The Molecular Tactics of a Crystal

by Baron William Thomson Kelvin

Fig. 14.

[§ 38.] This asymmetric double crystal becomes simply the well-known symmetrical ‘twin-crystal’[11] in the particular case in which each of the constituent molecules is symmetrical on the two sides of a plane through it parallel to the plane of our diagrams, and also on the two sides of some plane perpendicular to this plane. We see, in fact, that in this case if we cut in two the double crystal by the plane of Fig. 14, and turn one part ideally through 180° round the intersection of these two planes, we bring it into perfect coincidence with the other part.

This we readily understand by looking at Fig. 14, in which the solid shown in outline may be either an egg-shaped figure of revolution, or may be such a figure flattened by compression perpendicular to the plane of the diagram. The most readily chosen and the most stable resting-places for the constituents of each successive layer might be the wider hollows p′ q′ r′: and therefore if, from a single layer to begin with, the assemblage were to grow by layer after layer added to it on each side, it might probably grow as a twin-crystal. But it might also be that the presence of a molecule in the wider hollow p′ q′ r′ on one side, might render the occupation of the corresponding hollow on the other side by another molecule less probable, or even impossible. Hence, according to the configuration and the molecular forces of the particular crystalline molecule in natural crystallization, there may be necessarily, or almost necessarily, the twin, when growth proceeds simultaneously on the two sides: or the twin growth may be impossible, because the first occupation of the wider hollows on one side, may compel the continuity of the crystalline quality throughout, by leaving only the narrower hollows p q r free for occupation by molecules attaching themselves on the other side.

§ 39. Or the character of the crystalline molecule may be such that when the assemblage grows by the addition of layer after layer on one side only, with a not very strongly decided preference to the wider hollows p′ q′ r′, some change of circumstances may cause the molecules of one layer to place themselves in a hollow p q r. The molecules in the next layer after this would find the hollows p′ q′ r′ occupied on the far side, and would thus have a bias in favour of the hollows p q r. Thus layer after layer might be added, constituting a twinned portion of the growth, growing, however, with less strong security for continued homogeneousness than when the crystal was growing, as at first, by occupation of the wider hollows p′ q′ r′. A slight disturbance might again occur, causing the molecules of a fresh layer to settle, not in the narrow hollows p q r, but in the wider hollows p′ q′ r′, notwithstanding the nearness of molecules already occupying the wider hollows on the other side. Disturbances such as these occurring irregularly during the growth of a crystal, might produce a large number of successive twinnings at parallel planes with irregular intervals between them, or a large number of twinnings in planes at equal intervals might be produced by some regular periodic disturbance occurring for a certain number of periods, and then ceasing. Whether regular and periodic, or irregular, the tendency would be that the number of twinnings should be even, and that after the disturbances cease the crystal should go on growing in the first manner, because of the permanent bias in favour of the wider hollows p′ q′ r′. These changes of molecular tactics, which we have been necessarily led to by the consideration of the fortuitous concourse of molecules, are no doubt exemplified in a large variety of twinnings and counter-twinnings found in natural minerals. In the artificial crystallization of chlorate of potash they are of frequent occurrence, as is proved, not only by the twinnings and counter-twinnings readily seen in the crystalline forms, but also by the brilliant iridescence observed in many of the crystals found among a large multitude, which was investigated scientifically by Sir George Stokes ten years ago, and described in a communication to the Royal Society ‘On a remarkable phenomenon of crystalline reflection’ (Proc. R.S., vol. xxxviii, 1885, p. 174).

§ 40. A very interesting phenomenon, presented by what was originally a clear homogeneous crystal of chlorate of potash, and was altered by heating to about 245°-248° Cent., which I am able to show you through the kindness of Lord Rayleigh, and of its discoverer, Mr. Madan, presents another very wonderful case of changing molecular tactics, most instructive in respect of the molecular constitution of elastic solids. When I hold this plate before you with the perpendicular to its plane inclined at 10° or more to your line of vision, you see a tinsel-like appearance, almost as bright as if it were a plate of polished silver, on this little area, which is a thin plate of chlorate of potash cemented for preservation between two pieces of glass; and, when I hold a light behind, you see that the little plate is almost perfectly opaque like metal foil. But now when I hold it nearly perpendicular to your line of vision the tinsel-like appearance is lost. You can see clearly through the plate, and you also see that very little light is reflected from it. As a result both of Mr. Madan’s own investigations, and further observations by himself, Lord Rayleigh came to the conclusion that the almost total reflection of white light which you see is due to the reflection of light at many interfacial planes between successive layers of twinned and counter-twinned crystal of small irregular thicknesses, and not to any splits or cavities or any other deviation from homogeneousness than that presented by homogeneous portions of oppositely twinned-crystals in thorough molecular contact at the interfaces.

