Concerning the Nature of Things, by William Henry Bragg

Lecture v

The Nature of Crystals: Ice and Snow

WHEN we look round to see what crystals we shall examine by our new X-ray analysis, the crystals of ice and snow at once strike our imagination. Water is one of the most obvious substances in the world: it affects our lives in numberless ways and We are interested in all the forms which it can assume. And again, from a scientific point of view we should like to discover the structure built with so simple a molecule, one oxygen and two hydrogens, and we might find that it was within our power to do so. But there is one very compelling reason in the beauty of the snow crystal, with its tracery so delicate and finished, and of the frost crystals on the window — pane, so quaint and charming in their outline. It is true that the blocks of ice that come from the freezing works are not remarkable for grace of outline, though there is a fascination in watching them slither across the pavement at the end of the ice-man’s pincers.

PLATE XVII.

plate17a

plate17b

By courtesy of the Chief of the U.S.A. Weather Bureau.

Snow crystals of various forms.
(From Monthly Weather Review, U.S.A.)

PLATE XVIII.

[By courtesy of the Dept. of Scientific Research of the Admiralty.

plate18a

A. Snow crystals. (From the Monthly Weather Bureau, U.S.A.)

plate18b

B. Ice flowers growing on the ice floes.

plate18c

C. Bundle of irregular prisms. From “The British Antarctic Expedition, 1910–1913.”)

The manufacture of commercial ice is too rapid to bring out the ice design: the crystalline structure is there, but the mass contains a multitude of tiny invisible crystals oriented in all directions, and is full of bubbles and sheets of air.

If we are to see what Nature will do if left to work out her design in peace, we must examine the snowflakes that fall in a hard northern winter. In England, we do not see the best crystals: it is not cold enough. Observers in other countries such as Sweden and America have many exquisite drawings, which are to be found scattered through physical and meteorological publications. Some of them are reproduced in Plates XVII and XVIII.

We can imagine the way in which the snow-flakes grow. One or two molecules of water become associated in the upper air; molecule after molecule adds itself to the growing, falling crystal, filling out the details of the pattern until at last the six — pointed snowflake rests gently on the ground. If the weather is cold the flake may continue to grow in the same way, and the crystals develop perfect little facets, which glitter like diamonds in the sunshine. When the snow crystal first forms, it is very often feathery; the six arms grow outwards and other little arms grow out from each of them to right and left, and from these yet smaller arms, and so on; all the arms joining each other at the angle of 60°, so that the whole is like a six-pointed star of fine lace. These feathery forms are peculiar to the early stage of crystallisation, and seem to be the consequence of sudden and rapid freezing. The arms stretch out from the centre because they have used up the nearer molecules that are ready to join up into the structure, and they must stretch out into new fields. This effect is often found in other cases of rapid crystallisation; a notable example is the formation of skeleton crystals of iron in the crucible of molten and cooling metal. If they are to be preserved, the rest of the liquid must be poured off before the crystal has had time to fill up vacant spaces. They are called “dendrites,” because they look something like trees, with trunks, big branches, small branches, and so on, but the angle at which two branches of an iron crystal join together is a right angle, not 60°, and the form is far from being as graceful as that of ice.

When the snow crystal has had time to grow, and there is an available supply of molecules, the gaps fill up, and the crystal becomes a hexagonal plate (Plate XVII B). Sometimes, it is supposed, the plates grow in that form from the beginning. Strange to say, these plates are often connected in pairs by a hexagonal prism; one plate is generally larger than the other, and the whole is like a fairy tea-table (Plate XVIII A). The prism appears also in the curious formations of Plate XVIII C, which is taken from Wright and Priestley’s “Glaciology,” British Antarctic Expedition, Fig. 41 1910–1913.

PLATE XIX.

plate19a

plate19b

The first picture is due to Mr. G. A. Clarke, and is taken from Mr. F. J. Whipple’s article on Meteorological Optics in the “Dictionary of Applied Physics,” Vol. iii., p. 529 (by courtesy of Messrs. Macmillan & Co.). It shows a halo and mock suns. The second picture is from an interesting original sketch in the possession of the Royal Institution: it shows the halo and the “sun-pillar.”

