STRUCTURE OF ORGANIC CRYSTALS

Sir W. H. Bragg, London1

I need not remind you that an organic molecule is a compound chiefly of carbon, oxygen, and hydrogen atoms, only in rare cases with the inclusion of atoms of some other kind; nor need I say also that the carbon atom plays the primary role in the structure of the organic molecule. Quantitatively, carbon constitutes an insignificant component part of the Earth. Half of the part of our planet known to us consists of oxygen, and a quarter of silicon; aluminium makes up a considerable part of the remaining quarter. Carbon, however, constitutes only a fraction of a percent of the whole Earth. Yet if we consider organic life on Earth, carbon proves to be the most important of all elements; it is the chief constituent of living nature. As to the structure of carbon, we know that it has a nucleus weighing 12 times as much as the nucleus of a hydrogen atom, and that the number of atoms contained in one gram by weight is expressed by the figure \(2 \times 10^{23}\). We know further that the carbon nucleus has a positive charge of such magnitude that 6 electrons are required in order to neutralize the charge of the nucleus by the negative charges associated with it. We know also that 2 of these electrons are very firmly bound to the nucleus and are probably situated very close to it; the other 4 electrons are held more loosely. These latter are often absent in our

terrestrial conditions. Bare nuclei, deprived of all electrons, can be found only in such places as the stars, where the temperature is immeasurably higher than any terrestrial temperature.

Of course, with such meager information one cannot go far in explaining the multifaceted role of the carbon atom. We all know well what work has been done by chemists in the field of organic chemistry during the past century. We look with astonishment at the science they have created; we are struck by the breadth and richness of the field of their work and by the dazzling character of the discoveries they have made. Yet here so much still needs explanation, and there is so little on which this explanation can be built. There is, of course, a certain connection between the peculiarities of the carbon atom, of which I have already spoken, and the role that this atom plays in the properties of the molecule. If one bears in mind the known tendency of carbon to bind four other atoms and never more, then the four most loosely bound electrons must have some relation to this tetravalence of carbon. Beyond this, little more can be said about any connection between the properties of the atom and certain known details of its structure. Chemists have prepared hundreds of thousands of different organic substances in which carbon is the principal element; the list of these compounds increases by several thousand a year. Some of them, in their significance, are of primary importance for living nature; most others are of accidental origin. It is difficult to imagine how such a large number of bodies can exist, each of which decomposes only into carbon and one or two other elements, and yet differs so sharply from other such bodies both in its properties and in its role in nature! Is it not possible to see here an analogy with the possibility of forming many words, having different meanings, from a small number of letters, or many melodies from a few notes? Or, perhaps, the carbon atom itself possesses certain other peculiarities—

...properties, leading to the formation of compounds, than those that we formerly ascribed to its structure? What can we say concerning the fact that, if we take a certain number of carbon atoms and a certain number of any other atoms, we shall have many ways by which the atoms can be grouped together, each compound possessing its own particular properties? The chemist can tell us much about the circumstances under which a molecule can be made and under which it cannot. Nevertheless, we are still very far from understanding the details of the picture of molecules encountering and reacting with one another, and also from having an idea of the geometrical conditions of encounter. We do not even know with sufficient accuracy the dimensions and details of the structure of molecules, except in a few cases; still less do we know about the course of reactions.

The chemist, as we know, attaches enormous importance to the geometry of molecular structure and believes that the properties of a molecule can vary within wide limits if its atoms are rearranged in space; this will be so even when the number of atoms remains unchanged. There exist, for example, three “pentanes,” which are expressed by the formula \(C_5H_{12}\) and which differ from one another in structure and, consequently, also in their properties.

