ELASTIC CONSTANTS AND LOSSES IN NICKEL 985 



for eddy current losses in sheets having the same thickness as the domain, 

 namely 



r-ix,fJR = Q,U ' (16) 



/ being the thickness of the slieet, juo the initial permeability, and R the 

 resistivity of the material (all in c.g.s. units). 



As noted below, the domain sizes calculated from the initial slope of the 

 b vs/ curve of Fig. 12, and from the frequency at which the maximum decre- 

 ment occurs, are respectively 0.035 mm and 0.045 mm (for plates). These 

 values agree quite well. The decrement curve is broader than would be cal- 

 culated from equation (1) for a single domain size. This agrees with the 

 optical measurements of domain size by WiUiams,^ which are shown by 

 Fig. 13. This indicates domain sizes from 0.01 to 0.2 mm. 



The maximum value for the decrement calculated from equation (1), 

 using the measured values, is 0.35 compared to the observed value of 0.11. 

 Part of this is due to the broadening of the peak caused by a distribution 

 of domain sizes, but part may also be due to the deviation of the actual 

 domain shape from a sheet which has been assumed in making the cal- 

 culations. 



The calculations of domain size are made in more detail as follows: 



According to Doring^^ the change in Young's modulus for nickel contain- 

 ing only small internal strains is related to the initial permeability, 7x0 , 

 as folio ws; 



A£ \\n (no - \)Es 



\_Cn — C12 4- 'icuj 



provided the averaging over all crystallites is carried out with constant 

 strain. (If constant stress is assumed, the fraction in brackets, equal to 

 1.76, is omitted.) For nickel Xm is 25 X 10~^, /« is 484, and the c's are the 

 elastic constants given in Table I. This equation holds for low frequencies 

 at which the shielding in single domains is negligibly small. When the re- 

 laxation effect of domain wall motion is considered* equation (18) has to be 

 multiphed by the factor 



1/(1 +/'//») " (19) 



The data of Fig. 12 give the values: 



AE 

 Eo = 1.83 X 10^2^ E, = 2.22 X lO^^ dynes/cm^ — = 0.21 (20) 



is 



for low frequencies. Using these in the above equation, the calculated value 



of juo is 320. A direct measurement* of no has been made for this rod and 



found to be 340, in good agreement with that deduced from the AE effect. 



* Measurements were made independently by Miss M. Goertz and Mr, P. P. Cioffi 

 in order to check this unusually high value. 



