We present an investigation of the collective magnetic behavior of nano-sized crystallites with dimension smaller than the critical diameter for mono-domain particles (below 54 nm for Fe_3O_4) and its close relationship with the particles' size and shape. The object of our work was Fe_3O_4, which is a classical case of a ferromagnetic spinel crystal structure and can be used to a certain extent as a model for other spinel solid solutions. We studied two types of powders with avarage grain size 38 nm (sample 1) and 6.5 nm (sample 2). Using high-resolution TEM (HRTEM), in both samples we observed grains with different shapes, namely, spherical, ellipsoidal and cubic. In sample 2, the content of spherical particles is about 80%, while grains with cubic shape predominate in sample 1 (about 85%). The samples were also examined by means of Moessbauer spectroscopy, X-ray diffractometry (XRD), ED, SEM and a vibrating-sample magnetometer (VSM).
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