ABSTRACTS OF TECHNICAL ARTICLES 773 



temperature variation of saturation magnetization, is discussed for ferro- 

 magnetic insulators and metals, with emphasis on its relation to the theory 

 of the energy of the Bloch interdomain wall. The analysis indicates that 

 spin-wave theory is of more general validity than the Heitler-London-Heisen- 

 berg model from which it was originally derived. Many properties of spin 

 waves of long wavelength can be derived without specialized assumptions, 

 by a field-theoretical treatment of the ferromagnetic material as a continuous 

 medium in which the densities of the three components of spin are regarded 

 as amplitudes of a quantized vector field. As applications, the effects 

 of anisotropy energy and magnetic forces are calculated; and it is shown 

 that the Holstein-Primakoff result for the field dependence of the saturation 

 magnetization can be derived in an elementary manner. An examination 

 of the conditions for vahdity of the field theory indicates that it should be 

 valid for insulators, and probably also for metals, independently of any 

 simplifying assumptions. The connection with the itinerant electron model 

 of a metal is discussed; it appears that this model is incomplete in that it 

 omits certain spin wave states which can be proved to exist, and that when 

 these are included, it will yield both a magnetization reversal proportional 

 to T^ and a specific heat proportional to T. Incidental results include some 

 insight into the relation between the exchange and Ising models for a two- 

 dimensional lattice, an upper limit to the effective exchange integral, and a 

 treatment of spin waves in rhombic lattices. 



Edticational Patterns in U. S. and England* M. J. Kelly^ J I. Engg. 

 Education, v. 41, pp. 358-361, Mar., 1951. 



A Barium Titanate Transducer Capable of Large Motion at an Ultrasonic 

 Frequency* W. P. Mason' and R. F. Wick^ Acoustical Soc. Am., JL, v. 

 23, pp. 209-214, Mar., 1951. 



Abstract — By using a barium titanate cylinder poled radially a length- 

 wise motion can be excited in the cylinder whose resonant frequency is con- 

 trolled by the length of the cylinder. By using a 4 percent lead titanate-barium 

 titanate combination, stresses up to 1000 pounds per square inch of cross- 

 sectional dimension and motions up to 50 parts in 10® times the length of 

 the cylinder are available for static or slowly varying voltages of 15,000 volts 

 per centimeter along the radial dimension. When such a cylinder is driven 

 at its resonant frequency, the maximum strain appears to be limited to 

 10~^ by heating considerations if no coohng is used. For a cylinder 12 centi- 

 meters long, which resonates at 18 kilocycles, this corresponds to a displace- 

 ment on each end of 3.9 X 10"'* cm, a particle velocity of 44 cm/sec and 

 an acceleration of 5 X 10* cm/sec/sec. All of these quantities can be en- 



* A reprint of this article may be obtained on request. 

 1 B. T. L. 