The prisms and plates and “tea-tables” are believed to be the cause of the mock suns and halos passing through it that are observed in high latitudes (Plate XIX). Suppose that the hexagon in Fig. 41 represents a section of one of these prisms or plates, and let ABCD be the path of a ray of light going through it. It is refracted at the points B and C; the ray is on the whole bent through an angle of at least 21° 50’, which is, in the language of physics, the angle of minimum deviation. If in Fig. 42 S be a source of light and E the eye, a ray from S is bent in going through P, and will enter the eye if P is properly placed. In the figure the prism is placed symmetrically, in which case it is known that the deviation SPE has its minimum value. Any prism lying between SPE and SP’E, such as Po, will bend the ray from S in such a direction that it cannot possibly get to the eye, no matter how the prism is placed. The eye cannot receive a refracted ray from any such prism. A prism P, may send light to the eye, Fig. 42 if it has an unsymmetrical position, as the figure shows; the angle of deviation has to be more than the minimum, and that is why the prism must be crookedly placed, as in the figure. If, therefore, an observer at E stands facing the sun at S, light will be seen to come from the directions PE and FE, and also other directions outside; but the latter will be relatively feeble, because most of the deviations are not far from the minimum value — the further they are from it, the fewer they are, in accordance with a known law of maximum or minimum values. Also there is no light at all from within PEP’, and the consequence is that the strong light of the minimum deviations is the more sharply defined.

This applies to rays coming from all directions round the sun; and so, on the whole, the observer must see a ring round the sun, sharp on the inside, rather more diffuse on the outer. For red light the angle PEP’ is rather smaller than for blue, so that the halo is not quite white, but is coloured, red on the inside, blue on the outside. The halo is observed if there are enough ice prisms in the air, just as a rainbow is seen if there is a sufficiently large number of drops of rain. When a ray of light goes into a raindrop and out again it is bent through an angle of more than two right angles, so that to see a rainbow one must have the sun at one’s back.

A little model may help to make this explanation clearer. The arc-lamp at S in the figure is the source, the eye is at E. Between S and E is a stand on which an arm is mounted; the latter carries a glass prism. The dimensions of the model are so adjusted that a ray of light refracted by the prism falls on E. If the arm swings Fig. 43 round J, the eye continues to be illuminated. If there were prisms all round the circle, the eye would see a circle of light round the central spot.

If for any reason the prisms tended to set themselves in certain positions only, the halo would be incomplete. Something of this kind actually happens. When a long prism falls through the air, the axis tends to set itself horizontally. If, however, it has the tables at the ends, as shown in Plate XVIII A, or if it is simply a hexagonal table which may be considered as a very short prism, its axis tends to become vertical, or, in other words, the table itself to become horizontal. This rather strange effect is in accordance with a well-known rule concerning the movement of bodies through gases or liquids. They tend to set themselves so as to offer as much opposition to the motion as possible. If we make a packet of two or three letters or post-cards, and drop them from a height, holding them horizontally and taking the hand quickly from underneath, they remain level throughout the fall. But if we let them fall edge first, they subsequently turn over and over. When we drop a white plate into the water, we see it swaying from side to side, but always tending to the horizontal position. The consequence is that the falling shower of ice crystals contains an undue proportion of vertical and horizontal crystals. Those parts of the halo which lie at the ends of the horizontal and vertical diameters are emphasised, and are like bright spots on the Fig. 44 ring: they are often spoken of as mock suns.

It is easy to show the tendency of the “tea-table” forms to become vertical as they fall. We make a number of models of ebonite and allow them to fall in a tall jar full of water. A very tall jar is the best, but even if the depth is not more than eighteen inches or so the tendency is quite obvious. Curiously enough, some of the bodies tend to fall with the plate leading the way, and some with the plate in the rear. The point was examined mathematically by Besson, who showed that when the diameter of the plate is small compared to the length of the prism, the plate tends to go first, and vice versa. We can prove this by experiment; it is best to hold the axis horizontally under the surface of the water and then let go.

The whole of the vertical line through the centre of the halo is often illuminated also, but this is due to a different reason altogether: it is caused by reflection at the flat surfaces of the snow crystals and plates. Consequently‘ the observer receives reflections of the sun from snowflakes at all altitudes, but they must all lie in a vertical plane through the sun. The bright vertical line is called a “sun-pillar.”

