal types of polyhedra—the cube, the hexagonal prism, the rhombic dodecahedron, and the cubic octahedron—from which, as Fedorov showed in his time, any geometrical models of crystalline grains may be obtained by deformation (\(d\) is the grain diameter).

TABLE 11

Model of the crystalline grain	Grain volume \(v_0\)	Grain surface \(S_0\)	\(\gamma=\beta\alpha-\dfrac{2}{3}\)
I. Cube	\(d^3\)	\(3d^2\)	3.000
II. Hexagonal prism	\(0.6495d^2h\)	\(0.64d^2+15dh\)	2.866
III. Rhombic dodecahedron	\(0.7071d^3\)	\(2.1213d^2\)	2.673
IV. Kelvin cubic octahedron	\(1.414d^3\)	\(3.350d^2\)	2.659

It is of very considerable interest to clarify the question of precisely which type of polyhedron most closely corresponds to real grains. To solve this question, Kaiser determines the surface of the interlayer corresponding to each of these types of grain models.

The interlayer surface per \(1\ \mathrm{cm}^3\):

\[ S = NS_0, \tag{1} \]

where \(N\) is the number of grains per unit volume, \(S_0\) is the surface of one grain. It follows from the table that in all four cases—

... cases (for a hexagonal prism, under the condition \(d=h\)) the volume and surface area of the grain may be written as:

\[ \left. \begin{aligned} v_o&=\alpha d^3\\ S_o&=\beta d^2 \end{aligned} \right\}. \tag{2} \]

On the other hand, the volume of a grain is the reciprocal of the number of grains per unit volume:

\[ v_o=\frac{1}{N}, \tag{3} \]

With the aid of equations (2) and (1) we can determine the surface area of the interlayer \(S\) as a function of only the number of grains \(N\). Indeed,

\[ S=\gamma \sqrt[3]{N}, \tag{4} \]

where \(\gamma=\beta\alpha^{-\frac{2}{3}}\).

The numerical values of the coefficient \(\gamma\) are given in the last column of Table 11. They show that (for a given number of grains \(N\)) the cubic model of the grain corresponds to the maximum extent of the intercrystalline interlayer, and the cubic octahedron to the minimum.

In reality, grains not only do not have a regular polyhedral shape, but also possess curvilinear surfaces; as models of real grains Kaiser chooses intermediate types of polyhedra—a hexagonal prism and a rhombic dodecahedron. He notes, moreover, that the relative error in calculating the surface area of the interlayer for grains of type I with respect to grains of type IV is 12.8%, of type II with respect to type IV—7.8%, and of type III with respect to type IV—0.53%.

To calculate the surface area of the interlayer \(S\), the number of grains \(N\) per unit volume must be known. Kaiser assumes that the minimum grain size is of the same order as the dimensions of the blocks of the mosaic structure, i.e., of the order of \(10^{-14}\,\text{cm}^3\). Hence \(N=10^{14}\), and the maximum possible extent of the interlayer is \(10^5\,\text{cm}^2\) per \(1\,\text{cm}^3\) of metal (\(10\,\text{m}^2\)).

Kaiser calculates the volume of the intercrystalline interlayer for two cases: a) on the assumption that the thickness of the interlayer \(\delta\) is of the same order as the grain diameter \(d\), and 2) for the case when \(\delta\) is considerably smaller than \(d\).

In the second column of Table 12 are written the volumes of the intercrystalline interlayer (per \(1\,\text{cm}^3\)) for various types of crystalline grains, calculated as the difference between the total volume and the volume occupied by the grain:

TABLE 12

Model of the crystalline grain	Volume of the interlayer per \(1\ \mathrm{cm}^3\) under the condition \(\delta \ll d\)	Volume of the interlayer per \(1\ \mathrm{cm}^3\) under the condition \(\delta \ll d\)
I. Cube	\(1 - Nd^3\)	\(\dfrac{3\delta}{d}\)
II. Hexagonal prism	\(1 - 0.6495\,Nd^2h\)	\(\left(\dfrac{1}{h}+\dfrac{4}{\sqrt{3}\cdot d}\right)\delta\)
III. Rhombic dodecahedron	\(1 - 0.7071\,Nd^3\)	\(\dfrac{3\delta}{d}\)
IV. Kelvin cubic octahedron	\(1 - 1.414\,Nd^3\)	\(\dfrac{2.37\,\delta}{d}\)

\[ v = 1 - Nv_o . \tag{5} \]

In the case when the thickness of the interlayer is very small, i.e. when the interlayer envelops the grains with a very thin layer, Kaiser determines its volume as the product of the interlayer thickness \(\delta\) and the surface \(N\) of the grains contained in a unit volume. The volumes of interlayers computed in this way for different types of grains:

\[ v = N\delta S_o \tag{6} \]

are given in the last column of Table 12.

