METALLIC CRYSTAL1

Harold Carpenter

Metals and alloys prepared by ordinary methods are aggregates of small allotriomorphic crystals. Pure metals usually consist of a large number of identical crystals. Alloys, however, usually contain crystals of two or more different kinds, although sometimes they consist of a single type of crystal. In both cases, metals prepared in the ordinary way contain from one hundred thousand to several million crystals in one cubic inch. Nevertheless, in all metals the individual crystal is the unit from which the aggregate is built. It is, therefore, the simplest form of a metal.

The size and shape of a crystal depend on the type of mold into which the liquid metal is poured and on the rate of cooling, so that in any given casting different types of crystals may be obtained. For example, when a steel ingot is cast, a layer of “chilled” crystals forms in contact with the surface of the mold. Next, the following layer is formed by long “columnar” crystals, which grow almost at right angles to the surface; and finally, in the interior, equiaxed crystals are formed, which are the result of the separation within the liquid of small crystals that grow until they come into contact and form mutual boundaries (Fig. 1). Along with this, on the surface—and sometimes also in the cavity formed as a result of the decrease in volume during solidification—

in the upper part of the ingot “skeletal” crystals grow. In the subsequent mechanical working to which the metal is subjected, these crystals change their shape. If the mechanical working is sufficiently severe, they are crushed, and ultimately complete recrystallization takes place, together with the birth of new crystals. Therefore, whether a given metal or alloy is used in the cast state or in a more or less worked form, it always consists of an aggregate of crystals.

Fig. 1. Section of a steel ingot showing the types of crystals. On the outside is a layer of small, “chilled” crystals. The middle layer is columnar crystals. The inner layer is equiaxed crystals.

The properties of metals and alloys in the ordinary state, accordingly, are the properties of these aggregates. As has already been noted, an individual crystal is the unit that forms these aggregates. If such a unit crystal possesses anisotropic properties, they might nevertheless fail to appear in a polycrystalline material if the individual crystallites are oriented in different directions and the anisotropic properties are thus masked. In addition to this, however, the properties of the boundaries of the crystals themselves must be taken into account. The finer the aggregate, the greater the area occupied by boundaries. It has long been known that the boundaries in a crystalline aggregate are stronger than the internal parts of a crystal. For example, in a tensile test the metallic fracture passes through the crystals, and not ob—

encompasses them. One of the commonest methods of increasing the strength of a metal or the size of a crystal consists in increasing their boundary surface by means of appropriate thermal and mechanical treatment. Therefore the properties of any given metal are not simply the resultant of the properties of the innumerable individual crystals that compose it, oriented in different positions, but rather resultants modified by the properties of the crystal boundaries.

If it were possible to study the properties of individual metallic crystals, the variables just mentioned would be eliminated, and the observations would have fundamental scientific significance. It would be possible to study the individual properties of the metallic crystals themselves, and the only variable would remain the orientation. In this way it would be possible to test whether the investigated properties of the crystal are directional. From the scientific point of view, the study of individual metallic crystals is therefore more valuable than the study of aggregates. However, because special conditions are required if one is to obtain a metal in the form of a single crystal, the direction of research in practice is the opposite.

About twelve years ago several investigators attempted to prepare a metallic single crystal. Considering the great scientific importance of obtaining single crystals, it may seem surprising that the attempt was not made earlier; but it is clear that it could not have been made with much hope of success until the technique of metallographic investigations had reached the necessary degree of perfection.

The problem of preparing a given piece of metal in the form of a single crystal theoretically admits at least three different methods of solution:

1) preparation of a crystal from the gaseous phase,
2) preparation of a crystal from the liquid phase,
3) transformation of a solid metal in the usual polycrystalline form of an aggregate into a single crystal.

Success has been achieved by all these routes. There are now nine methods for preparing single crystals—two from vapor, three from liquid, and four from the solid phase.

Each of these methods is an example of what may be called “controlled” crystallization, and the investigation of some particular metal is subdivided into three parts: a) the production of the crystal itself; b) determination of its orientation; and c) study of its properties. The last category can be further divided into two subgroups, according to whether the investigation includes distortion of the crystal or not.

PRODUCTION OF A SINGLE CRYSTAL FROM THE GAS PHASE

Two methods are used, both based on the technique developed in the manufacture of incandescent lamps for depositing metallic tungsten on a heated wire. One belongs to Coref \((^{1})\), the other to Van Arkel \((^{2})\). Both methods start with a single crystal obtained in another way. It serves as a nucleus and grows into a larger single crystal. As an example, one may describe the production of a single crystal of zirconium by J. H. de Boer and J. D. Fast \((^{3})\). The special interest of this method lies in the fact that it not only is simply capable of yielding the metal in single-crystalline form, but at first led to the production of the metal in its pure form, in which, in both mono- and polycrystalline form, the metal proved to be malleable, whereas previously it had always been obtained brittle. It is now known that the latter was due to the influence of small traces of contamination.

The principle of this method consists in depositing on a heated metallic filament of the metal under consideration by means of thermal dissociation of a volatile compound. A necessary condition for success is the existence, below the melting point of the metal being prepared, of a temperature interval at which the vapor pressure of the metal is less than the dissociation pressure of the metal. In this particular case the metallic filament was made of tungsten, and the volatile ...

Metallic Crystals

the compound was zirconium iodide. There is no need first to prepare zirconium iodide. A mixture of zirconium and iodine also serves well.