Ice when it forms quietly on a water surface exposed to the sky crystallises in a form analogous to that of the snow crystal, all the six-sided figures being horizontal. That it does so is not generally very obvious, though in books of Arctic exploration pictures are to be found of table ice breaking up into six-sided vertical columns, like the basalt columns of the Giant’s Causeway. It is also said that when the ice on a lake breaks up, it first divides into vertical columns, which for a time hold each other up; when, however, the ice begins to move, the collapse is rapid and the lake clears quickly.

In the accounts given by Antarctic explorers, it is especially mentioned that the ice on fresh-water lakes was found to be divided into six-sided prisms, all standing upright on the surface. The planes of separation were marked by lines of air bubbles. On the sea ice the formation of the crystals led to an expulsion of the salt which was deposited in the spaces between the crystals, and sometimes squeezed out above the top surface. The prisms were nearly free from salt inside, and fairly fresh water could be obtained if the outside Fig. 45 layers were first melted off. They were clear crystals, through which an observer might look at the rocks underneath as through tubes.

There is a very beautiful way of observing the crystalline structure of ice, which is described by Tyndall in his book on “Heat.”

A slab of clear ice is placed in the rays from an arc lamp and is focused on the screen, as in Fig. 45. The heat of the lantern begins to “undo” the crystals, which come to pieces in Fig. 45a the order inverse to that in which they were put together. Little six-rayed cavities appear and grow, looking like flowers of six petals, and other cavities having a fern-like form in which the fronds are inclined to the stem at an angle of 60°. Soon the whole screen is covered with these “flowers of ice,” as they are called: it looks like a beautiful carving in low relief. The ordinary commercial ice does not show the effect; there is a specially prepared “plate ice” which is fairly satisfactory. But the natural ice that is formed in the open at night-time is far better than anything frozen under the usual conditions of ice manufacture. Many disappointing trials were made to prepare a satisfactory experiment for these Christmas Lectures. After all, there was a kindly frost on the night before, and a young enthusiast rode out on his bicycle and collected from a pond a number of pieces which showed the effect splendidly. It is clearly essential that the ice should grow quietly; probably it is also a condition that the water should lose heat quietly at one face, as the water of a pond does on a still, frosty night.

A little black spot often appears in the centre of the ice flower. Tyndall was greatly interested in it, and explained its occurrence. When the ice melts within the block and a cavity is formed, the water due to the melting occupies less volume than the ice from which it came. Perhaps it holds together at first in a highly strained condition and fills as water the space it filled as ice. But if so the strain must be very great; it breaks away from the ice and shrinks to its natural volume. A vacuum is left, which acts as a tiny lens and diffuses the light that crosses it. Hence the black spot, which implies the absence of light going straight through the cavity.

plate20a

Plate XX A

This is due to Agassiz. It shows that the mass of glacier ice is an agglomeration of smaller blocks in which, when first laid down, the ice flowers would be in a horizontal plane. The blocks have now been heaved into various positions, and the flowers are seen some edgeways, some in full face, and in various other positions.

The ice flowers can be seen in glacier ice, where they are produced by the heat of the sun. When a glacier is formed by the contributions of ice from tributary glaciers or from blocks that have fallen in on the sides, the mass may consist of a pile of ice masses all frozen together, each of them showing ice flowers. The orientation of the flowers shows in each case the original lie of the block, for they are always formed in planes which were once horizontal. In the figure (Plate XX A), taken from an old volume by Agassiz, a section of glacier ice shows well the various positions of the cavities-some in full view, some on edge, and some in intermediate positions.

Let us now turn to the analysis of the structure of the ice crystal which X-rays have made possible. We must hope to find in it some explanation for its form and other physical properties which we have been considering. It turns out that the structure is something like that of diamond: there is the same symmetrical arrangement of four neighbours of like kind round every atom. In this case, it is the oxygen atom that stands at the centre of a tetrahedron, four other oxygen atoms lying at the four corners. There are, however, certain minor differences of structure. In the first place, in diamond the carbon atoms join on to each other. In ice there are the hydrogens to be placed. If we put one hydrogen between each pair of oxygens we shall have a symmetrical arrangement in which the atoms are in the proper numerical proportion. Every oxygen has four hydrogen neighbours, and every hydrogen has two oxygen neighbours, which implies that there are twice as many hydrogens as oxygens. A model showing the arrangement under these conditions is illustrated in Plate XX B, C. The large balls represent oxygen, the small represent hydrogen. It must be clearly understood that the X-ray methods do not measure the size of the oxygen atom, or of the hydrogen. All that they do is to find the distance between the centre of one oxygen and the centre of an oxygen neighbour, a distance which is the sum of the diameters of oxygen and hydrogen. The oxygen atom may take all the room, and the hydrogen none, because the hydrogen atom is supposed to hand over its electrons to the oxygen and be left a bare nucleus. No one can say how its size should then be represented. In making a model we must adopt some sizes for the balls which represent the atoms, and the model must be interpreted with the corresponding reservation.

