Concerning the Nature of Things, by William Henry Bragg

Lecture iv

The Nature of Crystals: Diamond

WE have seen that when the effects of movement overcome the forces of mutual attraction, the atoms and molecules have an independent existence and form a gas; and, further, that when the attractive forces are somewhat stronger or the effects of movement are somewhat less, the molecules may cling together and form a liquid. In this state we suppose that the connections between the molecules are loose enough to allow a molecule to change its position and its partners with ease. We have now to consider a final state in which the attractive forces have quite the upper hand. The bonds between the molecules are more numerous, and it may be stronger: each molecule is tied to its neighbours at more than one point of its structure, so that it is riveted into its place, and in this way the solid is formed.

Molecules differ very much from one another in their form and in the forces which they exert on one another. When the forces are strong, much movement is required to prevent them from binding the molecules into the solid: in other words, the melting point is comparatively high. Substances like diamond or tungsten, of which the filaments of electric lamps are made, are so tightly bound together that they must be raised to temperatures of several thousands of degrees centigrade before the molecules are forced to release their hold. Such substances as butter or naphthalene barely remain solid at ordinary temperatures; others, again, like carbon dioxide, still more oxygen or hydrogen, must be greatly reduced in temperature before solidification takes place. It is all a matter of the balance between the two opposing agencies, motion and mutual attraction, and it is easy to realise that the melting points of substances may differ very widely from each other. Furthermore, a molecule is not to be thought of as a body of vague and uncertain form exerting a loosely directed attraction on its neighbours. When two molecules are brought together they may or may not draw tightly together: everything will depend on the way they are presented to each other. Each molecule has a definite shape or outline, we may say; though in using these words we must remember that their meaning will require careful consideration when we look more closely into the matter. The molecules join together as if there were definite points of attachment on each, and the junction implied that the proper points were brought together. The action between them is not usually to be compared to the general attraction between two oppositely electrified bodies, but rather to the riveting together of two parts of a mechanical structure, such as two parts of an iron bridge. Just as in the latter case the parts must be brought into the proper relative positions so that the rivets can be dropped into their places, so we find two molecules of a solid substance tend to arrange themselves so that certain parts of one are fastened with considerable rigidity to the proper corresponding parts of the other. There may be more than one way in which molecules can be joined up, and in consequence different structures may be formed out of the same molecules; for example, there are different forms of sulphur, of quartz and of many other things. It often happens that one mode of arrangement is adopted at one temperature, and a different mode at another temperature.

The consequence is that when the molecule contains many atoms, and is, therefore, probably of complicated structure and curious form, the solid that is formed by their union is of a lace-like formation in space. We may compare it to a bridge formed of iron struts and stays; which is a very empty structure, because each member is peculiar in form, generally long and narrow, and is attached to the neighbouring members at definite points. Most organic substances, like naphthalene, or one of the solid paraffins, have such a complicated character, and the emptiness of the structure makes for a low density. Few organic substances are much heavier than water. When the molecules are less complicated, less irregular in outline, they may pack together more closely; if the molecule contains one or two atoms only, like the molecule of ruby, or iron pyrites, still more if it contains but one atom, atom and molecule being then equivalent terms, as in the case of gold or iron, then the packing may be very close, and we have relatively heavy substances.

The infinite variety in the properties of the solid materials we find in the world is really the expression of the infinite variety of the ways in which the atoms and molecules can be tied together, and of the strength of those ties. We

shall never thoroughly understand the materials that we put to use every day, not grasp their design, until we have found out at least the arrangement of the atoms and molecules in the solid, and are able to test the strength and other characteristics of the forces that hold them together.

Now, within the last few years the discovery of the X-rays has provided means by which we can look far down into the structure of solid, bodies, and observe in detail the design of their composition. We have advanced a whole stage towards our ideal purpose — that is to say, towards the position from which we can see why a material composed of such and such atoms has such and such characteristics, density, strength, elasticity, conductivity for heat or electricity, and so on; or, in other words, reacts in such and such ways to electricity or magnetism, or mechanical forces, or light or heat. How far our new powers will carry us, we do not yet know; but it is certain that they will take us far and give us a new insight into all the ways in which material things or structures are handled, consciously or unconsciously, it may be in some industrial process, or it may be in some action of a living organism. The new process is especially applicable to the

solid, and I hope to describe it in this and the following lectures, which deal especially with the solid state. It depends on the combined use of crystals and X-rays, and we must give a little consideration to each of these subjects. Let us take the crystal first.

Imagine a slowly cooling liquid to reach the stage of which I have already spoken, when the heat motions have decayed so far that the molecules or atoms begin to attach themselves rigidly together. They will lay themselves side by side, so arranged that the attractions of various points on the one for various points on the other are satisfied as far as possible. We can imagine two molecules, already tied together at one point, to swing about each other with diminishing movements until at last a second tie is made, quite suddenly, perhaps. Then it may be that a third tie is quickly made in the case of each molecule, linking it to the other of the two, or to a third; and so it becomes locked into position. Thus, as the liquid cools, molecule after molecule will take its place with others already locked together, and the solid grows.

