The crystal and defect structures of polar KBiNb₂O₇

Abstract

KBiNb₂O₇ was prepared from RbBiNb₂O₇ by a sequence of cation exchange reactions which first convert RbBiNb₂O₇ to LiBiNb₂O₇, before KBiNb₂O₇ is formed by a further K-for-Li cation exchange. A combination of neutron, synchrotron X-ray and electron diffraction data reveal that KBiNb₂O₇ adopts a polar, layered, perovskite structure (space group A11m) in which the BiNb₂O₇ layers are stacked in a (0, ½, z) arrangement, with the K⁺ cations located in half of the available 10-coordinate interlayer cation sites. The inversion symmetry of the phase is broken by a large displacement of the Bi³⁺ cations parallel to the y-axis. HAADF-STEM images reveal that KBiNb₂O₇ exhibits frequent stacking faults which convert the (0, ½, z) layer stacking to (½, 0, z) stacking and vice versa, essentially switching the x- and y-axes of the material. By fitting the complex diffraction peak shape of the SXRD data collected from KBiNb₂O₇ it is estimated that each layer has approximately a 9% chance of being defective – a high level which is attributed to the lack of cooperative NbO₆ tilting in the material, which limits the lattice strain associated with each fault.

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Introduction

Solid state compounds which exhibit non-centrosymmetric (NCS) crystal structures have been widely studied because they can exhibit physical properties such as ferroelectricity, piezoelectricity and second harmonic generation (SHG) which are forbidden by symmetry to centrosymmetric phases.^1,2 However, the preparation of acentric solid phases is challenging, principally because NCS crystal structures tend to be thermodynamically unstable with respect to centric alternatives, as these latter high symmetry structures exhibit more efficient packing.

The conventional method used to stabilize acentric structures is to make use of an electronic instability of a chemical subunit to break the inversion symmetry of the underlying centrosymmetric framework of a material. For example, instabilities such as the second-order Jahn–Teller (SOJT) distortion of octahedrally coordinated d⁰ transition metal cations (e.g. Ti⁴⁺ in BaTiO₃),^3–6 or the ‘off-centring’ distortions of ns² post-transition elements, often interpreted as stereoactive lone pairs (e.g. Bi³⁺ in BiFeO₃),^7–12 have been widely used to stabilize NCS crystal structures in complex oxide materials. However, the requirement to include these ‘polar chemical species’ limits the chemical constitution of NCS materials and makes it hard to include other properties such as magnetism in acentric phases.¹³

There has been much interest recently in a new class of acentric materials, the ‘hybrid-improper’ ferroelectrics, because their NCS crystal structures are not stabilized by specific polar chemical subunits. Instead the polar ground states of hybrid-improper ferroelectric phases are established by the presence of two non-polar structural distortion modes, which couple to, and stabilize, a third polar distortion mode.^14,15 This trilinear coupling of modes can stabilize polar NCS crystal structures without the assistance of local electronic instabilities, so offers the prospect of broadening the chemistry of NCS materials. It should be noted that the resulting polar materials are often referred to as ‘hybrid-improper ferroelectric phases’ because the ferroelectric polarisation which emerges at the paraelectric-to-ferroelectric phase transition of these materials need not be the primary order parameter of this phase transition.

The hybrid-improper mechanism has been observed to be responsible for the polar ground states of a number of A₃B₂O₇n = 2 Ruddlesden-Popper oxide phases. In these systems two low-energy, cooperative tilting distortions of the BO₆ octahedra combine to stabilize a third polar distortion mode (usually a polar displacement of the A-cations) to yield polar and potentially ferroelectric phases. Thus, the polar ground state structures of (Ca, Sr)₃Ti₂O₇,¹⁶ (Ca, Sr)₃Sn₂O₇ ¹⁷ Sr₃Zr₂O₇,¹⁸ and Ca₃Mn₂O₇ ¹⁹ have been attributed to the hybrid-improper stabilization mechanism.