A tungsten filament about \(40\,\mu\) in diameter was heated by an electric current to a temperature of \(1800^\circ\), measured with an optical pyrometer. The vessel in which the reaction took place was made of “Pyrex” glass, was placed in an electric furnace, and was heated to approximately \(600^\circ\text{C}\). The powders of zirconium and iodine combined, forming zirconium iodide, and this compound was then sublimed. It decomposed near the filament at \(1800^\circ\text{C}\), and zirconium was deposited on the filament. The free iodine combined with a new quantity of zirconium in the vessel, and this was repeated until a sufficient quantity of metal had been deposited. The incandescent filament cooled as the zirconium solidified, and the temperature was then determined through the strongly colored vapors of iodine and zirconium iodide.

The success of the experiment depends on the deposition of zirconium at the proper temperature. It was found that this temperature lies near \(1800^\circ\). The current increases from its initial value of \(0.25\) for a filament of \(40\,\mu\) to \(200\) amperes when the metal grows to a diameter of \(5\) mm. Whether the temperature of the incandescent filament rises or falls during the experiment depends on the external resistance. If it is small, the current strength is determined by the filament itself. As the filament grows, its resistance decreases in proportion to the square of its diameter, while cooling by radiation increases in proportion to the diameter. Therefore the temperature of the filament tends to rise, and this must be prevented by increasing the external resistance. Conversely, if the external resistance is large, it determines the current, and the zirconium rod, which gradually becomes thicker, tends to cool.

If the temperature of the filament is kept at \(1700^\circ\text{C}\), the deposited zirconium has a polycrystalline structure. Between \(1750^\circ\) and \(1850^\circ\text{C}\), the zirconium crystals are so large that only one is found in the cross-section of the wire, and the rod that has grown consists of single crystals of length

from 0.5 cm to 1.5 cm, arranged around the tungsten core. The crystals formed in this way prove to be hexagonal prisms. If the temperature is allowed to rise to 1900°, the zirconium at first grows very rapidly, but then reacts with the tungsten filament and forms a eutectic.

This method is convenient for preparing single crystals from refractory metals in lamp filaments. Van Arkel and de Boer applied it to titanium, hafnium, and thorium. Koref, together with Fischfeichtl (4), succeeded in preparing single crystals of molybdenum, tantalum, iron, zirconium, and titanium, using the same method. It is therefore possible, by one of these methods, to prepare single-crystal wire or a thin rod from refractory metals, provided that the vapors of the compound of the metal with iodine satisfy the conditions described above.

Obtaining a Single Crystal from the Liquid Phase

We shall confine ourselves to brief remarks on two methods in use. They are applied chiefly to obtaining single crystals from low-melting metals in vessels made of refractory glass, but may also be applied to metals and alloys with a higher melting temperature, of course in suitable vessels. The first method was invented by Czochralski (5), who prepared long, thin crystal filaments by drawing them at a special rate from the metal melted in a crucible, at a temperature slightly above the melting point. The metal is drawn upward with the aid of an auxiliary wire moving vertically at a constant speed. At several millimeters above the surface of the molten metal, solidification begins. The speed of motion of the auxiliary wire must be equal to the rate of crystallization. If it is too great, the crystal breaks; if it is too small, polycrystals are formed.

By this method crystals (0.5 mm in diameter) of lead, tin, and antimony were prepared. This method was

further developed by Gomper (1922) and by Mark, Polanyi and Schmid (1923). By the second method, which is the result of work by Tamann (1923), Obreimov and Shubnikov (1924), and Bridgman (1923–25), single crystals can be grown into rods 2.5 cm in diameter. In Bridgman’s method the molten metal, contained in a suitable closed tube of refractory glass or quartz, is slowly lowered in a vertical position into a tubular electric furnace, which keeps it at a temperature slightly above the melting point. The lower end of the tube is sharpened to a point; it is the first to emerge from the furnace. Solidification begins here and slowly spreads upward. Provided that the rate at which the tube is lowered is less than the rate of crystallization and is sufficiently slow for the latent heat to have time to dissipate, the metal usually crystallizes as a single crystal. In this way Bridgman prepared single crystals of tin, cadmium, zinc, antimony, bismuth, and tellurium. The success of this method is determined by the formation of a single nucleus, on which the cooling metal then crystallizes uniformly. If, however, crystallization begins at several centers, means can be indicated that ensure the formation of a single crystal. The best way is to draw out the lower part of the tube into a separate chamber, connected with the main part by a capillary 0.1 mm in diameter. The capillary acts as a filter and allows only one of the crystals that may form in the lower bulb to penetrate into the upper main part of the tube. This is precisely the crystal that grows and forms the single crystal. In Bridgman’s experiments the crystal grows in a vacuum, and the exclusion of all dissolved gases is therefore an essential condition for the success of this method. The rate of lowering depends both on the metal and on the dimensions of the tube. In the case of pieces 2.2 cm in diameter, a rate of 4 mm per hour proved the most suitable. For pieces of small diameter the rate can be increased to 60 cm per hour. Removal of the single-crystal piece from the tube requires great care—

tions. If the vessel is perfectly clean, the metal adheres and cannot be removed without destruction. Therefore the tube must be lubricated. The most convenient method is to rinse it with a heavy mineral oil and then wash it with petroleum ether. The tube is then heated; the ether is removed, leaving on the tube a thin film of oil, which prevents the metal from sticking. Davey (⁶) modified Bridgman’s method, using graphite tubes, and succeeded in making single crystals of copper 15 cm long and nearly 2.5 cm in diameter. Elam (⁷) showed that single crystals of copper, silver, and gold can be grown in graphite tubes and in an atmosphere of nitrogen. This method is especially favorable in that the metals obtained by it are quite sound, whereas those obtained by melting in vacuum are often prone to the formation of voids. Here, too, great care is required in removing the metals, especially soft ones, from the containing tube. In one case, when a single crystal of gold was being removed, it was found to have twisted into a spiral with three complete turns.

