Crystal Structure, Defects, Magnetic and Dielectric Properties of the

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Crystal Structure, Defects, Magnetic and Dielectric Properties of the Layered Bi3n+1Ti7Fe3n−3O9n+11 Perovskite-Anatase Intergrowths Dmitry Batuk,*,† Maria Batuk,† Dmitry S. Filimonov,‡ Konstantin V. Zakharov,§ Olga S. Volkova,§,∥,⊥ Alexander N. Vasiliev,§,∥,⊥ Oleg A. Tyablikov,‡ Joke Hadermann,† and Artem M. Abakumov†,‡,# †

Electron Microscopy for Material Science (EMAT), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium Chemistry Department, Moscow State University, 119991 Moscow, Russia § Physics Department, Moscow State University, 119991 Moscow, Russia ∥ Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002 Ekaterinburg, Russia ⊥ National University of Science and Technology “MISiS″, 119049 Moscow, Russia # Skolkovo Institute of Science and Technology, Nobel str. 3, 143026 Moscow, Russia ‡

S Supporting Information *

ABSTRACT: The Bi3n+1Ti7Fe3n−3O9n+11 materials are built of (001)p planeparallel perovskite blocks with a thickness of n (Ti,Fe)O6 octahedra, separated by periodic translational interfaces. The interfaces are based on anatase-like chains of edge-sharing (Ti,Fe)O6 octahedra. Together with the octahedra of the perovskite blocks, they create S-shaped tunnels stabilized by lone pair Bi3+ cations. In this work, the structure of the n = 4−6 Bi3n+1Ti7Fe3n−3O9n+11 homologues is analyzed in detail using advanced transmission electron microscopy, powder X-ray diffraction, and Mössbauer spectroscopy. The connectivity of the anatase-like chains to the perovskite blocks results in a 3ap periodicity along the interfaces, so that they can be located either on top of each other or with shifts of ±ap along [100]p. The ordered arrangement of the interfaces gives rise to orthorhombic Immm and monoclinic A2/m polymorphs with the unit cell parameters a = 3ap, b = bp, c = 2(n + 1)cp and a = 3ap, b = bp, c = 2(n + 1)cp − ap, respectively. While the n = 3 compound is orthorhombic, the monoclinic modification is more favorable in higher homologues. The Bi3n+1Ti7Fe3n−3O9n+11 structures demonstrate intricate patterns of atomic displacements in the perovskite blocks, which are supported by the stereochemical activity of the Bi3+ cations. These patterns are coupled to the cationic coordination of the oxygen atoms in the (Ti,Fe)O2 layers at the border of the perovskite blocks. The coupling is strong in the n = 3, 4 homologues, but gradually reduces with the increasing thickness of the perovskite blocks, so that, in the n = 6 compound, the dominant mode of atomic displacements is aligned along the interface planes. The displacements in the adjacent perovskite blocks tend to order antiparallel, resulting in an overall antipolar structure. The Bi3n+1Ti7Fe3n−3O9n+11 materials demonstrate an unusual diversity of structure defects. The n = 4−6 homologues are robust antiferromagnets below TN = 135, 220, and 295 K, respectively. They show a high dielectric constant that weakly increases with temperature and is relatively insensitive to the Ti/Fe ratio.

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INTRODUCTION Although perovskite (ABO3) is one of the simplest structure types of complex oxides, perovskite-based compounds can demonstrate extreme structural complexity. Structural and electronic instabilities, ordering of point vacancies and planar defects, formation of intergrowths and stacking faults and, particularly, various combinations of these factors result in a remarkable diversity of the perovskite crystal chemistry.1,2 Perovskite-based homologous series have been studied for decades, but apparently there is still room for exploring new materials constructed of 2D perovskite modules separated by planar interfaces of various kinds. Recently, being inspired by a transmission electron microscopy investigation of highly unusual antiphase boundaries in the (Bi0.85Nd0.15)(Ti0.1Fe0.9)O3 perovskites,3,4 we discovered a perovskite-based homologous series Bi3n+1Ti7Fe3n−3O9n+11.5 In this series, complex (001)p © XXXX American Chemical Society

interfaces (the subscript p refers to the perovskite sublattice) slice the perovskite structure into parallel slabs with a thickness of n (Ti,Fe)O6 octahedra (Figure 1). The interfaces are based on anatase-like chains of edge-sharing (Ti,Fe)O6 octahedra running along the [010]p direction. These chains are connected to the octahedra of the perovskite blocks by sharing corners on one side and edges on the other. This connectivity shifts the neighboring perovskite blocks relative to each other over a vector 1/2[110]p. Upon going from one chain to another along the [100]p direction, the edge- and corner- connectivity to the perovskite blocks alternates, resulting in the 3ap periodicity of the structure along this direction. The chains together with the octahedra of the perovskite blocks create S-shaped tunnels, Received: October 24, 2016

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DOI: 10.1021/acs.inorgchem.6b02559 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

also report on the magnetic and dielectric properties of the materials, demonstrating that they show robust antiferromagnetism with the Néel temperature increasing concomitantly with the Fe3+ content and high dielectric constant relatively insensitive to the Ti/Fe ratio.