§ 41. When the primitive clear crystal was first heated very gradually by Madan to near its melting-point (359° according to Carnelly), it remained clear, and only acquired the tinsel appearance after it had cooled to about 245° or 248°[12]. Rayleigh found that if a crystal thus altered was again and again heated it always lost the tinsel appearance, and became perfectly clear at some temperature considerably below the melting-point, and regained it at about the same temperature in cooling. It seems, therefore, certain that at temperatures above 248°, and below the melting-point, the molecules had so much of thermal motions as to keep them hovering about the positions of p q r, p′ q′ r′, of our diagrams, but not enough to do away with the rigidity of the solid; and that when cooled below 248° the molecules were allowed to settle in one or other of the two configurations, but with little of bias for one in preference to the other. It is certainly a very remarkable fact in Natural History, discovered by these observations, that, when the molecules come together to form a crystal out of the watery solution, there should be so much more decided a bias in favour of continued homogeneousness of the assemblage than when, by cooling, they are allowed to settle from their agitations in a rigid, but nearly melting, solid.

§ 42. But even in crystallization from watery solution of chlorate of potash the bias in favour of thorough homogeneousness is not in every contingency decisive. In the first place, beginning, as the formation seems to begin, from a single molecular plane layer such as that ideally shown in [Fig. 14], it goes on, not to make a homogeneous crystal on the two sides of this layer, but probably always so as to form a twin-crystal on its two sides, exactly as described in [§ 38], and, if so, certainly for the reason there stated. This is what Madan calls the ‘inveterate tendency to produce twins (such as would assuredly drive a Malthus to despair)[13]’; and it is to this that he alludes as ‘the inevitable twin-plate’ in the passage from his paper given in the foot-note to § 41 above.

§ 43. In the second place, I must tell you that many of the crystals produced from the watery solution by the ordinary process of slow evaporation and crystallization, show twinnings and counter-twinnings at irregular intervals in the otherwise homogeneous crystal on either one or both sides of the main central twin-plane, which henceforth, for brevity, I shall call (adopting the hypothesis already explained, which seems to me undoubtedly true) the ‘initial plane.’ Each twinning is followed, I believe, by a counter-twinning at a very short distance from it; at all events Lord Rayleigh’s observations[14] prove that the whole number of twinnings and counter-twinnings in a thin disturbed stratum of the crystal on one side of the main central twin-plane is generally, perhaps always, even; so that, except through some comparatively very small part or parts of the whole thickness, the crystal on either side of the middle or initial plane is homogeneous. This is exactly the generally regular growth which I have described to you (§ 39) as interrupted occasionally or accidentally by some unexplained disturbing cause, but with an essential bias to the homogeneous continuance of the more easy or natural one of the two configurations.

§ 44. I have now great pleasure in showing you a most interesting collection of the iridescent crystals of chlorate of potash, each carefully mounted for preservation between two glass plates, which have been kindly lent to us for this evening by Mr. Madan. In March, 1854, Dr. W. Bird Herapath sent to Prof. Stokes some crystals of chlorate of potash showing the brilliant and beautiful colours you now see, and, thirty years later, Prof. E. J. Mills recalled his attention to the subject by sending him ‘a fine collection of splendidly coloured crystals of chlorate of potash of considerable size, several of the plates having an area of a square inch or more, and all of them being thick enough to handle without difficulty.’ The consequence was that Stokes made a searching examination into the character of the phenomenon, and gave the short, but splendidly interesting, communication to the Royal Society of which I have already told you. The existence of these beautifully coloured crystals had been well known to chemical manufacturers for a long time, but it does not appear that any mention of them was to be found in any scientific journal or treatise prior to Stokes’ paper of 1885. He found that the colour was due to twinnings and counter-twinnings in a very thin disturbed stratum of the crystal showing itself by a very fine line, dark or glistening, according to the direction of the incident light when a transverse section of the plate of crystal was examined in a microscope. By comparison with a spore of lycopodium he estimated that the breadth of this line, and therefore the thickness of the disturbed stratum of the crystal, ranged somewhere about the one-thousandth of an inch. He found that the stratum was visibly thicker in those crystals which showed red colour than in those which showed blue. He concluded that ‘the seat of the coloration is certainly a thin twinned stratum’ (that is to say, a homogeneous portion of crystal between a twinning and a counter-twinning), and found that ‘a single twin-plane does not show anything of the kind.’