Possible Coexistence of Rotational and Ferroelectric Lattice Distortions in Rhombohedral PZT

The competitions between ferroelectric and rotational instabilities in rhombohedral PZT near x = 0.5 are investigated using first principles density functional supercell calculations. As expected, we find a strong ferroelectric instability. However, we also find a substantial R-point rotational instability, close to but not as deep as the ferroelectric one. This is similar to the situation in pure PbZrO_3. These two instabilities are both strongly pressure dependent, but in opposite directions so that lattice compression of less than 1% is sufficient to change their ordering. Because of this, local stress fields due to B-site cation disorder may lead to coexistence of both types of instability are likely present in the alloy near the morphotropic phase boundary.