Or it may be that a solid substance forms out of a solution in which it has been dissolved. The solution evaporates and the molecules meet each

other more often, so that their association is encouraged. When the liquid has entirely disappeared, the substance is all solid. If the evaporation has been slow, the molecules as they wander on their way through the solution come to places where already a few molecules have tied themselves together, and join up with them, quietly and deliberately arranging themselves before they finally settle down, or refusing to take their places before they are presented to each other in the right way.

We can well imagine that under such circumstances a regularity in the arrangement will ensue. Suppose that a flat fig26 body, shaped like A, had four centres of attraction, two positive and two negative, arranged as shown. If we had to lay a number of such bodies on a flat surface, and so join them together that a positive and a negative centre lay always close to one another, we might arrive at some such arrangement as is shown in Fig. 26.

Whatever arrangement we adopted we should naturally find in the result a certain regularity, as in the figure. And apparently Nature works in some such way: the molecules lie side by side in an ordered array. The point is of fundamental importance. Order and regularity are the consequence of the complete fulfilment of the attractions which the atoms or molecules exert on one another. When the structure has grown to a size which renders it visible in the microscope, or even to the naked eye, the regularity is manifest in the form of the solid body: it is what we call a crystal. It is bounded by a number of plane faces, often highly polished in appearance, so that the crystal has a certain charm due partly to glitter and sparkle, partly to perfect regularity of outline. We feel that some mystery and beauty must underlie the characteristics that please us, and indeed that is the case. Nature is telling us how she arranges the molecules when given full opportunity. There are but two or three in her unit of pattern, and when the unit is complete it contains every property of the whole crystal, because there is nothing to follow but the repetition of the first design. Through the crystal, therefore, we look down into the first structures of Nature, though our eyes cannot read what is there without the use, so to speak, of strong spectacles, which are the X-ray methods. A few crystal forms are shown in Plate XIII.

Plate XIII.

plate13

Crystalline forms.

A. Sulphur trioxide crystals which have grown from vapour in a glass vessel. B. Erythritol crystal, grown from solution. C. Ammonium chloride: ideal and distorted cubical crystals from solution containing urea. D. Crystal forms: Quercite; Cocosite. E. Crystal forms: Alizarin; Rubidium alum; Sodium chloride; Ammonium cobalt suphate; Phthalic acid. F.Ammonium chloride: fern-leaf crystals (octohedral) and cubical crystals from solution containing urea.

There are three stages in the arrangements of matter: the single atom as we find it in helium fig27 gas; the molecule as it is studied by the chemist; and the crystal unit which we now examine by X-ray analysis. To take an example, there are the atoms of silicon or of Oxygen. The moluul: of silicon dioxide contains one unit of silicon and two units of oxygen, arranged, no doubt, in some special way. Lastly, there is the substance quartz, of which the crystal unit consists of three molecules of silicon dioxide, arranged, again, in a special fashion which we now know has a certain screw-like character. The quartz crystal contains an innumerable multiplication of these units. Each of the units has all the properties of quartz, and, in fact, is quartz; but a separate molecule of silicon dioxide is not quartz. For example, one of the best-known properties of quartz is its power of rotating the plane of polarisation of light, and this property is associated with the screw which is to be found in the crystal unit. It takes three molecules to make the screw. If we insert pegs into a round stick as in the figure, and make all the pegs the same in every particular — that is to say, if our unit of pattern contains one peg only — we may form an arrangement like A. With two pegs to the unit of pattern we can make an arrangement like B, or Be. With three pegs to the unit of pattern we may make one as in C, which may twist either of two ways, C1 or C,, or, as it is generally said, may be either right — handed or left-handed. The X-rays actually tell us that the quartz unit contains three molecules, and that they are arranged in a screw-like form, with which facts the form of the quartz crystal is in complete agreement, because there are two varieties in the form, as shown in Fig. 27A. In one there is a sequence in the faces x, s, r’ which screw oil to the right, while in the other they go to the left.

fig27a

Such a dual arrangement may be expected to be a consequence of the existence of the two kinds of screw, though we do not yet know enough to enable us to guess why these particular faces are prominent. Quartz or “rock crystal” was called “Krystallos” by the Greeks; the name was given to ice also, because the two substances were confused with each other. It is appropriate, therefore, that we should use quartz as an illustration of what is meant by crystal structure and the crystal unit.

