Possible coexistence of rotational and ferroelectric lattice distortions in rhombohedralPbZrxTi1−xO3

The competitions between ferroelectric and rotational instabilities in rhombohedral ${\mathrm{PbZr}}_x{\mathrm{Ti}}_{1-x}{\mathrm{O}}_3$ near $x=0.5\mathrm{}$ 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 ${\mathrm{PbZrO}}_3.$ 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, and 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.