the Spinel Group of Crystals* 311 



H, and C. J, K, and L are the three other atoms which lie 

 at the same distance from B as H does. H, J, K, and L 

 form a regular tetrahedron. The length of AB is 1*52 A.U., 

 and of BH 4*6 A.U., being three times as large as AB. The 

 (111) spacing is not shown directly in the figure, but is four 

 thirds of AB : a glance at the photograph of the model 

 shown in 'X-rays and Crystal Structure,' p. 107, will make 

 this clear. 



In magnetite the distance AB becomes 3*60 A.U., and 

 BD 10*80 A. U. In fig. 36 divalent iron atoms have replaced 

 the carbon atoms at A, B, H, J, and K ; L is not shown. 

 The oxygen tetrahedra are shown, and it will be observed 

 that there are two orientations, A, H, J, and K being of one 

 description and B of the other. The former replace atoms 

 belonging to one of the face-centred lattices of the diamond, 

 the latter corresponds to the other. So far as our arguments 

 have gone, the size of the tetrahedron has not entered into 

 consideration : it might be of any size, but is drawn small 

 enough to be clear of other atoms. The structure seems 

 easier to grasp when this is done. We shall come presently 

 to arguments which relate to the size, but they are based on 

 quite new considerations. We may anticipate so far as to 

 say that the oxygen tetrahedron is so much larger than it is 

 drawn in the figure that it takes in five divalent iron atoms 

 instead of one*. Probably it is not the same size in all the 

 crystals of the spinel group. 



Trivalent iron atoms are shown at D, E, F, and Gr. It will 

 be observed that the positions of the divalent and trivalent 

 atoms are essentially different. B lies inside a tetrahedron, 

 D lies between the bases of two tetrahedra and has connexions 

 with six oxygen atoms, whereas B has relation to four. This 

 difference is quite independent of the size of the tetrahedron; 

 if the latter is enlarged, other oxygen atoms than those shown 

 move toward the iron atoms and the neighbours change. 

 But it always remains true that the trivalent atom has three 

 neighbours to the divalent atom's two. 



Let us now take up the points we left undecided. The 

 trivalent iron atom might be halfway between A and B or 

 halfway between B and H, the latter being the position 

 adopted in the figure. The reason for placing it as shown is 

 derived from considerations of the (111) spectra, and in 



* Note added subsequently. I see that the disposition of the oxygen 

 atom here described as consisting of certain large tetrahedra pointing 

 towards each other may with equal exactness be described as consisting 

 of smaller tetrahedra each containing only one divalent iron atom and 

 pointing away from each other. 