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EXPERIMENTAL SECTION

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RESULTS

The Bi3n+1Ti7Fe3n−3O9n+11 (n = 4−7) materials were synthesized using a conventional solid-state reaction from Bi2O3 (Aldrich, 99.9%), TiO2 (anatase, Aldrich, ≥99.9%; rutile, Aldrich, 99.9%), and Fe2O3 (SigmaAldrich, ≥99.98%). The starting materials were thoroughly ground, pressed into pellets, and annealed in air at 800 °C for 10 h, then 3−5 times at 1000 °C for 20 h with intermediate regrindings. The cation composition was verified using energy-dispersive X-ray (EDX) analysis (Table S1) conducted on a JEOL 5510 scanning electron microscope equipped with an INCAx-sight 6587 system (Oxford Instruments). The X-ray powder diffraction (XPD) data of the n = 4−7 samples were acquired on a Huber G670 Guinier diffractometer (Cu Kα1 radiation; curved Ge(111) monochromator; image plate). The crystal structure analysis was done with the JANA2006 package.6 The structure of the n = 4−6 materials was studied in detail using transmission electron microscopy (TEM). Samples for TEM were prepared by grinding materials in ethanol and depositing a few drops of the suspensions onto holey carbon TEM grids. Electron diffraction (ED) patterns were acquired using an FEI Tecnai G2 microscope. High angle annular dark-field and annular bright-field scanning transmission electron microscopy (HAADF-STEM and ABF-STEM, respectively) images were acquired on a probe-aberration-corrected FEI Titan3 80−300 microscope operated at 300 kV. The distribution of Fe and Ti in the n = 6 structure was analyzed using atomic resolution electron energy loss spectroscopy (EELS) acquired in STEM mode. The STEM-EELS data were collected at 120 kV on a probe aberration corrected FEI Titan3 60−300 microscope equipped with a Gatan Enfinium ER spectrometer. Individual elemental distribution maps for Ti and Fe were generated by placing an integration window over the background-subtracted Ti-L2,3 and Fe-L2,3 absorption edges. All STEM experiments were conducted with a probe convergence semiangle of about 21 mrad and a probe current about 50 pA. 57 Fe Mössbauer spectroscopy was performed in a transmission mode using a constant acceleration spectrometer (MS1104, Rostovna-Donu, Russia). A 57Co/Rh γ-ray source was used for the measurements. The spectrometer was calibrated with standard α-Fe or sodium nitroprusside absorbers. All isomer shift values (IS) are referred to α-Fe. The spectra evaluation was carried out using “UnivemMS” and custom least-squares fitting software. The measurements were performed on the n = 4−6 samples enriched to 10 at. % of 57 Fe. Magnetic susceptibility was measured in the 2−300 K temperature range at B = 0.1 T in field-cooled and zero-field-cooled regimes by means of Physical Property measurements System and Magnetic Property Measurement System “Quantum Design”. The dielectric permittivity of the ceramics was studied as a function of temperature at frequencies 1−20 kHz on cylindrical samples of 8 mm in diameter and 1.3 mm in height using capacitance bridge Andeen Hagerling 2700A with field strength on the sample ∼ 15 V.

Figure 1. Crystal structure of Bi10Ti7Fe6O38, the n = 3 member of the Bi3n+1Ti7Fe3n−3O9n+11 homologous series. Perovskite blocks with the thickness of three (Ti,Fe)O6 octahedra are marked with brackets.

which are occupied by double columns of Bi3+ cations. Formally, the Bi3n+1Ti7Fe3n−3O9n+11 structures can be considered as intergrowths of 2D perovskite blocks and 1D fragments of the anatase structure, which are stabilized owing to the stereochemical activity of the lone electron pairs of the Bi3+ cations. A combination of powder diffraction and transmission electron microscopy techniques indicates that the homologues demonstrate an exceptionally rich and complicated microstructure. Numerous defects are caused by off-center displacements of the 6s2 Bi3+ and d0 Ti4+ cations and by stacking faults. The stacking faults are associated with the variations in the arrangement of the interfaces relative to each other and the variations in the thickness of the perovskite block. Of all the homologues, only the n = 3 Bi10Ti7Fe6O38 member was studied in detail. Due to dilution of the magnetic Fe3+ cations with nonmagnetic Ti4+, this material does not demonstrate longrange magnetic order down to 1.5 K. It exhibits a relatively high dielectric constant, which gradually increases with temperature. In this contribution, we provide a detailed structure investigation of the n = 4−6 members of the Bi3n+1Ti7Fe3n−3O9n+11 homologous series using transmission electron microscopy (TEM) supported with X-ray powder diffraction and Mössbauer spectroscopy. Advanced TEM is the method of choice in this case, because numerous structure defects of various kinds prevent accurate structure analysis using the full power of powder diffraction techniques. Using TEM, we provide symmetry analysis and structure models for the n = 4− 6 members, unveil the evolution of the deformation pattern of the perovskite blocks with increasing n, retrieve quantitative information on the polar atomic displacements in n = 6, and provide a complete characterization of the defect structures. We

Stacking Sequences of the Interfaces. In the Bi3n+1Ti7Fe3n−3O9n+11 materials, the [010] zone axis is the most informative crystallographic direction for the TEM observations. It provides a clear view of the stacking sequence of the perovskite blocks and the interfaces allowing the observation of fine structure details related to planar defects and atomic displacements. Typical [010] ED patterns of the n = 3−6 materials are shown in Figure 2. Consistent with the layered arrangement of the structures, they are composed of parallel B


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the Bi3n+1Ti7Fe3n−3O9n+11 structures (see Figure 12 in ref 5 and the explanation therein) as cp*/(n + 1). All four ED patterns contain features related to the violation of the perfect long-range ordered atomic arrangement in the materials. Reflections in the h,0,l: h ≠ 3m reciprocal lattice rows are smeared along the cp* direction. The smearing in the n = 3 structure is very weak, but it is strongly pronounced in the n = 4−6 materials, forming corresponding lines of modulated diffraction intensities. The smearing is indicative of numerous stacking faults associated with lateral displacements of the adjacent interfaces with respect to each other over a vector R = [±1/3,u,0], as can be derived from a condition that g·R = integer for the reflections g = h,0,l: h = 3m that remain sharp. The repeat period of the interfaces is 3ap along the [100] direction, and their connectivity to the perovskite blocks implies that the successive interfaces can be positioned in two different ways with respect to each other. They can be stacked (1) precisely on top of each other and (2) with a shift of 1ap along either [100] or [1̅00] direction (Figure S1 of the Supporting Information). Crystals with a single configuration of interface stacking produce ED patterns with sharp and discrete Bragg reflections. Intermixing of three possible configurations (i.e., with the displacement vectors R = 0, [100]p or [1̅00]p) gives rise to the modulated intensity lines in the h,0,l: h ≠ 3m reciprocal lattice rows. In the n = 3 Bi10Ti7Fe6O38 material, the interfaces are stacked straight on top of each other, which results in an orthorhombic lattice with the Immm symmetry and the lattice vectors a = 3ap, b = bp, c = 2(n + 1)cp = 8cp, where ap, bp, and cp are the basic vectors of the perovskite sublattice. Interfaces with [100]p/ [1̅00]p shifts were observed only as occasional planar defects.5 In the n = 4 Bi13Ti7Fe9O47 material, stacking of the interfaces with systematic and cumulative shifts becomes dominant. This gives rise to a monoclinic lattice with the A2/m symmetry and lattice vectors a = 3ap, b = bp, c = 2(n + 1)cp − ap = 10cp − ap (Figure 3). However, domains with “straight” stacking of the interfaces were also found in some crystals. The corresponding ED pattern can be indexed on the orthorhombic Immm lattice with the basic vectors a = 3ap, b = bp, c = 2(n + 1)cp = 10cp (Figure 3). The n = 5 and n = 6 materials also contain crystals with a fairly well ordered monoclinic configuration of the interfaces (Figure S2 of the Supporting Information), while no orthorhombic crystals were observed. The dominant forms of the Bi3n+1Ti7Fe3n−3O9n+11 structures are schematically illustrated in Figure 4. Generalizing, the Bi3n+1Ti7Fe3n−3O9n+11 structures can demonstrate two basic stacking modes of the interfaces, corresponding either to the orthorhombic Immm polymorph with the a = 3ap, b = bp, c = 2(n + 1)cp lattice vectors or to the monoclinic A2/m polymorph with the a = 3ap, b = bp, c = 2(n + 1)cp − ap lattice vectors. Patterns of Atomic Displacements. Besides the main reflection rows, the [010] ED patterns of the n = 3−5 materials contain lines of modulated diffuse intensity at the positions h/2,0,l: h = odd (Figure 2). For the n = 3 material Bi10Ti7Fe6O38, our detailed structure investigation using a combination of neutron powder diffraction and TEM revealed that these intensities originate from short-range ordered Bi offcenter displacements inside the perovskite blocks induced by the stereochemical activity of the Bi3+ cations.5 Apparently, the same type of displacements gives rise to the diffuse intensities in the [010] ED patterns of the n = 4, 5 structures. These displacements affect the projected distances between the Bi cation columns, which can be directly visualized in the [010]

