PHYSICS AND METALLURGY1

Walter Rosenhain, Teddington

Success in any specialized field of technology can be achieved most rapidly only when a harmonious connection has been established not only between science and technology in general, but also between individual disciplines that are close to one another. In particular, all of physics may be regarded as a single domain of knowledge, but our scientific and technical practice deals only with narrower divisions, and therefore runs the risk of failing to notice, or of overlooking, what lies outside that domain. Hence arise misunderstandings that hinder the general development of technology and science. This can happen especially easily when two different fields are simultaneously making rapid progress. We see such a sharp rise in the field of the newest physics, and we may demand of metallurgy an equally rapid development. This circumstance fully justifies the connection between physics and metallurgy—a close connection that is self-evident without lengthy discussion.

In the field of modern physics, the theory of the atom has developed especially rapidly. The speed and success of its development have given certain well-known physicists grounds to express the view that the “empirical” study of metals and alloys may be of very little significance, since, having studied atoms and their interactions, we can predict in advance

all the properties of any compound of atoms, and consequently the properties of individual metals or their alloys. We hope that this confidence in the rapid successes of theory will be justified in the near future. At present, however, we do not yet have the possibility of deriving, with sufficient accuracy, even the simplest properties of metals proceeding solely from atomic theory. On the contrary, as will be indicated below, these atomic theories of the structure of metals themselves rely on the fact that the results obtained with their aid by calculation more or less coincide with experimental results, often obtained with great difficulty. The exception is, perhaps, the determination of density, which in individual cases can be performed from calculation based on atomic weights and X-ray-measured parameters of crystals, and moreover with an accuracy far exceeding that of direct experimental measurement. However, this is only an application of new methods of measurement, and not a consequence of atomic theory.

The point of view of some physicists with respect to metallurgy is determined not only by the familiar overestimation of the future successes of theoretical physics, but also rests in part on familiarity with what modern practical metallurgy strives for and what it has already achieved. There is an opinion that our practical investigation of metals consists mainly in the fact that we mix and fuse all kinds of metals in all kinds of proportions and measure certain properties of them, important for practice, and moreover with quite insufficient accuracy. Such an idea is so caricatured that it is hard to believe that there exist physicists who can consider this picture to correspond to reality. It is possible that this is the reason why many physical measurements of metals and alloys are still encountered that completely leave aside the modern data on the study of metals. One need only look through the tables of “physical constants” of metals and alloys to see that the data presented in them very often differ greatly among themselves and from

in the majority of cases only because the state and properties of the substance under investigation had been established quite insufficiently. In exactly the same way one can find a whole series of works on questions of the variability of various physical properties of metals in which modern data concerning cold working, recrystallization, etc., are completely disregarded.

If we now examine more closely the connection between physics and metallurgy, it will turn out that, apart from the extremely important technical applications of metallurgy, the study of metals pursues two aims that are of very great importance for physicists. For, first of all, the study of metals provides physics with material for the construction of its great theories. This material is, on the one hand, purely material—the matter at issue is the preparation of metals: pure metals or single-crystal metals are needed by physicists in many delicate measurements. On the other hand, the physicist obtains precise data on the properties of metals and alloys, on the basis of which he can test the results of his theoretical constructions. Only a specialist in the investigation of metals, who is sufficiently well acquainted with the complex conditions governing the dependence of the physical properties of metallic substances on their exact composition and preliminary treatment, can successfully undertake such measurements. In any case, any physicist who wishes to engage in precise measurements on such substances must take upon himself the labor of becoming acquainted with this branch, or, at the very least, work in collaboration with metallurgical engineers. Owing to the absence of such collaboration, many results obtained in this area of research have proved almost useless.

