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CARAMELS & COLORINGS for all purposes. A. BOAKE, ROBERTS, & CO. (LIMITED). Stratford, London, E. CHEMICAL NEWS, June 20, 1913 THE GREAT Great Advance in Crystallography. CHEMICAL NEWS. VOL. CVII., No. 2795. ADVANCE IN CRYSTALLOGRAPHY.* By A. E. H. TUTTON, D.Sc., M.A, F.R.S. (Continued rom p. 280). HAVING thus arrived at a comprehensive idea of crystal structure on the assumption of each atom and each grosser space-lattice unit being only a point, as far as which we are on safe and assured ground, we may proceed to the consideration of the various ideas advanced concerning the character of the units of structure thus represented by points, that is, concerning the mode in which the space around the point is more or less filled up. The valency theory of Barlow and Pope considers the atomic point to be expanded into the sphere of the atom's influence, the relative size of which in any one substance is supposed to be proportional to the fundamental valency of the chemical element of which the atom is composed. The spheres are further assumed to be pressed together on crystallisation until they fill space, becoming thereby deformed into polyhedra. The theory of von Fedorów, on the other hand, considers the grosser or space lattice units to be parallelohedra; besides those corresponding to the 14 space-lattices there are 9 other parallelohedra (making 23 in all) composed of simple Sohnckian point systems compounded of interpenetrating space lattices. 289 space-lattice unit is polymolecular, the stereohedra being arranged to build up the main parallelohedron (the space lattice unit) on a definite plan, which may involve mirrorimage juxtaposition. For example, a rhombohedral system of stereohedra is shown on the screen (Fig. 5), consisting of two kinds, R and L, one sort being the mirror. image of the other. Each rhombohedron representing the combined system is composed of six stereohedra, three of each kind, and a series of points, similarly situated one within each stereohedron R, would constitute a Sohncke point system, while a "double-system" is obtained by adding a series similarly situated one within each stereohedron L. If a single point were taken to represent analogously each rhombohedral set of six stereohedra, we should have a rhombohedral space-lattice produced. The valency theory of Barlow and Pope may or may not in the sequel prove to be correct, and some facts have recently been brought forward by Barker which tend to show that it will not hold in many cases of inorganic substances. Barker, who has had the good fortune to have worked in St. Petersburg with von Fedorow for more than a year, shows that, as the lecturer has always held, the true unit of volume is the molecular or atomic volume, as determined for the particular substance itself. The molecular volume is determinable by dividing the molecular weight of the substance by the specific gravity of its crystals at a definite comparable temperature, such as 20° C., but the determination of the atomic volume offers peculiar difficulty, and so far only comparative and indirect methods have been employed, chiefly by Sollas. By taking the volumes of the spherical units to be proportional to the atomic volumes (not those of the element in the free state, as enormous compression occurs on combination), and also determining the amount of free inter All the 23 parallelohedra are arranged parallelwise, and fill space without interstices. There are, however, only four types, namely, the cube, the rhombic dodecahedron (which has a second vertically elongated variety), the cubooctahedron, and the hexagonal prism, the first three being all of cubic symmetry, and the fourth of obviously hexagonal symmetry. They are shown, including the second variety of the dodecahedron, in the next screen picture (Fig. 4). He further considers that all four may be homo geneously deformed into analogous parallelohedra of lower orders of symmetry, without ceasing to fill space when closely packed. Hence, von Fedorow concludes that all crystal structures are of either cubic or hexagonal type, including not only truly cubic and hexagonal crystals, but their deformed derivatives. The cubo-octahedron (e, Fig. 4) is identical with Lord Kelvin's "tetrakaidekahedron," the most general parallel-faced cell (a hepta parallelohedron) into which space can be regularly partitioned, and possessing the minimum surface for a given volume. Unlike the atomic polyhedra of Pope and Barlow, these parallelohedra of von Fedorow are either molecular or polymolecular, in the latter event being made up of a small