i;tl;i] on Great Advance in Crystallography 687 



for carbon and hydrogen be accepted, so also must those for the 

 relative volumes of the atoms of the halogens, sulphur, oxygen, 

 and nitrogen, his values being : F = 1 ; CI, Br, and 1 = 7 each ; 

 S = 6 ; = 2; and N = ;>. 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 2. Barker 

 shows that while in the binary sulphides, such as zinc sulphide ZnS, 

 the sulphur is probably of volume 2, in the sulphates, such as K.2^^4 

 and BaSO^, it is probably 6, as Traube insists ; this conclusion is 

 also in agreement with other work of Barker on some extraordinary 

 cases of isomorphism, including that of barium sulphate with potassium 

 perchlorate KCIO^, potassium permanganate KMn04, and the extra- 

 ordinary compound potassium borofluoride KBF^. 



While it would thus appear that the atomic volume (in the 

 substance itself, and including any interspace) is the 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 preponderating cubic and hexagonal crystal- 

 line 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 illus- 

 trate the case of zinc sulphide, and also the structure of that most 

 interesting simple compound, silicon dioxide SiO._,, 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 zinc and sulphur 

 are approximately equal, is that 16 molecules ZnS go to form the 

 grosser units 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 sameways 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 inter- 

 penetrating 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 cube face. For this is the 

 space-lattice corresponding to an assemblage of spheres of equal 

 volume in closest packing. The space-lattice in question is shown 