We may now ask ourselves why, if the natural arrangement of molecules is regular, we do not find all bodies in crystalline form. To this we must answer that in the first place a large perfect crystal must grow from a single nucleus. It is difficult to say what first arrests the relative motion of two or three molecules of the cooling liquid, joining them together and making a beginning to which other molecules become attached. Perhaps it is a mere accident of their meeting; perhaps some minute particle of foreign matter is present which serves as a base, or some irregularity on the wall of the containing vessel. If there are very many nuclei present in the liquid, very many crystals will grow; and since they are not likely to be orientated to each other when they meet, they will finally form an indefinite mass of small crystals, not a single crystal. They may be so small that to the eye the whole appears as a solid mass without any regularity of form. In order that a large perfect crystal should be formed, the arrangements must be such that the molecules find few centres on which to grow. And they must grow, usually, very slowly and quietly, so that each molecule has time to settle itself correctly in its proper place. The molecules must have enough movement to permit of this adjustment. These conditions are well shown in the methods which the crystallographer employs for the growth of crystals. If, for example, he is growing a large crystal of salt from a solution of brine, he will suspend a minute, well-formed crystal in the brine, and he will keep the temperature of the latter so carefully adjusted that the atoms of sodium and chlorine are only tempted to give up their freedom when they meet an assemblage of atoms already in perfect array — that is to say, when they come across the suspended crystal. If the solution is too hot, the fig28
Fig. 28. — The thermostat.
The temperature of the bath in which stand the bottles containing the growing crystals must be free from sudden and irregular variations, and must be slowly lowered day by day. The temperature is maintained by an electric heater: if it rises too high the current is turned off through the expansion of the liquids in the large thermometer which also stands in the bath. The rise of the mercury closes a circuit containing an electromagnet which pulls the switch. The clock is all the time lowering — very slowly — a wire to meet the mercury in the thermometer, so that the temperature at which the heating coil is turned off is being steadily diminished. The heater is at the bottom of the bath, and a stirrer is just above it.
suspended crystal will be dissolved in the unsaturated solution; if it is too cold, crystals will begin to grow at many points. Sometimes the liquid is kept in gentle movement so that various parts of it are brought to the suspended crystal in due turn. The principal conditions are time and quiet, a solution of the salt just ready to precipitate its contents, temperature and strength of solution being properly adjusted for the purpose, the presence of a small perfect crystal and the gentle movement of the solution past it. We do not, of course, quite understand how these or some such conditions come to be realised during the growth of a diamond or a ruby; but we find them to be necessary in the laboratory when we attempt to grow crystals ourselves.

When the conditions are fulfilled in part only, we may get a mass of minute crystals in disarray; we may even find a totally irregular structure — an amorphous substance, to employ the usual phrase. This alone would account for the seeming rarity of crystals, and we have also to bear in mind that many bodies are highly composite in character, consisting of many substances each of which has its own natural form. The X-rays show us that the crystal is not so rare as we have been inclined to think; that even in cases Where there is no obvious crystallisation Nature has been attempting to produce regular arrangements, and that we have missed them hitherto because our means of detecting them have been inefficient. The regularity of Nature’s arrangement is manifested in the visible crystal, but is also to be discovered elsewhere. It is this regularity which we shall see to be one of the foundation elements of the success of the new methods of analysis.

Let us now turn to the consideration of the X-rays. The reason of their ability to help us at this stage may first be given in general terms.

The X-rays are a form of light, from which they differ in wave length only. The light waves which are sent out by the sun or an electric light or a candle and are perceived by our eyes have a narrow range of magnitude. The length of the longest is about a thirty-thousandth of an inch, and of the shortest about half as much. These sizes are well suited to the purpose for which we employ them. Let us remember that when we see an object we do so by observing the alterations which the object makes in the light coming from the source and reaching our eyes by way of the object. Our eyes and brains have attained by long practice a marvellous skill in detecting and interpreting such changes. We may be unsuccessful, however, if the object is too small; and this is not only because a small object necessarily makes a small change in the light. There is a second and more subtle reason: the nature of the effect is changed when the dimensions of the object are about the same as the length of the wave, or are still less. Let us imagine ourselves to be walking on the seashore watching the incoming waves. We come in the course of our walk to a place where the strength of the waves is less, and when we look for the reason we observe a reef out to sea which is sheltering the beach. We have a parallel to an optical shadow: the distant storm which has raised the waves may be compared to the sun, the shore on which the waves beat is like the illuminated earth, and the reef is like a cloud which casts a shadow. The optical shadow enables us to detect the presence of the cloud, and the silence on the shore makes us suspect the presence of the reef. Now the dimensions of the reef are probably much greater than the length of the wave. If for the reef were substituted a pole planted in the bottom of the sea and standing out of the surface, the effect would be too small to observe. This is, of course, obvious. Even, however, if a very large number of poles were so planted in the sea so that the effect mounted up and was as great as that of the reef, the resulting shadow would tell us nothing about each individual pole. The diameter of the pole is too small compared with the length of the wave to impress any permanent characteristic on it; the wave sweeps by and closes up again and there is an end of it. If, however, the sea were smooth except for a tiny ripple caused by a breath of wind, each pole could cast a shadow which would persist for at least a short distance to the lee of the pole. The width of the ripple is less than the diameter of the pole, and there is therefore a shadow to each pole. Just so light waves sweeping over molecules much smaller than themselves receive no impressions which can be carried to the eye and brain so as to be perceived as the separate effects of the molecules. And it is no use trying to overcome our difficulty by any instrumental aids. The microscope increases our power of perceiving small things: with its help we may, perhaps, detect objects thousands of times smaller than we could perceive with the naked eye. But it fails when we try to see things which are of the same size as the wave length of light, and no increase in skill of manufacture will carry us further. But the X-rays are some ten thousand times finer than ordinary light, and, provided suitable and sensitive substitutes can be found for the eyes, may enable us to go ten thousand times deeper into the minuteness of structure. This brings us comfortably to the region of atoms and molecules, which have dimensions in the various directions of the order of a hundred-millionth of an inch, and this is also the order of the wave lengths of X-rays. Broadly speaking, the discovery of X-rays has increased the keenness of our vision ten thousand times, and We can now “see” the individual atoms and molecules.

