Crystals

One of the most deeply interesting aspects of a crystal, especially from the point of view of the history of crystallographic investigation, concerns the mysterious process of its growth from a solution (in a solvent) of the substance composing it. The story of the elucidation, as far as it has yet been accomplished, of the nature of crystallisation from solution in water is one of the most romantic which the whole of scientific progress can furnish. Again we are struck with the parallelism between crystals and living objects. For just as the discovery of bacteria, the infinitesimal germs of life, has given an immense impetus to our knowledge of disease and been blessed with most beneficent effects in combatting the ravages of the latter, so the discovery that crystal-germs of most common crystallised substances, of no larger size than bacteria, are floating about in our atmosphere, and ready at any time to drop into our solutions and, if the latter are in the proper receptive condition, to set them crystallising, is little less marvellous, and has had as profound an effect on our knowledge of the process of crystallisation. A true story, told to the Royal Society the other day, may serve to illustrate the point. A new chemical compound had been discovered, and at the time there could obviously be no crystal-germs, minute crystallites of the dimensions of possibly only a comparatively few chemical molecules, of this hitherto unknown substance floating about in the air. It was found impossible to obtain the deposition of crystals in the ordinary way, from solutions of the substance in its ordinary solvent, although they were in the condition of proper receptivity above referred to, on account of the absence of such germs in the air. But later on, when the air of the laboratory had become impregnated with such germs, on account of the daily handling of the substance in the laboratory, no difficulty was any longer found in obtaining good crystals quite readily from these solutions.

We are at first inclined to wonder whether such extraordinary statements can possibly be sober facts. Yet such is, indeed, the case, and it will be very well worth devoting a chapter to the story of how we have at length arrived at definite knowledge concerning the process of crystallisation from the state of solution in water. For water is the ordinary solvent from which we obtain our crystals, that is, such as are prepared artificially in the laboratory. The laws which have been discovered to hold for aqueous solutions are, however, equally applicable to the cases where other solvents are used, such for instance as the usual organic solvents like alcohol, ether, chloroform, and benzene.

The conditions under which crystallisation occurs from the liquid state, or from solution of the substance in a solvent, have been accurately determined experimentally by H. A. Miers,^[19] and they bear out in the main the predictions from theoretical considerations which were made by Ostwald.^[20] Taking first the case of crystallisation from solution, there are two distinct curves representing the degree of solubility of the solid substance and of supersolubility. The well-known ordinary solubility curve is obtained by taking the temperature for abscissæ and concentration for ordinates, so that any point on the curve indicates the amount of the solid substance which the solvent can hold in solution at that particular temperature. Now the fact that supersaturation may occur has long been established, the phenomenon being of frequent occurrence; and it is common knowledge that a supersaturated solution may be preserved for a long time without crystals being deposited from it, provided the liquid be maintained quietly at rest. Obviously, therefore, this condition of supersaturation ought to be represented by a second curve a few degrees lower as regards temperature than the solubility curve, and its conditions were fairly fully predicted by Ostwald, after collecting together and analysing the results of the experiments of Gernez, Lecoq de Boisbaudran, J. M. Thomson, de Coppet, Lefebvre, and Roozeboom. It was reserved for Miers, however, to discover a means of experimentally tracing this curve, by observations of the refractive index of the solution. The point at which the deposition of crystals from the supersaturated solution occurs is immediately indicated by a sudden change in the refraction of the liquid, the refractive index attaining its maximum value at the temperature of spontaneous crystallisation, and then dropping suddenly the moment the crystals begin to fall. Moreover, the solution at the same time records its own strength, for the refractive index varies directly as the amount of salt dissolved. The determination of the strength of the solution at the critical moment itself had previously proved an impossibility by ordinary methods.

Fig. 98 gives a general diagrammatic representation of Miers’ results for a typical crystalline substance soluble in water. S is the ordinary solubility curve, which may also be termed the “curve of crystallisation by inoculation.” For as soon as the solution reaches this condition of normal saturation it is liable to be caused to commence crystallising if a germ crystal, that is, a miniature crystallite floating in the air as dust, of the substance itself or of one isomorphous with it or capable of forming parallel growths with it, fall into the solution from the air. It has been a revelation to us that such minute crystallites of all common substances are scattered broadcast in our atmosphere, and that sooner or later one will introduce itself into any solution set to crystallise which is not sealed up or placed in a vessel with a filtering plug of cotton-wool in its neck or other aperture.