Layered perovskite oxides based on the A′AB₂O₇n = 2 Dion-Jacobson framework have also been shown to exhibit polar structures stabilized by trilinear coupling.²⁰ For example, CsNdM₂O₇ and RbNdM₂O₇ (M = Nb, Ta) have been observed to adopt polar ground states, with ferroelectric switching reported for the two niobium phases.^21–23

The extensive cation exchange chemistry exhibited by Dion-Jacobson phases allows a range of metastable layered perovskite phases to be prepared.²⁴ For example, the Rb⁺ cations in RbNdM₂O₇ (M = Nb, Ta) can be exchanged for K⁺, Na⁺ or Li⁺, allowing the whole range of A′NdNb₂O₇ (A′ = Cs, Rb, K, Na, Li) materials to be investigated.^25,26 This reveals that LiNdM₂O₇ and NaNdM₂O₇ adopt pseudo Ruddlesden-Popper structures with the lithium materials exhibiting polar ground states stabilized by trilinear coupling, in contrast to the centrosymmetric structures of the sodium phases – a difference which can be attributed to the differing cation ordering patterns present in the contrasting materials.²⁵ KNdNb₂O₇ and KNdTa₂O₇ adopt layered perovskite structures with an unusual (0, ½, z) stacking of the perovskite sheets which are separated by 6-coordinate prismatic K⁺ cations.²⁶ Structural analysis reveals these KNdM₂O₇ materials are polar, but in this instance the acentric ground state is stabilized by a ‘conventional’ SOJT distortion of the MO₆ units.

The conventional polar distortions of the KNdM₂O₇ phases highlight the fact that many of the complex oxides which exhibit hybrid-improper polar ground states also contain ‘polar chemical species’, such as octahedrally coordinated d⁰ transition-metal cations. Thus, in principle, these compounds could adopt polar structures stabilized by the SOJT distortions of these polar chemical groups, which are in competition with the observed polar structures stabilized by trilinear coupling. This competition can be seen clearly in the two pseudo Ruddlesden-Popper phases Li₂La(TaTi)O₇ and Na₂La(TiTa)O₇ in which the polar distortion of the lithium phase is stabilized by trilinear coupling, in contrast to that of the sodium phase which is consistent with a SOJT stabilization mechanism.²⁷

Recently, to investigate the effect of including ns² post-transition metal cations in hybrid-improper polar phases, we reported the structures of NaBiNb₂O₇ and LiBiNb₂O₇ which were prepared by cation exchange from the Dion-Jacobson phase RbBiNb₂O₇.²⁸ Here we complete the A′BiNb₂O₇ series with an investigation of KBiNb₂O₇.

Experimental

Synthesis

Samples of KBiNb₂O₇ were prepared by first synthesising RbBiNb₂O₇, converting this material to LiBiNb₂O₇via Li-for-Rb cation exchange,²⁸ and finally forming KBiNb₂O₇via a K-for-Li cation exchange reaction. Specifically, polycrystalline samples of RbBiNb₂O₇ were prepared by a solid-state ceramic synthesis method from suitable stoichiometric ratios of Bi₂O₃ (99 995%) and Nb₂O₅ (99.9985%, dried at 900 °C), which were ground together in an agate pestle and mortar and combined with 50% excess (to compensate for the loss due to volatilization at high temperature) of Rb₂CO₃ (99.8%). These mixtures were then placed in open-ended silica tubes and heated at 600 °C in air for 12 h. The samples were then reground and heated at 1000 °C for 6 h then 12 h and 2 further periods of 4 h with regrinding between heating cycles. Finally, the powder samples were washed with distilled water to remove any excess rubidium oxide and then dried in air at 120 °C for 12 h. This heating regime was required to avoid the formation of BiNbO₄.

LiBiNb₂O₇ was synthesized as described previously²⁸ by reacting RbBiNb₂O₇ with 10 mole-equivalents of LiNO₃ (99.98%) in open ended silica tubes at 360 °C in air, for two periods of 48 h. Between heating cycles, samples were washed with distilled water, dried for 12 h at 120 °C in air and then mixed with a further 10 mole-equivalents of LiNO₃. After the final heating step, all samples were washed with distilled water to remove the LiNO₃ and then dried for 12 h at 120 °C in air.

KBiNb₂O₇ was synthesized by reacting LiBiNb₂O₇ with 10 mole-equivalents of KNO₃ (99.995%) in open ended silica tubes at 400 °C in air, for two periods of 48 h. Between heating cycles, samples were washed with distilled water, dried for 12 h at 120 °C in air and then mixed with a further 10 mole-equivalents of KNO₃. After the final heating step, all samples were washed with distilled water to remove the excess KNO₃ and then dried for 12 h at 120 °C in air.

