  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.