We must now connect the X— rays with the crystal, and again we may first state the point in a broad way. Although the single molecule can now affect the X-rays just as in our analogy the single pole can cast a shadow of the fine ripples, yet the single effect is too minute. In the crystal, however, there is an enormous number of molecules in regular array, and it may happen that when a train of X-rays falls upon the crystal the effects on the various molecules are combined and so become sensible. Again, we may make use of an analogy. If a single soldier made some movement with his rifle and bayonet, it might happen that a flash in the sunlight, caused by the motion, was unobserved a mile away on account of its small magnitude. But if the soldier was one of a body of men marching in the same direction in close order, who all did the same thing at the same time, the combined effect might be easily seen. The fineness of X-rays makes it possible for each atom or molecule to have some effect, and the regular arrangement of the crystal adds all the effects together.

We may now consider more in detail the way in which the properties of X-rays and crystals are combined in the new method of analysis. The explanation is, perhaps, a little difficult, and I am trying to state both what precedes and what follows the explanation in such a manner that the explanation can be omitted by those who Wish to leave it for a time. It must, however, be mastered sooner or later by everyone who wishes to make use of the new methods.

PLATE XIV A.

plate14a

A. Diamond model.

The model shows only the arrangement, and says nothing about the size or shape of the carbon atom.

PLATE XIV B.

plate14b

B. Wallpaper.

The unit cell is outlined in two ways: (a) by thick lines, (b) by thin lines. The shape and content of the cell are exactly the same in the two cases, although the corners of the two cells are chosen differently.

We have seen that the atoms and molecules of a crystal are in regular array, and have even found reasons for expecting them to be so. Suppose that we stand before the papered wall of a room and consider the pattern upon it. It is a repetition of some unit (Plate XIV B). Mark one particular point of the pattern whenever it occurs; if a real marking is disallowed, a mental marking must suffice. It will be found that the marks lie on a diamond — or rhombus — shaped lattice, and that this lattice has the same form no matter what point of the pattern has been chosen for the marking. The rhombus will have fig29 different sizes and shapes in different wall — papers, though the four sides will always be equal or, it may be, the rhombus will be a rectangle, because no one could endure a wallpaper in which this was not the case. The whole pattern of marked points may be called a “lattice.” Each rhombus contains the substance of one whole unit of pattern with all its details, and no more.

The arrangement in space of the units of the crystal is like the arrangement on the wall of the unit of the wallpaper design, except that the plane lattice is replaced by a. “space lattice” (Fig. 29). Each little cell of the lattice is bounded by six faces, which are parallel in pairs. The cell can have any lengths of side and any angles; its simplest and most regular form is fig30 that of a cube. Each cell contains a full unit of pattern with all its details, and no more: it is the crystal unit, which possesses all the qualities of the crystal, however large the latter may be. In the case of quartz, for example, it has the special shape that is shown in Fig. 30, and it contains three molecules of silicon dioxide. This fact is readily determined by X— ray methods, and also the size and dimensions of the cell, as we shall see; but it is a far more difficult matter to discover the arrangement of the atoms and molecules within the cell.