Finally, one may point to yet another circumstance in which the study of metals renders physics no lesser service and may be useful in the future as well. If today modern physics is often regarded as mathematics and philosophy, nevertheless, in essence, physics has been and remains an experimental science, and its development, in the final analysis,

depends on the development of successes and skill in experiment. This, in turn, is to a significant degree conditioned by the achievements of technology and, especially, of metal technology. In most cases new apparatus is produced from new metallic substances which metallurgy has placed at the disposal of technicians and physicists. If, in the present state of affairs, experimental physics and technology were to refuse, in the construction of instruments and devices, to make use of the achievements of metallurgy, this would mean an enormous step backward. One need only recall the low coefficient of thermal expansion of tungsten or of nickel steel, of cobalt-manganese steel, etc. From this point of view, metallography may be considered a servant of physics, and it performs its service well. One need only ensure that its significance not remain underestimated.

It would not be difficult to indicate a whole further series of questions where physics and metallography come into contact, but lack of time compels us to keep within narrow bounds and to the more important questions. It would be very appropriate to note here that, although all of metallography, insofar as it considers the question of the composition of alloys, borders on chemistry and, in particular, on physical chemistry, nevertheless, on the whole, it may be considered a branch of physics dealing with the physics of metals. Therefore it would be pointless to expatiate further on how much metallography and the extraction of metals depend on physics. It is equally self-evident how valuable the cooperation of physicists is to the metallographer. The metallographer, of course, cannot claim that his narrow, limited field of activity can have the same significance as all of physics. But the broad stream of knowledge and research is fed from many sources, and among them metallography can occupy by no means the last place.

Looking back over all that has been set forth above, we may express some surprise at the fact that one of the newest achievements of the science of metals, representing enormous interest for pure physics, adjoins chem-

physical section of metallurgy. This is the question of obtaining metals in the state of the highest purity in the chemical sense. In recent years it has been more and more confirmed that, from the properties of metals usually regarded as “pure”—metals which nevertheless contain several hundredths of a percent of admixtures of various substances—one cannot with certainty draw conclusions about the properties of truly pure substances. This was shown, in particular, by the example of very pure zinc, which was obtained by researchers of the American Zinc Company in New Jersey (Pierce and others). In recent years, in the laboratory under my direction, it has been possible to obtain iron, manganese, and chromium in a very pure state, and moreover in quantities that make it possible to carry out a detailed study of their properties. For very pure iron we found that its transformation points undergo an entirely unexpected displacement, which may possibly be connected with the idea of the American Jensen concerning the possible absence of allotropic transformations in perfectly pure iron. As an example of the significance of obtaining pure metals from the point of view of physics, the case of chromium is especially interesting. Studying the action of very strong magnetic fields (about 1 million gauss), Kapitza in Cambridge recently investigated a whole series of the purest metals. It was found that the behavior of metals, in particular the change in their electrical resistance in a strong magnetic field, constitutes a very sensitive method for determining the purity of metallic specimens. To our great joy it turned out that not only did our specimen of chromium far surpass in purity all the other specimens he had, but that, thanks to the possibility of conducting an experiment with such a pure metal, Kapitza was able to subject his theoretical considerations to a severe test.

To avoid undue emphasis on my point of view, I shall now turn to questions where we are dealing with a closer interaction of physics and metallurgy, in particular to the very important question of the “internal struc-

of metals and alloys.” Here one should recall that metallurgists already in 1898–99 came to the conclusion that metals consist of aggregates of crystals, and that the mechanism of slip, to which metals owe their ability to be worked, was also discovered in 1889. Our knowledge of the crystalline structure of metals has become extraordinarily deeper in recent decades, thanks to the application of X-ray analysis methods. The production of large single crystals contributed greatly to this; in these questions there was indeed mutual cooperation between physicists and metallurgists. It should be emphasized that the results of new and powerful methods of investigation have significantly broadened and deepened the results obtained by older and more difficult methods, in almost all cases. New investigations open up the possibility of new points of view on material already at hand, and I value this possibility so highly that I permit myself here to touch upon these questions in somewhat greater detail.

