Quadruple superstructure with antiferroic ionic displacements in B i 1 − x S m x Fe O 3

Crystallographic and morphologic features of quadruple and double superstructures in $\mathrm{B}{\mathrm{i}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{m}}_{x}\mathrm{Fe}{\mathrm{O}}_{3}$ with $0\ensuremath{\le}x\ensuremath{\le}0.40$ were investigated by x-ray powder diffraction and transmission electron microscopy. The presence of a quadruple superstructure accompanied by antiferroic ionic displacements was found near the morphotropic phase boundary between the $R3c$ phase ($0lxl0.10$) and the Pnma phase ($0.25\ensuremath{\le}x\ensuremath{\le}0.40$). The quadruple superlattice phase coexists with a ferroelectric $R3c$ phase at $x=0.15$. These superstructures were found to originate from the freezing of multiple phonon modes related to transverse wave ionic displacements. These findings provide further insight towards understanding the complexity of rare-earth-doped $\mathrm{BiFe}{\mathrm{O}}_{3}$.