Suppose that we were able to look into a crystal along one of the cell edges of Fig. 29, and found ourselves able to represent what we saw in some such way as is shown in Fig. 31. There is a grouping of atoms associated with each point on the lattice, which grouping we represent by the entirely imaginary set of circles in the figure. The form of the grouping is of no account, nor its contents; it may contain any number of atoms and molecules, but the essential point is that an exactly similar group is associated with fig31 each point on the lattice, as in the design of the Wallpaper. Suppose a train of X-ray waves to strike the crystal; in Fig. 31. — A, they are represented by the line WW and the parallels to WW. When these waves strike the series of groupings strung along AA— each grouping is now represented by a single dot —— a new set of similar waves will start from every grouping, though the wave as a whole sweeps on, just as a row of posts planted in the sea would each become the centre of a disturbance when a wave passed by. At a little distance from the row AA these minor disturbances link themselves together in a connected set of waves, represented by the parallel lines M. The effect is analogous to the reflection of sound by a row of palings, or by a stretched piece of muslin. In all cases the bulk of the wave goes on, but there is a reflected wave which makes with the reflecting layer the same angle as the original waves. The reflected waves form a simple train, the same as the original as to wave length, but far weaker, of course: it might be thought that the reflection would simply be a confused mass of ripples, but it is not so. Quite close to the groupings there is some apparent confusion, but a little further along the track of the reflection the wavelets melt into the steadily moving train aa, etc.

fig32 Behind the row of groupings strung along AA there is another, exactly like the first, which is strung along BB (Fig. 32, B). The original waves, which experiment shows to be very little impaired by their passage over AA, sweep over BB in turn, and again there is a reflection represented by the group of parallel lines H2. Behind that there is a row CC forming a N train, a row DD forming a dd train, and so on.

As a rule the lines aa, bb, cc, do not coincide with each other. But if the wave length of the rays, the distance between AA and BB (which are really planes seen edgeways), and the angle at which the waves meet AA, BB are correctly adjusted to each other, then the lines aa, bb, etc., do coincide with each other. In actual practice thousands of reflecting planes come into play, and when the reflections all fit together in this way exactly, the whole reflection is strong. If the adjustment is incorrect as it is drawn in the diagram, the reflections do not add together into a sensible effect; some throw their crests, or what corresponds to the crests on a waterwave, into the hollows of other waves, and there is mutual interference and annulment. The adjustment has to be exceedingly exact, because there are so many reflecting planes, one behind the other. It is easy to find a formula which expresses the condition for correctness of adjustment, and therefore for reflection. The line A’B’B must be longer than AB by a whole number of wave lengths. If λ is the wave length, d the distance between planes, or spacing, as it is usually called, and θ the angle shown, then:—

nλ = A'B'B— AB = A'D— AB = DN = 2dsinθ, where n is any whole number.

fig33

It is not necessary, as I have stated already, for the reader to go through the calculation just given, from which the fundamental equation of the subject is derived.

The essential point is that if the direction of the original rays is gradually altered with respect to the planes AA, BB, etc., there will be no observable reflection until the proper inclination is reached; when this happens there is a sudden flash of reflection. The angle of inclination is observed; and when, as is always the case in crystal analysis, the wave length of the rays is known, it becomes possible to measure the spacing. The reflected rays cannot, of course, be detected by the eye, but they can make their mark on a photographic plate and be observed in other ways which need not be considered here. The instrument constructed for the purpose of the experiment is called an X-ray spectrometer. It measures the angles at which reflection occurs; and its observations are used to determine spacings in the first instance, and in the second the angles between the various planes of the crystal. For instance, it gives not only the spacings between AA, BB, but also between PP, QQ (see Fig. 32, B), and the angle between AA and PP. It gives, in fact, the dimensions and form of the unit cell. It is, in general, a simple matter to find by experiment the density of the crystal, and then we can find the weight of the matter contained in the cell. Since we always know the weight of the molecule, it is easy to find how many molecules go to the unit; as already stated, it is always a very small number. Moreover, the observations of the X-ray spectrometer give us some knowledge of the relative positions of the molecules that make up the unit of pattern. They would tell us far more than this if only we knew how to interpret them, but we are too inexperienced as yet. We have found our Rosetta Stone, but are as yet only learners of the new language.

The most important point to bear in mind is that the X-rays give us the distance between any sheet on which the atom groups are spread and the next sheet, which is exactly the same as the first, on which, therefore, another lot of atom groups is spread. This spacing is the same thing as the distance between two opposite faces of the unit cell. We can draw the cell in many ways by joining up different corners of the space lattice. There are not only three spacings to be measured in the crystal, but in reality any number of them; usually we are content to determine a few of them.

In a few cases the crystal analysis has already been carried so far that we know where every atom has its place in the unit of pattern. To get so far we have made use not only of our X-ray analysis, but of many facts of chemistry and physics. I shall not describe these further details, in any case; the general explanation I have given above will serve as a sufficient indication of the methods that have been followed. But I think we shall be interested in some of the results.