SS is the supersolubility curve, situated approximately 10° to the left of the solubility curve as regards temperature, but about as much above as regards concentration, so that the two curves usually run diagonally and more or less parallel to each other across the diagram. This supersolubility curve may be also called the “curve of spontaneous crystallisation,” for it represents the conditions under which alone crystals may begin to form without the initiating impulse of inoculation by a germ-crystallite. On the suggestion of Ostwald it is also termed the “metastable limit,” and the whole area between the solubility and supersolubility curves is named the area of metastability, that which represents the “metastable” condition of the solution. Within this area the conditions are those for the start of crystallisation by inoculation. The area beyond the supersolubility curve represents the “labile” state, in which the conditions are those for spontaneous crystallisation, inoculation being no longer necessary. These precise results will, it is hoped, be quite clear with the aid of Fig. 98.

Hence, when a cooling solution not quite saturated at the higher starting temperature is stirred in an open vessel a slight shower of crystals, started by inoculation, appears when the saturation point is reached, which Miers calls a “metastable shower,” corresponding to the ordinary solubility curve; the liquid then goes on cooling without depositing the main bulk of the excess which that curve indicates ought to be deposited, if it represent the whole truth. But when the temperature of the supersolubility curve about 10° lower is reached, a much more copious shower falls by spontaneous crystallisation, the “labile shower.”

In a closed vessel, such for instance as a glass tube sealed with the aid of the blowpipe after the introduction of the solution, on cooling after heating to a temperature superior to that of saturation, the first shower never falls at all, no amount of shaking inducing the deposition of crystals at the ordinary saturation point, proving that the slight shower of the experiment in the open vessel is due to crystal-germs introduced from the atmosphere. The second shower of crystals falls at the lower temperature just as before, however, at the temperature of the supersolubility curve, indicating that this shower is due in both cases to spontaneous crystallisation. Solutions thus enclosed in sealed tubes, to which inoculating dust crystals cannot have access, can never be made to crystallise at any temperature higher than that given by the supersolubility curve, however agitated, although they immediately do crystallise, if shaken, as soon as that temperature is reached during the cooling. If allowed to remain absolutely quiet, however, the temperature may fall considerably lower before any crystallisation occurs, the labile region being frequently well penetrated before this happens. When crystallisation does supervene, the temperature usually rises somewhat. After the labile shower has been deposited, the crystals continue to grow steadily further, until the metastable region has been traversed, and the saturation state is eventually reached, when final equilibrium is produced.

The proof that the crystals deposited in the metastable condition were started by the advent of atmospheric germ crystals—that is, by infinitesimal but perfectly structurally developed crystals, carried by their very lightness like the particles of dust which are only revealed in the path of a sunbeam as seen against a dark background—was afforded by a series of experiments with a mixture of two rare organic chemical preparations, salol (phenyl salicylate) a substance melting at 42.5°, and betol (β-naphthol salicylate) another melting at 92°, which Miers assumed were not likely to be present in ordinary air. The assumption proved well grounded, and the first shower never fell at all in the earlier experiments in which mixtures of these two substances were allowed to cool in open vessels, from the state of fusion. But very soon the air of the laboratory became impregnated with crystallites of both substances, due to the very operations themselves being carried on in contact with the air, and in the later experiments the first shower of crystals did fall. The experiments were really designed to effect the determination of the solubility curve for salol and betol in each other, that is, the freezing-point curve of their mixtures, and the discovery of the so-called “eutectic” point at which a mixture of constant composition solidifies at a definite temperature. But incidentally the experiments also served to establish similar laws for the production of crystals from the liquefied state, by cooling below the melting point, to those applying to crystallisation from solution. In the case of the mixtures of the substances the one of lower melting point acted as a solvent for the one of higher melting point, just as water does for salt. Two curves corresponding to the ordinary freezing point and to the limit of superfusion were established, analogous to the solubility and supersolubility curves. Pure salol alone proved to crystallise spontaneously at 33°, 9½° below its melting point, and the refractive index attained a maximum for this temperature. Betol spontaneously crystallised at 79°, 13° below its melting point.