number of identically or symmetrically similar sub-polyhedra, termed by him "stereohedra," which represent the chemical molecules, just as already explained, when the grosser A Discourse delivered at the Royal Institution of Great Britain, March 14, 1913, stitial space by comparative methods of calculation, Sollas has achieved some remarkable explanations of the crystallographic characters of the two polymorphous forms of silver iodide and of the three forms of titanium dioxide, rutile, anatase, and brookite. We have as yet no guidance from von Fedorow as to the nature of the atomic units and the volumes which they occupy. It would not be surprising if the valency volumes of Barlow and Pope, in the cases of those elements for which their theory appears to work in a satisfactory manner, turn out to be identical with the atomic volumes as determined by the method of Sollas. As regards the compounds of carbon and hydrogen, Barlow and Pope have been most successful in accounting for crystallographic and chemical relationships, and it is at least significant that both Le Bas, from experimental work on the molecular volumes of liquid hydrocarbons, and Traube from an entirely different point of view, concur in assigning the relative volumes 4 and I to carbon and hydrogen atoms in combination respectively. If Traube's results for carbon and hydrogen be accepted, so must also those for the relative volumes of the atoms of the halogens, sulphur, oxygen, and nitrogen, his values being: F =1; Cl, Br, and I=7 each; S=6; 0=2; and N=3. As regards oxygen and nitrogen, he agrees with Barlow and Pope, but the latter take all the halogens as of unit valency volume, and sulphur as of valency volume Barker shows that while in the binary sulphides, such as zinc sulphide ZnS, the sulphur is probably of volume 2. FIG. 5.-FEDOROW'S STEREOHedra. true effective volume concerned in crystal structure, and that it may be only a coincidence that, in the cases of a few prominent elements, it happens to be approximately proportional to the valencies of those elements (as certainly appears to be true in the cases of hydrogen and carbon, and possibly oxygen and nitrogen), there is a very considerable amount of the joint work of Barlow and Pope which is of permanent value. Their explanations of the pre ponderating cubic and hexagonal crystalline forms of the elements themselves, and of binary compounds such as ZnS, are doubtless correct, and it will be of great interest, in view of the next development to which attention must be called, to illustrate the case of zinc sulphide, and also the structure of that most interesting simple compound, silicon dioxide SiO2, quartz, which has been worked out in a very complete manner by Barlow. Barlow and Pope's idea of the structure of zinc blende, which merely assumes that the volumes of the atoms of FIG. 6.-SPACE-LATTICE OF CENTRED-FACE CUBE. zinc and sulphur are approximately equal, is that 16 molecules ZnS go to form the grosser unit of the crystal structure, the combined system or space lattice unit-that is, 16 atoms of zinc and 16 of sulphur. Only one zinc or one sulphur atom in every 16 is same ways orientated, and if we adopt von Groth's definition, we may give the structure of zinc blende as follows:-The crystals of zinc blende consist of two interpenetrating regular point-systems, one formed from zinc atoms, and the other from sulphur atoms; each of these two point-systems is built up from 16 interpenetrating space lattices, each of the latter being formed from zinc atoms or from sulphur atoms occupying parallel positions. All the 32 space-lattices of the combined system are geometrically identical. Barlow and Pope have shown that the space-lattice in zinc blende is the third cubic one, in which a point is situated at each cube corner and also in the centre of each FIG. 10.-THE Two VARIETIES OF QUARTZ CRYSTALS, cube face. For this is the space-lattice corresponding to LEFT-HANDED AND RIGHT-HANDED. CHEMICAL NEWS, Great Advance in Crystallography. an assemblage of spheres of equal volume in closest packing. The space-lattice in question is shown on the screen (Fig. 6), and a pair of models of the arrangement are illustrated in the next two pictures, in the first of which the points are expanded into spheres of considerable size, and in the second they appear still further expanded into actual contact. The third stage, in which the expansion proceeds until all interstices are filled up and the spheres are converted into polyhedra, is left to the imagination. In the second picture the mutual arrangement of the spheres of the two elements in zinc blende, zinc