X-ray analysis and topic axes of the Alkali sulphates, and their bearing on the theory of valency volumes

One of the most interesting facts brought to light in the course of the author’s crystallographical investigations of the rhombic sulphates and selenates of potassium, rubidium, cæsium, and ammonium, and of the monoclinic double salts containing those simple salts in combination with the sulphates and selenates of dyad-acting metals (Mg, Zn, Fe, Ni, Co. Mn, Cu, and Cd), is the approximation in structure which has invariably been observed between the rubidium salt of any group and the ammonium salt of that same group. This striking fact is again emphasised by the results for the nickel group of double selenates, laid before the Royal Society on the same day as this present communication, and of which an Abstract immediately precedes this paper. While considerable differences occur between the structural dimensions of the potassium, rubidium, and cæsium salts of the group—differences which have been shown to follow the order of the atomic weights of the alkali metals (K = 38⋅85, Rb = 84⋅9, Cs = 131⋅9, and Rb—K = 46, Cs—Rb = 47, Cs—K = 93, or twice 46), so that the rubidium salt is always intermediate—the ammonium salt has without exception proved to possess structural dimensions almost identical with those of the rubidium salt, the central member of the group. By structural dimensions are meant the directional dimensions and the total volume of the unit cell of the space-lattice, the same type of which is common to the whole rhombic or monoclinic isomorphous series. The total volume is represented by the molecular volume (the quotient of the molecular weight by the density of the crystal), and the three directional dimensions of the cell in space are known as the topic axial ratios, or topic axes. The experimental basis of the molecular volume (molecular weight being known) is a very accurate determination of the density of the most perfect attainable crystal. The topic axial ratios require for their calculation (in addition to the molecular volume) the crystal elements (crystal-axial angles and ratios), which are derived from very accurate measurements of the external interfacial angles of perfectly developed crystals. For a series of isomorphous salts, such as the rhombic normal sulphates of the alkali-metallic family group of the periodic classification, R2 SO4 , where R may be potassium, rubidium or cæsium, there can be no possible doubt that the type of structure, that is of space-lattice, is identical. Its symmetry is the same for all the members of the group, but the dimensions of the elementary cell vary progressively with the atomic weight or atomic number of the interchangeable alkali metals; and correspondingly the interfacial angles also differ slightly and progressively, in accordance with very definite rules which have been established by the author.