The structural properties and lattice instabilities of perovskites in the $(\mathrm{T}\mathrm{h},\mathrm{P}\mathrm{b},\mathrm{B}\mathrm{i},\mathrm{Y}){\mathrm{ScO}}_3$ system are investigated by first-principles density-functional calculations with the linearized augmented plane-wave method. In all cases, Th is found to be tetravalent on the perovskite A site. The electronic structures have substantial Sc-O hybridization, as well as both Pb-O covalency, as is common in Pb based transition-metal perovskites, and significant hybridization of nominally unoccupied Th p and d states with O p states. The calculations show that the ideal cubic perovskite structure is highly unstable in $(\mathrm{T}\mathrm{h},\mathrm{P}\mathrm{b}){\mathrm{ScO}}_3.$ The dominant instability is against rotation of the ${\mathrm{ScO}}_6$ octahedra, as is common in perovskites with small A-site cations as defined by the perovskite tolerance factor. However, there are also substantial, though weaker, instabilities against ferroelectric distortions. These are characterized by large shifts of the A-site ions against the surrounding O, especially for the Th. The tetragonal ferroelectric state is favored over a rhombohedral state, and in addition a large tetragonal $c/a$ ratio is found. At least for a particular ordering of the A-site ions we find that the ferroelectric and rotational distortions coexist, yielding a monoclinic symmetry ferroelectric ground state with rotated octahedra and a large Th off-centering. Calculations are also reported for ${\mathrm{BiScO}}_3$ and ${\mathrm{YScO}}_3$ in the perovskite structure. Considering only ferroelectric instabilities, these compounds show somewhat different anisotropies but both favor large $c/a$ ratios when tetragonal. The instability against rotation of the ${\mathrm{ScO}}_6$ octahedra is similar in energy to the ferroelectric instability in ${\mathrm{BiScO}}_3$ and substantially stronger than the ferroelectric instability in ${\mathrm{YScO}}_3.$ Trends in the lattice instabilities of $A{\mathrm{ScO}}_3$ perovskites are discussed in terms of these results. Of the systems considered, the most likely to show a piezoelectrically active morphotropic phase boundary is ${\mathrm{Th}}_{\left(1\mathrm{}-x\right)/2\mathrm{}}{\mathrm{Bi}}_x{\mathrm{Pb}}_{\left(1\mathrm{}-x\right)/2\mathrm{}}{\mathrm{ScO}}_3.$ Implications for practical piezoelectric materials are discussed.

• Received 29 January 2004

DOI:https://doi.org/10.1103/PhysRevB.69.174107