Lattice Parameter

Beyond the critical diameter of 80 nm, BaTiO₃ stabilises in a cubic structure. Figure.1 shows an increase in the lattice parameter when the average grain size goes down. It would thus seem that there is a grain size dependence in the volume of the unit cell of the crystal lattice. In fact, as we shall see later, this phenomenon is not, at least not for the main part, related to the reduction in size of the nanocrystals, but is due rather to the action of certain heat treatments used on their surfaces to control their size.

In some cases, a grain size dependence is observed in the parameters specifying the crystal structure. However, the few available examples are insufficient to conclude that this is a general effect, and a fortiori, cannot yet provide a full understanding.

Fig.1 Size dependence of the crystallographic lattice parameters a and  c For  BaTiO₃, at 25 ^◦C and standard atmospheric pressure in the powdered state