PRESENT STATUS OF FERROMAGNETIC THEORY 



87 



So far only the effects of stress on the orientation of domains in 

 medium and high fields have been considered. But stress has an 

 effect on the initial permeability also. It has been said already that in 

 ver>' weak fields a change in magnetization is attributed to a movement 

 of the boundaries between domains, the domains oriented nearly 

 parallel to the field growing at the expense of adjacent domains 

 oriented in less favorable directions. Such a growth obviously may 

 be hindered by strain. A relation has been derived " connecting the 

 initial permeability with the internal stress and other magnetic 

 quantities: 



_ 0.018(^ - jj-)^at. 



where mo is the initial permeability, (B — H)sat. and (^//Osat. are the 

 (ferric) induction and magnetostriction at saturation, and ai is the 

 average value of the internal stress in dynes per square centimeter. 



Even when there are no internal strains caused by impurities, in- 

 sufficient annealing, etc., there generally will be the strains of magneto- 

 striction itself, and these will hinder the growth of one domain at the 

 expense of another (Fig. 24). In this case the stress in the foregoing 



UNSTRAINED 





COMPRESSED 



Fig. 24 — Magnetostriction in the shaded region acts as a barrier to further change In 



magnetization. 



equation is equal to Young's modulus, E, multiplied by the magneto- 

 strictive strain, 



<Ti = £(A///)sat. 



and the former equation becomes 



Mo = 



0.018(5 



{my 



This equation really gives a theoretical upper limit for hq. These 

 theoretical limits and the highest observed values for iron-nickel alloys 

 are shown in Fig. 25. This indicates why the composition of the 

 "permalloy" having the highest initial permeability is very nearly 

 the same us that for which the magnetostriction is zero. 