Characterisation

X-ray powder diffraction data were collected using a PANalytical X′pert diffractometer incorporating an X′celerator position-sensitive detector (monochromatic Cu Kα₁ radiation). High-resolution synchrotron X-ray powder diffraction (SXRD) data were collected using the I11 instrument at the Diamond Light Source Ltd. Diffraction patterns were collected using Si-calibrated X-rays with an approximate wavelength of 0.825 Å from samples, sealed in 0.3 mm diameter borosilicate glass capillaries. Time-of-flight neutron powder diffraction (NPD) data were collected using the HRPD diffractometer at the ISIS neutron source from the samples loaded in 8 mm vanadium cans. Rietveld refinements were performed using the TOPAS Academic (V6).²⁹ The particle-size dependent second harmonic generation (SHG) response of samples was measured by grinding sintered pellets of material and then sieving the resulting powders into distinct particle size ranges (<20, 20–45, 45–63, 63–75, 75–90, 90–125 μm). SHG intensity was then recorded from each particle size range and compared to a standard sample of KH₂PO₄ (KDP) in the same particle size ranges. No index matching fluid was used in any of the experiments. A detailed description of the experimental setup and process has been reported previously.³⁰

Electron diffraction (ED) patterns were acquired on a FEI Tecnai transmission electron microscope (TEM) operated at 200 kV. High angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images were acquired using a probe aberration corrected FEI Titan 80–300 “cubed” microscope operated at 300 kV. Samples for TEM analysis were prepared in an argon-filled glove box by dipping a copper TEM grid into the ground dry powder. The grids were then transferred into the microscope using a vacuum transfer holder.

Simulated HAADF-STEM images were calculated using the QSTEM software.³¹

Results

Synthesis of KBiNb₂O₇

KBiNb₂O₇ could not be prepared by direct high-temperature synthesis. Reaction of K₂CO₃, Bi₂O₃ and Nb₂O₅ at 1100 °C primarily yielded the tetragonal tungsten bronze phase K₂BiNb₅O₁₅,³² indicating that the desired layered perovskite phase is metastable with respect to a mixture of the tetragonal tungsten bronze phase and Bi₂O₃. KBiNb₂O₇ could be prepared via K-for-Li cation exchange of LiBiNb₂O₇, as described above. It should be noted that unlike KNdNb₂O₇,²⁶ KBiNb₂O₇ could not be prepared via direct K-for-Rb cation exchange of the corresponding RbANb₂O₇ phase, with the synthesis of KBiNb₂O₇ only achieved via the reaction sequence RbBiNb₂O₇ to LiBiNb₂O₇ to KBiNb₂O₇, as LiBiNb₂O₇ itself can only be prepared via cation exchange from RbBiNb₂O₇.²⁸

Structural characterisation of KBiNb₂O₇

High resolution SXRD and NPD data collected from KBiNb₂O₇ was initially indexed using a monoclinic unit cell (a = 3.847 Å, b = 3.840 Å, c = 22.193 Å, γ = 90.80°). This unit cell is consistent with the aristotype unit cell of a (0, ½, z) stacked n = 2 layered perovskite.^33–35 However, on close inspection a series of small diffraction peaks were observed (Fig. S1, ESI†) which could only be indexed using an expanded unit cell (a = 7.694 Å, b = 3.840 Å, c = 22.193 Å, γ = 90.80°) which is an a′ ≈ 2a, b′ ≈ b, c′ ≈ c geometric expansion of the aristotype unit cell, with reflection conditions consistent with an A-centred unit cell.

Electron diffraction (ED) patterns collected from KBiNb₂O₇ (Fig. 1) show streaking along c*, indicative of stacking faults in the material (vide infra). Analysis of these patterns confirms the a′ ≈ 2a, b′ ≈ b, c′ ≈ c unit cell obtained from the SXRD and NPD data, with reflection conditions consistent with A-centring. Particle-size dependent SHG data (Fig. 2) reveals KBiNb₂O₇ has an SHG activity which is approximately 1.5 times that of KDP, and thus has a non-centrosymmetric crystal structure.

Fig. 1 Electron diffraction patterns collected from KBiNb₂O₇. The presence of ‘axis-switch’ stacking faults means the [010] and [100] zone axes are superimposed. The indicated spots in the [120] zone are due to overlap with another crystal.

Fig. 2 SHG activity as a function of particle size for KBiNb₂O₇ compared to a KDP standard.