and sul. phur, is indicated by the yellow colouring of the sulphur spheres and the grey tinting of those of zinc. The tetrahedral mode of derivation of the structure, accounting for the observed hemihedrism, is also shown in another slide (Fig. 7). The eight larger cubes which together form the grosser unit are each supposed to be occupied by four smaller cubes of the same element, arranged tetrahedrally, and of zinc and of sulphur alternately in different larger cubes; on replacing the little cubes by spheres in contact the model represented in the second picture is produced. Barlow's conception of quartz affords us an example in 291 out of each crystal, perpendicularly to the axis, and using the device of 24 mica sectors, due to S. P. Thompson, which between crossed Nicols, shows a black cross, the arms of which are deviated one sector to the right or left when the thin quartz plate is interposed, in accordance with the right or left-handed nature of the plate. Also the phenomenon of the bi quartz, and of the natural bi-quartzes often produced by twinning of right and left individuals, may be illustrated, terminating with some beautiful cases of repeated twinning, including amethyst. The imitation of the phenomena of the two varieties of quartz, by crossing strips of mica in a righthanded or a left-handed pile, as shown by Reusch, may also be referred to and demonstrated, as affording some definite proof that the mineral does possess an analogous helical structure, complementarily opposite in its two varieties. Now these two crystalline minerals, zinc blende and quartz, have been chosen advisedly as examples of crystal structure. For a remarkable series of experiments have recently been carried out by Laue, Friedrich, and Knipping at Munich, where the lecturer had the advantage of seeing FIG. 11.-APPARATUS OF FRIEDRICH, KNIPPING, AND LAUE FOR PASSING X-RAYS THROUGH CRYSTALS which the symmetry is trigonal, and of which there are two kinds possible, one of which is the mirror-image of the other, the two being helical in character and of the nature of right- and left-handed screws respectively. The two structures, as thus conceived, are represented in the next two slides (Figs. 8 and 9), the white spheres representing silicon atoms, and the black ones oxygen atoms, of which there are twice as many, corresponding to the formula SiO2. The helical character is clearly shown, the white spheres being obviously arranged in a right-handed screw in one picture and a left-handed screw in the other. Rightand left-handed quartz crystals are so well known that it will not be necessary to do more than illustrate the fact by one or two experiments. First of all, two slides are shown (reproduced together in Fig. 10), one of a right-handed crystal and the other of a left-handed one, each exhibiting the characteristic little faces s and x of the right and left trigonal bi-pyramids and right and left trigonal trapezohedra, modifying the right and left corners formed by the meeting of the faces of the rhombohedron r and hexagonal prism m. That the right-handed crystal shows rotation of the plane of polarisation of light to the right, and the lefthanded crystal optical rotation to the left, may be beautifully demonstrated by cutting a plate 1 mm. thick some of the first photographic results last summer. In these experiments X-rays were passed through crystals of various substances, notably zinc blende, and, in more recent experiments by Laue at Zurich, quartz. The issuing rays were received on a photographic plate, on which they recorded a pattern of spots having the symmetry (full holohedral) of the space lattice present as the foundation of the crystal structure. These interesting photographs thus afford the first experimental and visible proof of the truth of the structure assigned to crystals by geometricians and crystallographers. By the great kindness of Professor Laue it is possible to exhibit the original photographs obtained with zinc blende, and one just obtained with quartz, the results for which Professor Laue has not yet published. Dr. Friedrich has also most kindly sent four excellent lantern slides expressly for this lecture. In view of this further evidence of the richness of the original discovery by Sir William Crookes of the famous tube which is universally known by his name-producing under suitable circumstances of exhaustion the cathode rays when excited by the intermittent current from a Ruhmkorff coil, which rays, on their striking solid matter such as the soda glass walls of the tube, in turn give rise to the X-rays of Röntgen-it is fitting that some examples |