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CRYSTAL PHYSICS AND ISSUES OF METALLURGY
S. T. Konobeevsky.
In 1912 Laue was the first to obtain the phenomenon of diffraction of X-rays, using as a diffraction grating the natural lattice represented by a crystal. The measurements of Laue and especially of the Braggs initiated the analysis of the internal structure of the crystal, which came to be regarded as a three-dimensional system of points possessing a definite period in each of the three dimensions. Such a representation was not new; it had its roots in the theory of Bravais, who as early as 1848 expressed the idea that a space lattice must lie at the basis of the crystal. What was new, however, was that the centers of the space lattice, which in the theories of crystallographers had had a formal significance, after the experiments of the Braggs acquired a clear physical meaning. These points proved to be the centers of the atoms of the crystal.
The further development in the accuracy of X-ray investigation made it possible to introduce a certain correction into these ideas and compelled one to regard as the elementary particles of the lattice not atoms, but ions.
On the other hand, the modern theory of the atom, proceeding from Rutherford–Bohr ideas on the planetary structure of the atom from electrons—ideas that have received confirmation and support in almost all branches of physics and chemistry—makes it possible to take into account those forces which must manifest themselves between individual ions, and consequently also the forces binding the entire system of particles of the crystal.
Therefore a crystal can be calculated as a mechanical system, since both its structure and its internal bonds are known. The first attempt in this direction belongs to Born and his school. Born succeeded in calculating the internal energy of a number of crystals whose structure had been determined by the X-ray method, and in showing that at least the order of magnitude of the internal energy of the crystals investigated agrees with the experimental data1.
S. T. Konobeevsky
The dependence of the magnitude of the internal energy of a crystal on the distance between its particles makes it possible theoretically to derive the elastic properties of the crystal: the coefficient of elasticity, tensile strength, ultimate elongation, etc.
In part these conclusions of the theory have been fully justified, for example in the case of uniform compression; in part, however, they have sharply diverged from experiment. An especially sharp contradiction with experiment was obtained in calculating the ultimate load for rupture of a crystal, which in reality proved to be several hundred times smaller than what followed from theory.
Recently, however, A. F. Ioffe succeeded in showing that, for example in the case of rock salt, this discrepancy between theory and experiment is an accidental result and arises from the fact that the crystal is usually tested under improper conditions. By rupturing a column of rock salt under water, Ioffe was able to increase the load by a factor of 150 compared with the usual value before the crystal broke. Thus, apparently, it is also possible to “strengthen” a crystal, at least up to the limits of its theoretical strength.
It becomes evident that the results at which the physics of the crystal arrives should be taken into useful account by that area of practical knowledge which deals with the properties of a solid substance as a material—primarily by metallurgy.
The fine-crystalline structure of a technical metal does not present any obstacles to the application to it of the methods of X-ray analysis. First, the study of the spatial lattice of individual metallic crystals can be carried out by the method of Laue and the Braggs, since at the present time large crystals of many (more fusible) metals, such as, for example, Zn, Sn, Al, Cu, etc., are readily obtained; secondly, the same investigation can be carried out by the method of Debye and Scherrer, which consists in irradiating a microcrystalline medium with X-rays: the X-ray diagrams thus obtained make it possible easily to calculate the structure of the individual crystals of the mixture and, consequently, to analyze the crystals of a metal in its natural, “technical” state.
The theory of interaction of the particles of a metal, although it cannot yet be considered fully developed, is nevertheless also capable of providing certain foundations for calculating the elastic forces in metallic crystals.
Thus, with respect to a metallic crystal, theory is in the same position as with respect to any other: it makes it possible to derive its elastic properties purely mathematically from the structure of its lattice and the forces of interaction between ions.
However, the difference between the microcrystalline body which a metal is and an individual crystal also consists in the fact that, ac-
quite apart from the peculiarities that are connected with the structure and forces of the spatial lattice of individual crystals, here importance is also acquired by the size of the crystallites, their mutual orientation, the frequent presence not of one but of several crystalline phases, etc. The metal is, as it were, a complexly organized microcrystalline system, and this system is highly sensitive to thermal and mechanical influences. It is precisely for this reason that, when applied to a metal, expressions are still current that are not entirely free from anthropomorphic notions, borrowed from the language of biology: to age, to fatigue, to become poisoned, etc.
