${\mathrm{Bi}}_2{\mathrm{W}}_2{\mathrm{O}}_9$: A potentially antiferroelectric Aurivillius phase

Ferroelectric tungsten-based Aurivillius oxides are naturally stable superlattice structures, in which $A$-site deficient perovskite blocks ${\left[{\mathrm{W}}_n{\mathrm{O}}_{3n+1}\right]}^{-2}$ ($n=1,2,3,\cdots$) interleave with fluorite-like bismuth oxide layers ${\left[{\mathrm{Bi}}_2{\mathrm{O}}_2\right]}^{+2}$ along the $c$-axis. In the $n=2{\mathrm{Bi}}_2{\mathrm{W}}_2{\mathrm{O}}_9$ phase, an in-plane antipolar distortion dominates but there has been controversy as to the ground-state symmetry. Here we show, using a combination of first-principles density functional theory calculations and experiments, that the ground state is a nonpolar phase of $Pnab$ symmetry. We explore the energetics of metastable phases and the potential for antiferroelectricity in this $n=2$ Aurivillius phase.

Figure 1

The structure of ${\mathrm{Bi}}_2{\mathrm{W}}_2{\mathrm{O}}_9$ in (a) the aristotype paraelectric $I4/mmm$ phase and (b) the distorted orthorhombic $Pnab$ ground state showing rotation of ${\mathrm{WO}}_6$ octahedra about in-plane and out-of-plane axes and in-plane antipolar displacements of ${\mathrm{W}}^{6+}$ ions. Bi, W, and O ions are shown in purple, gray, and red, respectively, and corner-linked ${\mathrm{WO}}_6$ octahedra are shown in gray.

Figure 2

Schematic illustration of atomic motions associated with the unstable phonon modes of the $I4/mmm$ phase of ${\mathrm{Bi}}_2{\mathrm{W}}_2{\mathrm{O}}_9$ (at high-symmetry points of the Brillouin zone). Rigid-layer modes (RL modes) are related to a nearly rigid motion of the ${\left[{\mathrm{Bi}}_2{\mathrm{O}}_2\right]}^{+2}$ layer with respect to the perovskite block [6, 15]. For modes involving polar and antipolar cationic displacements, oxygen atom motions are omitted for clarity. The [110] direction is that in the tetragonal primitive cell and corresponds to the $a$-axis in the orthorhombic cell.

Figure 3

Sketch of the most relevant metastable phases of ${\mathrm{Bi}}_2{\mathrm{W}}_2{\mathrm{O}}_9$. Each phase is identified by the combination of modes giving rise to it, its symmetry, and its energy ($\mathrm{\Delta }E$ in meV per formula unit) with respect to the $I4/mmm$ reference model. Contributions of the modes of a given symmetry to the total atomic distortion of each phase with respect to the $I4/mmm$ reference model are identified through color segments, with lengths proportional to the projection ($A{\alpha }_i$; see the main text) of these modes to the total distortion. A distinct color is affected to modes of distinct symmetry. When different modes of the same symmetry are contributing, only their total contribution is shown. The $Pna{2}_1$ phase from Ref. [11], although not a metastable phase in our computational framework, is included (darker gray box) for comparison.

Figure 4

(a) Rietveld refinement profiles from combined refinement using (a) XRPD data; (b) backscattered ${169}^{\circ }$ bank data ($\sim 0.6-2.6\AA d$-spacing range), including an enlarged view of low $d$-spacing range; (c) ${90}^{\circ }$ bank data ($\sim 0.8-3.8\AA d$-spacing range); and (d) ${30}^{\circ }$ bank data ($\sim 2.3-9\AA d$-spacing range) collected for ${\mathrm{Bi}}_2{\mathrm{W}}_2{\mathrm{O}}_9$ at room temperature using the $Pnab$ model. Observed and calculated (upper) and difference profiles are shown by blue, red, and gray lines, respectively. (b) Decomposition of the full atomic distortion with respect to the $I4/mmm$ reference model for the $Pna{2}_1$ phase of Ref. [11] (orange), the present $Pnab$ phase refined from our diffraction data (red), and the present $Pnab$ phase relaxed from first-principles calculations. The dashed boxes show the total distortion amplitudes ($A$), while the color segments show the respective contributions ($A{\alpha }_i$) of the modes of distinct symmetry.

Figure 5

Dielectric measurements on sintered pellets of ${\mathrm{Bi}}_2{\mathrm{W}}_2{\mathrm{O}}_9$, (a) showing polarization and (b) showing leakage current with applied field at various temperatures; (c) and (d) show polarization and current density for fields up to $\pm 250$ kV ${\mathrm{cm}}^{-1}$ at $-40{}^{\circ }\mathrm{C}$.