The discovery of the local effect produced by the two kinds, positive and negative, of chemical replacement, has a profound bearing on crystal structure. For it is thereby rendered certain that the atoms are fixed in the crystal edifice, and therefore in the molecule in the solid state. It becomes obvious that the atoms—in their stereometric positions in the molecule, being thus fixed in the solid crystal when the molecules set themselves rigidly in the regular organisation of the space-lattice—form the points of the regular point-system of the crystal structure, which determines to which of the thirty-two classes of symmetry the crystal shall belong. Any movement of the atoms in the crystal, other than that which accompanies change of temperature, and possibly change of pressure, is thus improbable; and this experimental proof of their fixity, afforded by the fact that definitely orientated changes accompany the replacement of particular atoms, also doubtless indicates that the latter are located in the particular directions along which the changes of exterior angle and of internal structural dimensions are observed to occur. Stereo-chemistry, which has made such enormous advances during the last few years, thus becomes of even greater importance than Wislicenus and its other originators ever dreamt of.
Within the atoms in the crystal the constituent electronic corpuscles may be and probably are in rapid movement, and such physical effects as have hitherto been ascribed to movement of the atoms within the crystal are doubtless due to movement of the electronic corpuscles within them, the sphere of influence of the atom itself being fixed in space in the solid crystal, and being doubtless defined by the area within which the corpuscular movements occur.
Fig. 60.—Diagram illustrating Progressive Change of Crystal Angles in Isomorphous Series.
Three illustrations of the law of change of the crystal properties with variation of the atomic weight of the determinative elements of an isomorphous series may be given, and will serve to render the practical meaning of the generalisation clearer. The first is a diagrammatic representation, in Fig. 60 (in a very exaggerated manner as the real change would be inappreciable on the scale drawn), of the change of angle on replacing the potassium in potassium sulphate, K2SO4, or selenate, K2SeO4, by rubidium or cæsium. The inner crystal outline, a vertical section, is that of the potassium salt. The vertical lines represent the intersections of the two faces of the brachypinakoid b = {010} with a vertical plane parallel to the macropinakoid a = {100}; the horizontal lines represent the intersection of the two faces of the basal plane c = {001} with the same vertical plane; and the oblique lines represent the intersection of the vertical plane with the four faces of the dome form q = {011}, which are inclined to both b and c planes. The diagram is thus designed to show the variation of the inclination of these latter dome faces to the two rectangular axial plane faces b and c. The outer crystal outline represents a similar section of a crystal of the corresponding cæsium salt, and the middle outline that of a crystal of the rubidium salt.
The progressive alteration of the angle of the q-face will be obvious, the direction of the change being correct, but the amount of change, as already stated, being much exaggerated; in reality it never reaches a degree between the two extreme (potassium and cæsium) salts. It will be remembered that the respective atomic weights of potassium, rubidium, and cæsium are 38·85, 84·9 and 131·9, when hydrogen equals 1, that of rubidium being almost exactly the mean.
Fig. 61.—Diagram illustrating Progressive Change of Double Retraction in Isomorphous Series.
The second illustration is taken from the optical properties. Fig. 61 represents graphically the regular diminution of double refraction (the difference between the two extreme indices of refraction α and γ) which accompanies increase of the atomic weight of the metal present. The diagram exhibits the closing up of the two spectra afforded by three analogously orientated 60°-prisms, one of each of the three salts, such as was used in determining two of the refractive indices of the salt. Each prism produces two refracted rays from the single ray furnished by the collimator of the spectrometer, and consequently two images of the signal-slit of the collimator when monochromatic light is used, or two spectra if white light be employed. The Websky signal-slit is narrow at the centre to enable an accurate allocation to the vertical cross-wire of the telescope to be made, but wide at its top and bottom ends, in order to transmit ample light, and Fig. 61 shows four images of this signal produced by each prism, namely, one R in red C-hydrogen light and another B in greenish-blue F-hydrogen light belonging to each of the two spectra, in order to locate the two ends of each of the latter, coloured monochromatic light of each of the two colours in turn and of the exact C and F wave-lengths having been fed to the spectrometer from the spectroscopic illuminator. It will be observed in the case of the top row that the two spectra, each indicated by the adjacent red and greenish-blue images, are well apart, the relative distance being about that actually observed in the case of potassium sulphate. They are nearer together, however, in the second row, which indicates what is observed in the case of the analogous rubidium salt, and in the lowest row representing the relative distances of the two spectra apart in the case of the cæsium salt, they are so close together as to overlap; for in this latter case the greenish-blue image of the left-hand spectrum, corresponding to the a index of refraction, occupies the same position as the image for yellow sodium light of the right-hand spectrum corresponding to γ would occupy in the case of cæsium sulphate, the a refractive index for F-light being 1·5660 and the γ index for Na-light being 1·5662. The progression of the alteration of the amount of the double refraction is thus very striking, as the atomic weight of the metal is varied.
The third illustration of the law of progression with atomic weight is also an optical one, and is taken from the monoclinic series of double sulphates and selenates. It indicates the rotation, with increase of the atomic weight of the metal, of the ellipsoid which graphically represents the optical properties, about the unique axis of symmetry, which is likewise an axis of optical symmetry, of the crystal. In the potassium salt the ellipsoid occupies the position indicated by the ellipse drawn in continuous line in Fig. 62, the section of the ellipsoid by the symmetry plane; the outline of a tabular crystal parallel to the symmetry plane is also given, as well as the axes of the crystal and of the ellipsoid lying in that plane.