Figure 2. Typical [010] ED patterns of the Bi3n+1Ti7Fe3n−3O9n+11 (n = 3−6) materials. Short arrows mark the a*p and c*p reciprocal lattice vectors of the perovskite sublattice. The numbers at the bottom of each ED pattern indicate the h0l reflection rows with the corresponding h indexes. White-outlined triangles indicate positions of the diffuse intensity streaks between the rows of the main reflections.

rows of Bragg reflections oriented along cp*, i.e., perpendicular to the (001)p interfaces. Along the ap* direction, the distance between the reflection rows is a*p /3, as defined by the 3ap periodicity of the interfaces along [100]. Within the rows (along cp*), the spacing between the reflections is inversely proportional to the thickness of the perovskite blocks and can be calculated from the repeated sequence of atomic layers in C


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in the [010] HAADF-STEM images can be easily recognized by the rows of double Bi columns occupying the S-shaped tunnels running along the [010] direction. The off-center displacements of the Bi columns cannot be easily discerned in the experimental images, but they can be visually enhanced by applying a Gaussian blur filter to the images (Figure 5, bottom). This operation does not affect the Bi column positions (Figure S3 of the Supporting Information), but increases their visible size, so that the relative variations in the Bi−Bi projected distances become more apparent. Visible variations in the Bi− Bi intercolumn separations are also confirmed by the analysis of the HAADF intensity profiles (Figure S3 of the Supporting Information). The [010] HAADF-STEM images of the Bi3n+1Ti7Fe3n−3O9n+11 structures after the Gaussian blurring demonstrate pronounced displacements of the Bi atomic columns in the perovskite blocks of the n = 3, n = 4 (both monoclinic and orthorhombic modifications), and n = 5 structures. As indicated by the h/2,0,l: h = odd positions of the diffuse intensity lines in the ED patterns, the repeat period of these displacements along [100] is 6ap, twice larger than the periodicity of the interfaces (3ap). In the n = 3 material, the cation displacements form only short-range ordered patterns giving rise to continuous diffuse intensity lines (Figure 2). However, in both modifications of the n = 4 structure, the displacements become rather long-range ordered, which transforms the corresponding diffuse intensity lines into rows of significantly broadened diffraction spots at the h/2,0,l: h = odd positions (Figures 2 and 3). In the n = 5 material, the long-range correlation between the atomic displacements is lost again, resulting in strongly pronounced diffuse intensities (Figure 2). The [010] ED pattern of the n = 6 Bi19Ti7Fe15O65 material does not demonstrate any observable diffuse intensities in the h/2,0,l: h = odd positions (Figure 2). In the corresponding [010] HAADF-STEM image, the projected Bi atomic columns in the perovskite blocks form a regular square pattern without any visible perturbations (Figure 5). It is noteworthy that, in all [010] HAADF-STEM images, the Bi atomic columns form very sharp well-defined dots, indicating that the off-center Bi displacements obey the translational symmetry of the structure along the [010] direction. Also, the Bi columns at the interfaces separating the perovskite blocks do not show pronounced variations, confirming that the diffuse intensities originate from the cation displacements inside the perovskite blocks. The HAADF-STEM images clearly reveal displacements of the Bi atomic columns with respect to each other. However, they do not provide information on the positions of the cations relative to the oxygen sublattice. To analyze the cation displacements within their respective coordination polyhedra, we employed high-resolution ABF-STEM imaging. The [010] HAADF-STEM and ABF-STEM images of the monoclinic modification of the n = 4 Bi13Ti7Fe9O47 material are shown in Figure 6. In the magnified fragment of the ABF-STEM image, the anionic sublattice of the perovskite blocks is highlighted with projections of the corresponding (Ti,Fe)O6 octahedra outlined using the visible positions of the O columns. To facilitate interpretation of the data, a schematic diagram at the bottom of Figure 6 shows the structure projection traced directly from the ABF-STEM image. The data reveal that the Bi columns exhibit systematic off-center displacements within their coordination polyhedra. In the outer BiO layer of the perovskite blocks, 2 out of 3 Bi atoms are shifted along [001]p toward the oxygen atoms connecting corner-sharing (Ti,Fe)O6

Figure 3. [010] ED patterns and corresponding high-resolution HAADF-STEM images for the monoclinic and orthorhombic modifications of the n = 4 Bi13Ti7Fe9O47 material. White lines on the HAADF-STEM images highlight the arrangement of the interfaces by tracing Bi atomic columns inside the perovskite blocks and the interfaces.

Figure 4. Schematic illustration of the dominant structures of the n = 3−6 Bi3n+1Ti7Fe3n−3O9n+11 homologues.

high-resolution HAADF-STEM images (Figure 5, top row). The brightest dots in these images correspond to the Bi atomic columns and the faint dots to the (Ti,Fe)O columns. The perovskite blocks appear as areas with a square arrangement of bright dots with faint dots centering the squares. The interfaces D


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Figure 5. High-resolution [010] HAADF-STEM images of the Bi3n+1Ti7Fe3n−3O9n+11 structures highlighting displacements of Bi atomic columns inside the perovskite blocks. The top row demonstrates the unfiltered experimental images. The same images after Gaussian blur filtering are shown in the bottom row. The length of the scale markers is 2 nm.

