A coherent model for the complex permeability in polycrystalline ferrites

It is demonstrated that a grain size dependence exists for the rotational permeability of a series of MnZn polycrystalline ferrites, analogous to that predicted by the Globus model for wall permeability. To account for this behavior, a model has been developed which considers crystalline ferrite grains with intrinsic complex permeability, mu /sub i/, surrounded by thin, nonmagnetic grain boundaries. The effectively measured permeability of the polycrystal ( mu /sub e/) is related in the model to the intrinsic permeability, the grain size (D), and the grain boundary thickness ( delta ) according to the equation mu /sub e/= mu /sub i/D/ mu /sub i/ delta +D. The almost linear dependence of permeability with grain size for fine-grained polycrystals emerges if one considers the limit where D is so small that D<< mu /sub i/ delta , and consequently mu /sub e/=D/ delta (providing delta remains constant). For large grains, where D>> mu /sub i/ delta , it is found that the model predicts a constant rotational permeability equivalent to that in a single crystal of the same material. In the situation where the intrinsic permeability of the ferrite displays a relaxational behavior and follows the Snoeks relationship, it is found that both the low-frequency permeability and the resonance frequency of the polycrystal are modified, but in a manner whereby the Snoeks relationship remains valid.<
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