Crystals

It has been shown in the last chapter how Mitscherlich discovered the principle of isomorphism, as applying to the cases of substances so closely related that their interchangeable chemical elements are members of the same family group; and also how the principle enabled him to determine the chemical constitution of two hitherto unknown acids which he isolated, selenic H₂SeO₄ and permanganic HMnO₄. For he observed that the selenates were isomorphous with the sulphates, and the permanganates with the perchlorates. It was further made clear that the principle as bequeathed to us by Mitscherlich was only defined in very general terms, and its details have only recently been precisely decided.

Before proceeding further (in Chapter X.) with the elucidation of the true nature of isomorphism, however, some important crystallographic relationships between substances less closely related than family analogues must be referred to, as the outcome of a series of investigations by von Groth, chiefly between the derivatives of the hydrocarbon benzene. Also, some suggestive results obtained by the author from an investigation of an organic homologous series, that is, one the members of which differ by the regular addition of a CH₃ group, may be briefly referred to.

The interval between the work of Mitscherlich and that of von Groth was one of doubt, discouragement, and somewhat of discredit for chemical crystallography. The chemists Laurent^[3] and Nicklès^[4] carried out during the years from 1842 to 1849 measurements of numerous organic substances and of some inorganic compounds, the former chiefly halogen or other derivatives of particular hydrocarbons or salts of homologous fatty acids. Laurent, for instance, found that naphthalene tetrachloride, C₁₀H₈.Cl₄, and chloronaphthalene tetrachloride, C₁₀H₇Cl.Cl₄, crystallise in different systems, the former in the monoclinic and the latter in the rhombic system. Yet the primary prism angles of the two are less than a degree different, namely, 109° 0′ and 109° 45′. Laurent named this kind of similarity “hemimorphism,” a most unfortunate term as it was already employed in crystallography in its other well-known geometrical significance, that is, to denote a crystal differently terminated at the two ends of an axis. Many other like similarities were discovered by Laurent, and he again coined an objectionable term, now discarded, to represent the cases of similarity extending over more than the same system, namely, “isomeromorphism.”

Nicklès observed similar facts in connection with the barium salts of the fatty acids, which crystallise in different systems with different amounts of water of crystallisation. But their prism angles are all within a couple of degrees of each other, varying from 98° to 100°. Thus the phenomenon of “isogonism,” a term much less objectionable than those invented by Laurent, appears to be a common observance not only for different kinds of derivatives of the same original hydrocarbon or other organic nucleus, but also for the case of homologous series. But Nicklès missed the real point by including salts with different amounts of water, which, it will be shown later, entirely upset the crystalline structure. When this is eliminated the resemblance between true similarly constituted homologues, differing by regular increments of CH₃, is very much closer than would appear from Nicklès’ results.

Unfortunately, some of the work of Laurent and Nicklès was not carried out with the care and accuracy which is indispensable for researches which are to retain permanent value, and critics were not slow to arise. Kopp,^[5] in 1849, unmercifully exposed these failings, so that the real kernel of the work, which was of considerable value, came into discredit.

Pasteur,^[6] however, in 1848, besides the important observations regarding enantiomorphism, to be described in Chapter XI., had noticed similar zonal likenesses between related tartrates, amounting only therefore to isogonism and not to isomorphism; for here again the system often differed, particularly when the members of a series compared differed in their water of crystallisation. Thus there was ample evidence of a really significant series of facts in the work of these authors, but they were not properly arranged and explained.

So high was the feeling against the whole subject carried, however, after Kopp’s memoir, that had it not been for the steadying influence of Rammelsberg and Marignac, who themselves carried out many crystallographic measurements as new substances continued to be discovered with great rapidity, the science would have suffered a serious set-back. Moreover, even Rammelsberg was led astray in the direction of the views of the chemists of the time, that isomorphism could be extended over the crystal system. Frankenheim, whose discovery of the space-lattice, to be referred to in the next chapter, will ever render his name famous, strongly opposed this view. Delafosse, on the other hand, recognised some truth in both views, and assumed that there were two kinds of isomorphism, that of Mitscherlich on the one hand, and the broader one of Laurent on the other hand, and that in the case of the latter kind the overstepping of the system is no bar.