periphery, the Bi displacements also gain an orthogonal component along the [001]p direction, toward the interfaces. The [100]p and [001]p displacement components are ordered in polar and antipolar fashion, respectively. Thus, the perovskite blocks in the n = 6 material acquire dipole moments oriented along either [100] or [1̅00]. The projected directions of the electric polarization in the perovskite blocks are schematically indicated in the image with arrows. The polarization is also supported by the shifts of (Ti,Fe) cations away from the centers of their oxygen octahedra in the same direction as the displacements of the neighboring Bi atoms. This results in a configuration of the perovskite blocks reminiscent of the PbTiO3 structure. The polar atomic displacements in the neighboring perovskite blocks can be either parallel or antiparallel, with a certain tendency to an antipolar arrangement (Figure 7 and Figure S7 of the Supporting Information). Also, it is seemingly unaffected by the position of the interfaces with respect to each other. Distribution of Ti and Fe. We used atomic resolution electron energy loss spectroscopy (STEM-EELS) to analyze how the increasing thickness of the perovskite blocks affects the Fe3+ and Ti4+ distribution in the structure. The Fe and Ti STEM-EELS elemental maps for the n = 6 Bi19Ti7Fe15O65 material are demonstrated and compared to those of the n = 3 Bi10Ti7Fe6O38 structure in Figure 8. In the n = 3 structure, which has three (Ti,Fe)O2 layers in the perovskite blocks, Ti4+ is concentrated in the central layer. Although the outer layers are more populated with the Fe3+ cations, they still demonstrate considerable presence of Ti4+ in the octahedra that are connected to the anatase-like chains of the interfaces by sharing edges (note the “base” of the triangular octahedral units in Figure 8, also compare with schematic structure diagrams in Figure 4). The n = 6 material demonstrates a somewhat similar distribution of Ti4+/Fe3+ in the perovskite blocks: Ti4+ is primarily concentrated in the center, while the outer (Ti,Fe)O2

octahedra. The remaining Bi columns are shifted primarily along the [100] and [1̅00] directions and do not demonstrate pronounced components along the [001]p direction. These Bi positions are located in the immediate vicinity of the triangular units of the edge-sharing (Ti,Fe)O6 octahedra, where the anatase-like chains are connected to the perovskite blocks. In the BiO layer at the center of the perovskite block, the direction of the Bi-off center displacements varies from one atomic column to another. However, they are not completely random; it can be recognized that they exhibit a periodicity of 6ap along the [100] direction (note the Bi columns marked with asterisks). The Bi displacements also affect the coordination of the O and (Ti,Fe) atomic species. In Figure 6, one can notice that the displacements of the O columns correlate with the Bi off-center displacements and cause deformations of the (Ti,Fe)O6 octahedra. Within the octahedra, the (Ti,Fe) columns shift away from the O atoms, which form short Bi− O distances. The same type of the perovskite block distortions can be found in the orthorhombic modifications of the n = 4 Bi 13 Ti 7 Fe 9 O 47 material (Figure S4 of the Supporting Information), in the n = 3 Bi10Ti7Fe6O38 structure (Figure S5 of the Supporting Information and the results of structure refinement in ref 5), and in the n = 5 Bi16Ti7Fe12O56 material (Figure S6 of the Supporting Information). Complementary [010] HAADF-STEM and ABF-STEM images of the n = 6 Bi19Ti7Fe15O65 structure are shown in Figure 7. Masking of the (Ti,Fe)O6 octahedra in the perovskite blocks reveals that the stereochemical activity of the Bi3+ cations is also well pronounced in this material. However, unlike the n = 3−5 structures, the Bi off-center displacements in the n = 6 structure become more uniform. A magnified fragment of the ABF-STEM image in Figure 7 demonstrates that, at the center of the perovskite blocks, the displacements of the Bi columns are confined to the (001)p planes having a significant component along the [100]p direction. On the E


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Figure 6. [010] complementary HAADF-STEM and ABF-STEM images of monoclinic n = 4 Bi13Ti7Fe9O47. The HAADF-STEM image is shown as acquired, and the ABF-STEM image is shown after low pass filtering to remove scanning noise. In the magnified fragment of the ABF-STEM image, projected (Ti,Fe)O6 octahedra are outlined based on the visible positions of the O columns. The central (Ti,Fe) atomic columns are encircled. Bi columns reside in the cuboctahedral sites between the octahedra. The schematic structure projection at the bottom is produced by tracing the atomic positions directly from the ABF-STEM image. Arrows mark strongly pronounced [001]p displacements of the Bi atoms in the outer BiO layers of the perovskite block. Asterisks mark Bi columns forming very distinct up and down configurations, as part of the intricate Bi displacement pattern with a period of 6ap visible in the HAADF-STEM images (Figure 5). Figure 7. [010] HAADF-STEM and ABF-STEM images of the n = 6 Bi19Ti7Fe15O65 material. The projected (Ti,Fe)O6 octahedra are masked in the ABF-STEM image with squares. In the magnified fragment of the ABF-STEM image, the octahedra are outlined, highlighting polar displacements of both Bi and (Ti,Fe)O atomic columns. The arrows indicate the direction of polar cation displacement in the perovskite blocks. The HAADF-STEM image is shown as acquired and the ABF-STEM image − after low-pass filtering.

layers are depleted for Ti4+. However, compared to the n = 3 structure, the material shows a noticeably weaker presence of Ti4+ cations in the base octahedra of the triangular octahedral units. In both structures, the octahedra at the vertices of the triangular units are connected to the Ti-rich octahedra, which are situated right at the central plane of the interfaces. The data in Figure 8 clearly demonstrate that the segregation of Ti in these positions is more pronounced in the n = 6 structure. This highlights that the increasing thickness of the perovskite blocks enforces the cation ordering at the interfaces, so that the Ti-rich columns at the center of the interfaces become more prominent. Such cation ordering further confirms our earlier finding that the formation of the interfaces requires B cations with higher formal charge to compensate for the A-cation deficiency at the interfaces.5

Structure Defects. The Bi3n+1Ti7Fe3n−3O9n+11 materials demonstrate a variety of structure defects. One type of defects has been already mentioned, i.e., stacking faults associated with the lateral shifts of the interfaces relative to each other (Figure 9). Besides, all investigated materials contain occasional inclusions of perovskite blocks with thicknesses corresponding to structures with smaller and larger n (Figure 9). As n increases, these defects become more prominent. Their presence can even be recognized in the ED pattern of the n F


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Figure 10. HAADF-STEM images of a crystal in the n = 6 sample showing coherent intergrowth of the domains with the [100] and [010] orientations. The perovskite block, where the intergrowth occurs, is marked with a star.