Two general cases of crystallisation are shown by the dotted curves ABCD and ABE in Fig. 98. The first, represented by ABCD, is the case of a supersaturated solution, made by adding the salt to hot water, being allowed to cool slowly while stirred. The solution cools from A to B without anything visibly happening, no crystal-germ falling into the solution until B is reached, somewhere well within the metastable region. When the germ has fallen in, however, crystals begin to appear as a slight shower at B, and from B to C they continue to grow slowly. On reaching the labile condition at C a cloud of crystals, the heavy shower, is deposited, and the concentration falls rapidly to D on the solubility curve, generally with slight rise of temperature.

The second case is the important one employed by the author in the investigations which will be found described in his “Crystalline Structure and Chemical Constitution” (Macmillan & Co., 1910), for the purpose of producing crystals of high perfection for goniometrical investigation. The method can be confidently recommended as the one best adapted to afford good measurable crystals, and is of quite general application. The solution is made up so as to be in the metastable condition, that is, only slightly supersaturated for the ordinary temperatures. Eventually, while the solution is at rest in a protected place, free from draughts or vibration, and after it has cooled to the temperature of the air, a crystal-germ enters, followed probably by others; each forms a centre of crystal growth, which proceeds very slowly and deliberately, keeping pace with the evaporation in such a manner that the labile condition is never reached. The natural result is the production of very well-formed crystals bounded by excellent faces, truly plane and free from striation or distortion.

When the operation is arranged to occur during the night, as will usually be the case, the solution being set out to crystallise in a quiet and protected place on the previous afternoon or evening, the slight fall of temperature during the night gently assists the process and almost ensures a good crop of a few well-formed crystals large enough for goniometrical purposes next morning. They should be removed before the temperature begins to rise again with the advent of the sun, dried with blotting paper and by air exposure for a short time, and stored in a miniature bottle labelled with the name or formula of the substance and the date of collection of the crop. In such cases the labile state is never reached, and the course of the crystallisation is represented by the curve BE. The whole conditions for the curve ABE, however, would correspond to much lower temperatures, such as those given at the foot of the diagram below the word “temperature,” rather than to the upper row of temperature abscissæ suitable for the other purposes of the diagram already referred to. Crystallisation might well begin about 13° or 14°, as shown at B, and the liquid would cool a couple of degrees or more during the night while crystallisation was steadily proceeding, until equilibrium was reached at E on the solubility curve.

The diagram does not represent any substance in particular, but is a perfectly general one, corresponding to the facts observed with most of the very varied salts worked with by Miers and those of which the author has had experience. The exact temperatures and concentrations will, of course, differ for each substance.

A beautiful experimental demonstration of crystallisation from the metastable and labile conditions of solution respectively is afforded by potassium bichromate, K₂Cr₂O₇. When deposited slowly from a metastable solution under conditions of quietude, this salt is slowly deposited in bright orange coloured and excellently formed crystals, often of considerable size, belonging to the triclinic system of symmetry; they are bounded by good pinakoidal (pairs of parallel) faces intersecting in sharp edges. But when the crystallisation occurs from a labile solution, being much more rapid, it takes the form of feathery or arborescent branching skeletal growths, there being inadequate time for the formation of well-developed crystals.

Fig. 99, Plate XXI., is a photographic reproduction of well-formed crystals of potassium bichromate, grown from a solution in the metastable condition on a microscope slip, just as they are seen through the microscope in the slow act of formation, employing a 1½ inch objective. The crystallisation had been started by germ crystals of the salt falling in from the air, after which the drop, placed within the ring of hardened gold size on the slide, had been covered with a cover-glass, under which the crystallisation had proceeded with sufficient slowness to enable a successful photograph to be taken, when the camera was subsequently attached above the vertically arranged microscope. An upright micrographic apparatus had been designed by the author specially for this photography of growing crystals, many of the results of which are reproduced in this book.

Fig. 100 is the reproduction of another photograph taken under similar conditions, but employing a hot and somewhat more concentrated solution of potassium bichromate, and making the exposure at the moment when, in the particular field chosen, a rapid labile crystallisation was just completing itself, the rapidity of growth of the feathery skeletal crystals having just become arrested. Indeed, the branches are frequently terminated by small well-formed crystals, the rapid growth having been succeeded by a final slow crystallisation where the solution had discharged its labile excess and attained once more the metastable condition.

