Frequency Dependence of Elastic Constants and Losses 



in Nickel 



By R. M. BOZORTH, W. P. MASON and H. J. McSKIMIN 



The elastic constants of nickel crystals, and their variation with magnetic field 

 (AE effect), have been measured by a 10-megacycle ultrasonic pulsing method. 

 The constants of three crystals agree well with one another when the crystals are 

 magnetically saturated, but vary with domain distribution when demagnetized. 

 The maximum ZLE effect observed is much less (3%) than has been observed at 

 lower frequencies (20%). By measuring the A£ effect and the decrement of poly- 

 crystalline rods at low frequencies, it is shown that the small effect observed at 

 10 megacycles is due to a relaxation in the domain wall motion due to micro- 

 eddy-current damping. 



From the initial slope of the decrement-frequency curve, and also from the 

 frequency of maximum decrement, the size of the average domain is found to be 

 about 0.04 mm. Actual domains in single nickel crystals have been observed 

 optically by Williams, who finds domain widths of 0.02 to 0.2 mm. 



THE three elastic constants of nickel have been determined in several 

 single crystals by measuring the velocity of pulses of elastic waves of 

 frequency 10 mc/s and duration 0.001 sec. The method has been described 

 by McSkimin^ and the preliminary results on nickel have already been re- 

 ported briefly .2 



It is well known that Young's modulus, E, increases with magnetization, 

 and changes in E (the "A£ effect") by 15 to 30 per cent have been observed 

 at room temperature and changes by greater amounts at higher tempera- 

 tures.^ It was surprising to find then, in our own experiments at 10 mc, that 

 the greatest change was only about 3 per cent. It then occurred to us that, 

 at such a high frequency, relaxation of the domain wall motion by micro- 

 eddy-current damping might be expected. This led to the investigation of 

 the frequency dependence of A£ and of the logarithmic decrement, 5, in 

 polycrystalline nickel, and the results obtained support the theory and give 

 information about domain size, as described below. Calculations'* based on 

 the equations of domain wall motion give results which agree with the ex- 

 periments. 



A number of experiments' have already established the existence of micro- 

 eddy-current losses in magnetic materials subjected to elastic vibrations. 

 These losses have their origin in the local stress-induced changes of mag- 

 netization of the domains of which magnetic materials are composed. The 

 change in magnetization of one domain will give rise to eddy-currents around 

 it and in it, and the consequent loss in energy depends on the frequency / 

 and the resistivity i?, and on the size and shape of the region in which the 

 change in magnetization occurs. These losses are in addition to the macro- 



970 