Figure 8. STEM-EELS maps showing the distribution of Fe and Ti in the n = 3 Bi10Ti7Fe6O38, and n = 6 Bi19Ti7Fe15O65 structures. Triangles highlight typical structure fragments, where the anatase-like chains of the interfaces are connected to the perovskite blocks by sharing edges and give rise to characteristic Fe-rich triangular units of edge-sharing (Ti,Fe)O6 octahedra.

zig-zag configuration of Bi atoms. In the [010] HAADF-STEM images, they appear as pairs of closely projected bright dots, while in the [100] HAADF-STEM images, they are seen as a zig-zag pattern between the perovskite blocks. The existence of such twins in the higher members of the Bi3n+1Ti7Fe3n−3O9n+11 series reflects that the ap and bp parameters of the perovskite sublattice become closer with the increasing thickness of the perovskite blocks, which is also confirmed by XPD analysis (see below). HAADF-STEM images in Figure 11 illustrate that the thickness of the perovskite blocks can change abruptly within the crystal, giving rise to sideway steps of the interfaces. The steps in Figure 11a (type 1) are associated with fragments of four (Ti,Fe)O atomic columns. Apparently, these defects are very similar to those observed by McLaren et al. in Nd- and Ticodoped BiFeO3, which are based on Fe-rich edge-sharing quadruple (Ti,Fe)O6 octahedral chains.7 Figure 11b demonstrates that there are at least two other types of interface steps that can be realized in the Bi3n+1Ti7Fe3n−3O9n+11 structures. Steps of type 2 also contain quadruple (Ti,Fe)O6 octahedral chains, which, in this case, are accompanied by groups of four Bi columns with a zig-zag arrangement. Steps of type 3 eliminate a single anatase-like chain, so that the interface shifts are associated with groups of four Bi columns. In these fragments, two pairs of Bi columns with a configuration of “straight” interfaces are shifted relative to each other over 1cp. It is remarkable that, in most cases, the interface steps occur cooperatively (Figure 11), which indicates that there is a weak interaction between these defects, e.g., through the strain field in the crystal lattice induced by their presence. An HAADF-STEM image in Figure 12a demonstrates that the fragments with a zig-zag arrangement of the Bi columns similar to those found in the steps of type 2 (Figure 11) are occasionally present as inclusions in the regular “straight” interfaces. Although they are reminiscent of the zig-zag arrangement of Bi columns at the regular interfaces viewed along the [100] direction, a careful examination (Figure S8 of

Figure 9. [010] HAADF-STEM images of the n = 4 (a) and n = 6 (b) materials demonstrating areas with numerous stacking faults in the interface arrangement, which also contain perovskite blocks of different thickness (the numbers mark the corresponding n values).

= 6 material in Figure 2: variations in the thickness of the perovskite block give rise to weak diffuse intensity streaks along the c* direction in the h,0,l: h = 3m reflection rows, as opposed to the reflection smearing in the h,0,l: h ≠ 3m rows due to faults in the stacking of the interfaces. The increasing thickness of the perovskite blocks promotes coherent intergrowths of structure domains with the [100] and [010] orientations (Figure 10), which can be considered as 90° rotation twins. Double Bi columns inside the S-shaped tunnels at the interfaces create a G


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Figure 12. [010] HAAD-STEM images demonstrating (a) interface defects with a zig-zag arrangement of the Bi columns and (b, c) dislocation-like defects introducing thickness variation of the perovskite blocks.

perovskite blocks but introduce perovskite lamellas of smaller thickness, demonstrating a dislocation-like behavior. X-ray Powder Diffraction. Owing to the numerous defects present in the Bi3n+1Ti7Fe3n−3O9n+11 materials, the quality of the XPD data rapidly deteriorates with n, which prevents accurate structure refinement. Nevertheless, profile fitting using structure models derived from the TEM data provides valuable information on the lattice parameters and verifies the proposed atomic arrangement. In the first step, we attempted the Rietveld refinement using the structure models, where, for each n = 4−7 material, we tested both orthorhombic and monoclinic models. Because of a large number of refineable parameters and rather poor quality of the diffraction data, we refined atomic parameters of the cation positions only. Parameters of the relevant starting models for the n = 4−6 materials (Figure 4) and the models after the refinement are listed in Tables S2−S4 of the Supporting Information. Corresponding theoretical XPD patterns are compared to the experimental profiles in Figure S10 of the Supporting Information. In the final step, we fitted the profiles using the LeBail method. The cell parameters of the n = 3−7 materials determined in this way are listed in Table S5 of the Supporting Information. The table also contains the cell parameters of the perovskite sublattice estimated from simple geometrical relations, ap = a/3, bp = b, and cp ≈ c sin(β)/(2n + 2). The n = 4−7 XPD profiles after the LeBail fit are shown in Figure S11 in the Supporting Information.

Figure 11. [010] HAADF-STEM images demonstrating three different types of sideway steps at the interfaces in the Bi3n+1Ti7Fe3n−3O9n+11 materials, which introduce cooperative variations in the thickness of the perovskite blocks (marked with the corresponding n numbers).

the Supporting Information) reveals two significant differences: (1) the Bi column intensities in the defects are stronger, indicating that these columns have the same composition as the Bi columns in the perovskite blocks, and (2) the projected distances between Bi layers are noticeably shorter in the defects than in the double Bi columns of the regular interfaces. It can be recognized that the configuration of these “zig-zag” defects is similar to the α-PbO arrangement typically found in the (A2O2) fragments of the Aurivillius-type structures.8 This is also validated by corresponding HAADF-STEM image simulations (Figure S9 of the Supporting Information). The HAADFSTEM images in Figure 12b,c indicate that the “zig-zag” defects can be associated with the thickness variations of the perovskite blocks. Unlike the steps in Figure 11, such structure fragments do not simply exchange the thicknesses of the adjacent H


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Inorganic Chemistry The XPD data confirm that the monoclinic structures are dominant in the n = 4 and n = 5 materials. The profile fitting using the corresponding models provides a notably better fit of the patterns (Figure S11 of the Supporting Information). The fitting of the XPD profiles of the n = 6 and 7 samples using monoclinic and orthorhombic structures gave rather similar results. Slightly better fit for the monoclinic model could be attributed solely to the larger number of variable parameters. The evolution of the perovskite basic cell parameters for the Bi3n+1Ti7Fe3n−3O9n+11 structures with the increasing thickness of the perovskite blocks is illustrated in Figure 13. In the n = 3−5

Figure 14. Mö ssbauer spectra of n = 4−6 Bi3n+1Ti7Fe3n−3O9n+11 materials in the paramagnetic state.