Combining the information above, we can deduce that KBiNb₂O₇ adopts a crystal structure described in an A-centred, non-centrosymmetric monoclinic space group. This gives 3 candidates: A11a (#9), A11m (#8) and A112 (#5) with unit cell settings chosen to preserve the z-axis as the stacking direction. Structural models were constructed in these three space groups and refined against the NPD data collected at room temperature. The diffraction data show strongly hkl-dependent peak shapes as shown in Fig. S2 in the ESI,† which arises from stacking faults in the material as discussed later. At this stage of the structural refinement no attempt was made to include stacking faults in the structural model, with the hkl-dependent peak width modelled by a 6^th order spherical harmonic,³⁶ which led to a significant improvement in the fit to the data.

A comparison of fitting statistics reveals that the A112 model fits the data poorly (wR_p = 10.2) and yields a chemically implausible structure for KBiNb₂O₇, so this model was rejected. The fitting parameters from the refinement of A11m (wR_p = 8.43) and A11a (wR_p = 8.50) symmetry models are comparable. A close inspection of the refined A11a model reveals many atoms located on general symmetry positions refine to locations for which the z-parameter is zero, within error, consistent with the presence of a mirror plane perpendicular to the z-axis at this position, suggesting the A11m space group is a better symmetry description of KBiNb₂O₇. In addition, an analysis of the bond valence sums (BVS)^37,38 revealed the A11m model yielded more chemically realistic values for the K⁺, Nb⁵⁺ and Bi³⁺ cations than the A11a model. These observations indicate that the A11m model is a better choice for the room temperature structure of KBiNb₂O₇ than the A11a symmetry model. Full details of the refined A11m model of KBiNb₂O₇ are given in Table 1, with selected bond lengths in Table S2† and a plot of the observed and calculated data shown in Fig. 3. It should be noted that the rather large thermal displacement parameters detailed in Table 1 are attributed to the stacking disorder exhibited by the phase, as described below.

Fig. 3 Observed, calculated and difference plots from the structural refinement of KBiNb₂O₇ against NPD data collected at room temperature. Excluded regions remove contributions from an unidentified impurity phase.

Table 1 Parameters from the structural refinement of KBiNb₂O₇ against NPD data collected at room temperature

Atom	Site	x	y	z	Occ.	Biso (Å^2)
KBiNb2O7 – space group A11m (#8). a = 7.6735(3) Å, b = 3.8437(2) Å, c = 22.1699(9) Å, γ = 90.806(1), V = 653.83(5) Å^3, formula weight = 545.89 g mol^−1, temperature: 298 K. Rp = 7.54%, wRp = 8.43%.
K1	4b	0.003(3)	0.967(6)	0.1963(6)	½	3.2(1)
K2	4b	0.501(3)	0.966(5)	0.1965(5)	½	3.2(1)
Bi1	2a	0.0204(1)	0.066(4)	0	1	6.3(4)
Bi2	2a	0.5205(1)	0.932(4)	0	1	6.3(4)
Nb1	4b	0.251(1)	0.001(1)	0.3958(1)	1	4.2(1)
Nb2	4b	0.750(1)	0.999(1)	0.3957(1)	1	4.2(1)
O1	2a	0.214(1)	0.524(4)	0	1	5.3(2)
O2	2a	0.713(1)	0.475(4)	0	1	5.3(2)
O3	4b	0.001(1)	0.962(5)	0.4130(6)	1	6.8(3)
O4	4b	0.499(1)	0.038(5)	0.4132(5)	1	6.8(3)
O5	4b	0.275(1)	0.009(4)	0.3160(3)	1	5.9(2)
O6	4b	0.774(1)	0.008(4)	0.3159(3)	1	5.9(2)
O7	4b	0.2907(9)	0.993(1)	0.0889(2)	1	4.3(2)
O8	4b	0.7905(9)	0.994(1)	0.0888(2)	1	4.3(2)

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Microstructural characterisation of KBiNb₂O₇

The SXRD and NPD data collected from KBiNb₂O₇ exhibit very strong hkl-dependent broadening, which can be seen clearly in Fig. 3 and accounts for the relatively poor fit to the data. In addition, ED patterns show extensive streaking parallel to the c* direction (Fig. 1). Together these observations suggest KBiNb₂O₇ exhibits some variety of stacking fault disorder. To investigate the nature of the stacking faults a series of HAADF-STEM images were collected.

