**Nanoscale clustering of Mn _{x}Fe_{3−x}O_{4} particles studied by small-angle neutron scattering**

A series of Mn_{x}Fe_{3−x}O_{4}(0≤x≤1) nanoparticles was successfully synthesized via a simple coprecipitation method. The starting material was a natural magnetite purified from local iron sand. Crystallite nanoparticles were produced by drying without using a high calcination temperature. Rietveld analysis of the X-ray diffractometry (XRD) data for all samples demonstrated that the Mn ions partially substituted the Fe ions in the spinel cubic structure of the Fe_{3}O_{4} to form Mn_{x}Fe_{3−x}O_{4} phases. We applied two lognormal spherical and single mass fractal models to the analysis of the small-angle neutron scattering (SANS) data and revealed that the primary Mn_{x}Fe_{3−x}O_{4} particles ranged in size from 1.5 to 3.8 nm and formed three-dimensional clusters as secondary structures.

SANS curves and fitting model of the Mn_{x}Fe_{3−x}O_{4}(0≤x≤1) nanoparticles. The data were shifted for clarity. Thecirclesrepresent the SANS data, and thesolid linesrepresent the fitting model using the two lognormal spherical model and the single mass fractal model.

Result of the fits for the SANS data (above) for the nanoparticles with x =0,0.25, 0.50, 0.75 and 1.

The HRTEM image of Mn_{0.5}Fe_{2.5}O_{4} sample; the green circles represent the primary particles, and the yellow circles represent the secondary particles.