?o8 



NATURE 



[November 14, 1912 



direct rays. Outside the square of spots were 

 others of a fainter character, also arranged with 

 similar cubic symmetry, and there was also a 

 faint square of spots inside the intense square, 

 nearer to the latter than to the larg-e central spot. 

 The tetragonal nature of the axis of symmetry 

 along which the Rontgen rays were travelling- 

 through the crystal is most strikingly apparent 

 in the photograph. One recognises at once also 

 the presence of two perpendicular planes of sym- 

 metry in the arrangement of the spots. In fact, 

 \he figure corresponds to the holohedral or full 

 symmetry (class 32) of the cubic system, in spite 

 of the fact that zinc blende belongs to the hexakis- 

 tetrahedral class 31 (one of the so-called hemi- 

 hedral classes) of cubic symmetry. Now this in- 

 teresting fact affords the most beautiful and 

 perfect proof that it is the space-lattice (Raum- 

 gitter) of the crystal structure which is affording 

 the figure, and that no other property than this 

 space-lattice is concerned. For space-lattices 

 alone always possess holohedral symmetry, and 

 they determine the crystal system and angles and 

 obedience with the law of rational indices. Inter- 

 penetrations, translations, and coincidence-move- 

 ments of space-lattices, which afford those of the 

 sixty-five Sohncke regular point-systems which 

 account for the simpler cases of hemihedrism 

 (types of crystals of lower than holohedral sym- 

 metry), are here obviously not concerned; still 

 more emphatically, if possible, is this true of the 

 165 yet more complicated point-systems involving 

 mirror-image symmetry made known to us by von 

 Fedorow and Barlow. 



In other words, it is not the stereographic 

 arrangement of the elementary atoms which is 

 revealed by the photographs, but the underlying 

 space-lattice, which is arrived at by taking the 

 atoms of the same chemical element which are 

 similarly (sameways, identically) situated through- 

 out the whole structure. This may either mean 

 (in very simple cases) taking a similarly situated 

 atom in each chemical molecule, or (more 

 generally) one such atom in a croup of molecules. 

 In the case of zinc blende, if Pope and Barlow's 

 conception of the structure be correct,^ only one 

 zinc or sulphur atom in every group of sixteen 

 molecules is thus sameways orientated, thirty-two 

 atoms (sixteen of zinc and sixteen of sulphur) 

 going to form the complete, double, regular point- 

 system (each atom being considered as a point, 

 and the sixteen atoms of each element forming a 

 simple regular point-system). 



In order to be quite clear, the definition of 

 crystal structure may be quoted which was given 

 Ijy Prof, von Groth at the 1904 meeting of the 

 British Association. Mr. Barlow has since ampli- 

 fied the statement so as to include the more com- 

 plicated cases, but as these are not concerned in 

 ihe case of zinc blende the definition is fully 

 adequate for our purpose. 



A crystal — considered as indefinitely extended — con- 

 sists of n interpenetrating regular point-systems, each 

 of which is formed from similar atoms ; each of these 



Journ.Chem. Soc. Tran*., 1907, xci., H71 and 1178 ; see particularly 

 Fig. 17 on p. ri7i and Fig. i on p. 1152. 



NO. 2246, VOL. 90] 



poirit-systems is built up from n interpenetrating space- 

 lattices, each of the latter being formed from similar 

 atoms occupying parallel positions. All the space- 

 lattices of the combined system are geometricallv 

 identical or are characterised by the same elementary 

 parallelepipedon. 



Now the combined system of zinc blende is prob- 

 ably that of the type 63 of Sohncke, and gaj of 

 Barlow, and in their 1907 memoir, alreadv alluded 

 to. Pope and Barlow describe the probable con- 

 stitution of the crystals of this substance, on the 

 basis of their assumption that the spheres of 

 influence of the zinc and sulphur atoms are 

 approximately equal, the fundamental acting 

 valency of both elements being here considered as 

 dyadic. If the spheres of influence of the zinc 

 and sulphur atoms, or the parallelohedra into 

 which they are compressed when the interstitial 

 spaces are removed in attaining their closest 

 packed arrangement, were quite equal, the sym- 

 metry would be cubic holohedral ; but the slight 

 difference in size and the different effect of com- 

 pression on the atoms of the two elements 

 degrades the symmetry into the hexakis-tetra- 

 hedral class 31, next lower in the cubic system. 

 This constitution of the crystals of the simple 

 binary compounds, such as zinc sulphide, does 

 not depend, however, on- Pope and Barlow's ver- 

 sion of the theory of crystal structure; for the 

 sizes of the spheres of influence of the atoms of 

 the two elements are assumed to be approximately 

 equal, just as is the case when valency is not con- 

 sidered to enter into the problem. It is equally 

 the probable one according to the theory of von 

 Fedorow, based on parallelohedra of cubic and 

 hypohexagonal types, which has led him to the 

 remarkable advance in crystallochemical analysis 

 described by the writer in Nature of July. 18 

 (P- 503) ; and as the parallelohedron of von 

 Fedorow represents the combined system (that of 

 Pope and Barlow only representing a single atom), 

 its central representative point is a point of the 

 space-lattice itself. The definition of von Groth 

 is thus equally applicable to both versions. 



Thus we are dealing with a crystal supposed to be 

 constructed of two interpenetrating regular point- 

 systems (type No. 63 of Sohncke), corresponding to 

 zinc and sulphur atoms respectively ; each of these is 

 composed of sixteen interpenetrating space-lattices, 

 each and all formed from one of the two elements 

 only, and composed of atoms of that element occu- 

 pying parallel positions. All the thirty-two space- 

 lattices of the double or combined system are 

 geometrically identical, and are characterised by 

 the same elementary parallelepipedon, a cube in 

 this case of zinc blende. Hence one tvpe of space- 

 lattice characterises the whole crystal, and it is 

 this space-lattice, formed by similar (consisting of 

 the same element) and simiilarly situated atoms, 

 which has apparently afforded the photograph of 

 spots showing holohedral cubic symmetry. This 

 is equally true whether the structure attributed by 

 Pope and Barlow to zinc blende, or a less com- 

 plicated one, be the correct structure. 



These are the crystallographical facts which 

 must be taken into account in any discussion as 



