THE QUANTUM PHYSICS OF SOLIDS 685 



third filled. To the left of the crossing of the bands, Kimball finds 

 that both bands contain four states per atom so that the lower is filled 

 and the upper is empty. The actual spacing in diamond occurs to 

 the left of the crossover and, as we shall see in the next paper, the 

 resultant filled band and empty band arrangement explains the ab- 

 sence of electrical conductivity for diamond. The diagram suggests 

 an explanation for the conductivity in graphite; one of the lattice 

 constants of graphite is known to be larger than the abscissa of the 

 crossover of Fig. 17; hence in graphite there are partially filled bands 

 and conduction. 



The general downward trend of the bands in Fig. 17 indicates a 

 strong binding energy for diamond; but quantitative calculations of 

 the total energy have not been made. 



The type of binding involved in diamond is quite like the binding 

 of metals save that, owing to the absence of partially filled bands, 

 there is no electrical conductivity. In both cases the energy arises 

 from the lowering of energy levels as the atoms come together. In 

 chemical terminology the binding of diamond is referred to as "ho- 

 mopolar" signifying that the atoms are all similarly charged, or rather 

 uncharged. In crystals containing ions rather than neutral atoms, 

 the cohesion is due largely to electrostatic forces and one refers to 

 binding as " heteropolar " or "ionic." 



Energy Bands and Binding Energies of Ionic Crystals 



The energy band theory can be applied to the calculation of the 

 binding energy of ionic crystals. Before discussing this application, 

 however, it will be instructive to examine a somewhat simpler ap- 

 proach to the problem. 



A sodium chloride molecule consists of a sodium ion and a chlorine 

 ion. These ions have charges of +e and —e respectively and have a 

 mutual electrostatic energy of 



-J. (5) 



where r is their distance of separation. This electrostatic energy, 

 which we shall refer to as the "coulomb energy," decreases with de- 

 creasing interatomic distance. If the ions are close together, as they 

 are in a molecule, the energy of encroachment due to the overlapping 

 of their closed shells must be considered; this energy increases with 

 decreasing interatomic distance. The equilibrium distance is the one 

 that makes the total energy, coulomb plus encroachment, a minimum. 