As a supplement to the analysis of metallic crystals considered from the standpoint of their internal structure, there must therefore appear the investigation of the entire crystalline mass of the metal as a whole, the discovery of the law or the elucidation of the character of the arrangement in the metal of the grains composing it. In individual cases this problem too is solved by methods of roentgenographic analysis. Thus, the determination of microcrystalline structures in metals subjected to homogeneous deformation (drawing, rolling) presents no special difficulties and can be carried through to completion.
Nevertheless, the question of the strength of metals is not covered theoretically only by Born’s theory, by the analysis of their spatial lattice, and by the analysis of the microstructure. This is connected chiefly with the fact that a metal is a plastic and viscous body. Its elastic properties are characterized not so much by the ultimate load necessary for rupture as by the limit of perfect elasticity, when the metal begins to flow and residual deformation appears in it. This property of plasticity is not directly connected with the microcrystalline structure of the metal; it belongs, to an even greater degree, to individual metallic crystals.
The mechanism of deformation of metallic crystals is one of the essential questions of theoretical metallography. It is also important because the deformation of metallic crystals is invariably accompanied by an increase in the elastic limit, i.e., it leads to what in practice is called the strengthening of the metal.
At the present time there exist side by side two theories which attempt to explain the property of metal flow, and at the same time that remarkable phenomenon of strengthening which is connected with its cold working. One of them is vigorously defended by Czochralski, the other was proposed by G. Tammann and his school.
Czochralski’s theory—the so-called theory of distortion (Verlagerungstheorie)—rests on facts of a metallographic character. The disappearance of the characteristic granular structure of a metal under strong mechanical working, the absence of clearly expressed figures of [[unclear: continuation cut off at page bottom]]
etching on its polished sections and, conversely, the appearance of a fibrous structure, for example in rolled metals, serves, in Czochralski’s opinion, as an indication that the crystalline structure of the metal in these cases undergoes a profound change, and that the regular structure of the space lattice is disrupted. If before deformation of the crystal its ions were arranged along straight lines, then after it these straight lines bend and intertwine like wood fibers1. Such a state cannot be called wholly amorphous, but neither is it crystalline, since the crystalline state is characterized by a regular lattice, which is the result of equilibrium of the forces between the ions and corresponds to the minimum of the potential energy of the crystal. Indeed, in some cases it may be observed that the internal energy of a metal worked by a cold process changes; this is revealed, for example, in changes in the electrochemical potential, solubility, and also in the conductivity and specific gravity of the metal. It should be said, however, that these changes are not so great as to testify to that profound distortion of the space lattice which, according to Czochralski, occurs in the metal during rolling or drawing.
Fig. 1.
Czochralski’s theory comes into contradiction with the results of X-ray investigation by the method of Debye and Scherrer. Thus, when even very strongly rolled plates of metal are irradiated, a clear interference pattern is always observed in the form of a series of rings (see Fig. 1), indicating the crystalline structure of the metal; only the width of the interference rings in some cases becomes greater, indicating an extremely strong subdivision of the crystallites. The method proposed by Debye for calculating the size of crystallites from the broadening of the interference bands gives for them a value of approximately \(10^{-6}\)—\(10^{-7}\). Czochralski’s attempt to explain the appearance of a peculiar radial figure around the central spot (the so-called phenomenon of asterism) in strongly rolled metal plates or drawn wires by reflection of X-rays from deformed internal faces of the crystal is not justified from the physical point of view and is based chiefly—
based on rather unconvincing and superficial analogies with radiographs of elastically deformed crystals (for example, mica plates). We shall see below that this phenomenon speaks much more precisely in favor of the theory of Tammann, who stands at the point of view opposite to Chokralski’s.
The theory of slip (Gleitungstheorie), advanced by Tammann and shared by the majority of physicists concerned with questions of the structure of metals, takes the view that a metal both before treatment and after it is physically one and the same body, preserving most of its physical properties and merely undergoing changes in its elastic properties. The crystalline lattice is not deformed, and the change in the shape of metallic crystals takes place by means of special slips, in which separate layers of the crystal participate, and, at higher degrees of deformation, also by the crushing of large crystals, which divide into smaller parts that nevertheless retain their normal crystalline structure.