Plate XX

plate20b

B. The model is made of balls of two colours, the white representing oxygens and the black hydrogens.

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C. A smaller section of the ice model, showing the grouping of the oxygens and hydrogens.

There is a second point of difference between diamond and ice which is subtler and more difficult to realise; but it is worth while trying to understand it. If the reader finds it too difficult to grasp, he may leave it out without any fear of losing the thread of the story.

Suppose that we are looking down on the diamond model from above, and we see a single puckered layer, as in Fig. 46, A. The carbon atoms are marked as 1, if they lie directly on the base of the crystal, and as 1’ if they are the atoms which are somewhat raised above their neighbours in the layer. Take another layer exactly like the first, and write 2 everywhere instead of 1, and place it on the first, so that each 2 comes over a 1’— that is to say, an atom in the lower level of the second layer comes over an atom in the higher level of the first. This is what happens in diamond. The combination is shown in Fig. 46, B, where 1’2 means that the atom 2 lies over the atom 1’. Now take a third layer, which Fig. 46 we may denote by using 3’s, and lay this so that 3 comes over 2’. We then get the arrangement of Fig. 46, C, and when this is repeated over and over again, in the same order 1 2 3 1 2 3, we get the diamond structure.

If new we begin again with a layer of r’s, but take as the arrangement of a layer of 2’s that which is shown in Fig. 46, D— which, it must be carefully observed, is not the same as before; the layer of 2’s has been turned round in its ‘own plane through I8o°— we then repeat the first layer, and alternately have I and 2. This gives us the arrangement of the oxygens in ice. The structure is complete when we place a hydrogen between each pair of oxygens.

If we look at the picture of the ice model shown in Plate XX B, we may be able to realise the arrangement. Why one crystal should repeat continually a series of three layers, and the other of only two, we cannot imagine.

If we now look at the model of the ice structure we can see in it many interesting features which help to explain what we know of the properties of ice. The hexagonal structure is there, of course, and the emptiness of the model is surely connected with the lightness of ice and the featheriness of snow. Ice floats on water; we can see that the molecules of water when they join up in the crystal structure must take up more room than before, We could obviously crush the model together into a smaller space, and that is, no doubt, what happens when ice melts under pressure. There is a well-known experiment which illustrates the point. A block of ice is supported at its ends, and a fine wire carrying heavy weights is slung over it, as shown in Fig. 47. The wire proceeds to sink slowly into the ice, but as it does so the ice closes up behind it, and when, finally, the Fig. 47 wire makes its way right through the block and drops, with the weights, on the floor, the block is still whole. It would seem that the pressure of the wire on the block breaks down the structure of the ice, and some of the molecules are set free. In other words, a certain quantity of ice is melted under pressure and becomes water, which is squeezed out from under the wire and slips round to the vacant space above it. There it joins up again with the ice on either side. We can imagine the molecules as settling into their places, because on either side there is crystalline ice holding out hands to them. Crushed ice can be moulded under great pressure into various shapes. We may, for instance, make a crystal cup: we need two or Fig. 48 three boxwood moulds of the proper shape. In one we can form the upper portion of the cup, in another the stem, and in yet another the foot; then we join them together into one piece by holding them into position for a few moments. The moulds we use in making the cup shown in Fig. 48 were once used by Tyndall for the same purpose.

When Tyndall showed these experiments he was proposing a theory of the movement of glaciers, and employed them as an illustration of his arguments. Tyndall, we may remember, devoted a great deal of time to the measurement of glacier movements: he was interested in them both from the scientific point of view and from his devotion to mountaineering.