This experiment with potassium bichromate lends itself admirably to lantern demonstration with the projection microscope. When the drop of hot concentrated solution is first placed on the warmed microscope slip, and the latter laid on the stage, nothing visible on the screen happens for a minute or two, the solution becoming, however, more or less rapidly cooled. But suddenly, the drop having cooled sufficiently to bring the solution to the labile condition of supersaturation corresponding to the conditions for spontaneous crystallisation indicated by the supersolubility curve, arborescent or feathery growths begin to shoot out from various points in the field, often near the margin, and traverse the screen so rapidly that in a moment or two it is filled with them. The crystallisation then slows down once more, the labile shower of excess having become exhausted, and the terminations of the branches and ramifications begin to develop into good little crystals, which thus hang like fruit on a tree. The experiment is rendered the more brilliant and beautiful by the bright orange colour of the crystals.

In Fig. 101, Plate XI., facing page 88, a reproduction of a photograph of a similar crystallisation from a labile solution of ammonium chloride is given. This salt is also particularly suitable for screen demonstrations. The beautiful skeletal ramifications follow the axial directions of the cubic axes, ammonium chloride crystallising in the pentagonal-icositetrahedral class of the cubic system. Good crystals may, however, be very slowly grown from metastable solutions, and they usually exhibit as the principal forms the icositetrahedron (predominating), cube, octahedron, rhombic dodecahedron, and the class-distinguishing pentagonal icositetrahedron. The rapid growths by spontaneous crystallisation of labile solutions, however, invariably take the form of the rectangularly branching feathery crystals shown in Fig. 101.

Further light has been thrown on the act of crystallisation by another most interesting research of Miers concerning “vicinal faces,”^[21] such as the three very low pyramid faces (forming a very flat triakis octahedron) which often replace each octahedron face on a crystal of alum which has been grown somewhat rapidly. The author has frequently observed this phenomenon in the course of the numerous crystallisations required for the investigation of the sulphates and selenates. It may be described in general terms as the replacement of primary faces possessing the simplest rational indices by faces having such high indices that it is doubtful whether they ought really to be represented by indices at all. The number of such vicinal faces which replace the simple face depends on the symmetry of the crystal, to which, of course, they conform. Thus, while three such vicinal faces replace an octahedral face, and two replace the face of a tetragonal prism, the simple primary prism face of a rhombic or monoclinic crystal would only be replaced by one, which may have a deformation of as much as even 30′ from the correct position of the prism face, and on either side of it. Indeed it is possible for a whole succession of such vicinal faces to be developed within the degree of arc which may in extreme cases separate the limiting values on each side of the prism face, and such are often seen and make up the well-known bundle of images afforded on the goniometer by a bad face, a face which would cause the author at once to reject the whole crystal for measurement purposes. One of the faces, even in cases such as alum or a tetragonal crystal, where three or two might have equal values as regards the symmetry, generally predominates, and affords a very much more brilliant image of the goniometer signal than the others in the bundle, so that an unwary observer might easily come to the conclusion that this was the really valid image corresponding to the octahedron face or to the simple primary prism face, or whatever particular face was expected in the neighbourhood indicated by the bundle of images. Obviously, however, it might only be one of three or two equally valid faces of a vicinal form, which had grown predominatingly during the last period of growth previous to removal from the mother liquor.

The explanation of this interesting phenomenon of the production of vicinal faces is one intimately connected with the structure of crystals, and it forms one of the strongest confirmations of the correctness of the theory of crystal structure the basis of which is the molecular space-lattice. Miers is in full agreement with the author in emphasising the importance of the space-lattice formed by the “points” representative of the molecules, and analogously chosen in the molecules. He says: “Whatever structures may be necessary to account for other features of crystals, there is little doubt that we are justified in regarding their faces as the planes of a space-lattice.”^[22] Now Wulff,^[23] who has contributed very considerably to our knowledge of the nature of the act of crystallisation, has proved, from his own investigations and those of Weyberg, carried out at his suggestion in his laboratory at Warsaw,^[24] that faces of greatest reticular density, that is, those along which the points of the space-lattice are most thickly strewn, are those which grow the most slowly, and therefore are the best developed. This latter will be obvious on a little consideration, for the faces of less reticular density which grow more, tend in doing so to extend the boundaries of the faces of greatest reticular density, and thus to enlarge those faces. Hence the usual planes on a crystal must be those of high reticular density; and these are such as are represented by the simplest indices, the faces most dense of all in points being the primary ones.

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.