DIAMONDS — LOGIE 371 



Some idea as to why there should be these differences in bond- 

 ing energy can be gained by imagining the crystal to be assembled 

 from a group of atoms which are initially far apart. We imagine the 

 atoms to be brought closer and closer together until they are at the 

 characteristic lattice spacing. Binding energy, wliich is so large in 

 the case of the diamond, comes about because the electrons lower 

 their energy as the atoms get closer. It was shown earlier that the 

 energy of the electrons was less if they were closer to the nucleus, 

 and this is precisely what happens when the atoms are brought 

 together to form a solid. The valence electrons in the crystal are 

 never very far from some atomic nucleus and their potential energy 

 is thus much reduced. They are making better use of the positively 

 charged cores by staying closer to them. 



While the potential energy has been lowered, what has happened 

 to the kinetic energy? All the valence electrons caiuiot have zero 

 kinetic energy without violating the exclusion principle. This princi- 

 ple states simply that no two electrons may occupy one and the same 

 quantum state. If it were not for a law of this nature, all the electrons 

 would drop to the lowest energy level and the structure of the periodic 

 table, the diversity of the elements, and this audience would not exist. 

 In order to dispose of all the valence electrons in the crystal and yet 

 have at most one electron per quantum state, a large range of momenta 

 and therefore of kinetic energies must be f oimd among the electrons. 

 The band of energy states required to accommodate the electrons and 

 the number of states which are occupied can be calculated using 

 Fermi-Dirac statistics. The average kinetic energy per electron then 

 turns out to be somewhat larger in the solid than in the gas. However, 

 there still remains a net loss of energy for the atom as a whole. The 

 binding forces arise then because the gain of kinetic energy does not 

 completely offset the loss of potential energy. The net change is 

 greater if the difference in the size of the atom and of the ion core 

 is large. This explains the difference in the cohesive energy of the 

 group IV elements and the fact that the binding energies are lowered 

 as the atomic number is increased. 



It has been remarked that the bonding in diamond is covalent. In 

 the simplest terms, this means that a valence electron from one atom 

 is shared with the adjacent atom and none of them is free to move 

 through the crystal. The situation is usually represented by an 

 energy band diagram lil^e figure 6. Each band represents a group of 

 closely spaced energy states in which the electrons may be. These 

 energy bands have their counterpart in the discrete energy levels of 

 the free atom. Just as the quantum conditions allow only certain 

 widely separated energy levels in the atom, so also there are energy 

 bands in the crystal which are separated from one another by "for- 