Obtaining a Single Crystal from the Solid Phase

Here the problem consists in transforming a polycrystalline metal into a single-crystalline one. Success in this case was achieved by making use of an observation made by Sauveur (⁸) in 1912. He showed that, by careful stretching and subsequent heating of certain metals, crystals of large size can be obtained, and proposed the existence of a critical stress at which the largest crystals can be obtained. Later Reder (⁹), Chappell (¹⁰), Jeffries (¹¹), and Hanson (¹²) showed that if a metal is subjected to local deformation and then heated, then at a small distance from the point where the stress is greatest exceptionally large crystals are formed. If a forged specimen is used, then it already contains a stress gradient, and the largest crystals always form within the region of stress, and the farther from the region of maximum stress the higher the temperature.

Siligman and Williams \((^{13})\) stretched a previously heated aluminum sheet to various dimensions and found that, when heated to a certain temperature, small deformations had no effect. However, above this temperature large crystals were formed, and as the deformation increased the crystals decreased in size. The crystals obtained by this method were very large in comparison with the crystals of the original metal; some of them reached \(1.5\ \mathrm{cm}\).

Single-crystal test specimens of aluminum, obtained from polycrystalline metal, were first produced by the following treatment \((^{14})\): 1. The metal was first completely softened, recrystallized, and transformed into new equiaxed crystals, possibly of more uniform size. The most suitable size proved to be 36 per \(1\ \mathrm{mm}^2\). This condition was achieved by heating the metal for six hours at \(550^\circ\). 2. These crystals then had to be stretched to the required dimensions. The exact degree of stretching for aluminum was 2.4 tons per square inch, which corresponded to an elongation of \(1.0\%\) over three inches. 3. The stretched crystal was then heated so that the potential possibility of growth caused by stretching was fully realized. This final heat treatment begins at \(450^\circ\), and the temperature is raised by \(25^\circ\) per day to \(550^\circ\). Finally it is raised to \(600^\circ\) in one hour, in order to complete the absorption of the small crystals on the surface, which remain at lower temperatures.

The boundaries of the single crystal thus obtained extend at each end, in the form of an irregular surface, up to the head of the test specimen (Fig. 2). In this way a single-crystal piece of aluminum was prepared—its diameter was 0.564 inch and its length about [[unclear: number]] inches. A single-crystal ingot, 0.798 inch in diameter, was transformed into a single crystal 4 inches long. In this way more than seven million original crystals can grow together into one crystal. How delicate the process of selecting the proper amount of stretching is may be judged from the fact that the exact amount of stretching can be deter-

…determined only for each fresh melt of aluminum, even if the metal was of one and the same “working” composition. On the average, one experiment out of four leads to the production of a single crystal. Let us give an illustration: the result of treating twenty polycrystalline test specimens was as follows: seven were transformed into single crystals, eight into two crystals, four into [[unclear: three]], and one into four. This method was successfully applied by Edwards and Pfeil (15) to the production of large iron crystals; it was also used by Miss Elam (14) for obtaining single crystals of a solid solution of zinc in aluminum. Schaller and Orbig employed it for producing single-crystal wires of tungsten and molybdenum, while Althertum prepared single-crystal bars of tungsten by utilizing the special action of water vapor on small tungsten crystals at high temperature. The production of single-crystal test specimens from polycrystalline metal by the method of critical stress arising on heating is a much more complicated process than the preparation of single crystals directly from vapor or liquid.

Fig. 2. A. Specimen consisting of two crystals, end to end. B. Specimen consisting of a single crystal. Boundary dimensions at each end are the width of the head of the test specimen. One third natural size.

Deformation of a metal is possible owing to the existence of “atomic planes” in each crystal. These are those planes…

which can slip and flow over one another. In a single-crystal bar, where the orientation is uniform, nothing impedes this sliding of the planes. But in a polycrystalline bar, where the crystals are oriented differently, the motions are quite different. The first crystals in which the sliding of layers begins are those oriented so that they present the least resistance to tension. However, the degree of yielding is limited, since these crystals are fixed by a kind of framework formed by the other crystals. Hardening occurs along the slip planes, and the motion ceases. After this, limited slip occurs in other crystals, which now present the least resistance to stretching, but they too in turn eventually become fixed. The process is then repeated in other crystals. The final result, in this case, is a bending of the cleavage planes. According to Van Liempt \(^{17}\), “in this way stresses arise in the crystal, since the original distances between atoms change and the electron lattice is distorted. The deformed metal is in an unstable state. This instability increases in particular places as the stretching increases. If the deformed metal is now subjected to the action of a high temperature, it will tend to return to a stable state.”

