GRANULAR STRUCTURE OF SOLIDS

W. G. Bragg, London¹)

A cursory review of the research works published in the scientific journals of the present day shows that a very considerable number of them are devoted to objects which are too small to be examined in detail under a microscope, but which at the same time are too large to be conveniently studied by X-ray methods. We encounter such objects in all branches of research: in medicine, in technology, etc. The peculiarities of these magnitudes make the study of them a very interesting subject and at the same time an exceptionally difficult one. The solution of the question of these magnitudes is urgently necessary, and the insufficiency of our knowledge of them greatly retards the development of many branches of knowledge.

The microscope makes it possible to discover objects with dimensions down to several hundred angstroms in diameter, but it does not make it possible to discern the details of these objects. Besides the microscope, we also have other optical methods for detecting such objects. Thus, Langmuir has recently shown that it is possible to establish the polarization effect of films having a thickness not exceeding several tens of angstroms. However, this method too, which establishes the order of the corresponding magnitudes, does not make it possible to discern details.

X-ray methods, in the sense of the order of the magnitudes investigated, go too far. The wavelengths used are such that they make it possible to measure, with great accuracy, the mutual distances of atoms and molecules in a crystalline substance, but their field of view is too limited and does not make it possible to discern the details of larger structures. Thus there is a gap in the means of investigation, and it is remarkable that this gap systematically makes itself felt in a whole series of questions.

We encounter magnitudes of this order in particular in the field of metallurgy and metallography. Their exceptional importance became especially evident after we had obtained fairly detailed information about the atomic structure of metals and their alloys. X-ray methods give very detailed information about the details

¹) Nature, 140, 954, 1937, translation by N. V. Belov.

of the structure of crystals of iron and its alloys; however, this knowledge proves insufficient for predicting the properties of a steel specimen. As was emphasized by Smekal1, solids, in particular metals, possess properties that are completely determined by the crystalline structure. These properties are insensitive to the treatment of the steel in one or another period preceding the history of the specimen. A very large number of other properties prove to depend on the preceding history and can be varied within wide limits depending on the treatment. Such are the tensile strength of the metal, ductility, hardness, and also electrical and magnetic properties—that is, precisely all the qualities of a metallic specimen most important in practice. The microscope showed long ago that a metal is an aggregate of grains. The conditions under which this aggregate arises also determine those properties named above as dependent on the preceding history. The details of this dependence are at present very difficult to establish precisely because the corresponding objects fall within a range that has not yet permitted their direct observation.

Theoretical metallurgy long ago arrived at the conclusion that every specimen of a metal or metallic alloy is composed of small groupings of atoms and represents a combination of these groups, which may be called crystallites, since the arrangement of atoms within each of them is perfectly regular. The corresponding X-ray diffraction patterns are quite regular, and the lines of the powder diagram are just as perfectly clear and sharp. Thus, Gough and Wood, in their investigations of metal fatigue caused by the cyclic repetition (in some experiments up to several million times) of an applied stress, found that the visible grains of the metal were gradually destroyed and reached a certain limiting size, which was determined by the magnitude of the applied force. Rupture in some region occurred after the disintegration into separate crystallites had ended. This destruction did not consist in the separation of some atoms from others, i.e., it did not lead to the complete disintegration of the specimen, but to its division into the smallest crystals, the magnitudes of which were grouped more or less closely around some average. This conclusion was supported by the thicknesses of the lines of the corresponding X-ray patterns, with a certain definite limit reached upon destruction of the material. The existence of these mean values makes it possible to conclude that the sizes of the crystallites are somehow connected with numerical quantities characterizing the shape and sizes of the atoms of the metals themselves. As an analogy one may point to the formation of benzene rings of definite shape and definite dimensions from atoms

GRANULAR STRUCTURE OF SOLIDS

carbon, each of which is characterized by its own tetrahedrality.