Glaciers descend from the snow-covered mountains, glide along the valleys, and pour out into the plains almost as if they were fluid: a very viscous, treacly fluid, because the motion is so slow — a few inches a day or even less in some cases, many feet a day in others. That which has always excited wonder and interest is the stateliness of the motion, and the strange way in which a substance so brittle and crystalline can flow like a river, can move round the corners of a valley, or fall over a cliff and yet remain whole. In Tyndall’s time much consideration was given to a theory which supposed that the glacier melted internally in places where the strain was great, and that the water thus formed [slipped away, relieving the pressure. It would freeze again, it was said, if it made its way into empty cracks or spaces where there was no longer the pressure required to keep it molten. Thus the glacier would, in a way, contract where compressed and expand elsewhere, and so accommodate itself to its bed. The explanation seems to offer difficulties when we think of the glaciers in the Arctic or Antarctic which also flow, though the temperature is so low that no conceivable pressure would bring about any melting.

It is possible that when we look a little more closely into the behaviour of a crystalline structure we shall find another way of conceiving how the motion takes place: not so very different in reality from the view that Tyndall maintained, but not so open to criticism. There are many substances that can be made to flow like a glacier: metals can be squirted through holes; wires can be drawn; plates can be rolled. Even the surface of glass, or of a perfect crystal such as Iceland spar, can be made to “flow,” as Sir George Beilby has shown. Now all these things are crystalline; if we did not know it before, the X— rays have emphasised the fact for us. And they are just as crystalline after the flow as before. We shall see some examples when we come to speak of the metals. The substance accommodates itself to pressure, changing its shape as it does so. Whole layers of atoms or molecules are momentarily uprooted from their places, ride over the tops — so to speak — of the atoms on which they lie, and settle down into a new position, or perhaps are kept on the move for some time. When they settle down again for a moment the crystal is perfect once more, and when they are uprooted, the bonds are broken as if the substance was going to melt. This must be especially the case when, as in ice, the substance contracts on melting, when the bonds, breaking under pressure, let the atoms and molecules take up positions in which less space is occupied than before. When a piece of metal is bent or squeezed into a new form, the crystals of which it is made, whether few or many, are “sheared”— that is to say, one part slides on another part; and we can understand how many successive “shears” can bring about any change of shape. So it may be in the case of ice: both shearing and melting may be called into play during the change of shape. The “shearing” of ice has often been observed. A block of ice is cut from the ice that has formed naturally on the surface Fig. 49 of the water. If such a block is supported at its ends, and lies in the same position which it had when it grew, it bends under a weight, just as a beam would (Fig. 49, A). If it is turned on its edge and placed so that the layers which were horizontal are now vertical, and their plane is parallel to the line joining the supports (Fig. 49, B), then the block yields very little indeed. If the planes that were horizontal are perpendicular to the line joining the support they slide on one another, and the ice block is altered in shape (Fig. 49, C). If under pressure and local melting a few molecules are set sufficiently free to move as a liquid into a new place, they will, as in the case of the wire, readily join on to the ice structure on either side, simply because a place is always waiting for them. But we can look on the effect in the general sense as due to the movement of the planes over one another.

It is curious to see with what readiness pieces of ice join together. If we rest one fairly flat piece on another for a few moments, we can, keeping hold of the latter piece, turn the pair upside down, and the added piece does not fall. When two pieces of ice are held together under water, even warm water, they join together.

We may now go back to the consideration of the peculiar chain molecules of carbon atoms which, from want of time, we were obliged to leave over from the last lecture. When we considered the structure of the diamond, We saw that there was a certain arrangement of the carbon atoms which was found everywhere within it. It was an arrangement of six atoms in the form of a ring. We saw that a similar arrangement formed the basis of the so-called benzene ring, which is a molecule formed by ringing the six — sided carbon ring with six hydrogen atoms; and that a very large number of other important molecules were founded on the same arrangement, the hydrogen atoms being replaced by various other atoms or groups of atoms. The study of these molecules is the purpose of one of the great branches of organic chemistry. The molecules form substances which are called “aromatic,” because many of them have a fragrant smell.

There is a second great branch of organic chemistry, which deals with substances of a different kind. They are called “aliphatic,” the word implying that they are well represented by oils and fats. The chemist has been able to prove that in this case the molecule is formed of a chain of carbon atoms, to which various atoms, particularly hydrogens, may be attached along its length and at its end. The ring was obvious in the diamond structure. It seems, from recent experiments, that we may find the chain also in the diamond; so that the diamond contains the essentials of both the great branches.