The critical-stress method consists in stretching the crystals of an aggregate in such a way that, upon heating, only one of the crystals recrystallizes and forms a nucleus. As heating continues, the remaining crystals, which are in an unstable state, gradually recrystallize and join the single nucleus. Therefore, in the end, a single-crystal bar is obtained. If, however, the bar is heated at a higher temperature, then a certain number of the stretched crystals recrystallize, forming nuclei, and each of them will act as a crystallization center. The result will be a bar containing as many crystals as

how many nuclei there were. One cannot be certain that at the first moment only one unstable crystal recrystallizes; for this reason, in a series of experiments only some of the bars prove to be single crystals. This method makes it possible to grow crystals of the desired dimensions from polycrystalline aggregates; it is only necessary to establish the degree of tension and the temperature according to the required conditions. In this respect it is the most suitable method for obtaining large crystals. Moreover, it is completely independent of the melting point of the metal or alloy. In another sense, however, it is more limited, since it depends on the response of the crystal lattice to tension and on the instability of the metal or alloy, which leads to the formation of twin crystals upon heating. If such instability exists, then single crystals cannot be prepared by this method.

Orientation of Crystals in Single-Crystal Test Specimens

The only satisfactory method for determining the orientation of crystals is X-ray analysis. The initial method for determining the axes of a crystal was developed by Müller (18). It requires the preparation of a bar with a square cross-section and the photographing of reflections from the crystal planes. A special device is required for fastening the bar so that it can be rotated about a vertical axis and photographed in the desired position. Müller found that the reflection from unstressed bars is quite sharp and distinct and is obtained within a small interval of setting angles; whereas, if the bars are stretched, the reflection becomes “shaggy” and becomes possible over a wide interval of angles of incidence, with the width of the interval increasing as the distortion of the bar increases. In Müller’s method, data can be obtained only about a very thin surface layer of the test specimen. The measurements that he made on various parts of the surface show, however,

that this layer has the same orientation relative to the plane of reference over the whole surface. Therefore it seems probable that the very same state of affairs is preserved also in the interior of the rod.

I shall now briefly touch upon two questions to which the method of X-ray analysis gives definite answers.

1) Are the single crystals obtained by the methods I have described perfect crystals in the sense that the orientation of their atoms everywhere uniformly corresponds to the symmetry of the crystal, and are they free from stresses? Of course, owing to the method of preparation, they generally cannot possess an external form, but possess only the internal symmetry of the crystal. An exception is the case when single crystals are prepared from vapors; here, provided suitable conditions are maintained, crystalline wires exhibit the external forms of crystals. Single-crystal rods and wires prepared from vapor or liquid prove, in all tests, to be perfect crystals. This is just what was to be expected, especially in the latter case, where the crystals are deposited from a liquid during slow cooling, in which there are no tensions. But it is interesting that the reflections obtained from an aluminum single-crystal specimen grown from a polycrystalline solid by the method of critical tension and heating prove to be perfectly sharp and indicate a complete absence of stresses, at any rate in the outer layers of the crystal. This follows from the fact that the slight stress produced in obtaining the crystal is completely removed during the prolonged heat treatment to which the specimen is subjected. This conclusion is supported by the fact that, when such a bar is slightly distorted, the X-ray reflections at once become less clean.

2) Do crystals grow more readily in some definite position than in others, i.e., do they have a preferred orientation? As regards crystals obtained from the gaseous phase, we have no data in favor of such a conclusion. Bridgman concluded that

a favorable position for growth from the liquid is that in which the principal plane of cleavage is parallel to the axis of the crystal, and he showed that in the case of large crystals of antimony not a single specimen was found which was oriented otherwise. This, however, does not fix the orientation of the crystal, since this cleavage plane may have any orientation within \(180^\circ\) about the casting axis. Miss Elam showed that, in the case of rods of copper, silver, and gold grown from the liquid, there are no separate preferred positions. Considerable changes of position were also found by her in the case of crystals grown by the method of stretching and heat treatment \((^{19})\). Orientations were determined for twenty-nine aluminum, twelve aluminum-zinc, and ten iron single-crystal specimens. In the case of aluminum a great variety of orientations was found, since it turned out that the position of the axes is scattered over a wide interval, but most crystals prefer an arrangement near the \((110)\) axis, and not a single one had chosen a position near the \((111)\) or \((100)\) axes (Fig. 3). Moreover, it was found that the same holds for aluminum test specimens consisting of four crystals. In the aluminum-zinc alloy a great variety of orientations was also found, but here the \((110)\) axis was avoided. Five out of the twelve were found in a position near the \((100)\) axis. In the case of iron, a wide range of positions was found among ten crystals. The \((110)\) axis was avoided, but nevertheless no preferred orientation was found. As a result, it is clear that in the case of fifty-one crys-

Fig. 3. Shows the great variety of orientations encountered among twenty-nine single-crystal specimens of aluminum. \((111)\) — octahedral; \((110)\) — rhombododecahedral; \((100)\) — cubic.

steel, whose positions had been determined, the method of pulling and heat treatment does not fix the orientation of the crystal, although certain positions are avoided. Growth, it seems, proceeds equally easily in many positions. The positions that are avoided are undoubtedly those in which growth is especially difficult.

The problem of growing a single-crystal specimen in a desired position has only recently been taken up, and some successes have been achieved \((^{20})\).