Such information about the structure of molecules, obtained by means of chemical methods, is usually expressed by very convenient formulas. Let us take, for example, the molecule of dibenzyl. It is a compound of 14 carbon and 14 hydrogen atoms. When it is not required to know the arrangement of atoms in the molecule, one writes the simple formula \(C_{14}H_{14}\). But if one wishes, by means of a formula, to express also the structure of the molecule, then one writes it thus: \(C_6H_5 \cdot CH_2 \cdot CH_2 \cdot C_6H_5\), or, in more detailed form:

\[ \begin{array}{cccccccccccccc} & & H & & H & & H & H & & & H & & H & \\ & & \backslash & & / & & | & | & & / & & \backslash & & \\ H & - & C & & C & - & C & - & C & - & C & & C & - H \\ & & / & \backslash & & & | & | & & \backslash & & / & & \\ & C & & C & - & C & & C & - & C & & C & & \\ & / & & \backslash & & & | & | & & / & & \backslash & & \\ H & & & H & & & H & H & H & & & H & & \end{array} \]

Each of these two modes of expression means that two benzene nuclei, or carbon hexagons, are joined together by means of a short chain of two carbon atoms, the hydrogen atoms being attached at different positions in the manner indicated.

However, this formula tells us nothing about the actual dimensions of the whole molecule and of its individual parts. There are 28 atoms in the molecule. If the center of each atom could be regarded as a sufficient indication of the position of the atom in space, then, in order to determine the shape of the molecule and its position with respect to the coordinate axes, it would be necessary to know 84 coordinates. To determine only a single shape, a smaller number of coordinates would be required, since the general orientation of the molecule and its position with respect to the aforementioned axes would be immaterial. Even here, however, we would have a number of coordinates equal to 78. All this would be so if we had not altogether reckoned with the possibility that each atom may have a form which must be taken into account. It is true that the scheme given above is a very convenient expression of known facts and, moreover, even indicates how their explanation may depend on the structure. Thus, for example, it correctly shows that some of the carbon atoms belonging to the molecule can with equal ease be deprived of their hydrogen atoms and receive in place of the latter other atoms, or groups of atoms; or, for example, that some of the carbon atoms differ from one another in this respect; or, finally, that where such replacement of hydrogen atoms has occurred, it will be more difficult to apply the same replacement to neighboring atoms, since spatial conditions hinder this. It is obvious, however, that all this represents an extremely limited range of information concerning the properties of the molecule, yielding in the aggregate something like its representation on a diagram. We must know all the details of the structure in order that we may better understand the reactions of molecules and, as far as possible, be able to control them. Ultimately we may hope that we shall be able to depict the plan and the relative dispo-

THE STRUCTURE OF ORGANIC CRYSTALS

the arrangement of the parts of a molecule, just as we draw the plan of a house, showing its horizontal and vertical projection. Finally, we must be able to represent the interrelations of the various parts of the molecule, and not only that, but also the properties of each separate part, thus explaining how they depend on the composition and arrangement of the whole system. It is easy to see how far, after all, we have advanced in this respect. What is there in the formula of dibenzyl—if we take this simple example—that expresses the fact that this substance melts at 52°C? And yet this is only one among the multitude of its properties!

It may be said that the aim of physics and chemistry is to explain, as far as possible, the properties of substances by using for this purpose the properties of the atoms of which these substances are composed. There exist 92 kinds of atoms and an infinite number of kinds of substances. The importance of the molecule lies in the fact that it stands midway between the atom and the substance. A small group of atoms—remarkably small, generally speaking!—is joined together into a separate unit, which may undergo many changes in conditions without itself changing. When dibenzyl melts, its molecules remain undamaged; between them only those bonds are broken which firmly held them together, while those are preserved which prevent the complete disintegration of the group. Each molecule, during so strong a change of conditions, preserves its properties, its composition, and, very probably, also the principal characteristic features of its form. If a molecule is less constant, then determining its structure is not so important and is of no great interest. On the Sun, where molecules do not exist at all, there can be no question of any great variety of animate and inanimate forms, such as exists on Earth.

The organic molecule is, in this respect, especially independent. The group of atoms contained in it is closely bound together, but the strong bonds that would determine its cohesion with other molecules, even of the same substance, do not exist here. Inorga-

A chemical molecule presents the complete opposite, for it is often bound to neighboring molecules so strongly that it loses its individuality, as, for example, in the case of quartz. In those cases where this occurs, a considerable temperature is required in order to break such a solid body down into molecules; quartz does not melt in the flame of a blowpipe. On the other hand, the melting points of organic substances are usually very low, and many of them at ordinary temperatures are in the liquid state. We shall now see what features of the structure of an organic molecule account for this peculiarity of it.