Figure 13. Cell parameters of the perovskite sublattice in the Bi3n+1Ti7Fe3n−3O9n+11 materials determined from the XPD data. Note a distinct bend between n = 5 and n = 6 visible in all curves.

of the magnetic structure, which is hindered by high complexity of the structure and numerous structure defects. Magnetic and Dielectric Properties. Temperature dependencies of the magnetic susceptibility χ(T) for the n = 4−6 Bi3n+1Ti7Fe3n−3O9n+11 samples are shown in Figure 15. All compounds demonstrate kinks in the χ(T) curves that can be attributed to the formation of a magnetically ordered state. The χ(T) curve measured in a zero-field-cooled (ZFC) regime for n

structures, the parameters change linearly with n, so that cp gradually decreases, bp slightly increases, and the ap parameter stays nearly the same. Although, for the n = 6 and n = 7 materials, the trends continue, the cell parameters demonstrate steeper variation between n = 5 and n = 6. Apparently, these results correlate with the TEM data, which reveal pronounced changes in the direction of the Bi off-center displacements in the perovskite blocks of the structures. 57 Fe Mössbauer Spectroscopy. The n = 4−6 Bi3n+1Ti7Fe3n−3O9n+11 compounds were analyzed using the 57Fe Mössbauer spectroscopy. Paramagnetic spectra of the n = 4− 6 materials are demonstrated in Figure 14. As confirmed by the magnetic measurements, the TN gradually increases with n, so the spectra for n = 4, 5 were acquired at room temperature of 298 K, and for n = 6 − at 348 K. The fitting parameters are listed in Table S6 of the Supporting Information. For all structures, the isomer shift of the doublets is about 0.38 mm/s, which is consistent with the Fe3+ species in octahedral oxygen coordination.9 The n = 4, 5 spectra are fitted with two overlapping paramagnetic doublets, which can be qualitatively attributed to Fe atoms in the (Ti,Fe)O6 octahedra sharing only corners and the octahedra sharing at least one of the edges with other octahedra. For the n = 6 compound, the spectrum is fitted with a single broadened doublet. In this structure, two types of the Fe octahedral positions are unresolved, which contributes to the line broadening. At low temperature, the n = 4−6 materials undergo transition into a magnetically ordered state. The corresponding Mössbauer spectra collected at 78 K demonstrate multiple magnetically split components (Figure S12 and Table S7 of the Supporting Information). They indicate high complexity of the superexchange interactions in these materials. Mixing of magnetic Fe3+ cations and nonmagnetic Ti4+ cations in the same (Ti,Fe) positions can give rise to sophisticated patterns of spin ordering. The detailed analysis of the Mössbauer spectra requires a complete solution

Figure 15. Temperature dependencies of magnetic susceptibility of Bi13Ti7Fe9O47, Bi16Ti7Fe12O56, and Bi19Ti7Fe15O65 measured in fieldcooled (FC, open circles) and zero-field-cooled (ZFC, filled circles) regimes. Large and small arrows indicate temperatures of magnetic ordering of main and impurity phases. I


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Inorganic Chemistry

are suppressed (Figure S13 of the Supporting Information), which can be due to a diffuse phase transition at higher temperatures with strong frequency dispersion, i.e., some kind of (anti)ferroelectric order.

= 4 Bi13Ti7Fe9O47 demonstrates a robust transition to an antiferromagnetically (AFM) ordered state below the Néel temperature TN = 135 K. Another, less pronounced, AFM transition is observed at TN = 220 K. The nature of this transition can be understood comparing the χ(T) curves for the Bi13Ti7Fe9O47 and Bi16Ti7Fe12O56 samples. The AFM transition at TN = 220 K dominates in the Bi16Ti7Fe12O56 sample, demonstrating remarkable similarity of the ZFC and FC curves between the two samples. The Bi16Ti7Fe12O56 curve also shows a secondary AFM transition at even higher temperature TN = 295 K. Taking into account the presence of the intergrowth defects of perovskite blocks with different thicknesses, we attribute the transitions at different TN to Bi3n+1Ti7Fe3n−3O9n+11 domains with different n coexisting in the samples. In the Bi13Ti7Fe9O47 sample, the n = 4 homologue dominates and the n = 5 blocks are locally present; thus, the transitions at 135 and 220 K can be assigned to the n = 4 and n = 5 materials, respectively. In the Bi16Ti7Fe12O56 sample, the n = 5 homologue becomes the main phase and the n = 6 blocks appear as defects causing the minor AFM transition at 295 K. Indeed, the transition at TN = 295 K is the only magnetic transition observed in the n = 6 Bi19Ti7Fe15O65 sample. The Néel temperature of the homologues increases concomitantly with n, which is consistent with the increasing content of the magnetic Fe3+ cations in the structures. For all the n = 4−6 homologues, a divergence of the FC and ZFC curves that sets in at TN is indicative of a disorder in the magnetic subsystem due to random distribution of magnetic Fe3+ and nonmagnetic Ti4+ ions in the octahedral positions. Results of dielectric permittivity ε(T) measurements for the n = 3−6 Bi3n+1Ti7Fe3n−3O9n+11 samples are shown in Figure 16

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DISCUSSION The TEM data unequivocally demonstrate that the Bi3+ cations inside the perovskite blocks exhibit pronounced stereochemical activity. Cooperative Bi displacements away from the center of their respective BiO12 cuboctahedra are clearly visible in the ABF-STEM images (Figures 6, 7, and Figures S4−S6 of the Supporting Information). These displacements follow the translational symmetry of the structure along [010] and create distinct cation displacement patterns within the ac plane, which are visible in the HAADF-STEM images (Figure 5). In these patterns, the Bi columns demonstrate local correlations: there are no two neighboring perovskite cells where the Bi3+ cations are displaced toward the same group of O atoms. The same type of correlations were observed in the anion deficient perovskites (Pb1−zSrz)1−xFe1+xO3−y modulated with periodic crystallographic shear planes.11 They can be understood considering that the stereochemical activity of the lone pair Bi3+ cations originates from the specific Bi−O bonding. It involves covalent mixing of the cation 6s2 orbitals with the oxygen 2p orbitals, giving rise to the corresponding bonding and antibonding states.12 In the asymmetric coordination, unoccupied cation 6p orbitals can interact with these antibonding states, minimizing the energy of the system. This orbital stabilization creates an asymmetric electron density around the lone pair cation, which has a characteristic lobeshaped distribution directed into the structural void. Strongly covalent Bi−O interactions force two Bi atoms to avoid formation of short Bi−O bonds with the same O atoms. This creates a competition for the same O 2p orbitals between the Bi cations in the adjacent perovskite unit cells, which stabilizes the observed patterns of atomic displacements. The atomic displacement patterns in the n = 4−6 Bi3n+1Ti7Fe3n−3O9n+11 structures systematically change with n. As the thickness of the perovskite blocks increases to n = 6, the configuration of the perovskite blocks becomes similar to the PbTiO3 structure, with the polar axis confined to the [100] direction. To analyze the polar distortion of the perovskite blocks, we estimated the amplitude of Bi off-center displacements along the ap axis directly from the ABF-STEM image shown in Figure 7. We measured the ABF intensity profiles along the BiO layers and fitted them using the Fityk program13 with two sets of Gaussian peaks, corresponding to the Bi and O atomic columns, respectively (Figure S14 of the Supporting Information). We calculated the amplitude of Bi off-center displacements as a shift from the geometrical center between two adjacent O columns. The analysis reveals that the amplitudes of Bi displacements in different BiO layers of the same perovskite blocks are very similar, e.g., 56(6), 60(3), 55(3), 59(3), and 53(5) pm for the layers 1−5 in perovskite block 1, respectively (Figure 7, Figure S14 of the Supporting Information). The averaged Bi displacements in different perovskite blocks with parallel orientation of polarization are also very similar. Thus, the values for the perovskite blocks 1, 3, 4, and 6 (Figure 7) are 57(3), 52(3), 56(3), and 53(3) pm, respectively, whereas the values in blocks 2 and 5, with the polarization in the opposite direction, are 39(2) and 35(2) pm, respectively. The difference in the values for the perovskite blocks with antiparallel polarizations is likely attributed to slight

