1920] on Crystal Structure 195 



from these positions without destroying the symmetry of the structure, 

 and their exact positions are therefore defined. Such structures 

 are illustrated by the models of potassium chloride and zincblende in 

 Plates I. and II. 



In contrast to this, the positions of the sulphur atoms in the 

 crystal of iron pyrites, FeS 2 , are denned by symmetry alone. Plate I., 

 fig. a, and Figs. 1 and 2 illustrate this structure. The sulphur atoms 

 lie on certain axes of three-fold symmetry, illustrated by the model, and 

 every atom occupies the same relative position along the appropriate 

 axis, but this position must be determined by quantitative investi- 

 gations of the diffraction of the rays. The ratio of the parts into 

 which the cube axis is divided by the centre of the sulphur atom may 

 be taken as the parameter fixing its position, and this parameter may 

 have any value. In the case of the ruby, A1 2 3 , two parameters are 

 necessary to define the crystal structure ; in quartz, Si0 2 , four para- 

 meters must be determined. The complexity of the crystal structure, 

 and the difficulty of analysing it, increase greatly with the number of 

 these parameters, and it is this which has limited to the simpler forms 

 the types of crystal so far worked out. 



4. In trying to find some method of simplifying the analysis of 

 these complex structures, the author has been led to a manner of 

 regarding the crystalline structure which is similar to the well-known 

 theory proposed in 1906 by Barlow and Pope. Barlow and Pope 

 pictured the atoms of a crystal as an assemblage of spheres, packed 

 together tightly, the volume of the space in the crystal structure 

 occupied by the sphere representing any atom being proportional to 

 the valency of the atom. We now know the atomic arrangement of 

 a number of crystals, and we know that the disposition of the atoms 

 predicted by the " Valency Volume " theory, though in some cases it 

 has been found to hold, is in general different to that which the 

 X-rays have enabled us to discover. Nevertheless, Barlow and Pope's 

 models of crystal structures may be modified so as to apply to 

 crystals by substituting, for the valency volume law, one which assigns 

 to the sphere representing any atom a constant size characteristic of 

 that atom. 



5. This may be illustrated by the iron pyrites structure already 

 referred to. In this structure the iron atoms are situated on a face- 

 centred cubic lattice. If the unit cube of this lattice be subdivided 

 into eight cubes of half the linear dimensions, each of these latter 

 will have an iron atom situated at four of its eight corners. Fig. 1 

 represents such a unit of the structure, the iron atoms being at the 

 corners of A, C, H and F. One diagonal of each cube, the diagonal 

 AG in the figure, is an axis of threefold symmetry, and the sulphur 

 atom lies at some position along this axis. Since each corner of the 

 cube is a centre of symmetry, there will correspond to the sulphur 

 atom centred at Sj a similar atom at S , where S X G = S 2 Gr. A pair 

 of sulphur atoms are thus associated with each cube corner, since one 



o 2 