The existence of such slips is revealed already in microscopic observation of polycrystalline metals subjected to compression; the consequence of these slips is that individual grains of the metal become covered with a series of parallel striations—each of them representing the boundary of two neighboring layers shifted somewhat with respect to one another (Fig. 2).
Fig. 2.
Still more convincing in this case are experiments with single-crystal metals. If a single-crystal zinc wire is stretched, it becomes covered with oblique notches and is clearly divided into layers which, slipping, give the round wire, upon further stretching, the form of a flat ribbon.
Very important here is the circumstance that the displacement of the layers is accompanied by their rotation, so that a zinc rod deformed by stretching can no longer be regarded as a single crystal.
The fact of the slip of individual layers in metallic crystals is so well known to metallographers that even Chokralski does not consider it necessary to deny it; he indicates only that shifts like those described are characteristic merely of the initial stage of deformation of a crystal, and that subsequently a new mechanism of ion displacement takes their place, one no longer having a regular character:
because the rows of shifting ions cease to be straight lines, the structure of the lattice is disrupted.
However, the fact that crystallographically determined slip planes are preserved even with a very considerable change in the shape of metallic crystals is proved by the study of diffraction X-ray photographs of strongly rolled metal plates (see Fig. 3). Here one may observe a characteristic change in the Debye–Scherrer pattern, consisting in the fact that the rings corresponding to definite internal faces of the microcrystals split into a series of maxima which, with the proper orientation of the plate with respect to the beam, have a strictly symmetrical arrangement.
Fig. 3.
When not monochromatic but white X-ray light is used, the phenomenon of asterism can also be observed; however, from this alone it cannot be interpreted in Chochralski’s sense, since the arrangement of the rays is strictly regular and symmetrical, indicating not a disorderly arrangement of the diffraction centers of the lattice, but, on the contrary, a certain statistically ordered placement of the reflecting crystals in the thickness of the metal.
If the Debye–Scherrer rings arise as a consequence of the uniform distribution of the axes of the microcrystals over two degrees of freedom, corresponding to rotation about two mutually perpendicular axes, then the X-ray photographs of rolled metals indicate that one crystallographically definite axis in all the crystals remains parallel to the direction of rolling of the metal plate, and that the rotation of the microcrystals takes place around this axis1.
The meaning of this kind of structure becomes clear if one takes into account the probable mechanism of the shifts of microcrystals during rolling. An individual crystal must break up into a multitude of layers, turned relative to one another according to the rule of a screw, while the slip plane, by virtue of the mechanical conditions, is established perpendicular to the direction of rolling. Determining from the X-ray photograph the angles formed by the axis of orientation with the principal faces
crystal, we also easily determine the indices of the slip plane. In the case when the X-ray photograph is taken on a cylindrical film of radius \(R\), the maxima are arranged along horizontal lines (zones of the 1st, 2nd, ... \(h\)-th order), and the sum \(h_1^2+h_2^2+h_3^2\) can be calculated from the formula:
\[ \frac{Z^2}{R^2+Z^2}=\frac{\lambda^2}{a^2}\frac{n}{\sum_{i=3} h_i^2}, \]
where \(Z\) is the distance of the maximum of the 1st, 2nd, ... \(n\)-th order from the equatorial line of the X-ray photograph, \(\lambda\) is the wavelength, and \(a\) is the lattice parameter (in the case of a regular system of crystals).
In this way one can, for example, find that in crystals of Al, Cu, Ag and certain other metals, which have a cubic lattice with centered faces, the slip plane has the indices 211. In crystals of \(\alpha\)-iron the slip plane is the plane of the rhombic dodecahedron 110, etc. \(^1\)
Slip and rotation of layers in metallic crystals need not necessarily be accompanied by destruction of the crystal. The cohesive forces between the displaced parts of the crystal are preserved. In the case of a simple translation, the matter proceeds in such a way that each successive layer is displaced relative to the preceding one by an integral number of lattice periods, and, consequently, the crystal changes its form while at the same time remaining one whole crystal. Twin crystals may also arise in a similar way; traces of them can often be detected on sections of metals that have undergone slight deformation. But translation accompanied by rotation also should not lead to the destruction of the crystal, but rather to an improvement of its mechanical qualities, since, owing to the angular displacement of the layers, additional stresses arise between them, making the system more elastic. In this, in all probability, should be seen the cause of that strengthening of metals which occurs during cold working of them by mechanical means.