The study of the crystal lattices of metals and alloys pursued chiefly the aim of establishing the structure of the various kinds of crystals that constitute the phases of series of alloys. Investigations of this kind have yielded very much for the study of certain series of alloys. But they apparently gave rise to the thought that X-ray investigations by themselves are quite sufficient for studying the structure of a system. Against this I could object that the presence of very small amounts of a second and third phase on an X-ray photograph may be only very slightly noticeable, or not noticeable at all. The determination of solubility limits, i.e., of the formation of mixed crystals with the largest lattice parameter, also seems somewhat bold, since in doing so one must assume that the expansion and contraction of the lattice, even near the solubility limit, remains proportional to the concentration; and this, in my view, is rather unlikely. These remarks, of course, are not intended to diminish the significance of X-ray methods of investigation, but only point to the necessity of their simultaneous application, together with new

...by new research methods, old ones, tested many times.

An even more important application than that which radiographic methods of investigation find and may still find in the study of alloys is obtained when considering the fundamental problem of metallography, which at the same time is one of the most important problems of physics: the question of the exact correspondence between the structure of a metal and an alloy and their physical properties. From this problem, which embraces all questions—strength, capacity for working, hardening during treatment, etc.—I shall select only certain questions and theories that may be regarded as general problems for the physics of metallography. Among them, the question of the internal structure of “mixed crystals” and the related question of “intermetallic compounds” may be especially interesting.

As early as 1922/23 I pointed out that in mixed crystals the “dissolved” atoms occupy the places of individual atoms of the basic substance, and somewhat later this assumption was confirmed experimentally by Owen and Preston on a whole series of alloys forming mixed crystals. Then several other investigators, among them Bain in America, came to the same conclusion and obtained new evidence in its favor. On the other hand, Westgren and his collaborators showed that in mixed crystals of iron and carbon the replacement of iron atoms by carbon atoms is hardly possible. This, however, represents a special case which, although it is of very great importance, may, in a general consideration, be temporarily singled out and left aside.

In those cases where mixed crystals are formed by substitution, this substitution cannot take place without certain changes. And indeed, as I pointed out already in 1923, one of the principal changes is a distortion of the crystal lattice, which may occur because the force field of the foreign atom is not exactly equal to the field of an atom of the basic substance. But with the emergence of

of these lattice distortions (Figs. 1a, 1b, and 2) we can readily explain many features typical of mixed crystals, for example, the lowering of the melting temperature, the temperature interval between the beginning and end of melting or solidification, the slow increase in hardness and tensile strength in a series of mixed crystals with gradually increasing concentration, and that increased hardness with which the onset of the transition to a mixed crystal is associated. Even the difficult question of electrical conductivity finds some explanation from this point of view. However

Fig. 1a and 1b. Schematic representation of a “normal” and a “distorted” lattice of the simplest form. The “distortion” is represented here as an expansion of the lattice at the center caused by a foreign atom.

we cannot go into these questions in greater detail, since that would take us too far afield, and I shall confine myself here to only two points.

If physicists are now no longer satisfied with the model of the atom proposed by Rutherford and Bohr, and, following de Broglie and Schrödinger, make use of wave mechanics, which can be expressed only in mathematical formulas and almost does not permit a visual physical interpretation, nevertheless the representation of the atom as a certain entity consisting of a positive nucleus surrounded by electrons can still be retained as a first approximation. If, for the sake of clarity, we speak of electrons or electronic orbits, then we may assume that in a disturbed crystal-

in the lattice there exists a certain state of equilibrium which provides, for each atom, at least statistically, a symmetrical field. The electronic orbits must also be imagined as being in a state of stable symmetry.