We considered a few examples of the ring in the last lecture, but left the chain until today. The chain is formed of any number of links, each of which, in general, is made out of one atom of carbon and two atoms of hydrogen; and the ends are formed of various groups of atoms, of which some are very common and give to the chain well-known characteristics. In the simplest case the ends are formed of hydrogen atoms, and we have then the hydrocarbon or paraffin molecule. The symbol of pentane, for example, is written by the chemist as follows:—

Pentane is an inflammable liquid used in standard lamps — that is to say, lamps which serve as a standard of comparison for other lamps, because they burn with a steady and constant flame. The diagram is intended to represent the way in which the various atoms are attached to one another. Each carbon is joined to four other atoms. The carbon atom cannot link up closely to more than four, so that the molecule cannot be added to without first breaking it somewhere. It is said to be saturated. In the diagram it is represented as lying altogether in one plane, partly because of convenience of drawing, partly because so little is known of its actual arrangement. One of the objects of the X-ray analysis is to determine the relative positions of the atoms in a molecule more accurately than has been possible hitherto, and to measure the linear dimensions. In the case of these long — chain molecules, the X-rays have recently had an unexpected’ success. In order to express this additional knowledge, we really need a model or a sketch in perspective; a model of the probable form of the pentane molecule is shown in Plate XXI A.

PLATE XXI.

plate21a

A. Model of a hydrogen chain. pentane, containing five carbon atoms. The larger balls represent carbon atoms, the smaller hydrogens.

plate21b

B. An X-ray spectrum of the hydrocarbon containing 13 carbons obtained by the method shown in Fig. 52. (Muller.)

plate21c

C. The model shows the arrangement of sodium and chlorine atoms in rock-salt: the dark balls represent sodium, the white chlorine, or vice versa. Only arrangement is shown: there is no attempt to show the size or shape of the atom.

Many members of the paraffin series are found mixed together in petroleum wells. They are inflammable, because they readily break up under the proper stimulus in the presence of oxygen, and the atoms rush into fresh combinations, developing great heat in doing so. The shortest member of the series contains only one link. It is a gas, called methane or marsh gas, represented thus:—

It bubbles up from stagnant water containing vegetable matter in decay. As the chain grows longer, the substance holds together better. Pentane, with five links, is a liquid at ordinary temperatures and boils at 36° C.; pentadecane, with fifteen links, boils at 257° C., while penta-cosane, with twenty-five links, is solid at ordinary temperatures and melts at 54° C. The long molecules are supposed to have a tendency to lie side by side, like matches in a box; we shall see that this view is strongly supported by the X-ray results. It may, therefore, be expected that the longer they are, the greater the forces required to tear them apart; so that for this reason alone the longer the chain the higher its boiling point and melting point. As a class they have no strong hold on each other: the boiling and melting points are low. The cloak of hydrogens with which they are covered seems to hinder their association with other molecules such as those of acids. In fact, the word paraffin is derived from two Latin words meaning “little” and “affinity.” But, as I have already said, they join up very readily with oxygen under the proper circumstances.

The behaviour of these chains is greatly altered if we take off an end group and put on a different one. By substituting for one of the end hydrogens a certain group, containing a carbon, two oxygens and a hydrogen, we get another highly important series of compounds called the “fatty acids.” The group is known as the carboxyl group. Here again the chain may be of any length. When there is only one carbon in it, the chemist represents it thus:—

meaning that of the four bonds which carbon can exert, drawing four other atoms to itself, one goes to a hydrogen, another to an oxygen which carries a hydrogen, and two go to a separate oxygen, binding it very tightly. This substance is formic acid, which is secreted by ants, and has a very irritating action on the skin, as we all know. When a fresh link is added to the chain, we have acetic acid, which gives acidity to vinegar; in fact, the name is derived from the Latin word for vinegar. The formula is no:—

Butyric acid has four carbons; it is the substance that gives to rancid butter its peculiar taste and smell. Lauric acid has twelve carbons, and is found in laurel oil and cocoanut oil. Myristic acid has fourteen, and is found in the butters of mace and nutmeg. All these are liquids. Palmitic acid, found in palm oil, has sixteen, and stearic has eighteen. The last two are solids at ordinary temperatures. They are used in the manufacture of stearine candles, and, slightly modified, are the most important constituents of animal fat.

The alcohols constitute another of these chain series. They are formed from the paraffins by taking off a hydrogen from one end and replacing it by an oxygen and a hydrogen in combination.

Thus:—

is the ordinary alcohol.

