Influence of the Grain Size Distribution

The grain size influences crucially the remanence and coer-civity of nanostructured materials. Indeed, in large grains, internal magnetization distribution with domain walls at the grain boundary may be formed. Calculations of Ref. [111], by using randomly oriented anisotropy distribution, inplane magnetization, and equal-size grains in Fe14Nd25 magnets showed that in interacting grains, the remanence enhancement (with respect to that for noninteracting grains) increases with the average grain diameter, and this is more prominent for grains with diameter <20 nm. However, coer-civity also is significantly reduced. This is explained by means of competitive effects between magnetocrystalline anisotropy and exchange interaction at the grain boundary. Only the magnetic moments within the boundary region, which is of the order of the domain wall, could enhance remanence; its volume fraction is more significant for small grains. However, these strongly inhomogeneous microstructures favor the nucleation of reversed domains and, therefore, decrease the coercivity. Figure 17 presents the grain size dependence of the demagnetization curves, the distribution of the magnetization for NdFeB soft-hard magnets, and the magnetization distribution at the remanence. More inhomogeneous magnetization structures at the boundaries of large grains are clearly observed.

Similarly, for Co nanoelements [128], three grain sizes without size dispersion were investigated. The nanoelements, consisted of 8-nm grains, exhibit strongly pinned magnetization until the coercive field is reached and, consequently, is a very squared loop. In larger grains (12-nm Co), the reversible magnetization changes occur inside grains (within the boundary region) in the field prior to the coercive one that resulted in Barkhausen jumps. It was observed, during the simulation, that the magnetization within individual grains was strongly uniform in the case of 8-nm grains and less homogeneous in the case of 12-nm grains.

In reality, the nanostructured materials typically present a log-normal grain-size distribution. It has been showed that a small dispersion of the grain sizes may lead to an enhanced remanence and may preserve a high coercive field [111].

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