the Spinel Group of Crystals 



313 



particular the fact that the first order spectrum is so very- 

 small. We gather from this fact that two sets of planes 

 occur alternately at half the actual (111) spacing, and 

 nearly balance one another. If we place the trivalent atom 

 halfway between every pair of divalent neighbours such as 

 A and B, we obtain the two sets of planes we want, but one 

 set is so much stronger than the other that it would be hard 

 to explain the weakness of the first order reflexion. If we 

 place it as shown, viz., halfway between B and H, we again 

 obtain the two sets of planes (it is rather hard to see without 

 -a model), but one consists of a single plane with three atoms 

 in it, and the other three planes fairly close together each 

 with a single atom. Thus they nearly balance, and so we 

 make the first order reflexion small. In all this we are 

 neglecting the oxygen atoms, it is true. But they are so 

 much lighter than the iron atoms that it seems unlikely that 

 they can make much difference. 



Let us next consider the size of the oxygen tetrahedron. 

 So far as we have gone we have made such a distribution of 

 the atoms in the crystal that the distribution in the (111) 

 planes will be found to be as shown in fig. 4 ; the distance 



Fig. 4. 



3oc 



3TT 



3F* 



3 Fe" OFe'O Fe'3 



3fd 



from 3Fe"' to 3Fe"' being 4'80 A.U. The constituent of 

 two molecules are employed to represent the arrangement. 

 We may represent the effect of such a distribution in 

 the manner employed by W. L. Bragg in previous papers. 

 Take the central Fe'" plane as the zero plane. We have 

 then 



(1) The central Fe'" plane. 



(2) Two Fe" planes having phases tt/4 and — tt/4 respec- 



tively. 



(3) One 3Fe'" plane having a phase ir : the other is only 



a repeat of the first. 



