2G8 Dr. A. C. Crehore on the Construction of the 



It may be objected that it is not sufficient to calculate the 

 forces upon a single atom ; but it may be shown that 

 the example calculated is representative of all atoms, owing- to 

 the symmetry of the crystal. Referring to fig. 2, the atom 

 represents any one of the crosses, meaning that the axis 

 points down, perpendicular to the paper. One-quarter of 

 the total number of atoms in this plane are crosses, and an 

 inspection shows that we must obtain the same result for 

 any one of these crosses ; and the same remark will apply to 

 everyone of the different planes. That is to say, our selected 

 atom really represents one-quarter of all the atoms in the 

 crystal. Had we started with one of the other atoms, for 

 example, that just below in fig. 2, we should have used the 

 sets of planes perpendicular to this arrow. The crystal may 

 be built up as well of parallel planes perpendicular to this 

 arrow as of those perpendicular to any other arrow, each 

 plane being an exact duplicate of fig. 2. The atom 

 is therefore representative of every atom in the whole 

 crystal. 



A word of caution seems advisable lest attempts be made 

 to apply this result for the diamond to other crystals whose 

 atoms are arranged in a similar way. A case in point is 

 crystal zincblende, ZnS. It has been showm by X-ray 

 analysis * that the structure of this crystal is like the 

 diamond, zinc atoms replacing the carbon atoms in one set 

 of tetrahedra and sulphur atoms replacing the carbon atoms 

 in the other, interpenetrating, set of tetrahedra. The zinc 

 atom, according to the theory, has a ring of only two elec- 

 trons at its centre and the sulphur atom a single electron. 

 The general equations (20), (24), and (25), so far developed, 

 do not apply to the case where each atom has one or two 

 electrons at the centre. They do apply to give the force of 

 the zinc on the sulphur because there is presumably no syn- 

 chronous rotation in such a combination, but not to the case 

 of the zinc on the zinc or the sulphur on the sulphur. To 

 be more explicit, if the selected atom in fig. 8 is zinc, then 

 the atoms in planes +2 and —2 are also zinc. So far as we 

 know, therefore, we have no right to say that these planes 

 cancel each other, as was the case with the diamond, because 

 we do not know that the forces of these atoms cancel in pairs. 

 The phase angles of the single electron in sulphur and the 

 double electron in zinc come into the account, and render 

 the solution of the problem far more complicated than in the 

 case of the diamond, where the equilibrium is independent of 



* W. H. Bragg, Roy. Soc. Proc, ser. A. lxxxix. pp. 430-438, Jan. 1, 

 1914. 