Molecules can exist as independent individuals in the state of vapor, or gas; a certain number of such individuals always exists also in the presence of a more condensed liquid phase. Their number is noticeable even in the case of some solids: for example, individual molecules of naphthalene detach themselves from the solid mass and, under suitable conditions, reunite with it again. We do not have a large amount of data for determining the form of a molecule when it moves independently and freely in space; a little information can be obtained from the determination of the viscosity of vapor, and then only in a very limited number of cases; some information can be obtained with the aid of optical methods, but the explanation of optical observations presents great difficulties. When molecules are joined together, as, for example, in the case of a liquid, by means of bonds that are easily formed and destroyed and at the same time are never all released at once, their action on one another, or on those molecules which are bound to them, can evidently be very varied. Such actions and counteractions are precisely the chief object of study for the chemist, and his observations up to the very latest time have been the chief source of his knowledge.

When molecules are sufficiently deprived of their usual motion, which is known to us as thermal motion, they are held motionless by their mutual bonds.

together and constitute a solid body. In this case, molecules of one and the same kind are most firmly bound to one another when they are grouped together in a special regular lattice characteristic of the given molecule. There is only one definite way in which the molecules can be satisfactorily arranged with respect to one another, so that this arrangement could be compared with a puzzle. However, the comparison with a puzzle is inadequate, for in it there are no repeating elements of the lattice, whereas the lattice is precisely the most distinctive feature of an aggregate of molecules of a given kind. There exists a certain element of the lattice, which consists of a small number of molecules and which is repeated in all directions in space; and this perfectly exact repetition is the cause of that regular form which we call crystalline. When a substance crystallizes from a solution, or solidifies from the molten state, or assumes a solid form through gradual growth from its vapor, the molecules of the substance tend to arrange themselves one beside another in perfect order. One after another they take their places and build up a plane lattice. We can imagine that free molecules, being in disordered motion, continuously fall upon the already formed surface of the crystal, as a result of which each of them enters the sphere of action of free bonds and is held by the crystal. Very often, however—and perhaps in the majority of cases—this retention of new molecules proves temporary, for by no means all of them fall into a position corresponding to their greatest stability. When they are held in a perfect manner, the crystal grows.

As I have already said, the number of molecules in an element of the lattice is generally very small, especially in the case of organic molecules. Usually there are either two or four of them, although three is also not infrequent; six and eight occur much more rarely. It is curious, incidentally, that the repetition of so small a number of these complex molecules must form a lattice. Indeed, one must imagine—

to see that they are particles too awkward for them to be fitted well to one another, so that several of them are required in order to obtain a compact element of the lattice.

When a molecule is immured somewhere in the middle of a crystal, it is, of course, outside the sphere of external influences, so that one might think that its shape and structure do not play a great role. This, however, is not so. A solid body possesses strength, viscosity, optical activity, and many other properties; all these properties must depend entirely on the properties of the molecule itself. Of course, one should not suppose that the molecules of which the crystal is built possess exactly the same peculiarities as are characteristic, in part, of the free molecules of a liquid or of the completely free molecules of a gas. Nevertheless, as the method of X-ray analysis, of which I shall speak here, shows, the difference in the properties of molecules found in the three phases is not especially great. This is an exceedingly important fact, and it would be a great pity if, while using an exact and definite method of analysis with the aid of X-rays, we could not obtain this valuable information. Consequently, this new method of analysis is of great significance not only because it can give us indications as to the structure of the solid body, but also because we see in it an auxiliary means for the study of liquids and gases.

But perhaps the most important and, of course, most highly interesting conditions in which a molecule can find itself are those corresponding to the boundary layers between the solid and liquid phases, between the solid and gaseous phases, and between the liquid and gaseous phases. In the final analysis, it is precisely on such surfaces that the most important processes take place. Reactions on the surfaces of solid bodies play an exceedingly large role in nature. Every student of biology is well acquainted with them. In recent years we have acquired knowledge indicating the necessity of studying these surface actions, and in connection with this a large branch of chemical science has developed—colloid chemistry. It is concerned with the study of

chiefly what is called the disperse phase, or, in other words, conditions under which one substance is distributed in another in a state of extreme subdivision. In this case the magnitude of the surface that separates one substance from the other is, of course, very large, so that surface actions are especially intense.