The coloration of a substance depends to a certain degree on the electrons and their orbits, because these determine which light waves are absorbed and which will be reflected. In a symmetrical, undisturbed state, each atom gives normal reflection and absorption of rays. In the majority of metals only very weak selective absorption is observed, so that they appear “white” or “colorless.” In individual cases (copper and gold) a vivid coloration appears. What, then, must happen to the coloration of a metal in an alloy or, at first, in mixed crystals? As has already been said above, a distortion of the lattice must occur, accompanied by the asymmetric insertion of a certain number of atoms and, at the same time, by a small but substantial change in the atom itself, i.e., in the electronic orbits, and consequently also a change in coloration. This change, apparently, always proceeds in the direction of decolorization, which also explains why alloys of “white” metals are never colored. However, decolorization upon alloying is explained not only by the dilution of colored atoms. The addition of 10 or at least 15% Ni to copper decolorizes the latter almost completely, whereas 40% Zn is still insufficient for this. If we turn to the idea of the lattice and the deformation of atoms, then all these phenomena become intelligible. Let us compare three metals—zinc, aluminum, and tin—in their action on the coloration of copper. We shall find here an approximate proportionality between the solubility limit (the limit of mix-

Fig. 2. Schematic representation of lattice distortion by introducing a foreign atom (as in Fig. 1b), but the distortion here consists of contraction of the lattice.

tion of crystals) of α-mixed crystals and the capacity for decolorization. The limit of mixing of crystals depends for the most part on the degree of distortion caused by each introduced atom of the dissolved metal, and it is this same distortion, according to the explanation proposed here, that causes the change in color. All three of the metals named have the common property of expanding the copper lattice. By contrast, metals of the nickel type, which contract the lattice and raise the melting point, apparently produce comparatively strong decolorization; however, here too there is a dependence on the degree of lattice disturbance, as is shown by the comparison of nickel with cobalt.

The theory of distortion presented here gives an explanation of yet another very interesting phenomenon of coloration observed in alloys. If, in a series of alloys, the limit of formation of mixed crystals is reached—for the given kind of mixed crystals—then, from the point of view of the theory of distortion, this means that the highest degree of lattice distortion has been reached, or that, at the very least, some other arrangement of atoms is possible which has a lower potential than the most strongly altered lattice of the mixed crystals. In this case a new phase is formed and, except in those cases when a chemical compound with an especially low potential is formed, the formation of the new phase must be imagined as follows: the base metal receives a new lattice form. This form is such that, if the lattice were built only of atoms of the base metal, it would have a higher potential than the lattice of the normal form. In reality, however, owing to the presence of a comparatively large number of foreign atoms, and because the new form of arrangement of the foreign atoms is better adapted to these inclusions, this lattice gives a lower potential. Consequently, in the new phase at first—that is, at the concentration at which it is initially formed—the disturbance of the lattice is less than in the saturated mixed crystals of the former phase.

If such considerations are correct, then we must

one should expect that, in a number of alloys, upon passing from saturated mixed crystals to the neighboring phase, a reversal should be observed in the change of coloration that appears when the concentration of mixed crystals is increased. In fact, such a reversal of color is clearly visible in alloys of copper with zinc. With an increase in zinc content, the color of copper passes through a light golden shade to a greenish-yellow one, which appears when saturation by \(\alpha\)-mixed crystals is reached. With the onset of the \(\beta\)-phase the color becomes noticeably redder, i.e. the greenish-yellow color becomes golden, in order, with a further increase in zinc concentration, again to become more yellow. Only when the \(\gamma\)-phase appears does the alloy become quite pale.

In order to provide proof of the correctness of this explanation of the phenomenon described—one that is, to the highest degree, remarkable—it would be necessary to undertake precise measurement of the color of alloys, and not only of alloys of copper and zinc, but also of other, more or less strongly colored metals. This, however, is an exceedingly difficult task, because it is necessary here to work with surfaces completely free of oxides, and with such surfaces as have no mechanical damage whatsoever, i.e. to make them suitable for optical measurements. Here there arises a problem whose solution depends entirely on the joint work of physicists and metallurgists.