Kaiser uses relations (5) and (6) to calculate the relative fraction of impurities contained in the intercrystalline interlayer. In doing so, he assumes that the interlayer consists entirely of impurity.

The relative amount of impurity insoluble in the grains, i.e. forming the interlayer, is \(f\):

\[ f = \frac{\rho v}{\rho_o}, \tag{7} \]

where \(\rho_o\) is the density of the metal, \(\rho\) is the density of the material of the interlayer, and \(v\) is the volume of the interlayer per \(1\ \mathrm{cm}^3\).

For the case of a sufficiently thin interlayer:

\[ f = \frac{\rho}{\rho_o} S_o N\delta = \frac{\rho}{\rho_o}\, S_o\, \frac{\delta}{v_o}. \tag{8} \]

With the aid of this relation Kaiser calculates the concentration of impurity that is necessary so that, for a given grain size, each of them would be surrounded by a continuous monomolecular film of the interlayer. To simplify the calculation he uses here the cubic model of the grain, for which:

\[ f=\frac{3\rho}{\rho_0}\frac{\delta}{d} \]

(\(d\)—grain diameter).

Figure 27 gives curves of the dependence of the percentage content of impurity, \(f\), corresponding to the formation of a closed shell, on the grain diameter \(d\) for certain oxides, namely: CoO in cobalt, FeO in iron, CuO in copper, and Al\(_2\)O\(_3\) in aluminum. From these curves it follows that, in the case of grains whose diameter is of the order of \(0.1\) mm, the presence of \(0.001\%\) impurity is sufficient for the formation of a continuous intercrystalline film.

Fig. 27

Kayser believes that in real polycrystals the thickness of the intercrystalline interlayer is of the order of 10–100 atomic distances; accordingly, at \(d=0.1\) mm the amount of insoluble oxides must be raised to \(0.01\)–\(0.1\%\).

The smaller the grain size, the greater the amount of impurities that must be present in the metal in order for the formation of a “shell” around each of the grains to be possible. Thus, for example, in the case of a monomolecular film:

\[ \begin{array}{rcccc} \text{for } d &= 1\ \text{mm} & 0.1\ \text{mm} & 0.01\ \text{mm} & 0.001\ \text{mm};\\ f &= 0.0001 & 0.001 & 0.01 & 0.1 \end{array} \]

(The total amount of impurities in the material in some cases must, of course, be somewhat higher, since the impurity may partially dissolve in the grains).

CONCLUSION

Let us now try to draw some conclusions.

Tammann’s experiments directly proved that in real polycrystals there exists a quite real intercrystalline interlayer, which is not a two-atomic layer (as Dunn and Triff assumed), but a layer at least several thousand atoms thick.

These experiments showed at the same time that the intercrystalline interlayer is the place of preferential concentration of foreign inclusions. The presence of impurities in the interlayer is also evidenced by the phenomenon of destruction of polycrystalline materials along grain boundaries as a result of add-

NATURE OF INTERCRYSTALLINE INTERLAYERS

of certain impurities into the melt of the corresponding metal.

The experimental data presented in the preceding chapter indicate that the physical properties of the intercrystalline interlayer differ from the physical properties of a regular crystal lattice.

First of all, the intercrystalline interlayer has a density lower than that of the grain. This fact refutes Mayer’s theory of a denser “o-phase.” The reduced density of the intercrystalline interlayer indicates that the atoms in it are arranged less regularly than in the crystalline grain.

The regular arrangement of atoms in a normal crystal lattice corresponds, as is known, to the minimum value of the energy of the system; a less ordered structure corresponds to an increased value of the energy, and in this case the energy of the system is the higher, the greater the degree of “disorder” in it.

From this one may draw the natural conclusion that the atoms of the interlayer possess an increased energy in comparison with the atoms of the grain.

These conclusions are excellently confirmed by experimental material, namely:

1. Since the intrinsic energy of the atoms of the interlayer is increased, a smaller additional energy (the so-called activation energy) must be imparted to them in order to dislodge them from their equilibrium position than in the case of a regular crystal lattice.

Indeed, as we have already seen, the etchability (solubility), and also the evaporability of the interlayer, are higher than the etchability and evaporability of the crystalline grain1.

1. A consequence of the reduced activation energy must be an increased value of the diffusion coefficient, which in this case can be determined in the usual way as:

\[ D = D_o e^{\frac{U}{kT}}, \tag{1} \]

where \(U\) is the activation energy (the height of the potential barrier separating two neighboring equilibrium positions). This conclusion, as we know (see § 15), is also confirmed by experiment.

1. The intercrystalline interlayer, as a less ordered zone, must have an increased resistance to shear in comparison with the grain.

