﻿the Electron Theory of Solids. 6G3 



c. A type where the lattices are built up of units which 

 are not electrified ; such units are probably molecules 

 containing two or more atoms, though in certain 

 cases they may be single atoms. The characteristic of 

 the type is that each unit has sufficient electrons 

 bound to it to make it electrically neutral, and that 

 each electron remains attached to a particular atom. 

 Thus where an electric force acts on the system there 

 is no tendency to make the unit move in one direction 

 rather than the opposite, so that the substance cannot 

 conduct electricity. 



Metallic Conduction. 



We now pass on to consider why it is that the arrange- 

 ment of atoms and electrons in type a is in many cases, 

 though not in all, connected with the property of metallic 

 conduction. The consideration of the frequencies of the 

 vibrations of the electrons in a lattice will, I think, throw 

 light on this connexion. I showed (Phil. Mag. April 1922, 

 p. 721) that these frequencies may extend over a very wide 

 range of values as the type of displacement of the electrons 

 is altered. Thus, if all the electrons in a region whose linear 

 dimensions are large compared with 2d, the distance between 

 two electrons, have the same displacement relatively to the 

 atoms, the frequency n of the vibrations for the alkali metals 

 is given by the equation 



mp 2 ==-384c.* 2 /<* 4 (1) 



This frequency, even in the case of the univalent element, 

 corresponds to that of light in the visible part of the 

 spectrum ; for elements of greater valency it is far in the 

 ultra-violet. This is also the frequency with which a single 

 electron vibrates if the surrounding atoms and electrons are 

 fixed. As those frequencies are so great very little energy 

 will go into them at ordinary temperatures, and they will 

 have little or no effect on the specific heat of the solid. 



There are, however, other types of vibration for which the 

 periods may be very long. Thus if all the electrons on a 

 certain line of the lattice are displaced along the lattice by 

 the same amount, while those on adjacent lattices are 

 displaced in the opposite direction, the frequency is given by 

 the equation 



2 -384c. e* 5-2e s ,-. 



thus we see that only under certain conditions is the ex- 

 pression for p 2 positive, and it is only under these that the 