As a result of the stresses arising between the separate layers of the crystal, certain displacements must occur in the lattice, of course of an exclusively elastic character. By partly bending the slip surfaces, they can hinder further slip along definite surfaces, which, when the character of the deformation is irregular (for example, during forging), leads to the appearance in each of the crystallites of new slip planes (it is clear that these new planes will belong to the same group of crystallographically determined faces) and, consequently, to further subdivision of the crystallites of the metal. Apparently, by such elastic deformations of the lattice one should
\(^1\) See S. Konobeevsky, On the crystalline structure of rolled plates of Fe and Ni. Journal of Applied Physics, vol. II, issue 1–2, Moscow, 1925.
explain the anomalous broadening of spectral lines recently observed by V. Arkel1 on X-ray diffraction photographs of tungsten wire.
A rarer case of an anomalous interference pattern was observed by the author in investigating the crystalline structure of rolled nickel (Fig. 4). It must be thought, however, that in this case the matter is not so much deformation as that limiting crushing, when the normal conditions of diffraction, owing to the approach of the metal to the amorphous type, no longer obtain.
Fig. 4.
Thus, since the experimental data make it possible to choose between the two theories, one must recognize Tammann’s point of view as the more substantiated and consider that the most essential role in the mechanism of plastic deformation of a metal is played by the internal sliding of layers in metallic crystals.
From the theoretical side the phenomenon of sliding is still very little elucidated. The planes of sliding, as they are determined from experiment, apparently have nothing in common with the cleavage planes, that is, with those planes along which the crystal is most readily split. Their very position in the crystal lattice, if the latter is regarded as a lattice of atomic centers, is in no way distinguished. Without doubt, the selection of precisely these planes must be connected with a definite orientation of the electron orbits in the ions of the lattice, whose force field we, of course, have no grounds whatever to regard as isotropic. However, at present there is too little data for the characterization of this field.
Since the plastic properties of a metal are connected with the existence of slip planes, the elastic limit for a whole metallic crystal directly characterizes the magnitude of the internal friction during the sliding of its layers, and an increase of this friction must, of course, be accompanied by a rise in the elastic limit. Such a phenomenon is well known; it is observed, for example, in the formation of solid solutions.
Solid solutions have in many cases been investigated by the X-ray method. In general they are of two types.
In one case the particles of the dissolved substance take the place of the ions of the host, forming a kind of mixed lattice. Since
if the effective volume of the particles of the dissolved substance and of the solvent is different, then the lattice parameter changes, although all the geometrical relations in it are preserved. Such a change is easily detected in the form of a change in the specific gravity of the alloy, which, for example, in the case of martensite—a solid solution of carbon in \(\alpha\)-iron of the type described—decreases in proportion to the increase in the percentage of C.
The question is debatable whether the particles of the dissolved component are distributed according to a definite periodic law in the lattice of the solvent, or whether they are arranged quite randomly. Tammann adheres to the first point of view, since in his opinion, in a number of certain solid solutions the internal energy of the crystals changes abruptly where the atomic percentages of one component are related to the other as \(n:8\) (\(n\) an integer) (see Fig. 5).
However, Bromé, investigating such crystals by X-rays, found no confirmation of Tammann’s views, so that, apparently, it cannot be considered that the particles of the dissolved substance are distributed in the lattice of the solvent in any definite order.
At the same time it is quite possible that these particles within the lattice possess a certain freedom of migration, at least at high temperature. This must explain the formation from one and the same alloy now of solid solutions, now of isomorphous mixtures or, in the case of metals, eutectics, depending on the method of heat treatment.
Fig. 5.