As noted above, the aristotype n = 2, (0, ½, z) layered perovskite structure adopted by KAB₂O₇ phases can be considered as a hybrid of the (0, 0, z) stacked Dion-Jacobson framework and the (½, ½, z) stacked Ruddlesden-Popper framework. HAADF-STEM images collected from KBiNb₂O₇ show that the BiNb₂O₇ perovskite sheets in KBiNb₂O₇ adopt an evenly spaced stacking sequence. However, close inspection shows that the stacking exhibits frequent ‘faults’ in which the (0, ½, z) stacking changes to a (½, 0, z) and vice versa, as shown in Fig. 4. This type of stacking fault corresponds to a switching of the x- and y-axes in the aristotype structure, and from the HAADF-STEM images these faults appear to be prevalent throughout the KBiNb₂O₇ sample measured.

Fig. 4 (a) HAADF-STEM image collected from KBiNb₂O₇. Green bracket shows stacking of BiNb₂O₇ sheets corresponding to [010] zone. Red bracket shows stacking corresponding to [100] zone. Superimposed spheres correspond to Bi (green), Nb (orange) and K (blue) atoms. Inset shows simulated [100] image of KBiNb₂O₇. (b) Representation of the 90° stacking fault in KBiNb₂O₇.

In an attempt to quantify the frequency of this stacking fault, the structural model obtained from the NPD data was modified to introduce this ‘axis-switch’ stacking fault with a frequency defined by a variable, FF (Fault Frequency), which describes the probability that at any potassium layer there will be a change from (0, ½, z) stacking to (½, 0, z) stacking or vice versa, as described in detail in the ESI.† A series of models with different values of FF were refined against the SXRD data, whilst keeping the atomic coordinates of the model static, to find the value of FF which best fitted the data. The introduction of this fault description led to a great improvement in the fit to the data as shown in Fig. 5. As shown in Fig. 6, the best fit to the SXRD data was obtained with a value of FF = 0.09, which corresponds to a 9% chance of a stacking fault occurring between any particular pair of perovskite double sheets. This faulting probability appears to be in line with the number of faults observed in the HAADF-STEM images. Attempts to perform an analogous analysis using the NPD data were hampered by the complex double-exponential peak shape of the time-of-flight instrument.

Fig. 5 Observed calculated a difference plots from the structural refinement of KBiNb₂O₇ (bottom) with and (top) without 90° stacking fault description.

Fig. 6 Plot of Goodness of fit (GOF) parameter against Fault Frequency (FF) determined by fitting to SXRD data.

Discussion

KBiNb₂O₇ adopts a layered structure in which the BiNb₂O₇ perovskite double sheets are stacked in a (0, ½, z) manner, with the K⁺ cations adopting a disordered arrangement within half of the 10-coordinate sites in the interlayer region. The BiNb₂O₇ sheets do not adopt a cooperative tilting distortion of the NbO₆ units, but are distorted by a large alternating displacement of the Bi³⁺ cations along the y-axis, as shown in Fig. 7. This low-symmetry, polar crystal structure differs markedly from other members of the A′BiNb₂O₇ (A′ = Cs, Rb, Na, Li) series. We can gain some insight into the interactions which lead to this low symmetry structure by examining how the structures of other phases in the A′BiNb₂O₇ series, and related A′NdNb₂O₇ series, evolve on changing the A′-cation.

Fig. 7 The crystal structures of KBiNb₂O₇ and KNdNb₂O₇. Purple, green, orange, grey and red spheres represent K, Bi, Nb, Nd and O respectively.

As described previously,^21,25,26 the stacking of the NdNb₂O₇ perovskite sheets and the cooperative tilting of the NbO₆ units in the A′NdNb₂O₇ series of layered perovskite phases, can be rationalised on the basis of simultaneously satisfying the bonding requirements of both the A′ and Nd³⁺ cations.

It can be observed that as the size of the A′-cations declines across the A′NdNb₂O₇ series, so does the A′ coordination number in the resulting framework, from 8-fold (A′ = Cs, Rb) to 6-fold (A′ = K) to 4-fold (A′ = Na, Li). This change is facilitated by a change in the layer stacking type, from (0, 0, z) Dion-Jacobson stacking (A′ = Cs, Rb) to (0, ½, z) stacking (A′ = K) to (½, ½, z) Ruddlesden-Popper stacking (A′ = Na, Li). Thus, the structural evolution of the A′NdNb₂O₇ series can be simply rationalized on the basis of the A′-cation size.

