Quadruple superstructure with antiferroic ionic displacements in $\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{m}}_x\mathrm{Fe}{\mathrm{O}}_3$

Crystallographic and morphologic features of quadruple and double superstructures in $\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{m}}_x\mathrm{Fe}{\mathrm{O}}_3$ with $0\le x\le 0.40$ 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 ($0<x<0.10$) and the Pnma phase ($0.25\le x\le 0.40$). 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 $\mathrm{BiFe}{\mathrm{O}}_3$.

Figure 1

Powder x-ray diffraction patterns measured in $\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{m}}_x\mathrm{Fe}{\mathrm{O}}_3$ with compositions between $x=0.00$ and 0.40 at room temperature. R, O, and QSL indicate the rhombohedral, orthorhombic, and quadruple superlattice phases, respectively. All the indices are based on the cubic perovskite structure.

Figure 2

Powder x-ray diffraction patterns measured at various temperatures on heating in $\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{m}}_x\mathrm{Fe}{\mathrm{O}}_3$ with different Sm compositions: (a) $x=0.05$, (b) $x=0.15$, and (c) $x=0.30$. R, O, and QSL indicate the rhombohedral, orthorhombic, and QSL phases, respectively. All the indices are based on the cubic perovskite structure.

Figure 3

Schematic phase diagram obtained from powder x-ray diffraction patterns on heating. The squares $(\square )$ and circles $(◯)$ represent phase transition temperatures from $R3c$ to Pnma and from QSL to Pnma structures, respectively. The solid lines are drawn as a visual guide, and the dashed line implies the coexistence of $R3c$ and QSL phases observed by TEM.

Figure 4

(a) Bright-field image taken of $\mathrm{B}{\mathrm{i}}_{0.85}\mathrm{S}{\mathrm{m}}_{0.15}\mathrm{Fe}{\mathrm{O}}_3$ at room temperature. (b) and (c) Electron diffraction patterns from regions I and II, respectively. The electron incidence is parallel to the $\left[1\overline{1}0\right]$ direction.

Figure 5

Electron diffraction patterns obtained at room temperature with the electron incidences parallel to (a) [001], (b) [100], (c) $\left[1\overline{1}0\right]$, and (d) [110] directions. (e) Schematic three-dimensional reciprocal lattice constructed from electron diffraction patterns with various electron incidences. The large, medium, and small spheres represent the fundamental, double, and quadruple superlattice reflection spots, respectively. Each inset depicts the cross-sectional plane of the reciprocal lattice corresponding to the electron diffraction pattern, and the right front lower corner of the cubic lattice is chosen as the origin of 0 0 0.

Figure 6

Schematics of possible ionic displacements associated with the frozen transverse wave normal vibration modes with (a) ${\mathrm{\Sigma }}_3$, (b) ${\mathrm{\Delta }}_5$, (c) $M_5^{\prime }$, and (d) ${\mathrm{\Lambda }}_3$ irreducible representations, in $m\overline{3}m$ point group for the perovskite-type structure. The inset shows the projection view of (a) along the $c$ axis. The large and small spheres represent Bi and Fe ions, respectively, and the arrows denote directions of ionic displacements. (e) $\left[1\overline{1}0\right]$ and (f) [110] schematic diffraction patterns obtained from cross-sectional planes of the three-dimensional reciprocal lattice. The large, medium, and small circles represent the reciprocal positions of the fundamental, double superlattice, and QSL spots, respectively.