The question of the very existence of these crystallites, of their nature and of their role has been studied very vigorously over the last several years, and at the present time we have a whole series of theories of the so-called mosaic structure of crystals. The first theories attempted to connect this mosaic structure with the so-called superstructure, which required the correct arrangement of crystallites even in the case of a pure metal. These theories, however, soon had to be abandoned, since they attempted to derive the secondary dimensions of the structure of metals from the primary atomic ones. Bürgher proposed that the granular structure of metals is a consequence of specific growth conditions, when different crystallization processes collide with one another and combine throughout the whole mass of the substance in the most peculiar manner. Such a structure, however, would lead exclusively to static formations, which is not in agreement with metallurgical experience. In particular, the well-known Taylor theory of the hardening of metals by means of appropriate treatment necessarily requires the existence of crystallites. The question remains unclear to this day, although it is extremely important, since, as has been indicated, almost all the most important properties of metals depend to a large extent precisely on the granular structure of the given specimen, and the corresponding grains—crystallites—are the main focus of research on the metallic state at the present time.

We encounter exactly the same state of affairs in the study of other materials as well. Thus, in April 1937, at the International Congress on the Testing of Materials held in London, it turned out that a very considerable part of the papers presented dealt precisely with this question of the granular structure of the most diverse substances. Thus, in the extensive field of fibrous materials, an individual fiber is entirely analogous to a grain of metal, and the central concern of research on fibrous minerals is now reduced to the study of these microfibers, or fibrils. In all colloidal questions, in exactly the same way, the essential matters are the properties and the conditions of origin of the corresponding grains. Analogously, in materials originating from living organisms, the focus of attention is the cell and its parts, and it should be noted that it is precisely with these elements of structure that the manifestation of life itself is connected. Finally, in the field of dielectrics and lubricating substances, their most important properties are likewise determined by groupings of atoms and molecules.

In recent years we have witnessed an entirely exceptional shift in the field of the application of one or another metal, in connection with the fact that the changes in the structure of solids occurring in them over time must be taken into account more acutely. The question of the so-called “creep” of materials is now one of the fundamental ones for the designer. Its great role is determined by two reasons. First, the development of machine technology has required much more

greater correspondence of some parts with others and smaller tolerances than had previously been possible. In particular, this applies to modern turbines and internal-combustion engines. With the precise fitting of parts that is required in these machines, a creep of the order of 1:1000 is already a serious obstacle to the operation of the machine. Secondly, one must take into account the fact that the use of high temperatures greatly intensifies the creep of the material. It seems beyond doubt that every material, with the exception of single crystals, is characterized by a slow but continuous change in its structure. At any given moment some of the molecules jump over those barriers which keep them in the hardened state and pass into the state corresponding to equilibrium. As a consequence, new crystallization centers arise, while the former ones spread farther and farther. Such jumping of atoms and molecules must, of course, be facilitated by external forces applied to samples of the metal. Figuratively speaking, one may say that each part of a solid body, over a more or less short interval of time, becomes liquid; in connection with this, the atoms of this region become capable of displacements, the range of which is determined by the stabilizing role of the neighboring grains.

The laws of the corresponding motions are extremely complex, and the information available, despite all its importance, is still extremely scanty. Bailey, who was a pioneer in these questions, established that the addition of 1% chromium to 0.5% molybdenum steel increases the initial resistance to creep only up to a certain definite temperature, above which the effect of the addition becomes the opposite. It is very probable that the introduction of chromium atoms leads to a certain mutual interlacing of the grains, and the latter are strengthened until their own structure is disturbed. Upon passing a certain temperature limit, when the structure of the grains themselves begins to change, this motion becomes, in accordance with the general rule, more facilitated in the case of the more complex composition of the alloy. Obviously, in this case the effect of chromium will be negative. Such an explanation, however natural it may be, may prove not to correspond to reality upon a detailed study of the question. In any case, it is clear that before us lies one of the most interesting questions, where physics and chemistry must meet.