First of all let us take the diamond, which is a prince among crystals. It is not only a beautiful and valuable gem, but in its structure it teaches us many things concerning the most fundamental truths of chemistry, particularly organic chemistry. Only one atom, that of carbon, goes to the building of the diamond; but that atom is of vital interest to us. It is a fundamental constituent of foods and fuels, dyes and explosives, of our own bodies and many other things. The structure of the diamond is remarkably simple, though, like all constructions in space, it is difficult to comprehend quickly. We are so accustomed to drawings on the flat, paper and pencil are so handy, that our minds easily grasp the details of a plane design. But we cannot draw in space; we can only construct models at much cost of time and energy, and so our power of conceiving arrangements in space is feeble from want of practice. A few have the natural gift, and some, being crystallographers, have trained themselves to think in three dimensions. Most of us find a great difficulty in our first efforts to realise the arrangements of the atoms and molecules of the crystal. Nevertheless, the diamond structure shown in Plate XIV A will become clear at the cost of a little consideration.

The black balls represent carbon atoms, in respect to position only, not in any way as to size and form, of which we know very little. Every carbon atom is at the centre of gravity of four others; these four lie at the corners of a four-cornered pyramid or tetrahedron, and the first carbon atom is, of course, at the same distance from each of them. We have reason to believe that the ties between the atoms are very strong, and there is only one form of tie throughout the whole structure. In its uniform simplicity and regularity we can surely see the reason why the diamond is placed in the highest class on the scale of hardness. If it is pressed against any other crystal it is the atoms of the latter that must give way, not the atoms of the diamond. The diamond has a cleavage plane. In the figure it is parallel to the plane of the table on which the model stands; there are four such planes, one parallel to each face of the four-faced pyramid. The model can be turned over so as to rest on any one of the four faces, and looks exactly the same in each position. The distance between the centres of two neighbouring carbons is F54, Angstrom Units; this unit is the hundred-millionth of a centimetre. It does not seem surprising that this particular plane should be the cleavage plane, because it cuts straight across the vertical connections between the horizontal layers that appear in the figure. Each of the layers may be described as a puckered hexagonal network. The crystal may, of course, be considered as an arrangement of layers parallel to any one of the four faces of the tetrahedron, not merely the face on which the model happens to stand.

PLATE XV.

plate15a

[By courtesy of Joseph Asscher & Cie.

A. The Cullinan diamond split into three pieces.
It was originally as large as a small fist.

plate15b

[By courtesy of Joseph Asscher & Cie.

B. The table and tools used for splitting the diamond.

The existence of this cleavage is well known to diamond cutters, who save themselves much labour by taking advantage of it. In the Tower of London are shown the tools wherewith the great Cullinan diamond was split during its “cutting.” Plate XV A shows the diamond in three pieces; and XV B the tools used in splitting it. It is possible to cleave a diamond in yet another plane, which contains any one edge of the tetrahedron and is perpendicular to the other edge; but the operation is difficult and rarely used.

When we consider the diamond construction we cannot but notice the striking appearance, in every part of the model, of an arrangement of the carbon atoms in a ring of hexagonal — or six-sided — form. If we take one of these rings out from the model, it has the appearance of Plate XVI B, 2: a perfect hexagon when viewed from above, but not a flat ring.

Now the ring of six carbon atoms has already a famous place in chemistry. No one has ever seen the ring: it is too small. But the chemist has inferred its existence by arguments which are most ingenious and most interesting. Even those of us who are not chemists may find no great difficulty in acquiring some understanding of them. For instance, it was well known in the middle of last century that certain molecules could be formed in which the fundamental structure consisted of carbon atoms in a row or chain, and that hydrogen atoms could be attached to the various carbon atoms in such a way that every carbon atom had four other atoms attached to it. That was known because the molecule could not be made to take on any more hydrogens: it was full, or, as the chemists say, “saturated,” because a single carbon atom is “saturated” when it has four other atoms attached to it, as, for example, in marsh gas or methane (CH,). The relative number of carbons and hydrogens was exactly what would be expected on this hypothesis. With six carbon atoms there ought to be fourteen hydrogen atoms, as the diagram shows, and this is found by experiment to be the case. These substances are called the “parafiins” (see the latter part of the next lecture); the various members of the series having different numbers of carbons in the chain. The particular substance shown in the figure is called hexane.

PLATE XVI.

plate16a

A. The layers of the graphite crystal.

(a) and (c) are similar in all respects, but (b) is like (a) when turned round through two right angles in its own plane about any such vertical line as is drawn in the figure.

plate16b

B. Possible forms of the benzene ring (see p. 152).
No hydrogens are shown.

Now in 1825 Faraday isolated a certain substance from the residue found in gas retorts, which he called bicarburet of hydrogen; it is now known as benzene. A few drops of Faraday’s first preparation are preserved as an historical treasure in the Royal Institution.