It is obvious that the action of a molecule belonging to the surface layer of a solid must depend entirely on what part of its surface is in contact with the surrounding space. The molecules on the surface of a crystal are arranged in a definite order, and what one of them does, its companions must do as well. Thus some entire face of a crystal must possess definite characteristic properties. Another face will already have different properties, and we shall have something like the picture presented to us when observing a group of soldiers on parade, so that this picture will depend on the point from which the observation is made. The bonds between molecules lying in a plane parallel to some face and molecules situated in the adjacent layer, parallel to that same face, must be comparatively weak, since the crystal easily splits along such a layer or, as it is said, along a cleavage plane. The weakness of these bonds may also lead to one part of the crystal sliding over another, so that in this case we are dealing with planes of slip. Cleavage planes can very often be found in organic crystals; we shall speak of the reasons when considering their structure. Slip planes are especially noticeable in metals. The deformation of metals under the influence of a force is chiefly the result of slip along various planes; this phenomenon has recently been studied with particular care in metallurgy.

Thus, in solids, liquids, and gases, besides the composition of the molecule, its form also plays a large role. This was known earlier as well, but modern physics and chemistry have found an especially firm basis for this assertion. Further, there is no doubt that the forms of molecules in the three phases are ...

at any rate very close to one another. But if all this is so, then we obtain a very broad justification for the method by means of which we carry out a thorough investigation of the form of the molecule in the crystal. This investigation has now been made possible thanks to the special application of X-rays.

I cannot now consider the complete theory and the details of the new methods, for this would take much time and would demand great concentration of attention. I shall confine myself only to the most general explanation of the method, after which I shall immediately pass on to some of the results that have so far been obtained.

My purpose is to give you an idea of the manner in which X-ray analysis supplements the knowledge of molecular structure obtained by the older chemical methods. First of all I wish to draw your attention to the conditions under which the application of the new method is possible.

In X-rays we have radiation which differs from light only quantitatively, but not in its nature. The wavelengths of the former are 1,000–10,000 times shorter than the wavelengths of light rays. We are now able to obtain beams of rays which may constitute a mixture of rays of different wavelengths, or may consist solely of a single wavelength. Our technique in this respect is very perfect.

A crystal, as we have already seen, is a system of molecules arranged in the form of a certain lattice. The element of this lattice is repeated with complete exactness in all directions.

We know, furthermore, that the wavelength of X-rays is comparable with the intervals between the elements of the crystal. To be more precise, I shall give figures. The wavelength of the X-rays usually used in analysis ranges from \( \tfrac{1}{2} \) of an Ångström unit to \( 1\tfrac{1}{2} \) such units. The distance from some point in an element of the crystal lattice to the same point in a neighboring element is approximately from 2–3 to 70 or 80 Å. Of course,

in some one crystal these distances in different directions must be different.

Under the existence of such-and-such conditions we may expect to discover the so-called diffraction. This is the very same effect with which we are all familiar in the visible region of ether waves. Light waves, in their length, are of the order of 0.001 mm; the longest of them are somewhat less than this value, while the shortest are approximately half the length of the longest. In nature there are very often cases of such a structure in which a certain regular repetition is, in magnitude, of just the same order as the wavelength of light; let us point, for example, to the regular sequence of bands on mother-of-pearl, or to the finest scales on the wings of butterflies or on the feathers of birds. In all such cases the objects appear to us either colored or painted with stripes or ribbons. Further, we see colored rings or bands when we look at a bright luminous point through a thin fabric. To these same phenomena should also be assigned the rings around the moon, observed when vapor is present in the air. In these cases the regularity consists in the equality of the diameters of the fibers, of the empty intervals in the fabric, and of the diameters of the particles of water.

One may say briefly: whenever periodic repetitions exist both in the radiation and in the substance through which the radiation passes, and both periodicities are comparable in their dimensions (more precisely, the periodic repetition in the substance must be the larger of the two), then the radiation scattered by the substance will not go in all directions (i.e., will not be diffuse), but will go either in the form of rings, or in the form of lines, or in the form of separate rays. When these rings, lines, or rays fall upon a photographic plate or into the eye, this order is embodied in a picture, which will be the diffraction picture.