A detailed study of cellulose fibers visible to the naked eye shows that they are composed of fibrils decreasing in size, which in turn consist of ellipsoidal units with dimensions from 1.5 to 1.1 μ. Each such unit, in turn, may be composed of several million cellulose chains. However, the details of this assembly remain unknown, just as do the properties of that sheath in which these millions of individual chains must be considered enclosed. Chemical analysis and X-ray examination have yielded a quite satisfactory model of the chain molecule of cellulose, as well as a certain

picture of other details of molecular structure. All the more sharply felt is the lack of information about larger groups, and also about the formation of fibrils, by whose properties, evidently, all the properties of fibrous materials are determined. If the corresponding fibril constitutes part of a living organism, then its change with time will obviously be its growth. But even a fibril that has already become part of some material probably possesses variability, which must have a substantial effect on the quality of the corresponding material.

Changes in grains or fibers may be both external and internal. The slow regrouping that accompanies recrystallization or devitrification obviously occurs at the expense of internal forces. But the quality of a material may also be strongly affected by surface changes caused by the reaction of the surface with surrounding atoms, for example by processes of corrosion or hydration.

Naturally, such surface changes play a more essential role the smaller the particles of the given substance are, which, incidentally, has long been known in colloid chemistry. This also includes, in particular, the extremely important question of how clay retains its water. X-ray analysis has made it possible to establish the detailed structure of individual crystals in clayey substances. The positions in this structure of individual atoms of oxygen, silicon, aluminum, magnesium, iron, and other constituent elements are known with very great accuracy. Apparently, however, all the known properties of clays are determined by the behavior of large flat aggregates of individual molecules of the clayey substance, having colloidal dimensions, i.e., precisely those dimensions that lie between the limits of visibility of the microscope and the limits of visibility of X-ray analysis.

In dielectrics, generally speaking, slow internal regroupings can be extremely accelerated by the electrical stresses to which the material is subjected. Electrical forces seem to seek out the weakest places for rupture, quite like the way in which a tensile force leads to the breaking of a chain at the weakest place in the structure. Therefore the corresponding changes in structure are extremely important. Of course, the designer’s ideal would be the “deacon’s stool,” constructed in such a way that in it every part is just as strong as every other, so that as a result, at the end of the stool’s service life, it becomes a heap of dust. Unfortunately, up to now this has not been possible to accomplish with any technical product, and however well balanced the design may be, the real structure may be destroyed as a result of continuous changes in the grains of its material.

It may be that the structure of gigantic protein molecules will suggest to us how to bridge the indicated gap in our means of investigation. It appears to be a very remarkable fact that the magnitudes of these molecules definitely fluctuate around certain averages, which in turn are in very simple relationships—

relations with one another. These molecules are not simple groups of atoms assembled according to the law of chance. Their definite formulas point to the existence of definite rules for the formation of these assemblages, which remain in force up to the attainment of a definite and unvarying final result. As may be concluded from the extensive experimental material, the addition of each further carbon atom is governed by strict geometrical laws, both with respect to distances and with respect to orientation. Rinch and other investigators have shown that long chains, composed of a regular alternation of two carbon atoms and one nitrogen atom, can combine, while observing the indicated regularities, into films enclosing definite volumes and having an external structure of linked hexagons; moreover, the dimensions of these films are limited to a certain set of definite values. It is very probable that in the present case we have an example of the way in which the groupings that interest us proceed from a few atoms up to the dimensions of grains, which constitute the central link of the problem that interests us. Some confirmation of the supposition that this is indeed the correct approach is provided by the unexpected strictness and definiteness of the rules governing the linking of these films in all those cases in which they can still be investigated by purely X-ray methods.

Knowledge of the structure of solid matter has now reached a very considerable degree of development, and the investigation has proceeded along lines that would have seemed unexpected to a researcher 1¼–2 decades ago. As has been indicated, the granular structure of matter now stands at the center of our attention, and we believe that it explains the most important properties of solid matter, not only from the standpoint of the application of solid matter in technology, but also in all manifestations of the structural activity of organisms. In all attempts to penetrate into the details of this structure there arises an extraordinarily large series of simultaneous scientific and technical problems, effecting in this field, as perhaps in no other, a close union of science and technology. It may be thought that these works will indeed lead to an exceptional development of our knowledge of the nature of the matter surrounding us.

1. An interesting exposition of Smekal’s theory and analogous theories is given in the last chapter of Juma-Rosery’s book Theory of Metals and Their Alloys, to be published shortly by ONTI. ↩