Mechanical Properties of Single Crystals

I have already pointed out the remarkable softness of single-crystal bars, which requires great caution in handling them and distinguishes them from the same metal in polycrystalline form. This is precisely what should be expected of a metal possessing the uniform orientation of a single crystal, and it provides rigorous proof that the bars are indeed single crystals. Since the work of Ewing and Rosenhain at the end of the last century it has been known that the plastic yielding of a metal is the consequence of slip along certain planes, along which it occurs with the least resistance. The ease with which single crystals of aluminum, copper, silver, and gold, and even of iron, are deformed is simply astonishing. Each of these metals bends easily, but, once bent to some extent, they require a greater force to return them to their former shape. This simply means that the crystal has hardened under the action of the distortion and that the uniform crystalline lattice of atoms has changed. Whether this is the consequence of uniform bending of crystalline planes, as Miss Elam and I suppose, or whether, as Gough, Hanson, and Wright suppose, it occurs because the distortion of the crystalline planes is such that the average curvature is small and the distortion has the character of “wrinkles,”—this question still cannot be finally resolved.

The softness of single-crystal bars indicates that

they can have only a very low limit of proportionality to the external force, and in general it arouses doubt as to the existence of such a limit. This point was carefully investigated by Gough, Hanson, and Wright (21) for aluminum. The limit of proportionality in tension in a polycrystalline bar is about one ton per square inch. These investigators found that no elastic limit exists, and that plastic extension occurs already under the influence of the smallest applied force. Further, from the slope of the load—extension diagram they concluded that there is no primary elasticity even in the range of loads from 10 to 40 English pounds. It is clear, therefore, that a well-defined elastic limit in polycrystalline metals is not a property of the metallic crystal, but, in the case of aluminum, a property of the aggregate.

Ordinary and commonly used metals belong to one of three types of crystalline structure: face-centered cubic, body-centered cubic, or hexagonal lattice. A characteristic feature of each of them is a very high degree of crystalline symmetry. They have certain common structural features. There are planes of atoms in which the nodes are closer to one another than to their neighbors in the nearest plane. Even in one and the same plane, however, there are certain lines along which the atoms are closer to one another than in other directions. When a crystal is stretched or compressed, it tends to yield along certain planes and along certain directions in which the binding forces of the crystal are weakest.

Aluminum Single Crystals

The deformation and subsequent fracture of specimens were first investigated in the case of aluminum. The first experiments were qualitative and revealed the directionality of the elastic properties of this metal. On the one hand, a round polycrystalline bar is stretched as an isotropic material.

It undergoes general stretching, breaks with a considerable reduction in area, and gives a cup-and-cone fracture (Fig. 4). This is the result of slip with bending. The transverse section of the specimen is round everywhere, although the surface is rough owing to the unequal distortion of small crystals oriented differently. On the other hand, the distortion of a round single-crystal bar under the influence of a tensile force makes it elliptical. As the distortion increases it leads to ever sharper ellipses. Finally, a certain state is reached in which an interesting characteristic lenticular figure appears, inclined at some angle to the longitudinal axis of the specimen. Finally the bar breaks in this region with a characteristic “wedge-shaped” fracture (Figs. 4 and 5).

Fig. 4. Upper half—fracture of a polycrystalline specimen, giving a cup and cone. Lower half—fracture of a single crystal, “wedge-shaped” fracture.

In this test the surface of the specimen is not rough, but mechanically etched by numerous lines, which are known as “slip ellipses.” Significant changes in ductility and ultimate tensile strength in different specimens proved to be the result of different orientations of the single crystals relative to the axis of the specimen. The ductility in some cases is almost three times greater than in polycrystalline specimens, while the tensile stress is considerably smaller and in no case exceeded 80% of the same tension in polycrystalline specimens.

The first complete mathematical and quantitative analysis of the deformation of a single-crystal metal was also carried out for aluminum and was the subject of the Bakerian Lecture by Taylor and Elam in 1923 (²²). The analysis

related to a square bar made from a round bar, each face being marked with scratches parallel to the axis of the specimen and with transverse scratches spaced 0.5 inch apart. The dimensions of the specimen tested were: \(1.0\ \text{cm} \times 1.0\ \text{cm} \times 20.0\ \text{cm}\). The faces were numbered 1, 2, 3, 4 in such a way that, when the specimen was placed in the testing machine, its faces appeared in this order as the machine was rotated counterclockwise. At each successive stage of the test the distances between the transverse marks were measured. The angles between the longitudinal and transverse scratches were also measured. In addition to this, the thickness of the specimen between pairs of opposite faces and the angles between adjacent faces were measured. This was sufficient to determine the nature of the deformations (Fig. 6).

Fig. 5. Shows the stages of deformation under tension of a single-crystal aluminum specimen.

These investigators found that up to 40% elongation the crystal is deformed by shear or slip along one plane. X-ray measurements revealed that this plane is the octahedral \((111)\). The direction of shear was also determined, namely along the three principal lines of atoms in the octahedral plane. When the specimens were stretched to an elongation greater than 40%, it was found that the deformation was no longer more a consequence of slip along a single plane. This was explained by the authors, who showed that the effect of shear is reduced to a rotation of the specimen axis relative to the crystal axis, in such a way that another octahedral plane comes into a position where its inclination to the axis becomes the same as that of the slip plane. Under these circumstances it is clear that slip can occur simultaneously along both planes, which was confirmed in this case (Fig. 7).

This investigation gives an explanation of the stretching of a round single-crystal aluminum test specimen.

into a very regular elliptical one. This proves to be the consequence of the sliding of the crystal along two conjugate planes. Thus a further important point is established. Until now the evidence for the sliding of metal had been purely qualitative. It had not been shown that the deformation in stretching of a crystal is such as it would be if produced by sliding.

