THE PHYSICAL BASIS OF FERROMAGNETISM 5 



the crystals. The circles represent the positions which centers of 

 atoms take up on an imaginary framework or lattice. Because of the 

 smallness of atomic dimensions only a small fraction of the atoms in a 

 crystal of ordinary size are shown, but the same pattern, the unit of 

 which is outlined by solid lines, extends throughout the whole of the 

 single crystal. The arrows indicate the directions of "easiest" mag- 

 netization, which are different for the two materials as may be noticed. 



In order to give a notion of the absolute and relative sizes of crystals 

 and domains and atoms with which magnetic processes are concerned, 

 it may be pointed out that a piece of ordinary iron a cubic centimeter 

 in volume may contain about 10,000 single crystals, and that each 

 crystal contains on the average 100,000 domains each with from lO^'* 

 to 10"^^ atoms. 



Although this article is not concerned primarily with the details of 

 the changes in magnetization that occur when a magnetic field is 

 applied, a brief description of such changes is desirable. In a crystal 

 of iron the directions of easy magnetization are parallel to the cubic 

 axes, that is, they are the six directions parallel to the edges of the 

 cube which represents the structure. When such a magnetic material 

 is unmagnetized as a whole a portion of one of the crystals in it may 

 be represented by the highly schematic Fig. 3(a). As shown, each 

 of the domains, represented by the arrows, circles and crosses, is 

 magnetized in one of the directions of easy magnetization, equal 

 numbers in each of the six directions. When a weak field is applied in 

 the direction indicated and its strength gradually increased to a high 

 value, the magnetizations of the domains change suddenly and their 

 directions approach coincidence with that of the magnetic field. This 

 is usually accomplished by the displacements of domain boundaries, 

 these moving so that some domains grow at the expense of others in 

 which the magnetization lies in a direction further from that of the 

 field. When the field has been increased to such a strength that 

 practically all the domains are oriented as shown in (b) and the crystal 

 is really just one large domain, a second process commences: the mag- 

 netization changes slowly in direction until finally it is parallel to the 

 field, and then changes no more. The material is then said to be 

 saturated, as shown in (c). 



Figure 3 is drawn to illustrate the changes in magnetization that 

 occur in a single crystal of iron. Iron as we ordinarily see it is com- 

 posed of a great many minute single crystals, but the changes in 

 magnetization that occur in each one of these crystals are just those 

 which have been described, the magnetization of the whole poly- 

 crystalline material being the sum of the magnetization of the parts. 