Hjortdahl,^[7] in the year 1865, supported the views of Delafosse more or less, at any rate so far as to assume the possibility of the existence of partial isomorphism, that is, of isogonism. He was very definite, however, against accepting the proposition that any general law could be applied. He himself discovered a partial similarity of angles in several homologous series of organic compounds.

About this time Sella^[8] uttered a warning which is one worthy of being prominently posted in every research laboratory, namely, that It is unwise to make hasty generalisations from the results of a small number of observations. Were this principle more generally followed, much greater progress would in the end be achieved, and without the discouragement and discredit which inevitably follows the detection of errors due to lack of broad experimental foundation. It is certainly an incontrovertible fact that only such generalisations as find themselves in accordance with all new but well-verified experimental facts as they are revealed can stand the test of time and become accepted universally as true laws of nature. And it is unreasonable to expect any generalisation to be of such a character unless it is already based on so large a number of facts that there is little fear of other new ones upsetting them.

Some order was, however, introduced into this chaotic state of chemical crystallography in the year 1870 by P. von Groth.^[9] He investigated systematically the derivatives of the hydrocarbon benzene, C₆H₆, many of which are excellently crystallising solids suitable for goniometrical measurement. He showed that although the crystal system may be and often is altered, yet there is a striking similarity in the angles between the faces of certain zones, which for the purposes of comparison he arranged to be parallel to each other in his descriptions of the crystals, so that the relationship would then consist in an elongation or a shortening of this particular zone axis, which was usually a crystallographic axis. He recognised that this was a totally different phenomenon from isomorphism, and called it “morphotropy.” Although it may possibly be permissible from one point of view to regard isomorphism as a particular case of complete morphotropy along all zones, such a course is not advisable, as morphotropic similarities are frequently of a comparatively loose and often indeed of a somewhat vague character, while isomorphous relationships are governed by very precise laws.

Thus von Groth showed first that benzene, C₆H₆, crystallises in the rhombic system with axial ratios a : b : c = 0.891 : 1 : 0.977. Next, that when one or two of the hydrogen atoms are replaced by hydroxyl OH groups the substances produced, phenol C₆H₅.OH and resorcinol C₆H₄(OH)₂, are found also to crystallise in the rhombic system, and in the second case, for which alone the axial ratios could be determined, the ratio a : b proved to be very similar, but the ratio c : b was different, the actual values being a : b : c = 0.910 : 1 : 0.540. Pyrocatechol, the isomer of resorcinol, also crystallises in the rhombic system, but the crystals have not been obtained sufficiently well formed to enable any deductions to be made from any measurements carried out with them.

Similarly, the nitro-derivatives of phenol, orthonitrophenol C₆H₄.OH.NO₂, dinitrophenol C₆H₃.OH.(NO₂)₂, and trinitrophenol C₆H₂.OH.(NO₂)₃, also crystallise in the rhombic system, and with the following respective axial ratios: 0.873 : 1 : 0.60; 10.933 : 1 : 0.753; 0.937 : 1 : 0.974. Again, the value for the ratio a : b is not very different from that of benzene itself, while the ratio c : b differs considerably in the first two cases. Similar relations were also found to hold good in the cases of meta-dinitrobenzene, C₆H₄(NO₂)₂, axial ratios 0.943 : 1 : 0.538, and trinitrobenzene, C₆H₃(NO₂)₃, which possesses the axial ratios 0.954 : 1 : 0.733.

The introduction of a chlorine or bromine atom or a CH₃ group in place of hydrogen was found by von Groth to produce more than the above effect, the symmetry being often lowered to monoclinic, a fact which had also been observed to occur in the cases of certain isomers of the substances quoted above, ortho-dinitrobenzene for instance. But it was nevertheless observed that the angles between the faces in the prism zone remained very similar, the angles between the faces of the primary prism (110) and (1̄10), for instance, only varying in eight such derivatives of all three types, whether rhombic or monoclinic, from 93° 45′ to 98° 51′.