Fig. 6. Diagram of markings and measurements of the deformation of a single-crystal test bar of aluminum.

Quantitative measurements in this work showed for the first time that this is precisely so, and Taylor and Elam were able in this way to complete the original discovery of Young and Rosengain.

Fig. 7. Shows the position of the specimen axis relative to the crystal axes at elongations of 0%, 20%, 30%, and 40%.

The second paper by Taylor and Elam (23) on the plastic tension and fracture of aluminum crystals contains a very interesting test. As a preliminary, they investigated by a similar method the deformation of other single-crys-

of steel bars, in which slip began along one plane and then, when the bar passed into the position of conjugate slip, continued along two planes. The authors predicted that if the crystallographic axis of an unstretched crystal was initially in such a position that double slip could occur, it ought to begin at once. Among a large number of crystals grown by me and Miss Elam, one was found whose axis came very close to this position. When it was deformed in tension, it was found that double slip began almost at once and continued throughout all further stretching. Not only this, but the magnitudes of the slip along the two planes were also practically equal, so that the axis of the specimen changed only slightly throughout the entire test. Another conclusion likewise followed from these tests, namely that, whatever the initial orientation of the crystal in the specimen, it always fractured in the very same position.

In such a case the question arises whether the single crystal remains such throughout the whole extension up to fracture, or whether it subdivides. Clarity on this question is provided by Müller’s paper (loc. cit.) on the character of the spots of reflected X-rays. In an unstretched specimen the reflected spots are very small and are obtained only within a narrow interval of reflection angles. When stretching begins, the region of reflection often increases, and the size of the reflected spots becomes larger.

Assuming that the specimen divides into small crystals, one may, from the dimensions of the reflected spots, make a rough estimate of the maximum angle between the surfaces of a pair of these small crystals. It was found that this angle sometimes reaches several degrees. Müller considers that this result indicates an actual subdivision of the test specimen into an aggregate of small crystals. However, in view of the fact that even after considerable stretching these crystallites remain almost in the same position, the specimen may still be regarded macroscopically as a single crystal. An X-ray photograph was made

the X-rays for that part of the specimen where it had broken. The picture obtained indicated the existence of relatively large crystals near the place of fracture. Hence it is clear that metallic crystals display great resistance to destruction by mechanical force.

It is well known that when a metal is deformed by tension, it breaks under a shearing force and that this has an inclination maximum of 45° to the long axis of the specimen. Assuming that aluminum were a stronger metal and that it could be broken by a shearing force along a single plane, and that we could find a single-crystal specimen whose cleavage plane is inclined at an angle of 45° to the long axis, we should expect that the fracture surface would not be a wedge, but a flat surface inclined at 45° to the specimen. Since we cannot do this with aluminum owing to its weakness, it seemed interesting to find out whether it could not be strengthened by making alloys with such an element as would not disturb the symmetry of the aluminum crystal, so that this alloy would possess the property of slipping along only one plane right up to fracture.

Miss Elam succeeded in doing this by dissolving 18.6% zinc in aluminum, and this despite the fact that the lattice of zinc is not cubic with centered faces, but hexagonal. This is a single-phase alloy. It was turned into a single-crystal specimen by the method of critical tension and heat treatment and was tested in tension. It elongated almost entirely along the principal slip plane, although there were also signs of a second plane, along which slip occurred at an angle of 90° to the first. Both planes form angles of 45° with the axis of the specimen (Fig. 8).

It is therefore clear that fracture occurred along the plane of maximum stress, which is in strict agreement with theory. So far as I am aware, this was the first time that it proved possible to carry out such a test.

Taylor and Farren, in a paper on the deformation of aluminum crystals under compression ($^{24}$), found that compression

has the same nature as stretching. It is the consequence of the sliding of a certain crystallographic plane in a certain crystallographic direction; the choice of which, out of twelve possible crystallographically similar types of slip, depends only on the components of the shearing force in the material and does not at all depend on whether the force normal to the slip surfaces is pressure or tension.

Fig. 8. Fracture of a single-crystal specimen of an aluminum-zinc alloy. The fracture occurred almost entirely along the principal cleavage plane, although there were also signs of fracture along a second plane at \(90^\circ\) to the first. Both planes form angles of \(45^\circ\) with the axis of the specimen.

Iron single crystals

The study of the deformation of iron single crystals has yielded results of exceptional interest. The lattice structure of this metal differs from that of aluminum. It proves to be cubic with centered cubes, i.e., there is one atom at each corner of the cube and one more at the center of the cube. The planes having the greatest number of atoms and the greatest distance between neighboring planes are not those of the lattice with centered faces. For this reason alone, the study of the deformation of an iron single crystal is important, but there is also a further reason. The slip bands of most metals, formed during plastic deformation, are straight, whereas in iron they are almost always curved. Almost all earlier investigators of this subject were surprised that an iron crystal has a slip plane which is a crystallographic plane, and they tried to bring the slip lines into correspondence with the traces of crystallographic planes. These attempts were unsuccessful, but the work of Osmond and Cartaud \((^{25})\) represents a remarkable exception. They noted—

