984 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



quency of the maximum value of 5 and the initial slope of the decrement 

 frequency curve are connected with definite domain sizes which can be 

 calculated approximately and compared with magnetic domain powder 

 patterns. 



Discussion 



Our determinations of the elastic constants may be discussed in relation to 

 the values obtained by others. The results reported by Honda and Shira- 

 kawa^° and Yamamoto" were unlcnown to us and unavailable at the time of 

 our preliminary communication. The data of the Japanese, converted from 

 5-constants to c-constants by the relations: 



^11 + ^12 

 ^11 — 2 . r, 2 



5il -r SiiSu — ^Si2 



_ -^12 (15) 



'^12 — 2 I o 2 



^11 + ^11^12 — ^^12 



Cu — 1/544 



are included with our data in Table II. 



As our experiments show, the 10 mc pulses that we used are so rapid that 

 micro-eddy-currents largely prevent the stress-induced changes in mag- 

 netization from penetrating the domains. Therefore the constants deter- 

 mined by this method are those for material almost saturated. The values 

 at saturation are independent of the initial domain distribution, and of the 

 ease with which the magnetization in the separate domains can be changed 

 by stress, consequently they are the more fundamental elastic constants of 

 the material. The variety of values for unmagnetized nickel is made evident 

 from the scatter in the ratios of LE/E that have been reported.' The varia- 

 tion in the values of the c-constants recently published is thus not surprising. 

 The values at saturation of the three crystals examined by us are in sub- 

 stantial agreement, as shown in Table II. They cannot be compared directly 

 with the results of the Japanese workers because the latter reported data 

 for unmagnetized crystals only and then E is sensitive to heat treatment 

 and domain configuration. 



As mentioned in the introduction, the damping of elastic vibrations by 

 micro-eddy-currents is proportional to the frequency at low frequencies 

 (Eq. 1) and it rises with frequency to a maximum and then declines toward 

 zero. The frequency at which the maximum occurs has been calculated^ 

 by using the equation of domain wall motion and evaluating the constants 

 from the initial permeability and the power loss caused by domain wall 

 motion. The maximum value of b comes at the same value as that calculated 



