ELASTIC CONSTANTS AND LOSSES IN NICKEL 971 



eddy-current losses, due to the relatively uniform changes in magnetization 

 of a magnetized specimen that occur during a change in stress. 



Calculations of the logarithmic decrement, 8i , attributable to micro- 

 eddy-currents, have been made by Becker and Doring^ and by one of the 

 writers.* According to these calculations when the material is composed of 

 plate-like domains of thickness /, in which magnetization changes by bound- 

 ary displacement, the decrement for nickel, which has its directions of easy 

 magnetization parallel to [ill] directions, is given by the relation 



^ Mo Es Xni r 5c44 T f/fo /.N 



Sn Icn - Cn + Scu] 1 + P/fl 



irR 



where /o , the relaxation frequency for domain wall motion is /o = ^ . ,3 



Is is the saturation magnetization, Es is the saturated value of Young's 

 modulus. Ho is the initial permeability, R the electrical resistivity, Xm the 

 saturation magnetostriction along the [111] direction, and Cn , Cn and Cu 

 the three elastic constants of nickel which are evaluated in this paper. For 

 low frequencies the initial slope of the decrement vs frequency curve is 



8^ ^ 24£, 111 t Xni f 5^44 T ,r.\ 



J SirRPs \_cii — cu -\- 3C44J 



As the frequency is increased the decrement rises to a maximum and then 

 declines asymptotically to zero. Both the initial slope of the 5 vs/ curve and 

 the frequency at which the maximum occurs are measures of the domain size. 

 The initial slope has already been used to evaluate the size of the domains 

 in 68 Permalloy.^ It is shown in the present work that the maximum occurs 

 in polycrystalline nickel at a frequency consistent with the dimensions of 

 domains observed by Williams and Walker® in single crystals of nickel. 



Elastic Constants and Damping in Single Crystals 



The nickel crystals used here were grown by slow cooling of the melt in a 

 molybdenum wound resistance furnace, by a method previously described.^ 

 They were cut with major surfaces parallel to (110) planes and were placed 

 between two fused quartz rods as shown in Fig. 1. Measurements of the 

 elastic constants were made as described in detail by McSkimin,^ by meas- 

 uring the velocity of propagation of 10 mc pulses. In order to obtain a num- 

 ber of reflections in the crystal, films of polystyrene approximately J wave- 

 length thick are placed between the rods and the nickel crystal. This has the 

 effect of lowering the impedances next to the nickel to small values and 

 hence nearly perfect reflections at the two surfaces are obtained. The fre- 

 quency is varied until successive reflections occur in phase, and the velocity 

 is then calculated from the frequency and the dimensions of the crystal. 