...types, that the slip lines which occur in an iron crystal subjected to tension are curves, and they could not find any relationship of these lines, taken as wholes or in parts, with crystallographic planes. Taylor and Elam studied deformation during tension of a single crystal of iron prepared by Edwards and Pfeil \((^{26})\). They concluded that when an iron crystal is deformed by tension, it does not slip along a crystallographic plane, but that the metal particles are fastened together along some crystallographic direction, and the resulting deformation may be likened to the deformation of a large bundle of rods sliding one past another. The rods are fastened together into groups or smaller bundles of irregular cross-section, and the slip lines appearing on the polished surface are the traces of these bundles on the surface. This conclusion was tested by Gough, who subjected a single crystal of iron to alternating torsional stress. The specimen ultimately broke from fatigue, measures being taken to avoid the appearance of cracks of very large size. Careful microscopic examination showed that the slip bands were quite different in different parts of the specimen, but all the bands could be described by the following three types: 1) a series of straight parallel bands; 2) two series of bands of different inclination, each of them straight or almost straight; 3) clearly “wavy” slip bands, having a well-defined mean inclination and limits of inclination, but which cannot be decomposed into a combination of straight bands. Gough’s analysis led him to the conclusion that iron slips along crystallographic planes, but slip does not always occur along a plane of a single type; it may take place along one of the planes \((112)\), \((110)\), or \((123)\). Only under very special conditions will any plane coincide with that in which the shearing force resolved along the octahedral direction is a maximum. Therefore, in general, slip will occur along two systems of planes simultaneously. This is what generally causes the curved form of the slip bands...

...strains and, in a very complicated form, is represented by double and “wavy” types of bands. This view of the deformation of iron single crystals is now for the most part accepted. The character of slip accounts for a most important property of iron, namely, its tendency to fracture with a fibrous break.

MAGNETIC CHARACTERISTICS

Plasticity is only one of the properties of a metal. It is of the greatest importance for metallurgists and engineers, but from the general point of view of physics all properties are important. By studying single crystals, physicists have come closer to the solution of many of their problems, and every year this form of metal is being used more and more widely as a means of obtaining new data on the fundamental properties of matter. Magnetic, electrical, thermal, and optical properties have been measured for crystals of many metals; nevertheless, it must be noted that the number of such works is small.

Investigations of the magnetic properties of an iron single crystal were carried out by Honda, Kaya, and Masiyama (27). They prepared single crystals of iron wire, measuring \(68.1\ \mathrm{mm} \times 2.4\ \mathrm{mm} \times 1.81\ \mathrm{mm}\), by the method of critical stretching and heating. They found that hysteresis losses in an iron single crystal amount to only one tenth of the losses in ordinary iron, and that these losses increase rapidly with an increase in the number of crystals per unit volume. The initial and maximum permeability of iron decreases with an increase in the number of crystals per unit volume. Five crystalline rods were prepared, of which three had an axis lying approximately in the \((100)\) plane and two in the \((110)\) plane. The magnetic elongation of the single-crystalline rods was measured, and the following observations were made: 1) the magnetic elongation of iron single crystals is usually very large in comparison with ordinary iron; 2) magnetic elongation along the tetragonal axis is always positive, whereas along the trigonal axis it is always negative; the curves of mag-

noticeable stretching of crystals for intermediate orientations are determined as the resultant of the indicated extensions and compressions; 3) magnetic elongation in ordinary polycrystalline iron is a difference effect arising from the extensions and compressions of the numerous crystals of random orientations.

The work of the Japanese investigators shows that hysteresis losses and permeability are functions of the number of crystals per unit volume, and that magnetic elongation is a direct property of the crystals.

A similar investigation was carried out by Gerlach (²⁸). The results obtained by him are in substantial agreement with those of Honda and his co-workers; moreover, Gerlach showed that the magnetic properties of single crystals are clearly directional. It was found that the initial permeability is greater in the tetragonal direction than in the diagonal direction, and that saturation in the tetragonal direction occurs at a lower magnetic-field strength than in the diagonal direction. Gerlach found that slight deformation produces considerable changes in the magnetic properties, and accounts for the small discrepancies between his results and Honda’s, owing to the presence in Honda’s experiments of small mechanical disturbances. Their effect is observed on the curve connecting the field intensity with the intensity of magnetization. The longitudinal magneto-ohmic effect in single crystals was investigated by Webster (²⁹). He measured the change in resistance in a longitudinal magnetic field for three different orientations of iron crystals. He found that, for the tetragonal direction, there is no change in resistance in a longitudinal magnetic field, whereas in the trigonal and diagonal directions the electrical resistance begins to change when the magnetic-field strength reaches 800 CGS. Various magnetic properties of nickel crystals were also studied, chiefly by Kaya. This investigator found that, up to magnetic-field strengths of 205 CGS, nickel crystals are isotropic, but above this magnetizing intensity they vary for differ-

of the directions of the applied field. The magnetic susceptibility decreases, in order, along the trigonal, digonal, and tetragonal axes. Meanwhile, for iron the reverse order is evident. The same investigator measured the change in the electrical resistance of a nickel single crystal in longitudinal and transverse magnetic fields. In a longitudinal magnetic field, each axial direction shows an increase in resistance, the magnitude of the increase decreasing in the order of the axes: (111), (110), and (100).

These results differ from those of Webster, who found no increase in resistance for the direction (100) in iron crystals. The magnetic elongation of nickel single crystals was measured by Masiyama. He found that, in a longitudinal field, the magnetic elongation is always negative for all fields and directions, and that the absolute magnitude of the contraction decreases in the order of the directions (100), (110), and (111). The transverse effect proves to be opposite to the longitudinal one.