And so we may go on, describing an immense number of substances, all consisting of links of CH,, with varying terminations. Sometimes one or more hydrogens are taken off the side of the chain and replaced by other atoms or atom groups; sometimes there are further complications. There is a fascination in the simplicity of the general principle and in the wonderful variety and influence of detail. Why should different plants or different animals, or different members of the same plant or animal, contain these carbon chains of different lengths, on which their own growth and properties and characteristics greatly depend? Of course, the whole effect rests, in the first place, on the properties of the carbon atom, and it is that which gives a peculiar interest to the crystal forms of carbon, diamond and graphite.

We may look again at the diamond model and ask ourselves whether we can see any skeleton form of the chain, just as we saw the skeleton of the ring. The model (Plate XIV A) shows that it can be cut into chains of any length and of this form:—

Fig. 50

in which the angle that recurs at every bend can be calculated to be 109° 28’. We might suppose this to be a simple form of the chain. We are only speculating, of course, trying to imagine possible solutions of our problems, which we may put to the test of experiment, and even when we seem to have a success, not counting too much upon it. If this were the chain, two hydrogens would naturally be attached to each carbon at points which, with the two points of attachment of its carbon neighbours, would make four points symmetrically arranged, like the four points at which each carbon atom is attached to its four neighbours in the diamond, as in Plate XXI A. This picture goes more into details than the form of illustration generally employed by the chemist; the latter is merely a representation on the flat, our new figure is in three dimensions. And no doubt the true figure is in three dimensions. The chemist has not drawn it so hitherto, because he has had no direct evidence as to how he ought to do it. We are trying to go one stage further; with some hesitation, because we are not perfect in the interpretation of our new methods, though very hopeful as to their value to us in the end.

In the last year or two we have been able to make accurate measurements of the lengths of the chain molecules by means of the X-rays. The discovery of the method arose from a curious accident. A certain crystal was under examination by X-rays, and because it was liable to suffer rapid deterioration from the moisture of the air, it was covered over with a thin layer of the solid paraffin which is generally used in laboratories as an electric insulator. Certain reflections of the X-rays were found which could not be reconciled with what was known. It was found that they were due to the paraffin. The commercial paraffin is a mixture of several of the fatty acid chains, and is not suitable for accurate experiment. It happened, however, that a certain enthusiastic student of organic chemistry, Dr. Le Sueur, had prepared a great number of these chain substances in a pure state, and these were fortunately available. Those and many others have now been examined, with very interesting and, on the whole, simple results.

The particular method is a good example of the way in which the X-rays can be used. A little of the solid substance is put on a piece of glass and pressed flat: We will consider the significance of the pressing in a moment. The substance is now, as it turns out, in layers parallel to the glass. The molecules in each layer are are???????

They may be represented as in Fig. 51, in which three layers are drawn. Each layer is perhaps a fifty-millionth of Fig. 51 an inch thick, and the thickness is proportional to the hydrocarbon length of the molecule. When a beam of X-rays is passed through such a sheet, composed of layers, a little is reflected by each layer, just as would happen in the case of a beam of light passing though a pile of glass plates. The principle of the experiment has already been described on p.:40. Suppose S is the source of the X-rays, and P1P, is the glass plate with its layers upon it. When the X-ray beam along SC falls on the plate at the proper angle, the reflection from the different layers are all in step and the reflection is strong. We may imagine the reflected ray going off on the line CR1, and making its mark at R1 on the photographic plate DD. If the plate is then turned round about the vertical line through C— the figure shows the experiment in plan — reflection as a whole ceases, because the separate reflections from the various layers get out of step and destroy each other. But when the plate has been turned sufficiently, another Fig. 52 general reflection appears, because the reflections from the different layers have got into step again. The first general reflection comes when the particular reflection from one layer is one wave-length behind or in advance of the reflection from the layers on either side of it; the next when there is a difference of two wave-lengths, and so on. Consequently the photographic plate when it is developed shows a whole series of such general reflections. Usually the plate is turned so as to throw reflections both above and below the line (Fig. 52). A central mark M is due to the direct action of the X-rays — this part of the plate is usually shielded, so that the direct action is not too strong — and all the different orders of reflection appear on either side. An actual example showing the reflection of a paraffin of 18 carbons is shown in Plate XXI B. It was obtained by Dr. Müller. It will be seen that the reflections are very well marked. It is possible to measure their distance apart with accuracy, and from this We calculate the thickness of one of the layers in the reflecting material. We cannot be quite sure that the molecules stand upright and perpendicular to the layer, but we have good grounds for supposing so, which we need not enter into here. We find that the length of the chain increases with perfect regularity as carbon links are added to it. We actually find that many of them have exactly the length we should expect if they were as represented in Fig. 50.