The molecule of this substance contains six carbon atoms like hexane, and six hydrogen atoms. It can be made to take on six more hydrogen atoms, twelve in all, but no more, and the new molecule then behaves chemically like hexane in respect to most of its properties. But it cannot have the same structure as hexane, because it has two hydrogen atoms less. The riddle was solved in 1867 by Kekulé, who suggested that the framework of benzene is a ring, not a chain, of Fig. 34 six carbon atoms; we may think of it as derived from the chain of Fig. 34. by the removal of the two hydrogen atoms at the ends and a bending of the chain round until the two ends meet and are joined up. We then have the structure shown in Fig. 35. Its chemical name is hexahydrobenzene. Benzene itself has only one hydrogen at Fig. 35 each corner of the hexagon. The carbon chain and the carbon ring are the foundations of the two great divisions of organic chemistry. Chain molecules are found not only in the paraffins, but in fats, oils, soaps and many other important groups of substances. The ring is the basis of many thousands of known molecules, including dyes and explosives, drugs such as quinine and saccharin; and so on.

The conception of the closed hexagonal ring leads at once to a simple and beautiful explanation of a number of remarkable chemical observations, of which we will consider one example. The benzene molecule consists of the hexagonal ring of carbon atoms, with one hydrogen at each corner. Each carbon atom has only three neighbours in this molecule: it can take on a fourth, so that on the whole there is room for six more atoms or groups of atoms, to be tied on at the corners. and these can be added. But the benzene molecule can exist contentedly enough without them. Taking the benzene molecule as it is, chemists find that they have the power to alter its constitution, pulling OH one or more of the hydrogen atoms, and substituting other atoms or groups of atoms. In a well — known and important case, a single hydrogen is removed and replaced by a group consisting of one carbon and three Fig. 36.-Toluene hydrogen atoms, known as the methyl group. The new molecule has the structure shown in Fig. 36, and is known as toluene, a very important substance, a liquid at ordinary temperatures. A second hydrogen can be removed from the ring molecule and replaced, let us say, by an atom of bromine; the new substance is known as bromotoluene. It is very remarkable that when this has been done three different substances are obtained, all having the same composition, viz. the six carbon atoms, four hydrogen atoms, one bromine atom and one methyl group which we will presume remains intact. How are we to explain the existence of these three, endowed with different properties, yet all having the same constitution? The ring hypothesis gives an immediate answer. There are three ways and no more of making the substitutions, which are shown in the figure. The bromine atom may be next to the methyl group, or next but one, or next but two.

The three molecules have different shapes, and therefore may be‘ expected to have different properties; and there is no doubt that there are Fig. 37. — Bromotoluene. actually the three different substances. Chemists have even been able to tell which is which. Many other similar examples could be given, but this one will suffice as an illustration of the significance of position as well as of composition, the three molecules differing only in the relative positions of the two things substituted. The methods of X-ray analysis are peculiarly fitted to deal with such differences as these, because they measure the dimensions of the unit of pattern into which two or more molecules are packed, and can detect the effects of altering the shape of the molecule. A little work of this kind has already been done.

It is very interesting to observe that in the’ case of chain molecules the number of carbon atoms is found to vary within wide limits; butyric acid, the substance characteristic of rancid butter, contains four carbon atoms, while palmitic acid, found in palm oil and other places, contains sixteen (see the latter part of the next lecture). On the other hand, the ring molecule of six carbon atoms occurs far more frequently than any other. It must be the easiest to form and the strongest in construction. Now the diamond, the only crystal, except graphite, which consists of carbon atoms only, is full of hexagonal rings. It is natural to suppose that the reason for the ring of six is to be found in the diamond structure. But the basis of the latter is simply the principle according to which each carbon atom is surrounded by four others symmetrically arranged round about it. The two lines which join a carbon atom to two of its neighbours are inclined to one another at an angle readily calculated to be 109° 28’. If in certain circumstances it is the rule that the junction of two carbon atoms with a third must always be made so as to show this angle, see Fig. 50, then the shortest ring that will close up contains six carbon atoms. (A model may be made to illustrate the point. Wooden balls of sufficiently regular form can be obtained in large numbers, being used in the manufacture of large buttons. Four holes are drilled at the proper places on each ball, and gramophone needles are used as connections. Models of diamond, and many forms of ring and chain molecules can then be put together.) Five carbon atoms in one plane nearly make a ring, because the angle of a pentagon is 108°. But if the angle is to be 109° 28’, it is necessary to take six, and to arrange them in the puckered form of Plate XVI B 2. Whether the benzene ring is actually puckered under all circumstances, or is sometimes flat, in which case the angle is 120° (Plate XVI B 1), or even has the shape shown in Plate XVI B 3, which is another form based on the tetrahedral angle, we find it difficult at present to say with any certainty. Experimental evidence is accumulating, but is not yet decisive as to this particular point; perhaps all three forms occur. Meanwhile, many facts emerge in the course of the ‘work which are definite and very interesting.