Electrical Conductivity

A considerable number of studies have been carried out on the electrical conductivity of single crystals, and in general it has been found that, for crystals belonging to the cubic system, the resistance is the same for all directions; for crystals of other systems it has been found that the greatest resistance lies in that direction of the planes in which slip occurs most readily. In comparing the differences between single-crystal and polycrystalline zinc bars with respect to thermal and electrical conductivity at temperatures from −250° to +100°, Lewis and Bidwell found that: 1) the thermal conductivity decreases smoothly, though not linearly, with increasing temperature; 2) zinc single crystals measured in the direction of the basal plane give, at 0°, a thermal conductivity 11–18% higher than polycrystalline bars. Bridgman directed numerous investigations on the conductivity and thermoelectromotive force

in the case of crystals of low symmetry. In 1926 he published an article on the thermal conductivity and thermoelectromotive force \((^{30})\) of single crystals of zinc, bismuth, cadmium, and tin. Both properties, it turns out, vary with the orientation of the crystal, and these variations were especially noted in the case of the thermoelectromotive force.

Applying improved methods for casting single crystals, which make it possible to obtain a wide range of orientations and more accurate means of measuring thermoelectromotive force and resistance, in 1928 \((^{31})\) he showed more clearly the relation between these properties and the orientation of the crystal. He found that the thermoelectromotive force is a linear function of \(\cos^2 \theta\), where \(\theta\) is the angle between the axis of the crystal and the length of the rod. This confirms the relation of Kelvin and Voigt, about which Bridgman, on the basis of his earlier work, had been doubtful.

Density

It was found that the density of iron single crystals is \(0.037\%\) greater than the density of the polycrystalline material, and that the density of aluminum single crystals is \(0.034\%\) greater than the density of the polycrystalline metal \((^{32})\).

Characteristics of the Electromotive Force

Measurements of the electrode potential of a single crystal of zinc were carried out at Yenching University (Peking) by Paul A. Anderson \((^{33})\). The results indicate that the principal cleavage plane of zinc—the basal pinacoid—gives constant and reproducible values of the electrode potential, and that these values are precisely those obtained in electrolytically deposited crystalline conglomerates. This result apparently indicates that, in an electrolytically deposited conglomerate, the crystals have a random orientation, and that the basal plane of the pinacoid has the maximum electrode potential among all planes. Attempts to prepare zinc

crystal with naturally developed secondary faces proved unsuccessful, and the measurements of electrode potential were made on an artificially prepared surface. The results obtained in this way indicate a qualitatively correct decrease in the potential with an increase in the angle between the plane under consideration and the principal cleavage plane.

Studies of the relation between the electrode potential and the density of atoms on various planes of a zinc crystal were carried out at the University of Latvia (³⁴). The results obtained in these investigations do not agree with those just mentioned, and no difference of potentials was found on the various artificially prepared planes.

It is very probable that the characteristics of the electromotive force of a metal change with the orientation of the surface on which the measurements are made, but it is difficult to measure the change of these characteristics on artificially prepared surfaces. The Latvian researchers attribute the negative results to this circumstance. They indicated that polishing, filing, and rubbing with emery pulverize the crystallographic surfaces and that the resulting structure is indeterminate and shows no differences in potentials, while etching with dilute acids acts on the surface very unevenly and does not yield definite planes. It is likely that the results obtained by Anderson are qualitatively correct, but their definite confirmation must await measurements of the electrode potential of naturally developed surfaces.

From the preceding results, and from those that it has not been possible to consider, it is clear that the mechanical and physical properties of metal single crystals, in the majority of cases, prove to be directional. This fact is most vividly illustrated in mechanical tests, since a single-crystal specimen, when subjected to deformation, assumes new and striking forms. In both groups, however, the properties of a single crystal depend on its orientation and differ from the properties of a crystalline aggregate. Mono-

crystalline alloys have been investigated to a lesser extent, but sufficiently for the same to be asserted of them.

Scientific research on metals in the future will take into account both states—the mono- and the polycrystalline—as well as the changes in any property that are obtained by varying the orientation of the crystal. This also includes the production of single crystals in desired positions; the field of research has only just been opened.

The information that mechanics and physics possess concerning the metallic crystal is still in an embryonic state. From the standpoint of pure science, single crystals of metal should be studied first of all. The study of a crystalline aggregate of some average size should follow at a later stage. Such knowledge will form the foundation for the scientific manufacture of metals and alloys possessing properties that can be established with precision and reliability.

LITERATURE

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1. Geiss and van Leimpt. Z. Metallkunde. July, 1925.

2. A. Müller. Proc. Roy. Soc. A. 105, pp. 500—506, 1924.

3. Elam. Phil. Mag. 50, pp. 507—520, September, 1925.

4. Goetz. Phys. Rev. 35, No. 2, January, 1930.

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9. Osmond and Cartaud. J. Iron and Steel Inst., No. 111, 1906.

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11. Honda, Kaya and Mashiyama. Sci. Rep. Tôhoku Imperial University, 1926.

12. Gerlach. Z. Physik. 1926—27.

13. Webster. Proc. Roy. Soc. A. 113, 1927.

14. Bridgman. Proc. Amer. Acad. of Science. 61. 1926.

15. Bridgman. Physical Rev. 31, No. 2, 1928.

16. Seisi Kaya. Kinzoku no Kenkyn, 5, 10, 1928.

17. Anderson. Nature, Jan. 12, p. 49, 1929.

18. Stranmanis. Nature, July 13, p. 56, 1929.

1. Suppl. to Nature, July 5, 1930, p. 17. ↩