The view expressed above, that the second phase in a sequence of alloys is simply an allotropic form of the base metal—a form whose purpose it is “more conveniently” to accommodate a larger number of foreign atoms—brings us to the most difficult question of the true nature of intermediate phases and to the question of the so-called intermetallic compounds.

In certain cases the question is resolved simply by determining the lattice parameters, because where there are crystals in which the distances between atoms are considerably smaller than the normal atomic radius, it is impossible not to conclude that a chemical compound is present.

...i.e., a closer interaction of atoms than in an ordinary lattice, which I shall call a “cohesion lattice.”

In such cases we have yet another criterion: such phases do not form mixed crystals at all with their components, or form very few of them. This result becomes more and more evident from year to year, as the solubility limit is determined ever more accurately. If in these compounds the interrelations of the atoms are in fact different, closer than in the cohesion lattice, then we must expect that here we can no longer replace such a tightly bound atom by an atom of another component. The formation of mixed crystals in binary systems would therefore be completely impossible. However, it must be remembered that this conclusion, strictly speaking, can be applied only to single crystals. In aggregates of crystals there is always the possibility of the presence of a small percentage of another component, since the possibility is not excluded that the distortion of the lattice, which always begins near the boundaries of individual crystallites, presents a convenient case for the introduction of foreign atoms.

On the other hand, one may cite a whole series of firmly established cases in which the formation of mixed crystals is associated with a distinctly expressed compound. These cases include, in particular, the substances called γ-phases, which have been studied by various investigators, especially by Westgren and his collaborators and by Bernal (the Davy-Faraday Laboratory in London). In these cases we encounter a fact of extraordinary structural complexity, since in individual cases the structural unit of the lattice consists of more than 50 atoms. Consequently, the atomic interactions of both components in such cases are by no means as simple as might be expected according to the usual laws of chemical compounds. It may be asserted that in alloys of copper with tin, instead of 4 atoms of copper per one atom of tin, there are 3 atoms of copper per 8 atoms of tin. The question must be raised whether here we are dealing with a special type of chemical compound, with

something intermediate between a “normal” compound and a mixed crystal, or else other explanations must be sought for this fact. In what follows I can point to one explanation of this phenomenon; I do not yet insist on its correctness, but it deserves attention because it considers the question from a new point of view and therefore may lead to the further development of ideas and experiments.

My collaborator Mary Gayler (M. Gayler) recently obtained, by my method—as has already been mentioned elsewhere—metallic manganese in a chemically very pure form. The metal prepared in this way served not only for the study of pure alloys of iron with manganese, but also for the exact determination of the lattice of these elements in two allotropic modifications. Both modifications, α- and β-manganese, have a rather complex lattice structure. The lattice structure of α-manganese was determined by Bradley in Manchester and later still more accurately by my collaborator Preston. In Figs. 3 and 4 models of the lattices of α- and β-manganese are presented. I draw particular attention to the obvious fact that these lattices, in the number of atoms in their structural unit and in the arrangement of the atoms within them, are very similar to the above-mentioned γ-phase. Therefore, with regard to α-manganese the question arises: how does it come about that the atoms of this metal are not only arranged in a very complex manner, but that their very arrangement is extremely similar to the structure of alloys of copper with tin? The solution of this question is much more difficult for the element manganese than for copper-tin compounds, because in the latter case we may take into account the difference between the atoms and their mutual incompatibility. In the case of manganese we cannot explain its structure by assuming a special “shape” of the atom (for example, ellipsoidal). One might suppose that in crystals of α-manganese there are two sharply different kinds of atoms, but such an assumption is not easy to reconcile with the clearly expressed transformation point of manganese.

The study of models of the manganese lattices leads to the ide—

... which suggests a certain explanation of all these questions. The model gives the impression as though, in this structure, there were sharply bounded atomic groups which, by means of individual atoms, would be linked into a whole filled with cubic cells. Such a structure can be explained simply, without invoking atoms of another kind for the explanation, by assuming that manganese—and, in the same sense, alloys of copper with tin in the solid state—forms a rather strongly associated molecule. This assumption contains nothing especially improbable.