Figure 16. Temperature dependencies of dielectric permittivity of Bi10Ti7Fe6O38, Bi13Ti7Fe9O47, Bi16Ti7Fe12O56, and Bi19Ti7Fe15O65 samples measured at frequency of 5 kHz.

and Figure S13 of the Supporting Information. Owing to very low electric conductivity, the samples demonstrate almost no signal in the imaginary part, so that the real part ε′ matches the total permittivity (ε). All compounds demonstrate rather large ε, which grows almost linearly with increasing temperature. Similar to other systems with lone pair cations and empty dshell cations, such as Bi2Ti4O12, high dielectric constants can be attributed to the off-center cations displacements and the deformation of the (Ti,Fe)O6 octahedra.10 The n = 4 and 5 compounds demonstrate more rapid increase of ε(T), while the n = 6 homologue slightly deviates from this tendency. This can be explained by more uniform Bi off-center displacements in Bi19Ti7Fe15O65. For higher frequencies, all ε(T) dependencies J


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Inorganic Chemistry

growth of the perovskite slabs with different thicknesses, because of the decreasing difference in free energy and chemical composition between the high-n homologues. However, there is an important difference between the Bi3n+1Ti7Fe3n−3O9n+11 series and other perovskite-based homologues, which is related to the periodicity of atomic arrangement within the interfaces. Neglecting possible superstructures (e.g., due to cooperative octahedral tilting distortion), the interfaces have the same periodicity ap as the perovskite blocks in all perovskite homologous series, but not in Bi3n+1Ti7Fe3n−3O9n+11. The 3ap periodicity of the interfaces along [100] in Bi3n+1Ti7Fe3n−3O9n+11 gives rise to more complex stacking faults arising from lateral shifts of the interfaces over +ap or −ap without substantial configurational changes, i.e., at low energy cost. Complete ordering of the interface stacking with respect to each other gives rise to the orthorhombic and monoclinic Bi3n+1Ti7Fe3n−3O9n+11 polymorphs with the interfaces stacked on top of each other and with systematic cumulative shifts, respectively. The orthorhombic configuration is only stable in the n = 3 material, while the monoclinic polymorphs are dominant in higher members of the series. The HAADF-STEM data for the n = 4 material, where both polymorphs coexist, indicate that the deformation patterns of the perovskite blocks are slightly different in the monoclinic and orthorhombic modifications. Therefore, one can consider that these subtle differences might be responsible for the stabilization of a particular polymorph. The n = 4−6 compounds demonstrate antiferromagnetic ordering, as detected with Mö ssbauer spectroscopy and magnetic susceptibility measurements. The Néel temperature rises concomitantly with n, because of the increasing concentration of magnetic Fe3+ cations. The Bi3n+1Ti7Fe3n−3O9n+11 materials combine antipolar electric ordering and antiferromagnetism. They provide an interesting playground for further optimization of their magnetic and dielectric properties and investigation of possible coupling between the magnetic and electric subsystems.

misorientation of the crystal with respect to the electron beam. The average Bi off-center displacements can be estimated at about 45 pm. This value is very similar to the Pb off-center displacements in PbTiO3 of 48.8(2) pm.14 The similarity between perovskite blocks of the n = 6 material and the tetragonal PbTiO3 structure is also corroborated by the analysis of the distortion of the perovskite sublattice. PbTiO 3 demonstrates pronounced tetragonal distortion with a = 3.902(3) Å and c = 4.156(3) Å.14 Parameters of the perovskite sublattice in the n = 6 Bi19Ti7Fe15O65 structure calculated from the XPD data are ap = 3.9594(2) Å, bp = 3.8950(2) Å, and cp = 4.051(1) Å (Figure 13 and Table S5 of the Supporting Information). However, the cp parameter determined in this way does not reflect the actual distortion of the perovskite blocks because of an unknown contribution of the interfaces between the perovskite blocks to this value. We obtained a more adequate estimate of the perovskite block distortion by measuring the spacing between the (Ti,Fe)O2 atomic layers directly from the TEM data. The resulting value is cp′ = 3.90(2) Å, which confirms that the perovskite blocks in the n = 6 structure demonstrate significant elongation of the perovskite subcell along ap, i.e., the direction of the electric polarization. The Bi3n+1Ti7Fe3n−3O9n+11 structures can be represented as coherent intergrowths of 2D perovskite blocks with 1D anataselike chains of edge-sharing (Ti,Fe)O 6 octahedra. The alternating corner- and edge-sharing connectivity of the chains to the perovskite blocks results in the 3ap periodicity of the structure along [100]p and significantly alters the metal−oxygen bonding in the outer (Ti,Fe)O2 layers of the perovskite blocks. In these layers, 3 out of 6 O atoms connect the octahedra along the ap direction; 2 of those O atoms are bonded to two B cations as in the conventional perovskite structure, but the remaining 1 O atom is bonded to three B cations, i.e., in the triangular units of edge-sharing of the (Ti,Fe)O6 octahedra. This difference directly affects the displacements of the Bi3+ cations in the perovskite blocks. They tend to move closer to the two-site bonded O atoms as their orbitals are more accessible for covalent bonding and move away from the threesite bonded O atoms (Figure 6). As a result, Bi3+ cation displacements in the outer BiO layers of the perovskite blocks follow the periodicity of the interfaces. This creates an intricate pattern of atomic displacements in the whole perovskite blocks owing to competing Bi−O interactions. The influence of the interfaces on the atomic arrangement of the perovskite blocks is the strongest for the n = 3 homologue and gradually diminishes with increasing n. In the n = 6 structure, only the outer layers are affected and the cooperative polar displacements become dominant. The ABF-STEM data (Figures 6, 7 and Figures S4− S6 of the Supporting Information) indicate that the three-site bonded O atoms in the outer (Ti,Fe)O2 layers become more favorable for the formation of short Bi−O bonds with the increasing thickness of the perovskite blocks. This correlates with the changing composition in the corresponding (Ti,Fe) positions. The STEM-EELS data (Figure 8) demonstrate that the concentration of Ti4+ in these positions steadily reduces with n. Apparently, the observed behavior is another illustration that the stereochemical activity of lone pair cations is sensitive to the O bonding with other cations.15 The Bi3n+1Ti7Fe3n−3O9n+11 homologues demonstrate certain similarity in the defect structure with other perovskite-based homologous series, such as Ruddlesden−Popper An+1BnO3n+1, Dion−Jacobson AnBnO3n+1, and Aurivillius Bi2An−1BnO3n+3.1 The increasing homologue number promotes abundant inter-