In the case of X-rays we cannot use our eyes to examine this picture, for our eyes are not adapted to see X-...

rays in any form whatever; but a photographic plate can record this effect. If we pass a beam of X-rays through a crystal with its regular arrangement of molecules and place a photographic plate behind the crystal, then on the plate we shall find a diffraction pattern. It will consist of a bright central spot exactly at the place where the primary beam of rays fell on the plate, and around it, in a definite order, are arranged spots of smaller size.

Fig. 1. Diffraction pattern for diamond. Laue method.

Different crystals give different arrangements of spots, since each crystal differs from other crystals in the nature of the molecules of which they consist and in the manner of their arrangement. Different orientations of the crystal with respect to the incident ray also give different pictures.

It proves entirely possible to proceed in the reverse direction, i.e., from the diffraction pattern to draw conclusions about the structure of the crystal, which is the cause of precisely this diffraction; therein lies the principle of the new method of analysis. The calculations are for the most part attended by difficulties, unless one wishes to confine oneself to the determination of a few simple measurements of the element of the crystal lattice. In the case of crystals possessing a very simple structure, a few such determinations may prove sufficient for carrying out the analysis. It must also be noted that our inability to explain the diffraction pattern with respect to many details of structure that we would like to know by no means signifies that there is any doubt or uncertainty in those determinations which the analysis makes so successfully. Extensive measurements of the lattice element are now easily made with an accuracy of up to one percent, and often can be carried to one per mille and even further.

Let us take one or two examples. In Fig. 1 is shown the diffraction pattern obtained as a result of the passage

beam of mixed X-rays through diamond. The explanation of such a regular pattern presents no particular difficulties. It leads to the structure shown in Fig. 2, where each black sphere denotes a carbon atom; to this it must be added that each atom is situated at the center of a regular tetrahedron formed by the four nearest neighbors of this atom. The distance between two such neighbors is 1.54 Å.

I shall not attempt to explain the transition from Fig. 1 to Fig. 2. For physicists, the determination of structure from a diffraction pattern is of enormous interest; but I shall speak only of the results. Be that as it may, we can see that the diffraction pattern must change with a change in structure, and indeed the character of certain changes is quite obvious. If, for example, the structure of the crystal is sufficiently simple, then the diffraction pattern will also be simple and perfectly regular; conversely, in the case of a complex structure, an apparent disorder is obtained in the diffraction pattern. Moreover, it is well known that if all dimensions of the crystalline system are simultaneously increased proportionally, then the diffraction pattern remains the same, only with more closely spaced dimensions, and vice versa. If this circumstance is illustrated by any of the examples given above, then the halo around the moon must be the larger, the smaller the particles of water vapor are in diameter.

Fig. 2. Model showing the structure of diamond.

This effect becomes strikingly clear in the case when we are dealing with X-rays. For example,

in Fig. 3 is shown the diffraction pattern obtained by continuous rotation of a simple small crystal about an axis perpendicular to the incident beam of X-rays of a single wavelength. This pattern differs from the pattern shown in Fig. 1, since it was obtained in another way. In the first case, during the action of the X-rays the crystal was at rest and the rays were mixed. Here, however, the X-rays were of only one wavelength, and since this restriction was too severe for developing the pattern, the necessary breadth was obtained by moving the crystal. Here rock salt was taken as the material; its simple structure is shown in Fig. 4. Let us now compare the pattern just considered with the pattern of a more complex crystal such as naphthalene (Fig. 5). There is no doubt that this pattern is much more complex: it is, as can be seen, full of spots, many of which crowd toward the center.

Fig. 3. Diffraction pattern for rock salt. Rotating-crystal method.