The crystallographic relationships of organic substances, however, are very much complicated by the possibilities of isomerism, the ortho, meta, and para compounds—corresponding to the replacement of the two hydrogen atoms attached to two adjacent, alternate, or opposite carbon atoms respectively, of the six forming the benzene ring—generally differing extensively and sometimes completely in crystalline form. Consequently, the phenomenon of morphotropy is best considered quite independently of isomorphism.

An interesting intermediate case between morphotropy and true isomorphism was investigated by the author in the year 1890, namely, a series of homologous organic compounds differing by regular increments of the organic radicle CH₃. They were prepared by Prof. Japp and Dr Klingemann, and consisted of the methyl, CH₃, ethyl, C₂H₅, and propyl, C₃H₇, derivatives of the substance triphenyl pyrrholone, all of them being solids crystallising well. The problem was somewhat complicated by the development of polymorphism, the methyl, ethyl, and propyl compounds having each been found to be dimorphous, and not improbably trimorphous, but only two varieties of each salt were obtained in crystals adequately perfect for measurement. That the production of these different forms was due to polymorphism and not to chemical isomerism (different arrangement of the chemical atoms in the molecule) was shown by the fact that one variety could be obtained from the other by simply altering the conditions of crystallisation from the same solvent. Their identical chemical composition was established by direct analysis.

The methyl (CH₃) compound crystallised in rhombohedra and in triclinic prisms. The ethyl (C₂H₅) derivative was deposited in triclinic prisms exactly resembling those of the methyl compound in habit and disposition of faces. A crystal of the triclinic methyl derivative which would represent equally well the ethyl compound is shown in Fig. 56. The angles also of the crystals of the two substances are so similar that one might infer the existence of true and complete isomorphism. The actual angular differences rarely exceeded three degrees.

Besides the triclinic form the ethyl derivative was also obtained in monoclinic crystals, one of which is represented in Fig. 57. This illustration might serve equally well, however, for a corresponding monoclinic form of the propyl (C₃H₇) derivative, and the angles of these two monoclinic ethyl and propyl compounds are even closer than those of the triclinic methyl and ethyl derivatives, the closeness increasing with the advent of symmetry.

This similarity of angles in the cases of the two pairs of triclinic and monoclinic compounds is not only true about particular zones, but about all the zones, so that it is a case isomorphism rather than of isogonism (morphotropy). The similarity of optical properties is also very close, and so much so in the cases of the monoclinic crystals of ethyl and propyl triphenyl pyrrholone that both exhibit very high dispersion of the optic axes. In the case of the propyl derivative the difference between the apparent angle of the optic axes for red lithium light and for green thallium light amounts to 11°. In the case of the ethyl compound this difference is enhanced so considerably that the crystals afford a remarkable instance of dispersion of the optic axes in crossed axial planes, resembling the case of gypsum discovered by Mitscherlich and described in the last chapter, except that the sensitiveness is to change of wave-length in the illuminating light rather than to change of temperature. The optic axial plane is perpendicular to the symmetry plane for lithium and sodium light, as it is also in the case of the propyl compound; but in the ethyl derivative it crosses over for thallium light and rays beyond that towards the violet, into a plane at right angles to the former plane, namely, the symmetry plane itself. The total dispersion between the two axes as separated in the one plane for red light, and as separated in the other perpendicular plane for blue light, is more than 70°. Fig. 58, Plate XIII., shows the nature of the interference figures afforded in convergent polarised light of different wave-lengths by a section-plate perpendicular to the first median line. The figure at f represents what is observed in white light, as far as is possible by a drawing in black and white. It consists of a series of concave coloured curves, falling in between the arms of the cross, and looping round the axes, a figure very much like that afforded by brookite and triple tartrate of ammonium, potassium, and sodium, the substances already mentioned in Chapter VII. as being similarly very sensitive to change of wave-length. The figure in red monochromatic lithium light is shown at a in Fig. 58, and that for yellow sodium light at b, the axes being now much closer together. On changing to green thallium light the line joining the optic axes becomes vertical instead of horizontal, as shown at d.

