Lattice instabilities and ferroelectricity in A ScO₃ perovskite alloys

The structural properties and lattice instabilities of perovskites in the (Th,Pb,Bi,Y)ScO₃ 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 (Th,Pb)ScO₃. The dominant instability is against rotation of the ScO₆ 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 BiScO₃ and YScO₃ 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 ScO₆ octahedra is similar in energy to the ferroelectric instability in BiScO₃ and substantially stronger than the ferroelectric instability in YScO₃. Trends in the lattice instabilities of AScO₃ perovskites are discussed in terms of these results. Of the systems considered, the most likely to show a piezoelectrically active morphotropic phase boundary is Th_(1-x)Bi_xPb _(1-x)/2aScO₃. Implications for practical piezoelectric materials are discussed.