The whole series of experiments of this kind bears out the idea that the chemist has formed as to the shape of these molecules: his representation has been wonderfully correct. The X-rays have given precision to the idea, suggesting also that the molecule must be drawn in three dimensions, and at the same time measuring the length. I may add that the sideways dimensions can be measured also.

We may now go back to the curious point that we get much better X-ray reflections if the material is pressed on to the glass plate. It seems likely that it naturally forms flakes, and in each flake the molecules are perpendicular to the flake. They join together side by side, as I have already said, and hold together much better in this union than one flake holds to another. This last linking is affected by the ties at the ends of the molecules, and these are much weaker. It is exactly the same effect as we found in graphite, where flakes held together strongly as flakes, but slid easily on one another. It is this that gives the greasy, slippery feeling both to the greases and fats and to graphite. When pressure is applied to the material, the layers are squeezed flat, just as when graphite is rubbed on a surface, and the X-ray reflections are good because the layers are made to lie regularly. When the material is melted and cooled again, the layers are broken up, and though, no doubt, they are formed again, they lie irregularly; the X-ray reflection is then poor. We find the same effect in the case of gold leaf, as we shall see in the next lecture.

There is another curious property of the long-chain molecules which is worth our consideration. The paraffin chain has hydrogens at both ends. Each flake is one molecule thick. But in the case of the fatty acids (p. 188), the X-rays show that there are two molecules in the layer, end to end. This is, indeed, to be expected, because it is known that a carboxyl group has a tendency to join up with another of its own kind. Consequently the chains attach themselves together in pairs, forming a chain of double length, the ends of which are hydrogens; the two carboxyl groups are in the centre. This result is obtained from the X-ray measurements. Here again the X-rays confirm a chemical conclusion and throw a fresh light upon it.

There is a type of crystal structure which, differing entirely from those that we have considered already, is of such great importance that we must not pass it by. The crystals of ordinary salt are good examples.

Sometimes, as we have already seen, a molecule is formed from two atoms, of which one, being greedy for an additional electron, has satisfied itself at the expense of the other atom. The latter, before the transference, has held one electron in a loose binding. For example, chlorine has seventeen electrons: two in an innermost shell or coating, and eight in the next shell. In the outer shell there are seven, and the chlorine atom exerts a great force, tending to complete the shell, which when full contains eight. It will then present the external appearance of argon. Sodium has eleven electrons normally: two in the inner-most shell and eight in the next, but only one in the outer shell instead of the seven in chlorine. The sodium atom has no tight hold on this odd electron, so the chlorine takes it. The sodium atom then has the external appearance of a neon atom. (See p. 76.)

The two atoms are now charged electrically; the chlorine is negative, because it has one negative charge over and above its proper number, and the sodium is positive, because it has one too few. The governing principle in the growth of the crystal is the attempt on the part of the atoms to satisfy as fully as possible the mutual attraction of the positive sodiums and the negative chlorines. The system of packing which Nature adopts is that in which each chlorine is surrounded by six sodiums and vice versa. It is shown in Plate XXI C. It is very simple — a cubic arrangement in which each of the lines of atoms that are parallel to the edges consists of sodium and chlorine atoms alternately. The white balls may represent chlorine and the black sodium, or vice versa. It is because of this arrangement that salt crystallises from brine in cubic form. The crystals are not necessarily cubes, but are rectangular blocks, all faces of which are of the same type. The frequent differences between their sizes and appearances are merely accidents of growth. Very many crystals are built on this principle: in particular all the salts of the metals, in which the metal has lost one or more electrons, and the remainder of the molecule, as a group, has gained them. The resulting structure is not always so simple as that of salt, because, for instance, the group may be more irregular in outline than the single chlorine. In calcite, the metal atom calcium loses two electrons to the group CO,, and the result is the rhomb of Iceland spar. It is still true that each metal atom is surrounded by six negatively charged bodies, and each of the latter by six metal atoms; the crystal is no longer rectangular, because the CO, group is not round.

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