A similar sequence of structures is adopted by some members of the A′BiNb₂O₇ series, with the A′ = Cs, Rb, Li phases being isostructural to their A′NdNb₂O₇ analogues. These isostructural relationships are perhaps a little unexpected given the preference for 6s² Bi³⁺ cations to adopt asymmetric coordinations in contrast to the more symmetric environments favored by Nd³⁺. However, in the case of the Cs, Rb and Li phases, the large magnitude tilting distortions exhibited by the ANb₂O₇ sheets, which are required to simultaneously satisfy the coordination requirements of the A′ and Nd³⁺ cations, lower the symmetry of the A-cation sites (by way of the trilinear coupled hybrid improper mechanism)^14,20 to the ..m point symmetry favored by Bi³⁺.²⁸ Thus, perhaps coincidentally, Nd³⁺ and Bi³⁺ can be accommodated in the same structural frameworks, despite the contrasting features (Nd³⁺ small size; Bi³⁺ non-spherical geometry) of the two ions.

However, the differing coordination preferences of Nd³⁺ and Bi³⁺ do lead to a small difference in the structures of NaNdNb₂O₇ and NaBiNb₂O₇.^25,28 Both NaANb₂O₇ phases adopt a (½, ½, z) stacking of the ANb₂O₇ layers, with Na⁺ cations ordered in 4-coordinate sites in the interlayer region. However, the relatively large size of Na⁺ means that NaNdNb₂O₇ adopts a small magnitude a⁻b⁰c⁰/b⁰a⁻c⁰ tilting distortion (space group P4₂/mnm) with the Nd³⁺ cation accommodated on a site of m.2m point symmetry. This site symmetry appears to be incompatible with the coordination requirements of Bi³⁺ as NaBiNb₂O₇ adopts a much larger magnitude a⁻a⁻c⁺/a⁻a⁻-c⁺ tilting distortion (space group P2₁2₁2₁), despite Bi³⁺ being larger than Nd³⁺, which lowers the point symmetry of the Bi³⁺ cations to that of a general position, yielding an asymmetric bismuth coordination environment, suggesting that the change in structure occurs in response to an off-centring distortion of the Bi³⁺ cations.

In light of the analysis above, we can rationalise the much more significant structural differences between KNdNb₂O₇ and KBiNb₂O₇. KNdNb₂O₇ adopts a (0, ½, z) stacking pattern of the NdNb₂O₇ sheets, which themselves exhibit a cooperative a⁰b⁺c⁰/a⁰–b⁺c⁰ tilting scheme to best accommodate the K⁺ cations, which are ordered within half of the available 6-coordinate trigonal prismatic sites in the interlayer region of the structure as shown in Fig. 7. As noted above, KBiNb₂O₇ also exhibits a (0, ½, z) stacking pattern of the ANb₂O₇ perovskite sheets, however the remaining structural details are strongly contrasting: the K⁺ cations in KBiNb₂O₇ adopt a disordered arrangement within half of the 10-coordinate sites in the interlayer region and no cooperative tilting distortion is observed in the BiNb₂O₇ layers, which are instead distorted by a large alternating displacement of the Bi³⁺ cations, shown in Fig. 7.

Again the structural differences between the neodymium and bismuth phases can be attributed to the coordination preferences of the Nd³⁺ and Bi³⁺ cations. The a⁰b⁺c⁰/a⁰–b⁺c⁰ tilting distortion exhibited by the NdNb₂O₇ sheets in KNdNb₂O₇ results in a 222 point symmetry site for the Nd³⁺ cations. As noted above, such a high symmetry site appears to be incompatible with the asymmetric coordination environments adopted by Bi³⁺ – a statement supported by the observation that the Bi³⁺ sites in KBiNb₂O₇ have ..m point symmetry. Thus, we can attribute the change in structure on replacing Nd³⁺ with Bi³⁺ within the KANb₂O₇ framework to the preference for asymmetric environments exhibited by 6s² Bi³⁺ cations. It is worth noting however, that in contrast to the simple change in tilting pattern on Bi³⁺-for-Nd³⁺ substitution exhibited by the NaANb₂O₇ framework, the potassium system undergoes a much more dramatic change in structure on the introduction of bismuth, with the K⁺ coordination site and the ANb₂O₇ layer distortion changing. The resulting structure of KBiNb₂O₇ has a highly distorted BiNb₂O₇ layer in which the NbO₆ units are deformed from their expected octahedral geometry. This low symmetry arrangement suggests that it is difficult to satisfy the coordination preference of K⁺ and Bi³⁺ simultaneously in this (0, ½, z) framework, with the observed structure being the best compromise. As a consequence the inversion symmetry breaking in the non-centrosymmetric structure of KBiNb₂O₇ can be attributed to an SOJT-like distortion driven by the 6s² electronic configuration of Bi³⁺, in contrast to KNdNb₂O₇ where the inversion symmetry breaking is attributed to an SOJT-like distortion driven by the Nb⁵⁺ cations.²⁶

