I replace the iron ion with a rare earth ion of concentration between 0 and 0.2. The particle size decreased till a concentration 0.12 and then increased again for a concentration 0.2. The synthesis method used is co-precipitation.
It is interesting that the particle size decreases initially up to 0.12 of rare earth element. However the size increases on further doping. This might be due to the fact that at higher concentration of rare element the inter ionic interaction becomes dominating factor.
The metal ions you precipitate can be regarded as clusters attracting water molecules to different extents depending on ionic radius and charge. High charge and small radius are the strongest metal cations, attracting the greatest shell spheres of organized water. By light scattering you can approximate the size of the clusters, which with precipitation will form your doped ferrite. The size of the clusters are also depending on the concentrations, and possibly you are passing some transition here. The system is also dependent on the media you use for the enforced precipitation, meaning that if you use ammonia instead of sodium hydroxide, then your particle size average will go towards smaller particles. 40 nm average generate close to 10 nm average for the same system when I make pure magnetite.