When, instead of employing monochromatic flames, the spectroscopic monochromatic illuminator (Fig. 75, page 193), described by the author some years ago to the Royal Society, is employed to illuminate the polariscope, the source of light being the electric arc, the change of the figure from that given by the extreme red of the spectrum to that afforded by the violet may be beautifully followed, and the exact wave-length in the greenish yellow determined for which the crossing occurs and an apparently uniaxial figure of circular rings and rectangular cross is produced. For it is possible with the aid of this illuminator directly to observe the production of the uniaxial figure. The wave-length is either directly afforded by the graduation of the fine-adjustment micrometric drum or is obtained from a curve of wave-lengths, constructed to correspond to the circle readings of the illuminator. The appearance of the interference figure for this critical wave-length is shown at c in Fig. 58. The remaining figure at e represents the appearance when a mixture of sodium and thallium light is employed, which clearly indicates the four extreme axial positions, and assists in elucidating the nature of the figure f exhibited in white light.

The second form of the propyl derivative belongs to the rhombic system, and a similar rhombic form of the ethyl compound was once obtained, but lost again on attempting to recrystallise.

These interesting relationships of the homologous methyl, ethyl, and propyl derivatives of triphenyl pyrrholone thus appear to form a connecting link between cases of isogonism or morphotropy and of true isomorphism.

We are now, therefore, in a position to approach the question of true isomorphism, and as leading up to the fuller treatment of the subject in Chapter X. we may conclude this chapter by referring first to one important investigation in which the necessity for extreme accuracy of measurement and perfection of material was fully appreciated. This was an admirable research carried out in the years 1887 and 1888 by H. A. Miers^[10] on the red silver minerals, proustite, sulpharsenite of silver, Ag₃AsS₃, and pyrargyrite, the analogous sulphantimonite of silver, Ag₃SbS₃, which afforded a further indication of the existence of real small differences of angle between the members of truly isomorphous series. These two minerals form exceptionally beautiful crystals belonging to the trigonal system, the hexagonal prism being always a prominent form, terminated by the primary and other rhombohedra, scalenohedra and various pyramidal forms, many of the crystals being exceedingly rich in faces. When the crystals are freshly obtained from the dark recesses of the silver mine they are very lustrous and transparent, but they are gradually affected by light, like many silver compounds, and require to be stored in the dark in order to preserve their transparency. A magnificent crystal of proustite from Chili is one of the finest objects in the British Museum at South Kensington, but is rarely seen on account of the necessity for preservation from light. Pyrargyrite is generally dark grey in appearance, and affords a reddish-purple “streak” (colour of the powder on scratching or pulverising). Proustite, however, possesses a beautiful scarlet-vermilion colour, and affords a very bright red streak.

Now these two beautiful minerals are obviously analogous compounds of the same metal, silver, with the sulpho-acid of two elements, arsenic and antimony, belonging strictly to the same family group, the nitrogen-phosphorus group, of the periodic classification of the elements according to Mendeleéff. Consequently, they should be perfectly isomorphous. Miers has shown in a most complete manner that they are so, that they occur in very perfect crystals of similar habit belonging to the same class of the trigonal system, the ditrigonal polar class, both minerals being hemimorphic, that is, showing different forms at the two terminations, in accordance with the symmetry of the polar class of the trigonal system. But the angles of the two substances were not found to be identical, although constant for each compound within one minute of arc, there being slight but very real differences, which are very well typified by the principal angle in each case, that of the primary rhombohedron. In the case of proustite it is 72° 12′, while the rhombohedron angle of pyrargyrite is 71° 22′.

This interesting and beautiful investigation of Miers thus gave us an inkling of the truth, that small angular differences do exist between the members of isomorphous compounds. It paved the way for, and indeed partly suggested, the author’s systematic investigation of the sulphates, selenates, and double salts of the alkali series of metals, a brief account of the main results of which will be given in Chapter X.