An example of the second type of solid solutions may be austenite (a solution of carbon in \(\gamma\)-iron), in which, according to the investigations of Westgren \(^{1}\) and Wever \(^{2}\), the carbon particles do not replace the iron ions forming the face-centered cubic lattice, but are wedged into the spaces between these ions, leaving the lattice of the iron ions unchanged and only moving them somewhat apart. Experiment shows that in this case the change in density as a function of the increase in the atomic percentage of carbon is also expressed approximately—
\(^{1}\) Zeit. f. phys. Chem. 102, 1922.
\(^{2}\) Mitteilungen a. d. K. Wilhelm Inst. f. Eisenforschung. Dusseldorf III-45, 1922.
…a straight line, but having a smaller slope with respect to the abscissa axis (the abscissa axis is atomic percent carbon).
Both martensite and austenite differ from pure iron by a considerably higher elastic limit. If elasticity depends on the magnitude of friction along the shear planes, then it is obvious that in solid solutions slip is impeded. It is retarded by the inclusion of foreign atoms in the lattice.
Such retardation is self-evident in crystals similar to austenite. Whatever the slip plane in crystals of γ-iron may be, it is clear that the inclusion of foreign particles within the lattice must produce the same effect as the pouring of sand between rubbing surfaces. The motion of the slipping layers will be greatly impeded. It goes without saying that the quantity of this sand need not be large in order to create already noticeable friction, and this is reflected in the fact that, in the field of metallic alloys, sometimes a very small amount of one or another component produces a strong strengthening effect.
The same phenomenon of friction between slipping layers will also be observed in the case of solid solutions similar to martensite.
The replacement of the ions of the host by particles of the dissolved component, having a different effective volume and, possibly, a different symmetry of the force field, must lead to the result that the slip planes of the pure metal, formerly “smooth,” now become as it were rough, owing to which slip is impeded.
Since, apparently, one should ascribe to the elements of the space lattice the capacity for migration, here, perhaps, lies the key to explaining the still little-understood phenomena of “fatigue” of a metal under rapidly alternating shocks applied to it, which lead to such a rearrangement of the dissolved particles as “liberates” certain slip planes and makes possible the appearance of residual deformation.
A systematic study of the influence of various impurities on the mechanism of slip in metallic crystals may be carried out both by means of microscopic investigation of polished sections and with the aid of X-ray analysis.
It should provide the metallurgist with guiding indications as to the relation between the chemical composition of an alloy and its technical properties, and therefore, perhaps, also outline a certain theoretical path toward solving its practical problems. Here should lie the first boundary that, for the time being, separates the domains of crystallophysics and metallurgy.
The second boundary passes where questions of the strength of a metal are connected with the character of its microcrystalline structure. The elastic limit for a metal treated by a cold method, as a rule, always increases, but in such cases as rolling or drawing
wire, the elastic properties also depend on direction. Thus, the elasticity along the fibers of a rolled metal is different from that perpendicular to them. Knowledge of the final structure of the crystalline mass of a metal under one or another method of mechanical working can therefore provide indications of those manipulations that are capable of imparting to the product the required strength and resistance in any desired direction.
Crystal physics must here, as it were, help the metallurgist to construct a skeleton that reinforces the “working” directions in the metal.
The third task confronting the physics of metals is the creation of a detailed and exhaustive theory of the structure of metallic crystals, including an explanation of the mechanism of slip. This theory must provide a basis for calculating all the elastic properties of metallic crystals and, consequently, establish the concept of the theoretical strength of a metal. It is not impossible that this theoretical strength will prove different from the strength that a metal exhibits under ordinary conditions; this, in turn, may advance scientific and technical work toward finding new conditions that make it possible to strengthen metal, just as Joffe succeeded in “strengthening” a crystal of rock salt.
These are only the most probable and direct paths along which solid-state physics must approach the urgent problems of metallurgy. But a whole series of other problems as well, which modern technology continually poses to metallurgy, makes it urgently necessary to enlist the aid of precise methods of physical research. The production of alloys with particular magnetic properties, the manufacture of stainless steel, of low-melting and refractory metals, and so forth—all this domain, in which art, ingenuity, and chance still prevail, must be placed upon a firm and reliable theoretical foundation.