Indeed, in the case of naphthalene the pattern is too intricate to be fully explained in the present state of our knowledge. However, we can note here certain very important details of structure. From this pattern and from others obtained for the same crystal placed in another position, we can learn the exact size and shape of the element of the crystal system; we can show that two molecules take part in the structure of the crystal and that they are alternately arranged—

are assumed to lie side by side with one another. The chemist depicts for us the picture of the naphthalene molecule in the form shown in the following scheme:

\[ \begin{array}{ccccccccc} & & \mathrm{H} & & & \mathrm{H} & & & \\ & & | & & & | & & & \\ \mathrm{H} & - & \mathrm{C} & - & \mathrm{C} & - & \mathrm{C} & - & \mathrm{H} \\ & & | & & | & & | & & \\ \mathrm{H} & - & \mathrm{C} & - & \mathrm{C} & - & \mathrm{C} & - & \mathrm{H} \\ & & & \backslash & & / & & & \\ & & & \mathrm{C} & - & \mathrm{C} & & & \\ & & & | & & | & & & \\ & & & \mathrm{H} & & \mathrm{H} & & & \end{array} \]

It tells us that the carbon atoms are arranged in the form of two hexagonal rings and are bordered by hydrogen atoms. The picture given to us by the chemist is, to a certain extent, conventional; however, in emphasizing this limitation, the chemist, as we now see, has proved excessively cautious. Indeed, we can now measure distances in the system by various methods and show that not only is the general scheme of the plane represented by the chemist correct—which we never doubted—but also that this scheme may rather be called a plan than a diagram.

Fig. 4. Model showing the structure of rock salt.

However, it cannot be perfectly as symmetrical as the diagram shows. Two molecules in an element of the system can be distinguished from one another by means of X-rays.

from one another, which could not have been done if they had the same appearance from all points of view. They are completely identical until they are included in the crystalline system, but each of them is, to a certain extent, asymmetric, so that after placing it in position by different routes the two positions can be distinguished from one another.

An enormous number of organic crystals consist of one or several such hexagonal rings of carbon atoms. They form classes of compounds of extraordinary importance.

Fig. 5. Diffraction pattern for naphthalene; rotating-crystal method.

These include: dyes, explosives, and many drugs such as salicylic acid or quinine. We are making great progress in our attempts to discover the exact details of the structure of these crystals; however, this is a very difficult task. We are making much greater progress in studying another class of organic compounds, which also includes a large series of substances. These are the so-called long-chain compounds. These include fats, oils, paraffins, and others; many of them play a predominant role in animal and plant organisms. When analysis by means of X-rays was applied to the study of organic substances

STRUCTURE OF ORGANIC CRYSTALS

For the first time, ring compounds seemed more convenient for study, since their crystals are much better formed. It turned out, however, that compounds with long chains are more suitable—and this despite the fact that a piece of fat looks entirely non-crystalline. But X-rays can see much better than our eyes. They reveal crystalline structure where we see nothing. Let us take, for example, one of the ordinary substances: if a small amount of stearic acid is smeared over a smooth plate, then, as it turns out, the long molecules are arranged far from being in such disorder as, for instance, a batch of pins on the tray of a peddler; their arrangement may rather be likened to matches in a box. Chemists have long known about these substances; they also know that in each molecule the carbon atoms are built into a chain, forming the links of this chain. The results obtained by means of X-ray investigation are in full agreement with this general proposition and, moreover, give many additional indications concerning the details of the picture. Eighteen carbon atoms form the links of the stearic-acid chain; three hydrogen atoms are bound to one of the terminal carbon atoms, forming together with this atom the so-called “methyl” group; to the carbon atom at the other end there are attached one oxygen atom and a small separate chain consisting of one more oxygen atom and one hydrogen atom, which together with the terminal carbon atom is called the “carboxyl group.” To each of the remaining 16 carbon atoms there are attached 2 hydrogen atoms. All these facts have been proved by chemical methods.

Stearic acid is an extremely important substance. But it is only one member of a group of substances which differ from one another only in the length of the chain, and all these substances play a greater or lesser role in nature. Formic acid, with one carbon atom, bears witness to this by its very name. The same applies to acetic acid, which has 2 carbon atoms, and to butyric acid, with 4 carbon atoms.

