Hot-deformed anisotropic Nd$-$Fe$-$B nanocrystalline magnets have been subjected to the grain-boundary diffusion process (GBDP) using a $mathrm{Pr}_{70}mathrm{Cu}_{30}$ eutectic alloy. The resulting grain microstructure, consisting of shape-anisotropic Nd$-$Fe$-$B nanocrystals surrounded by a Pr$-$Cu-rich intergranular grain-boundary phase, has been investigated using unpolarized small-angle neutron scattering (SANS) and very small-angle neutron scattering (VSANS). The neutron data have been analyzed using the generalized Guinier-Porod model and by computing model-independently the distance distribution function. We find that the GBDP results in a change of the geometry of the scattering particles:~In the small-$q$ regime the scattering from the as-prepared sample exhibits a slope of about $2$, which is characteristic for the scattering from two-dimensional platelet-shaped objects, while the GBDP sample manifests a slope of about $1$, which is the scattering signature of one-dimensional elongated objects. The evolution of the Porod exponent indicates the smoothing of the grain surfaces due to the GBDP, which is accompanied by an increase of the coercivity.
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