THE QUANTUM PHYSICS OF SOLIDS 



691 



atom is closely prescribed. For a given volume per atom, as we have 

 seen above, the close-packed arrangements are the ones which give 

 the largest separation between neighboring positive ions; and since the 

 positive ions repel each other, the close-packed arrangements will 

 give the lowest energies. This accounts for the fact that the custom- 



k 



3/. 





CL- 



% 



Fig. 19 — Electron charge densities in crystals. The numerical values give the 

 number of electrons per atom in the space corresponding to each intensity of shading. 



(A) In diamond. 



(B) In magnesium. 



(C) In sodium chloride, 



ary metallic lattices are the body-centered cubic lattice, the face- 

 centered cubic, and the close-packed hexagonal. A further discussion 

 of this physical picture of the nature of the metallic state will be given 

 in the third paper of this series. In Fig. 19B we show qualitatively 

 the electron density of metallic Mg according to Grimm.^^ It is seen 

 that the valence electrons give a uniform negative charge in which 

 the positive ions are embedded. 



We have seen in the preceding section that the band theory of the 

 alkali halides is essentially equivalent to the ionic theory. A large 

 fund of evidence attests to the validity of the ionic theory, one item 

 being the electron concentrations determined for sodium chloride by 

 BrilP^ and his collaborators. These are represented in Fig. 19C; we 



^^ Loc. cit. 

 2* Loc. cit. 