Indeed, the presence of interlayers in a polycrystalline aggregate causes retardation (“blocking”) of shears at the boundaries of crystalline grains. As a result of disor—

orderliness of the intercrystalline interlayer, shear formation in it is, in general, apparently impossible.

1. In the presence of external forces, diffusion of atoms of the intercrystalline interlayer may acquire a directional character, i.e. viscous flow may arise in it.

To characterize the capacity of the interlayer for viscous flow, a definite coefficient of viscosity may be assigned to it:

\[ \eta = \eta_0 e^{\frac{U}{kT}} \tag{2} \]

where \(U\) has the same meaning as in relation (1).

We obtained some indications of the possibility of viscous flow along grain boundaries when considering data on the “creep” of polycrystalline materials.

The relation between the rate of deformation of a specimen under the action of externally applied stresses and the rate of any flow along the intercrystalline interlayer apparently also determines the position of the “equicohesive” temperature of the given metal.

The whole body of these data testifies to a disordered arrangement of the atoms of the intercrystalline interlayer.

The question of whether the atoms in it are arranged in a completely arbitrary manner (an amorphous phase), or whether the equilibrium position of each of them is uniquely determined by the mutual orientation of the surrounding grains (a “transition” zone), cannot, however, be resolved on the basis of this experimental material.

Chalmers’ work cited in § 17\({}^{67}\) was undertaken by him with the special aim of clarifying the question of the character of the structure of the intercrystalline interlayer.

Chalmers notes that if the intercrystalline interlayer were amorphous, then its properties should be completely independent of the mutual orientation of the grains of the material. The physical properties of a “transition” zone, however, should be completely determined by the mutual orientation of the crystallographic axes of neighboring grains.

The experimentally observed dependence of the elastic limit of tin “bicrystals” on the mutual orientation of the grains of the specimen is regarded by Chalmers as direct proof of the existence of a zone transitional with respect to the two adjacent grains.

Chalmers’ conclusions are based, however, as we know, on the notion that in polycrystalline tin the volume effect of “blocking” of shears by grains of different orientation is absent, and that only the intercrystalline interlayer as such is responsible for the retardation of the process of shear formation at grain boundaries. The possibility of complete

The exclusion of the effect of volume blocking seems to us, however, doubtful.

Attempts to solve the question of the structure of the intercrystalline interlayer by the method of electron diffraction, as we have already seen, have also, unfortunately, not been crowned with success.

Let us consider, however, briefly the conditions for the formation of an intercrystalline interlayer during the crystallization of a metal from the melt.

Centers of crystallization arise at separate points of the melt quite independently of one another. Subsequently, the growth of each of the grains likewise proceeds independently of the growth of the other grains. At some moment two neighboring grains growing toward one another will approach to such a distance that the melt enclosed between them will come under the simultaneous action of atoms already belonging to each of these grains. The mutual orientation of the lattices of two neighboring grains may in this case be of the most varied kind.

In the regions of the melt adjacent to the grains, the atoms of the melt will tend to occupy positions that are equilibrium ones for the crystal lattice of the given grain.

Under such conditions it is difficult to imagine the possibility of the formation of a completely structureless (“amorphous”) intercrystalline interlayer.

The formation of the interlayer occurs as a result of the solidification of the melt between two orienting “substrates.”

The process of crystallization of a metal taking place on one such crystalline substrate is at present well studied.

One could cite many examples showing that, during the condensation of metal vapors, and also during the electrolytic deposition of metallic films on a metallic substrate surface, the orientation of the crystals of the substrate wholly and completely determines the orientation of the particles in the layer deposited on it. In some cases the influence of the substrate is so great that the deposited crystals assume orientations quite unusual for them. Thus, for example, according to Thomson’s experiments^73, a layer of silver obtained by electrodeposition on an etched copper surface assumes the orientation characteristic of the copper substrate.

Finch, Quarrell, and Wilman^74 (1935) studied the orientation of gold crystals obtained on various substrates by cathodic sputtering. When gold was deposited on the surface of glass, the gold crystals were arranged in a random manner; when deposited on platinum, however, gold of orientation (III) assumed the orientation of the platinum.

Of particular interest is the work of Finch and Zoner^75 (1936), who studied by the method of electron diffraction the structure and orientation of thin metallic films of Cu, Ni, Au, Ag,

Fe, Co, Sn, As, Sb, Bi, Pt, and α-brass, obtained on various metallic substrates by electrolytic deposition.

Preliminary experiments were carried out in order to determine what the normal orientation of a crystal is in various metallic films formed under conditions of electrodeposition. For this purpose, polished metal surfaces were used as substrates, on the assumption that the Beilby layer covering such surfaces is not capable of exerting an orienting influence on the crystals deposited upon it.