A further striking feature exhibited by KBiNb₂O₇ is the axis-switch stacking fault in which the (0, ½, z) stacking changes to (½, 0, z) stacking and vice versa. In principle, such a stacking fault should apply significant lattice strain to the materials. However, due to the lack of a cooperative NbO₆ tilting distortion, the lattice parameters of KBiNb₂O₇ are close to being metrically tetragonal (if the x-axis doubling due to the alternating Bi displacement is ignored) so the strain associated with the faulting should be minimal. Thus we can see that the prevalent axis-switch faults can be attributed to features of the crystal structure of the material.

Conclusions

The facile cation-exchange reactions exhibited by Dion-Jacobson phases allow a wide range of metastable, layered perovskite oxide phases to be prepared. In the case of the A′BiNb₂O₇ series this allows the competition between alternative polar ground states stabilized by either trilinear coupling, the SOJT distortions of Nb⁵⁺O₆ units, or the off-centring distortions of 6s² Bi³⁺, to be studied.

In the case of KBiNb₂O₇, we observe this phase is highly metastable, and can only be prepared through a 3-step reaction sequence. The phase produced differs significantly from the analogous Nd³⁺ phase, KNdNb₂O₇, both in the local coordination of the K⁺ cations and the deformation of the ANb₂O₇ perovskite double sheets. In addition KBiNb₂O₇ exhibits extensive ‘axis-switch’ stacking faults. These features combine to highlight the dominant influence of the off-centring distortions of the Bi³⁺ cations in this phase.

Author contributions

SM prepared the samples and performed the structural analysis, WZ and PSH collected the SHG data, MB and JH collected the microscopy data, ASG assisted with the collection of the NPD data, MAH conceived the study, wrote the manuscript and supervised the study.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Experiments at the Diamond Light Source were performed as part of the Block Allocation Group award “Oxford/Warwick Solid State Chemistry BAG to probe composition-structure–property relationships in solids” (CY25166). Experiments at the ISIS pulsed neutron facility were supported by a beam time allocation from the STFC (RB 2000148). SM thanks Somerville College for an Oxford Ryniker Lloyd scholarship. ‘PSH and WZ thank the National Science Foundation (DMR-2002319) and Welch Foundation (Grant E-1457) for support.

