The minimum size of oxide nanocrystals: phenomenological thermodynamic vs crystal-chemical approaches

The minimum crystallite size in a group of oxides has been analyzed as a function of their synthesis conditions, critical nucleus size and the crystal structure parameters. Nanocrystals were synthesized by solution combustion, hydrothermal synthesis and heat treatment in air of the precipitated hydroxides. Aluminum and iron oxides, titania and zirconia, cobalt ferrite, AFeO$_{3}$ ferrites (A = Bi, RE), Aurivillius phases Bi$_{m+1}$Ti$_{3}$Fe$_{m-3}$O$_{3m+3}$ ($m = 3$–$9$), as well as solid solutions based on these phases were chosen as the objects of the study. The presence of a correlation between the crystalline oxide unit cell parameters and the synthesized crystals minimum size is shown. A conclusion was made about the impossibility to use only the thermodynamic concept of the critical nucleus for determining the minimum possible particle size of a new phase in some cases of oxide nanocrystals synthesis. The paper demonstrates a necessity to use crystal-chemical criteria that complement the methods of phenomenological thermodynamics and kinetics for determining the minimum possible particle size of the resulting crystalline oxide phases synthesized under the considered conditions.