But it has been shown from the researches of Miers that vicinal faces are often produced in preference to these simple index planes of high density, and such vicinal faces, although the nearest (in angular position) of all possible faces to those simple index planes, are themselves of excessively low reticular density, so much so that if represented by indices at all they can only be indicated by very high numbers, not such as we are accustomed to consider as in keeping with the simple spirit of the law of rational indices. Taking the example worked out most fully by Miers, the octahedral crystals of alum, it is a fact that the cubic faces of highest reticular density are those of the cube itself, then come in order those of the rhombic dodecahedron and those of the octahedron. Hence, the density of octahedral faces is very high. But those of the very low triakis octahedron, which Miers finds to replace the octahedron faces so frequently as vicinal faces, are of excessively low reticular density.
Miers explains the appearance of the latter instead of octahedral faces by assuming that the supersaturated liquid in contact with the growing crystal consists of the particles (molecules) of salt uniformly mingled with those of water, the solvent, and that the act of crystallisation consists of the escape of the water and solidification of the salt. Consequently, the salt particles just before crystallisation cannot be so dense as they are along primary planes of the crystal, as they are separated by the water particles, which are presumably much more numerous. Hence it is that they are not deposited along the planes of high reticular density, but along vicinal planes of low density of points. For instance, he shows that the shower of salt particles upon a cube face would have to be so dense that there would be insufficient room for the water particles. The density in a cube face is 114 times as great as that in one of the vicinal planes observed. Now, 100 cubic centimetres of solid alum weigh 172 grammes, and 100 c.c. of the solution depositing crystals contain 9·74 grammes of alum. Thus the density of the growing crystal of alum is nearly 18 times that of the alum in the adjacent saturated solution.
Consequently the deposition of the salt particles, in a moderately quick crystallisation, when insufficient time is afforded for the deliberate escape of the water particles and for the orderly rearrangement of the salt particles, occurs along vicinal planes instead of along the primary planes. For it must not be forgotten that whenever it has the opportunity of coming into operation there is a directive molecular force of some kind, which controls the operation of crystallisation, and which undoubtedly attempts to cause, and given adequate time and scope succeeds in causing, the production of faces of high reticular density, the fundamentally important primary faces of lowest indices, and which are often those along which cleavage occurs. Wulff emphasises this in saying (loc. cit., p. 461): “Bei der Krystallisation orientiren sich die Molekeln auf den Flächen des Krystalles ganz gleichförmig durch den Einfluss der Richtkraft der Krystallisation.” The more rapidly the crystallisation occurs, however, the less chance is there for this force to attain its ultimate object. More will be said about this directive force in the next chapter, after we have studied the remarkable “liquid crystals” discovered by Lehmann.
This highly interesting explanation of Miers, supported as it is by the work of Wulff, and confirmed also in many respects by the observations of the author, whose great aim throughout his investigations has been to avoid the production of such vicinal faces, throws an important light on the nature of the act of crystallisation. It renders the reason clear why crystals which are very slowly grown from solutions only feebly supersaturated and under conditions of absolute rest, protected from either air currents or preventable earth tremors—conditions which the author has taken quite exceptional pains to procure for the preparation of the crystals used in the investigation of the sulphates and selenates of the rhombic simple salt series and monoclinic double salt series—are occasionally obtained quite free from any sign of such vicinal faces. They are small perfect individuals exhibiting primarily the faces of high reticular density, that is, the faces of the simple forms of low rational indices; and these faces are absolutely plane, affording one single brilliant image of the goniometer signal, which can be adjusted with great precision to the cross-wires of the telescope. For the slower the growth, the more time is afforded for the escape of the water molecules, and for the salt molecules to deposit themselves as directed by the molecular guiding force of crystallisation, along the planes of high reticular density. In many of his experiments Miers expressly stirred the solution, to prevent concentration currents, which had been considered by Wulff of importance in the process, from coming into play and causing unknown effects. Hence his experiments in which vicinal faces were produced are not comparable with the author’s slow growths.
The work of Miers assists in the proof that the constancy of angle to within one or two minutes of arc is a real property of the crystals of a substance. For previously the frequent presence of vicinal faces rather than the simple forms of high reticular density, and which had been mistaken for the latter, had caused Pfaff in 1878[[25]] and others to conclude that variations from the true crystal angle amounting to as much as 30′ were of common occurrence as the result of strain during deposition.
Brauns[[26]] in 1887 made a careful series of measurements of very good octahedral crystals of lead nitrate, and found 13′ 20″ the largest deviation of a good image from the theoretical position. He imputed it to the action of gravity as a disturbing cause during deposition. The researches of Miers have cleared away all this misconception, in proving that the bright images referred to, taken for those of the simple primary form, are not such at all, but vicinal faces of very low reticular density.
CHAPTER XVI
LIQUID CRYSTALS.
We have seen in the foregoing pages that a crystal is usually a solid, highly organised in a homogeneous manner, and, unless the symmetry be developed to its highest extent, the crystal then belonging to the cubic system, it is also in general anisotropic, that is, it exhibits double refraction. Section-plates of it, more or less thin according to the strength of the double refraction, exhibit colours in parallel polarised light, and show the phenomenon of a single optic axis, or of two optic axes, in convergent polarised light. Every variety of hardness, however, is displayed, from that of the diamond down to that of a crystal as soft as gypsum, and even softer. Moreover, many of the softer crystallised substances develop the property of permitting one layer to glide over another by gentle side pressure with a knife blade, when inserted in an edge or face in an attempt to cut the crystal. Calcite and ice, for instance, both possess such planes of gliding of the structural units over one another in layers. There are also the border line cases of crystals so soft as to be readily bent, and many well-known viscous substances crystallisable only with great difficulty, some of which form pliable crystals.
But in the year 1876 Lehmann discovered a new property in an already remarkable substance, iodide of silver, AgI, namely, that at temperatures superior to 146° C. it can flow like a viscous liquid, while exhibiting several of the properties which are characteristic of crystals. Silver iodide is dimorphous, exhibiting a hexagonal form at the ordinary temperature, which persists up to 146°. But during the heating to the latter temperature a regularly accelerating diminution of volume occurs, the feeble expansion in directions perpendicular to the axis being overbalanced by a considerable contraction along the axis, both quantities having been accurately measured so long ago as the year 1867 by Fizeau, by means of his delicate interference dilatometer. This contraction, so unusual an occurrence with increase of temperature, culminates at 146°, according to Mallard and Le Chatelier, in a sudden change of condition into a cubic modification, accompanied by absorption of heat. Now Lehmann, studying this cubic modification of silver iodide under a microscope which he had devised—specially adapted for observations at temperatures higher than the ordinary, by being supplied with the means of heating the object under observation—found that it was not only plastic, but actually a liquid.