Notes and references

1. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Oxford University Press, Oxford, 1991.
2. F. J. Nye, Physical Properties of Crystals, Oxford University Press, Oxford, UK, 1957.
3. R. E. Cohen, Nature, 1992, 358, 136–138.
4. M. Kunz and I. D. Brown, J. Solid State Chem., 1995, 115, 395–406.
5. S. K. Kang, H. Tang and T. A. Albright, J. Am. Chem. Soc., 1993, 115, 1971–1981.
6. R. G. Pearson, J. Mol. Struct.: THEOCHEM, 1983, 12, 25–34.
7. I. Lefebvre, M. Lannoo, G. Allan, A. Ibanez, J. Fourcade, J. C. Jumas and E. Beaurepaire, Phys. Rev. Lett., 1987, 59, 2471–2474.
8. I. Lefebvre, M. A. Szymanski, J. Olivier-Fourcade and J. C. Jumas, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 58, 1896–1906.
9. R. Seshadri and N. A. Hill, Chem. Mater., 2001, 13, 2892–2899.
10. M. W. Stoltzfus, P. M. Woodward, R. Seshadri, J. H. Klepeis and B. Bursten, Inorg. Chem., 2007, 46, 3839–3850.
11. G. W. Watson and S. C. Parker, J. Phys. Chem. B, 1999, 103, 1258–1262.
12. G. W. Watson, S. C. Parker and G. Kresse, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 8481–8486.
13. N. A. Hill, J. Phys. Chem. B, 2000, 104, 6694–6709.
14. N. A. Benedek and C. J. Fennie, Phys. Rev. Lett., 2011, 106, 107204.
15. N. A. Benedek, J. M. Rondinelli, H. Djani, P. Ghosez and P. Lightfoot, Dalton Trans., 2015, 44, 10543–10558.
16. Y. S. Oh, X. Luo, F. T. Huang, Y. Z. Wang and S. W. Cheong, Nat. Mater., 2015, 14, 407–413.
17. S. Yoshida, H. Akamatsu, R. Tsuji, O. Hernandez, H. Padmanabhan, A. Sen Gupta, A. S. Gibbs, K. Mibu, S. Murai, J. M. Rondinelli, V. Gopalan, K. Tanaka and K. Fujita, J. Am. Chem. Soc., 2018, 140, 15690–15700.
18. S. Yoshida, K. Fujita, H. Akamatsu, O. Hernandez, A. Sen Gupta, F. G. Brown, H. Padmanabhan, A. S. Gibbs, T. Kuge, R. Tsuji, S. Murai, J. M. Rondinelli, V. Gopalan and K. Tanaka, Adv. Funct. Mater., 2018, 28, 1801856.
19. M. F. Liu, Y. Zhang, L. F. Lin, L. Lin, S. W. Yang, X. Li, Y. Wang, S. Z. Li, Z. B. Yan, X. Z. Wang, X. G. Li, S. Dong and J. M. Liu, Appl. Phys. Lett., 2018, 113, 022902.
20. N. A. Benedek, Inorg. Chem., 2014, 53, 3769–3777.
21. T. Zhu, T. Cohen, A. S. Gibbs, W. Zhang, P. S. Halasyamani, M. A. Hayward and N. A. Benedek, Chem. Mater., 2017, 29, 9489–9497.
22. T. Zhu, A. S. Gibbs, N. A. Benedek and M. A. Hayward, Chem. Mater., 2020, 32, 4340–4346.
23. S. Asaki, H. Akamatsu, G. Hasegawa, T. Abe, Y. Nakahira, S. Yoshida, C. Moriyoshi and K. Hayashi, Jpn. J. Appl. Phys., 2020, 59, 6.
24. M. A. Hayward, in Comprehensive Inorganic Chemistry II, ed. J. Reedijk and K. R. Poeppelmeier, Elsevier, Oxford, 2013, vol. 2, pp. 417–453.
25. T. Zhu, G. Khalsa, D. M. Havas, A. S. Gibbs, W. Zhang, P. Halasyamani, N. A. Benedek and M. A. Hayward, Chem. Mater., 2018, 30, 8915–8924.
26. S. Mallick, A. S. Gibbs, W. G. Zhang, P. S. Halasyamani, N. A. Benedek and M. A. Hayward, Chem. Mater., 2020, 32, 7965–7972.
27. S. Mallick, A. D. Fortes, W. Zhang, P. S. Halasyamani and M. A. Hayward, Chem. Mater., 2021, 33, 2666–2672.
28. S. Mallick, G. Khalsa, J. Z. Kaaret, W. Zhang, M. Batuk, A. S. Gibbs, J. Hadermann, P. S. Halasyamani, N. A. Benedek and M. A. Hayward, Dalton Trans., 2021, 50, 15359.
29. A. A. Coelho, Bruker AXS, Karlsruhe, Germany, 2016.
30. K. M. Ok, E. O. Chi and P. S. Halasyamani, Chem. Soc. Rev., 2006, 35, 710–717.
31. C. Koch, Ph. D Thesis, Arizona state University, 2002.
32. M. Shimazu, Y. Tanokura and S. Tsutsumi, Jpn. J. Appl. Phys., Part 1, 1989, 28, 1877–1881.
33. J. Gopalakrishnan, V. Bhat and B. Raveau, Mater. Res. Bull., 1987, 22, 413–417.
34. M. Sato, J. Abo, T. Jin and M. Ohta, Solid State Ionics, 1992, 51, 85–89.
35. M. Sato, J. Abo, T. Jin and M. Ohta, J. Alloys Compd., 1993, 192, 81–83.
36. M. Jarvinen, J. Appl. Crystallogr., 1993, 26, 525–531.
37. N. E. Brese and M. O'Keeffee, Acta Crystallogr., Sect. B: Struct. Sci., 1991, 47, 192–197.
38. I. D. Brown and D. Altermatt, Acta Crystallogr., Sect. B: Struct. Sci., 1985, 41, 244–247.

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Footnote

† Electronic supplementary information (ESI) available: Full details of the structural and microstructural characterisation of KBiNb₂O₇. See DOI: 10.1039/d1dt04064b

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