704 BELL SYSTEM TECHNICAL JOURNAL 



Griineisen's law applies only to simple crystals; we shall see in the 

 next section that it is not applicable to the anomalous expansion asso- 

 ciated with ferromagnetic transformations nor is it applicable to the 

 abnormal expansions of the order-disorder transformations in alloys. 



Magnetic Effects 



In this section we return to a discussion of the energy band theory 

 and this time introduce the magnetic moment associated with the spin 

 of the electron. It is the spin magnetic moment which when added 

 to the concept of energy bands leads to explanations of para and 

 ferromagnetism. 



When a body is placed in a magnetic field it becomes magnetized; 

 in other words it acquires a magnetic moment. Ferromagnetic ma- 

 terials become very easily magnetized in the field with their magnetic 

 moments parallel to the field and they may remain magnetized after 

 the field is removed. Paramagnetic materials are also magnetized in 

 the direction of the field but only very weakly compared to ferro- 

 magnetic materials and only while they remain in the field. Diamag- 

 netic materials are magnetized in a direction opposite to the field and, 

 like paramagnetic substances, only weakly and while in the field. 

 These magnetic effects are produced by the electrons in two distinct 

 ways. In the first place, the motion of the electron as a whole pro- 

 duces a current and this current, like the ordinary macroscopic currents 

 in a wire, produces a magnetic field. Conversely, an externally ap- 

 plied magnetic field affects the motions of the electrons in a body and 

 can thereby magnetize it; this process accounts for the diamagnetism 

 of diamagnetic bodies but it may contribute to the paramagnetism as 

 well. It is not with this first way in which electrons can behave mag- 

 netically but rather with the second way, described below, that we 

 shall be concerned. The first way, which is mentioned for complete- 

 ness, involves a theory too complicated for treatment in this article. 

 In the second place, an electron can behave magnetically by virtue 

 of its spin : the rotation of the electron about its own axis produces 

 a magnetic moment which is anti-parallel — because the charge of 

 the electron is negative — to the angular momentum due to the spin. 

 A magnetic field tends to align the spin magnetic moments of the elec- 

 trons and to make them contribute to the paramagnetism. We shall 

 see below that this process accounts for the paramagnetism of non- 

 ferromagnetic metals. We shall see also that the magnetism of ferro- 

 magnetic bodies is due to the magnetic moment of the electron spin 

 but that the energy involved in the theory of ferromagnetism is not 

 an interaction betw^een the magnetic dipoles of the electrons but is 



