692 BELL SYSTEM TECHNICAL JOURNAL 



see that the electrons are closely held about the ions with very little 

 overlapping of the closed shells. 



In addition to the metallic, homopolar, and ionic bonds, there is still 

 another interatomic force known as the Van der Waals force — a very 

 weak force compared to the other three. We shall not discuss its 

 origin here except to say that it arises from the spontaneous and 

 mutual polarization of two atoms or molecules when in the neighbor- 

 hood of each other. It is responsible for the "a" term in the Van der 

 Waals equation for gases. When a crystal is formed from organic 

 molecules, such as a crystal of benzene, the forces holding them to- 

 gether are the weak Van der Waals forces. This is the reason why 

 "molecular crystals" have low melting points and binding energies. 

 Although the Van der Waals forces are much smaller than the other 

 three, they are not entirely negligible in comparison and in some of the 

 calculations referred to in the last section, their effects are included. 



It is interesting to note that in a single crystal of a given chemical 

 compound, several of the various forces may be operative at once in a 

 rather separable way. A classification of this sort for crystals has been 

 discussed by Grimm.^^ For example the crystal mica, which cleaves so 

 naturally into sheets, consists of planes of atoms bound together chiefly 

 by valence forces, the binding between the planes being due to ions 

 lying between and in the planes. Thus mica is held together in two 

 directions by strong valence forces and in the other by weaker ionic 

 forces. In asbestos the atoms are arranged in parallel rows, being held 

 together in the rows by valence forces; the rows, on the other hand, are 

 held to each other by ionic forces. The ionic bonds are more easily 

 broken and asbestos crystals exhibit a typical fibrous structure. Mica 

 and asbestos are intermediate members of a sequence of which diamond 

 with all valence binding and sodium chloride with all ionic binding 

 constitute the extremes. We shall give one more example: cellulose 

 consists of long chains of carbon, oxygen and hydrogen, the chains 

 held to each other by Van der Waals forces ; it is an example of valence 

 binding in one direction and Van der Waals binding in the other two. 



This section has been a digression, as the main purpose of these 

 papers is to illustrate the band theory of solids. It would hardly be 

 fair to concentrate on this, however, without pointing out, as has 

 been done in this section, that, although the band theory has great 

 generality, it is best adapted for a certain class of solids and that other 

 viewpoints are^more natural for solids outside of this class. 



25 Naturwissenschaften, 27, 1}_(1939). 