Fig. 3. Model of the lattice cell of α-manganese (after Preston).

Fig. 4. Model of the lattice cell of β-manganese (after Preston).

In ordinary space- or face-centered lattices, such as we have in copper, iron, etc., it is impossible to distinguish a “molecule.” Nevertheless, we must still think that these metals in the liquid state consist of associated groups of atoms, i.e., of molecules. Measurements of surface tension confirm this consideration. If, then, these molecules possess the property that they can, without any disturbance, fit—and moreover fit closely—into a space lattice, then this is what occurs upon solidification without any complica-

... and the process of crystallization reduces to a process of association, on a large scale. The same may also occur with the molecules of compounds, under the same basic condition, namely that the already existing molecules can readily fit into a dense lattice. It is evident, however, that there are very few forms that could in this way be spatially packed, and here the question arises—what will happen in the crystallization of a compound consisting of metal molecules, if the shape of the molecules and their dimensions are such that their packing into a regular dense lattice is impossible? Here two possibilities may present themselves; probably both are in fact realized. One of the possibilities is that, in the formation of the crystal, the molecules disintegrate and the atoms simply form the lattice anew. In such cases we could not, generally speaking, by any means—except perhaps the heat of crystallization—detect the process described. Such cases can be observed only when the bonds in the molecules are not very strong, so that in the formation of the lattice a lower potential is obtained. Where the compound is strong, the second possibility appears. It consists in this: ready-made molecules, with individual dissociated atoms, form a complex entity in which the molecules, with the aid of “free” atoms, enter into a lattice structure. This lattice is arranged in such a way that the “free” atoms completely fill the voids that remain when only the molecules are packed. The entire structure as a whole approaches a lattice with the densest packing, although with very considerable distortions of it. In this way I explain the complex structure of manganese and its striking similarity to the structure of copper-tin and many other compounds.

I should next like to draw your attention to two other circumstances. First, such an explanation makes the formation of mixed crystals in compounds of this kind quite understandable. In these, as in other compounds, it is not the atoms that are tightly bound in the molecule that are replaced, but precisely the “free” ones, which serve as the bond. Hence it may

be determined and reconciled with experimental data on the upper limit of mixing. Unfortunately, precise quantitative relations are lacking here. In any case, in such a lattice one may expect a higher solubility of both components than in a regular, densely packed structure of simple compounds. The same idea is also applicable to explaining the apparent deviation of compounds of this kind from the law of multiple proportions.

Finally, to all this one may add that the mode of crystal formation described here is not something unusual, because in the field of inorganic crystals we encounter a large number of such cases, for the crystallization of which the presence of water is required. The so-called water of crystallization, in this conception, serves in the crystal for the same purpose—to make possible the packing into a dense lattice of molecules of complex or inconvenient shape. In this sense the atoms referred to above as “free” may be called “metal of crystallization,” in exact correspondence with “water of crystallization,” as it occurs, for example, in copper sulfate. In both cases there had to be an unbound liquid medium as a factor assisting the formation of a lattice with the lowest possible potential. If, by delving into these questions, which seem to me especially important and interesting, I have aroused the suspicion that I have strayed too far from the bounds of the question of physics and metallurgy, then at least by this very fact I have emphasized the circumstance that only through the closest consideration of such questions is a deep mutual penetration of physics and metallurgy possible.

The considerations developed above concerning the internal structure of various kinds of crystals lead to the conclusion that the most important problems of metallurgy are at the same time the most profound questions of physics. Therefore both of them—the physicist and the metallurgist—must seek the solution of the problem jointly, if they wish to obtain it quickly and with the greatest reliability.

1. A speech delivered at the congress of the German Society for Metallurgy in Düsseldorf on September 7, 1929; printed in Zeitschr. f. Metallkunde, 22, 74, 1930. W. Rosenhain—director of the English “Institute of Metals.” Ed. ↩