310 Prof. W. H. Bragg on the Structure of 



divalent iron atom is the centre of the oxygen tetrahedron. 

 It might of course be multiplied by four, provided each was 

 placed at equal distances from four oxygen tetrahedra and 

 each such tetrahedron had shares in four iron atoms ; but 

 this comes to the same thing as the first suggestion, since, 

 owing to the peculiar diamond structure, a point which is 

 equally distant from four oxygen tetrahedra is itself the 

 centre of a tetrahedron. 



We have two iron atoms left. These cannot be assigned 

 entirely to a single tetrahedron so as to have the symmetries 

 required. But if they are increased to four, each being 

 placed on one of the four perpendiculars from the corners of 

 the tetrahedron on the opposite faces, and halfway between 

 two tetrahedra so as to be shared equally by them, every 

 condition of symmetry and spacing is fulfilled, for it has 

 already been shown that a properly oriented tetrahedron, 

 such as that on which the trivalent atoms now lie, may be 

 substituted for a single point centre without degrading the 

 symmetry or increasing the spacings. We conclude that this 

 is the real position of the trivalent atoms, and the structure 

 is complete, except as regards (1) a knowledge of the dimen- 

 sions of the tetrahedron and the determining whether two 

 neighbouring tetrahedra point towards or away from each 

 other, (2) a choice between two alternative positions of the 

 iron atom which we will discuss immediately. 



Fig. 3 a. 







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Arrangement of atoms on diamond. ABHC trigonal axis. 

 AB = 1-52A.U. BH = 4-56A.U. 



Avery good way to realize the stage we have reached is to 

 consider a small portion of the crystal consisting principally 

 of atoms lying along a trigonal axis. Fig. 3 a shows four 

 such atoms of carbon in the case of the diamond, viz., A, B, 