Table 13

Substrate material	Deposited metal	Orientation in the thin layer	Orientation in the thick layer
Polished surface of copper	Cu	Arbitrary	(110)
Polished surface of copper	Au	Arbitrary	(111)
Polished surface of copper	Ni	Arbitrary	(110)
Polished surface of copper	Fe	(111)	(111)
Polished surface of copper	α-brass	Arbitrary	(111) and (311)
Polished surface of copper	Pt	Arbitrary	(111)
Polished surface of copper	Sn	Arbitrary	(231)
Polished nickel	Ni	Arbitrary	(110)
Polished nickel	Au	Arbitrary	(111)
Polished gold	Au	Arbitrary	(111)

The results obtained in this way are given in Table 13. In the last two columns of the table are indicated the crystallographic indices of the planes oriented parallel to the surface of the substrate.

If the film of the deposited metal is sufficiently thin, the orientation of its crystals proves to be completely arbitrary. As the deposited layer becomes thicker, however, the crystals begin to orient themselves in a strictly definite manner.

Table 14 contains the results obtained when metallic films were deposited on unpolished metallic substrates. The latter, in turn, were obtained by electrolytic deposition on the corresponding metals. In this case the orientation of the crystals in the thin deposited layer is no longer arbitrary, but in almost all cases coincides with the orientation of the crystals of the substrate.

TABLE 14

Substrate material	Orientation of substrate crystals	Deposited metal	Orientation in a thin layer	Orientation in a thick layer
Electrolytic copper	(110)	Au	(110)	(111)
Electrolytic copper	(110)	Ni	(110)	(110)
Same	(110)	α—brass	(110)	(111) and (113)
Same	(110)	Fe	(100)	(111)
Electrolytic nickel	(110)	Cu	(110)	(110)
Electrolytic nickel	(110)	Au	(110)	(111)
Same	(110)	Fe	(100)	(111)
Electrolytic gold	(111)	Cu	(111) and (100)	(110)
Electrolytic gold	(111)	Pt	(111)	(111)
Same	(111)	Fe	(110)	(111)
Same	(111)	Sn	(110)	(231)

When the deposited film becomes sufficiently thick, the orienting influence of the substrate ceases to be felt, and the crystals acquire their usual orientation, characteristic of them when deposited on unpolished surfaces.

We thus see that the structure of the “crystalline substrate” completely determines the nature of the arrangement of the atoms adsorbed by it.

In view of the presence of a two-sided orienting action of crystalline grains, the atoms of the intercrystalline interlayer will not, however, be arranged in a strictly regular manner. They must form a certain “transition” zone, whose structure at a given temperature will be wholly and completely determined by the mutual orientation of the grains surrounding it.

This “transition” zone, unlike the crystal lattice of a grain, cannot be characterized by some constant lattice identical for all its regions. The distance between atoms in such a zone must change continuously from the lattice constant corresponding to the elements of the boundary surface of one of the grains to the lattice constant characterizing the second grain.

It may be assumed that the greater the difference in orientation of neighboring grains, the larger the region encompassed by the “transition” zone will be.

It should be noted that, in the region between grains, small embryos of crystalline grains may also become trapped—those that were contained in the melt and did not have time to join the aggregates of grains.

The schematic picture outlined here applies to the case of an absolutely pure metal.

Even the purest melt of a real metal, however, contains various impurities. As we have already seen, these impurities are concentrated at the grain boundaries, forming the main constituent of the intercrystalline interlayer of real polycrystals.

The presence of various impurities, both metallic and nonmetallic, must disrupt to an even greater degree the regularity of the arrangement of atoms in the “transition” zone. One may think, however, that even in this case it will possess certain elements of order, determined by the orienting influence of the surrounding grains.

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2. Osmond and Roberts-Asten, Trans. Roy. Soc., London, 187, 417, 1896.
3. Hartley, J. Inst. Metals, 37, 193, 1927.
4. Duncan, Met. Ind. (London), 24, 53, 1924.
5. Genders, J. Inst. Metals, 37, 215, 1927.
6. Carpenter and Elam, Proc. Roy. Soc., 100, 329, 1921; J. Iron and Steel Inst., 175, 1913.
7. Aston, Proc. Cambr. Phil. Soc., 23, 549, 1927.
8. Seumel, Z. Kristallographie, 93, 249, 1936.
9. Polanyi u. Schmid, Z. techn. Phys., 5, 580, 1924.
10. Chalmers, Proc. Roy. Soc., 162, 120, 1937; J. Inst. Metals, 61, 103, 1937.
11. Hanffstangel u. Hanemann, Z. Metallkunde, 112, 41, 1938.
12. Sauerwald, Z. Physik, 83, 483, 1933.
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16. Thompson, Proc. Roy. Soc., 133, 1, 1931.
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¹) For references Nos. 1–57, see Uspekhi fizicheskikh nauk, 22, 292, 1939.

1. These properties are, of course, also to a considerable extent due to the different chemical composition of the interlayer. ↩↩