I can show you the two conditions in one and the same drop by using a solution of common potassium bichromate. Crystals begin to grow at the edge of the drop where the liquid first becomes sufficiently strong, and continue to grow slowly in the evaporating liquid which is only slightly supersaturated. But in a few moments other parts of the drop which are thinner become so strongly supersaturated that they begin to crystallize spontaneously; and there you can witness the birth of new crystals which grow rapidly in all directions, because they are growing in a solution which is much stronger than that in which the first crystals are growing slowly.
Does not all this set one thinking? What is taking place we cannot tell, but we can only think of it as in some way analogous to the birth of a cloud; and in both instances we have to picture to ourselves minute invisible particles, of whose shape and size we know nothing, coming together and coalescing till they grow into a drop or a crystal that we can see. But why they do not begin to coalesce as soon as the liquid is supersaturated it is difficult to say. We have to conceive the alum solution as made up of moving particles of alum and of water, and it may be that the particles are constantly coalescing into minute groups, but as rapidly being broken up again, until a moment arrives at which the alum particles are sufficiently dense to cohere permanently; but how they attract one another and arrange themselves into the wonderful structure which makes a crystal, of this we are entirely ignorant. The question brings us back again to our initial mystery, how does the crystal actually grow?
But this is not all. I have said that all solutions seem to behave in the same way, and among them nitrate of soda, which we have already seen growing in perfect regularity on Iceland spar. It appears, however, from experiments made by Mr. Barker, Miss Isaac, M. Chevalier (who was another of my pupils), and myself, that Iceland spar behaves in this respect also exactly like nitrate of soda. In a solution which is supersaturated, but is not strong enough to crystallize spontaneously, not only will inoculation with a crystal of nitrate produce instant crystallization; but inoculation with a crystal of Iceland spar produces the same result. So we have a still more convincing proof of what I suggested a short time ago, that two crystals, which have structures so nearly identical that they can fit together, possess also the power of drawing each other from the liquid state into the solid form of a crystal. Whatever it is which conditions the fitting together of two structures must then also confer upon them this extraordinary power of making each other grow.
If I had more time, I should like to give an account of some of the more important discoveries that have been made about crystals during the last fifteen years, for they would make it easier to understand the present state of our knowledge concerning them. I will only refer to two: one is an experimental fact, and the other is a theoretical speculation, and both are connected with the subject that I have been discussing.
It was discovered shortly before that time, and has been found by many experiments since, that there are certain substances which are in a real sense crystals, although they are liquid; that is to say, they affect light in its passage through them just as solid crystals do.
These extraordinary substances, which had been investigated by Professor Lehmann, were first shown in England by Mr. Bowman and Mr. Hartley, who were then working in my laboratory, at a conversazione at the Royal Society, not long after their discovery, and I can well remember the interest with which they were witnessed by Sir George Stokes and others. We can only picture these liquids as consisting of particles which, while they are free to move in all directions, always continue to face the same way, like a group of dancers who in all their evolutions continue to face the audience, instead of turning as they move. When the mechanism which renders possible this remarkable behaviour is better understood, we may be sure that it will bring about a better understanding of the manner in which a solid crystal is constructed. The interesting thing about it is that here at any rate the particles are in violent movement instead of being comparatively stationary, as they are in a solid crystal.
One is naturally led to imagine that before any solution begins to crystallize in the solid form it passes into this liquid state, and that the particles have begun to set themselves and all to face the same way before they begin to cohere and to build themselves into a solid. But so far as I know there is no evidence in favour of this suggestion—a solution before solid crystals begin to appear does not behave like a liquid crystal, but remains an ordinary solution up to the last moment when new crystals are born in it or are started by inoculation with a crystal germ.
The other discovery, which is in the nature of a speculation, is that of another person whom I am proud to reckon among my former pupils, namely, Professor Pope of Cambridge, working in conjunction with Mr. Barlow. Mr. Barlow had already been referred to by Lord Kelvin in his Boyle Lecture as the author of ingenious researches upon the various ways in which materials can be packed together, and the different arrangements and structures which result from this packing.
These two workers have now propounded a theory according to which, if the various atoms which constitute a substance are represented by spheres whose sizes represent the valency of the atoms, and if these spheres are packed together as closely as they will go, the resulting structure will represent very nearly the structure of the crystal; and so it may be possible for the first time from a knowledge of the chemical constitution of a substance to predict the structure of its crystals and therefore the form in which it will crystallize. You remember the bee’s cell arrangement and the similar arrangement of balls got by placing a ball in each cell and then removing the cells. Another way of getting the same arrangement is to place a number of equal balls on a table and to squeeze them together until they are packed as closely as possible. This arrangement of closest packing, the arrangement of a pyramid of cannon-balls, is precisely the same as before, the one in which each ball on the table is in contact with six others. According to Pope and Barlow the atoms in a crystal simply pack themselves together as closely as possible, but instead of being equal in size they have generally to be represented as of different sizes according to their valencies. If we imagine the coalescence of atoms to form a crystal to be due to their mutual attraction, it is very reasonable to suppose that they will get as close together as is possible, and therefore that the ways of close packing are the ways of crystal structure. The theory therefore suggests a reason for the growth as well as for the shape of a crystal. I may remind you that the bee’s cell itself, which is in the world of life the thing that most nearly resembles crystalline structure, is due to this same principle of close packing; for in their efforts to get as closely together as possible the bees are constrained to get into the hexagonal arrangement. The bees crowd their heads together and to each bee’s head corresponds one cell.
On the other hand, Professor Sollas has brought forward some most suggestive and convincing speculations concerning certain crystals which are based upon the principle of open, and not close, packing. His model of silver iodide, for example, is well known in Oxford.