GRAIN-SIZE AVERAGE AND DISTRIBUTION EFFECTS ON MAGNETIC LOSSES AND THRESHOLD FIELDS IN NICKEL FERRITES AT MICROWAVE FREQUENCIES

Nickel ferrites with scaled average grain sizes and lognormal size distributions were prepared by hot-pressing and subsequent annealing and by conventional firing. Average grain sizes ranged from less than 1 to 10 μ. The dielectric loss, saturation magnetization, bulk density, and linewidth measurements confirmed that almost all samples were good nickel ferrites. Lognormal distributions allow with easy calculations to evaluate for each sample the fraction of grains having diameters below certain values that are critical for the loss mechanism. Orthogonal and parallel pump measurements of threshold fields at X band showed a very regular behavior with average grain sizes: ∥ hcrit varied from 80 Oe for 0.9-μ sample to 8 Oe for a 10-μ sample with a dependence of the type hcrit≈x̄-2 for x̄<2 μ, hcrit≈x̄-0.5 for x̄>2 μ. An analysis of the distribution of grains shows that ∥ hcrit increases steeply for samples having about 80% or more of the number of grains with sizes less than 3 μ. Regular behaviors of the imaginary part of the permeability (at Hdc≈4πMs/3) with average sizes are found at 9.23, 12.12, and 19.75 GHz: losses increase with decreasing grain sizes but not as much as threshold fields, with a dependence of the type μ″min≈x̄-0.5. The high-power figure of merit F*, measured on spheres at X band, increases with decreasing grain size from 0.07 to 0.26, thus encouraging the fine grain approach for microwave device applications. © 1969 The American Institute of Physics.