ELASTIC CONSTANTS AND LOSSES IN NICKEL 987 



2.5 X 10~^, and use of equation (2) with this and other appropriate values 

 indicates that the domain size is 



I = 0.035 mm, (21) 



as reported above. 



A check on this value can be obtained from the frequency, fm , corre- 

 sponding to the maximum of the 5 vs/ curve. If we use equation (16), 



/^o/n./^ = 0.13, (22) 



with/ = 1.5 X 10^ (Fig. 11), we find / = 0.045 mm, in reasonable agreement. 

 An actual photograph of domains in a single crystal of nickel, taken by H. 

 J. Wilhams and reproduced in Fig. 13, shows the presence of domains of 

 various sizes ranging from about 0.01 to 0.2 mm. Any such range in domain 

 sizes will naturally tend to flatten the maximum of the 6 vs / curve and, 

 on account of the form of the 6 vs / function, will push the maximum to a 

 higher frequency than that corresponding to the initial slope, and will give 

 a lower maximum value to the decrement frequency curve. 



The average domain size derived from our experiments is somewhat larger 

 than that previously obtained in 68 Permalloy.^ This may be expected, 

 for nickel has a very high magnetostriction and the movement of domain 

 boundaries by stress will be relatively large, possibly so large that the re- 

 gions swept over by the domain walls will correspond to whole domains of 

 the original domain structure, when the stresses are equal to those used in 

 our experiments. The domain size which we have determined is based on 

 this interpretation. 



APPENDIX 



METHOD OF MEASUREMENT— FORMULAE 



From transmission line theory (see reference of footnote 12) the ratio 

 of outputs, r, defined in the text and appHcable to the circuit of Fig. 9 is 

 given by 



r = cosh e/o + i (g + ^) sinh % (24) 



where Q = A -\- jB = propagation constant 



jSpco 

 Zq = - — , — — = characteristic impedance of rod 

 A -\r jB 



Zt = resistive terminating impedance provided by crystals 



5 = area of rod 



This expression may be expanded into real and imaginary parts and the 

 latter term set to zero in accordance with the condition of phase balance. 



