Abstract
The competitions between ferroelectric and rotational instabilities in rhombohedral ${\mathrm{PbZr}}_{x}{\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{O}}_{3}$ 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 ${\mathrm{PbZrO}}_{3}.$ 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.
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