The remarkable substance graphite is, like diamond, composed of carbon atoms only. It is much lighter, its density being 2’30 nearly; the density of diamond is 3‘52. Clearly, some rearrangement of the atoms has taken place in which the spacings between the atoms have on the average materially increased. The X— rays show that the increase has taken place entirely in one direction. There are layers in graphite as in the diamond structure (Plate XVI A). To one looking down on a layer from above it presents the same appearance of a hexagonal network; and moreover the side of the hexagon is almost exactly the same in length. But the distance between layer and layer has been greatly increased, and it is this change which has made the substance so much lighter. Recent experiments seem to show that the layers have been flattened out, so that each carbon is now surrounded by three atoms in its own plane. If the ties between the atoms in each layer have altered at all, they have at least not lost in strength; on the other hand, the ties between layer and layer are greatly weakened. For these reasons the layers slide over each other very easily, and at the same time each layer is tough in itself. It is the existence of these two conditions that makes graphite so good a lubricant; not only is the readiness to slip of importance, but also the fact that the layer does not easily break up into powder. When one slips on the black-leaded hearthstone, some of the layers are clinging to the stone and some to the sole of one’s boot; it is these layers that slide on one another. It is very curious that a single change — whose real nature is, however, a mystery — should convert the substance which is chosen as the type of hardness into one of the most efficient lubricators we possess.

Another set of facts which also supports the idea that the ring is a real thing, having dimensions which can be measured and allowed for, is to be found in the comparison of two crystals, naphthalene and anthracene. These substances are of the greatest importance in the dye industry, the former being used in the manufacture of artificial indigo, the latter in the manufacture of alizarin, which is the active constituent of madder.

Naphthalene is a common substance; to most of us it is no doubt familiar in the form of the white, strongly smelling balls which we put into drawers to keep the moth away. If naphthalene is dissolved in ether, and the solution allowed to dry off gradually, the crystals are readily formed.

In general appearance they resemble the crystals illustrated in Plate XIII D.

The chemist finds that naphthalene consists of a double benzene ring which we draw as in Fig. 38, A; anthracene is based on a treble ring, Fig. 38, B. When crystals of the two substances Fig. 38. — Naphthalene and Anthracene. are subjected to X-ray analysis, it is found that the unit of pattern contains two molecules and that the shape of the cell which contains the unit is as shown in Fig. 39. The dimensions of the cells are given below the figures. If the two cells are compared with each other, it is note-worthy that along two of the edges the cells are very nearly the same size; but that there is a great difference in respect to the third. The natural inference is that the double and treble ring molecules lie parallel to OC in the two cases, and’that the difference between 1118 and 8’69 is to be ascribed to the extra length of the molecule. The anthracene contains one more ring than diamond, which gives it the extra length, 2‘4.9. Now if we measure the width of the ring as it occurs in diamond, it is found to be 2’50. Thus we again find support for the View that the ring has a definite form, and nearly Fig. 39 constant dimensions; so that we have something to guide us in trying to discover the structure of a crystal of which the ring forms part. The X-rays tell us the size and form of the unit cell, and how many molecules it contains, as well as certain information about the relative positions of the molecules. If we know the size, more or less accurately, of the ring or rings which form part of the molecule, we can set out on the investigation of the structure, knowing that bodies of definite dimensions have to be fitted into cells of definite shape. Work of this kind is extraordinarily interesting, since it gives us new knowledge of the arrangements of the atoms in the organic molecules and of the forces that bind the atoms in the molecule and the molecule in the crystal. It is a new field of inquiry, in which some results are definite and clear, others more obscure and difficult to interpret until greater experience has been obtained.

The organic molecule appears to us so far as a light rigid framework, in itself tightly held together, but weakly joined to its neighbours in the crystal. Organic substances are nearly always light, not very much heavier than water. The fact that the density of naphthalene is only Pr 5 shows the emptiness of its structure. Even the diamond is full of holes, like a sponge. If the holes were filled up by other carbon atoms, the density of the diamond would be doubled, for each hole is just large enough to take one more carbon atom, and there are as many holes as there are atoms.

The weakness of the bonds that join molecule to molecule is the cause of the softness of the organic crystal and of the ease with which it can be melted. For the same reason naphthalene “sublimes”: it evaporates while in the solid state. Whole molecules are flung off from the solid, and form a vapour which may crystallise again in a cooler part of the containing vessel.

Fig. 40

Naphthalene and anthracene are flaky in structure: they have, as it is said, a well-developed cleavage. The dotted lines show the cleavage plane; clearly the molecules break away from each other more easily at the ends than at the sides. In each flake the molecules stand nearly upright, like corn leaning over in the wind.

The general conclusion to which we are led by these considerations is that the “benzene ring” is a real material object of definite form and dimension, which is built into crystalline structures with little alteration of form. We must now go on to consider the “chain” molecule: the basis of as great a section of organic chemistry as that which rests on the ring. As this lecture is already long enough, we can consider the chain in our next lecture, in addition to the ice crystal, which will be our main subject.

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