These substances differ considerably from one another in their properties, but in those cases where the chain is long, increasing it by one or two links does not entail any great difference. Indeed, various representatives of compounds with a long chain are very often found together in nature, as if indicating that more than one of them can be formed under identical circumstances. Palmitic acid, with its 16 carbon atoms, and stearic acid—with 18—occur together in animal

\[ \mathrm{H{-}C{-}C{-}C\cdots C{-}C(=O){-}O{-}H} \]

Scheme depicting the structure of the molecule of stearic acid.

fats, although the first of them is also a very important constituent part of palm oil, whence its name derives. The name of arachidic acid is given to the chain with twenty carbon atoms; it is found in peanuts. Behenic acid, with 22 links, is extracted from the seeds of certain plants. It has always seemed to me extremely curious that all these chains are so strongly predominant in organic nature and that different chain lengths are associated with different organisms.

X-rays tell us that these molecules have a tendency to arrange themselves side by side, like ears of grain in a field; in this way layers are formed in which the molecules are arranged across the layer. However, they are not positioned perpendicular to the layer, but somewhat inclined, exactly as ears of grain are inclined toward the ground when the wind blows across a field. A film of fat that we spread with our fingers consists of the thinnest layers, more or less parallel to the base on which the film has been applied. Each very thin layer is probably too thin for it to be visible even with the aid of a micro-

STRUCTURE OF ORGANIC CRYSTALS

itself is a small perfect crystal; all these layers are arranged like a deck of cards thrown in disorder onto a table, except that all the cards are nearly parallel to the surface of the table. The diffraction pattern obtained by means of X-rays is not as perfect as it would be in the case of a single good crystal, but nevertheless much information can be drawn from it.

All the molecules in any one layer are arranged in a perfectly definite manner—namely, like ears of grain in a field—but in the arrangement of many layers there is one remarkable feature. Alternating layers following one after another are disposed in the opposite way: the carboxyl groups of one layer are face to face with the carboxyl groups of the neighboring layer; the same also occurs in the case of the methyl groups. All this can be very well explained: it is known that carboxyl groups have a strong affinity for one another, which is in agreement with the observed arrangement of the layers. The double layers thus formed have methyl groups on both sides, between which there is weak attraction, so that the bonds between neighboring double layers must be weak. The layers can easily slide one over another, whence the slipperiness of fats and oils and their well-known lubricating properties become comprehensible. Indeed, the structure of these crystals is an essential condition for their being good lubricants. There must therefore exist layers which are held together as such, and others which can slide over one another. As strong as the bonds between two neighboring molecules in one layer must be, so weak will they be between the molecules in one layer and their nearest neighbors in the adjacent layer. Graphite is a first-class lubricating material, since its crystals likewise satisfy these conditions.

We can go further and, from the results of investigation by means of X-rays, derive a more detailed description

of the molecule itself. Its carbon atoms prove to be arranged not in a straight line, but in a zigzag, like the teeth of a saw, and the angle between neighboring zigzags is very close to the so-called tetrahedral angle, i.e. \(109^\circ 20'\) (Fig. 6). If we return to the diamond model, then everywhere on the surface we shall find the same zigzags. It must be remembered that each carbon atom lies at the center of gravity of four others, and the angle between the lines connecting the central atom with two of its neighbors will be the angle of the tetrahedron.

Many indications which we now possess have been obtained thanks to the fact that my colleagues Dr. Saville and Dr. Gilchrist have recently succeeded in growing a single crystal of stearic acid and of one or two other compounds of the same series. These crystals have given excellent diffraction patterns, which are being studied gradually and carefully.

Fig. 6. Arrangement of the carbon atoms in the chain of stearic acid.

The chemist has shown us how the properties of a long-chain molecule can be altered by removing one or more hydrogen atoms bordering its sides. The gaps may be left empty or may be saturated by adding atoms such as oxygen, or even side chains. At the same time, X-rays can show us precisely at which link in the chain the oxygen has been substituted.

One of the most curious facts concerning these substances is that long chains with an odd number of atoms are extremely rare in natural substances, although they can be made in the laboratory. Chains with an odd number of atoms have, generally speaking, a lower melting point; apparently this indicates that their structure is less strong. It seems quite ...

it is possible that, by means of a more detailed study of the crystalline structure, this circumstance can be explained, for the zigzag structure suggests that chains with an even and an odd number of atoms must show a difference in the manner in which they form the crystal.