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b02559. Results of the EDX analysis for the n = 3−7 Bi3n+1Ti7Fe3n−3O9n+11 materials; schematic illustration of possible interface stacking modes on the example of the Bi13Ti7Fe9O47 material; ED patterns of crystals with fairly well ordered monoclinic structure in the n = 5 and 6 materials; analysis of the Bi column intensities and Bi−Bi intercolumn separations in the experimental HAADFSTEM image (n = 4, monoclinic) and the same image after the Gaussian blur filtering; complementary [010] HAADF-STEM and ABF-STEM images for orthorhombic n = 4, n = 3, 5, and 6 structures; analysis of the Bi columns intensities and projected Bi−Bi separations in “zig-zag” defects together with simulation-based validation of the proposed Aurivillius-type atomic arrangement; parameters of monoclinic structure models of the n = 4−6 materials; theoretical XPD patterns of the n = 4−6 materials after the refinement of cation positions; results of the LeBail fitting of the XPD patterns of the n = 4−7 Bi3n+1Ti7Fe3n−3O9n+11 compounds using orthoK


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electron-pair cations on the orientation of crystallographic shear planes in anion-deficient perovskites. Inorg. Chem. 2013, 52, 10009−10020. (12) Walsh, A.; Payne, D. J.; Egdell, R. G.; Watson, G. W. Stereochemistry of post-transition metal oxides: revision of the classical lone pair model. Chem. Soc. Rev. 2011, 40, 4455−4463. (13) Wojdyr, M. Fityk: a general-purpose peak fitting program. J. Appl. Crystallogr. 2010, 43, 1126−1128. (14) Nelmes, R. J.; Kuhs, W. F. The crystal structure of tetragonal PbTiO3 at room temperature and at 700 K. Solid State Commun. 1985, 54, 721−723. (15) Stoltzfus, M. W.; Woodward, P. M.; Seshadri, R.; Klepeis, J.; Bursten, B. Structure and bonding in SnWO4, PbWO4, and BiVO4: lone pairs vs inert pairs. Inorg. Chem. 2007, 46, 3839−3850.

rhombic and monoclinic structures; cell parameters of relevant structure models for the n = 3−7 determined from the LeBail fitting; Mössbauer spectra of the n = 4−6 Bi3n+1Ti7Fe3n−3O9n+11 samples collected at 78 K; fitting parameters of the n = 4−6 Mössbauer spectra collected in paramagnetic (298 K, 348 K) and magnetically ordered (78 K) states; temperature dependencies of dielectric permittivity of the n = 5 and 6 samples collected at frequencies of 1, 5, and 20 kHz; fitting of ABF-STEM intensity profiles for the BiO layers in the perovskite blocks of the n = 6 structure (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Dmitry Batuk: 0000-0002-6384-6690 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the Russian Science Foundation (grant 14-13-00680).

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REFERENCES

(1) Mitchell, R. H. Perovskites: Modern and Ancient; Almaz Press Inc.: Ontario, Canada, 2002. (2) Abakumov, A. M.; Tsirlin, A. A.; Antipov, E. V. In Comprehensive Inorganic Chemistry II; Reedijk, J., Poeppelmeier, K., Eds.; Elsevier Ltd.: Amsterdam, 2013; Chapter 2, pp 1−40. (3) Wang, L. Q.; Schaffer, B.; MacLaren, I.; Miao, S.; Craven, A. J.; Reaney, I. M. Atomic scale structure and chemistry of anti-phase boundaries in (Bi0.85Nd0.15)(Fe0.9Ti0.1)O3 ceramics. J. Phys.: Conf. Ser. 2012, 371, 012036. (4) MacLaren, I.; Wang, L.; Morris, O.; Craven, A. J.; Stamps, R. L.; Schaffer, B.; Ramasse, Q. M.; Miao, S.; Kalantari, K.; Sterianou, I.; Reaney, I. M. Local stabilisation of polar order at charged antiphase boundaries in antiferroelectric (Bi0.85Nd0.15)(Ti0.1Fe0.9)O3. APL Mater. 2013, 1, 021102. (5) Batuk, D.; Tsirlin, A. A.; Filimonov, D. S.; Zakharov, K. V.; Volkova, O. S.; Vasiliev, A.; Hadermann, J.; Abakumov, A. M. Bi3n+1Ti7Fe3n‑3O9n+11 Homologous Series: Slicing Perovskite Structure with Planar Interfaces Containing Anatase-like Chains. Inorg. Chem. 2016, 55, 1245−1257. (6) Petříček, V.; Dušek, M.; Palatinus, L. Crystallographic Computing System JANA2006: General features. Z. Kristallogr. - Cryst. Mater. 2014, 229, 345−352. (7) MacLaren, I.; Wang, L.; Craven, A. J.; Ramasse, Q. M.; Schaffer, B.; Kalantari, K.; Reaney, I. M. The atomic structure and chemistry of Fe-rich steps on antiphase boundaries in Ti-doped Bi0.9Nd0.15FeO3. APL Mater. 2014, 2, 066106. (8) Frit, B.; Mercurio, J. P. The crystal chemistry and dielectric properties of the Aurivillius family of complex bismuth oxides with perovskite-like layered structures. J. Alloys Compd. 1992, 188, 27−35. (9) Menil, F. Systematic trends of the 57Fe Mössbauer isomer shifts in (FeOn) and (FeFn) polyhedra. Evidence of a new correlation between the isomer shift and the inductive effect of the competing bond T−X (→ Fe) (where X is O or F and T any element with a formal positive charge). J. Phys. Chem. Solids 1985, 46, 763−789. (10) Liu, J.; Duan, C.-G.; Yin, W.-G.; Mei, W. N.; Smith, R. W.; Hardy, J. R. Dielectric permittivity and electric modulus in Bi2Ti4O11. J. Chem. Phys. 2003, 119, 2812−2819. (11) Batuk, D.; Batuk, M.; Abakumov, A. M.; Tsirlin, A. A.; McCammon, C.; Dubrovinsky, L.; Hadermann, J. Effect of loneL


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