The Quantum Physics of Solids, I 

 The Energies of Electrons in Crystals 



By W. SHOCKLEY 



It is proposed to make this paper the first of a series of three 

 dealing with the quantum physics of solids. This one will 

 be concerned with the quantum states of electrons in crystals. 

 The discussion will commence with an introductory section devoted 

 to the failure of classical physics to account for phenomena of an 

 atomic scale. Next, the quantum theory of electrons in atoms 

 will be discussed, together with the resultant explanation of the 

 structure of the periodic table; this is designed to illustrate the 

 meaning of various quantum mechanical ideas which are important 

 in understanding solids. Furthermore, much of the detailed in- 

 formation about atomic quantum states of particular atoms will 

 be needed in the later discussion of the properties of certain solids. 

 As an introduction to the modification of the quantum states oc- 

 curring when atoms are put together to form a crystal, a short 

 section will be devoted to structure of diatomic molecules. The 

 next section will be concerned with quantum states for electrons 

 in crystals. Whereas in an atom there are a series of isolated 

 energies possible for an electron (corresponding to the various 

 quantum states), in a crystal there are bands of allowed energies. 

 This concept of energy bands is essential to the theory of crystals 

 in much the same way that the concept of energy levels is essential 

 to that of atoms. In terms of energy bands, the energy holding 

 crystals together can be interpreted on a common basis for a wide 

 variety of crystal types. This will be followed by a brief descrip- 

 tion of various crystal types and by a discussion of thermal proper- 

 ties in which the smallness of the electronic specific heat will be 

 shown. The last section will be devoted to a discussion of para 

 and ferromagnetism on the basis of the energy band picture. 



In the second paper, problems connected with electric currents 

 and the motion of electrons through crystals will be discussed. 

 This leads to the concept of the Brillouin zone which is complemen- 

 tary to that of the energy band, the two together forming the 

 basis for discussing the quantum states of electrons in crystals. 

 The third paper of the series will contain a comparison between 

 theory and experiment for the alkali metals, the principal emphasis 

 being placed upon the physical picture of the state of affairs in 

 these simple metals. 



Introduction 



^'' I '^HE parts of all homogeneal hard Bodies which fully touch one 



-■- another, stick together very strongly . . . I . . . infer from 



their Cohesion, that their Particles attract one another by some Force, 



which in immediate Contact is exceeding strong, at small distances 



645 