Recently it has been possible to establish clearly one extremely interesting circumstance. When the number of atoms in the chain is considerable, the terminal group of the chain occupies little space in comparison with the rest of it, so that the greater part of the crystal is built from the main part of the chain. Along these chains there exists a regular periodicity, since the zigzags are made up of repetitions in which two carbon atoms play a part. If there were no terminal groups at all in the compound, then in that case the most important elements of periodicity would already be present in the crystal; the diffraction pattern would then depict the features of the crystal in the usual way. Since the repetition would be small and very simple, the pattern would not contain a large number of spots, as I have already explained at the beginning. It would not show the complexity in the structure of crystals such as naphthalene, and would be similar to the pattern corresponding to rock salt. Furthermore, the terminal groups cannot exert a great influence on the diffraction pattern, for quantitatively they play an insignificant role in the structure of the crystal. Therefore, when we consider the diffraction pattern of such a system as stearic acid, we may expect that it will consist of a certain simple pattern with additions. Some spots and groups of spots in the diffraction pattern stand out very strongly, since they are caused by the presence of that periodicity in the structure of the crystal which is connected with the regular distribution of carbon atoms along the molecule. Alongside these spots there exists a multitude of weaker spots—the very ones that are caused by the regular repetition of terminal groups in the crystalline system. The crystal may thus be likened to a certain fabric with a special stripe repeating at regular intervals. These stripes are the layer of terminal groups of molecules. The periodicity of the fabric itself, with a small repe—

... corresponds to a small number of bright spots in the diffraction pattern. This second periodicity is more or less independent of the existence of the stripe, which, because of its infrequent repetition, leads to the appearance of a more complete pattern of many spots. However, some of these latter spots will closely coincide with the few spots that correspond to the simple pattern. This effect is clearly represented in some photographs obtained by Müller (Fig. 7).

Fig. 7. Diffraction pattern of stearic acid. Rotating-crystal method.

Thus a fat spot is far from being an amorphous body in which there is neither order nor definite form. It consists of a multitude of the thinnest layers, in each of which there exists a most perfect arrangement of molecules; chains of carbon atoms, each of which has its own outline, are arranged one alongside another, so that in the aggregate they form an entire layer which, in all probability, consists of many layers formed in this way; the intermediate layers of carboxyl and methyl groups are separated from one another by regular intervals. Further, all the properties of the substance depend not only on composition, but also on form, namely on the form of those elements of the system that correspond to the first case, and on the form of the entire system that is built from these elements.

If all this is supplemented with actual dimensions, then such, in general, will be the picture that until now we have obtained thanks to X-rays. But nevertheless it is still far from what we want to have and what we now hope for. The long chain with its special terminal groups has such great vital significance (these words may be taken in their literal sense) that the more we know about the details of its structure, the better we should understand those processes that constitute the subject of study of biology and biochemistry. I have had occasion to speak of one particular case. There are, of course, other cases as well: paraffins with methyl groups at both ends, which are the cause of the weakening of their activity and therefore must serve as a strong obstacle to all their attempts to combine with other molecules; further, one may mention alcohols, ketones, aldehydes, etc. Here one must also speak of the sugars, in which, although there is a more complex chain structure, there nevertheless exist many features characteristic of compounds with long chains; with respect to these important substances, nothing has yet been done by the X-ray method that would serve as a worthy complement to the new successes in the field of chemical research. Further, we have before us the continuation of the study of ring compounds, which were the first to attract attention, and we hope for rapid successes in this field. The experience we have gained in studying chains, although it was limited to them alone, increases our chances of success in studying rings; and indeed, quite recently we have made a great step forward.

I hope that from this brief survey it is perfectly clear that the X-ray method opens before us extensive possibilities for useful investigations. I also hope that the audience which I have had the honor to address will someday, in the future, show special interest in these questions and help in elucidating that picture which, thanks to these methods, is gradually being revealed.

1. A lecture in memory of Fison, delivered on March 13, 1928. The first paragraph of the lecture, not bearing directly on its subject, has been omitted. Ed. ↩