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. 2020 Sep 22;32(19):8700–8712. doi: 10.1021/acs.chemmater.0c03326

Tuning between Proper and Hybrid-Improper Mechanisms for Polar Behavior in CsLn2Ti2NbO10 Dion-Jacobson Phases

Vanessa A Cascos †, Jennifer Roberts-Watts †, Chloe Skingle †, Igor Levin ‡, Weiguo Zhang §, P Shiv Halasyamani §, Martin C Stennett ∥, Neil C Hyatt ∥, Eric Bousquet ⊥,*, Emma E McCabe †,*
PMCID: PMC7587150  PMID: 33122876

Abstract

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The Dion-Jacobson (DJ) family of perovskite-related materials have recently attracted interest due to their polar structures and properties, resulting from hybrid-improper mechanisms for ferroelectricity in n = 2 systems and from proper mechanisms in n = 3 CsBi2Ti2NbO10. We report here a combined experimental and computational study on analogous n = 3 CsLn2Ti2NbO10 (Ln = La, Nd) materials. Density functional theory calculations reveal the shallow energy landscape in these systems and give an understanding of the competing structural models suggested by neutron and electron diffraction studies. The structural disorder resulting from the shallow energy landscape breaks inversion symmetry at a local level, consistent with the observed second-harmonic generation. This study reveals the potential to tune between proper and hybrid-improper mechanisms by composition in the DJ family. The disorder and shallow energy landscape have implications for designing functional materials with properties reliant on competing low-energy phases such as relaxors and antiferroelectrics.

1. Introduction

Ferroelectrics are widely used in applications such as sonars and sensors,1 electrooptics,2 capacitors,3 and memory devices,4 making them materials of significant technological importance. From an academic perspective, the origins of their switchable polarization are fascinating as they hold the key to designing new classes of polar materials.5−7 In proper ferroelectrics, polar displacive distortions (e.g., of cations relative to anions in the structure) form the primary order parameter and drive the paraelectric–ferroelectric phase transition to give the polar, noncentrosymmetric phase.8 Such displacements are often favored by particular electronic configurations of ions (e.g., “inert pair” Bi3+, Pb2+ ions, and d0 transition metal ions). Alternatively, hybrid-improper mechanisms for ferroelectricity rely on coupling nonpolar distortions (such as rotations of octahedra in layered perovskite-related materials) to break inversion symmetry and stabilize polar displacements.9,10 This opens up the possibility of preparing new families of polar materials. These two mechanisms give distinctly different temperature-dependence of polar characteristics such as permittivity and therefore the possibility to tune the temperature scale and range of functional properties.

Families of layered perovskite-related materials are ideal systems in which to explore the mechanisms that give rise to polar structures.5 Recent work on hybrid-improper Ruddlesden–Popper phases11,12 has shown that nonpolar distortions such as octahedral rotations often give relatively small energy gains (compared with polar cation displacements in proper systems) and that different rotation modes can have similar energy gains. This gives a fairly shallow energy landscape with competing ground states and hence the potential to switch between phases giving more complex behavior such as antiferroelectricity,12 negative thermal expansion,13,14 and relaxor behavior.15 This provides a powerful motivation to understand the competition between different mechanisms/distortions and the consequences for structure and properties.

The Dion-Jacobson (DJ) family of perovskite-related materials have been a key focus for exploring hybrid-improper mechanisms for ferroelectricity.16 These layered materials, of general formula A′An-1BnO3n+1, are built up from perovskite-like layers (of corner-linked BO6 octahedra) n layers thick, separated by layers of large A′ ions (e.g., Cs+, Rb+). The A sites within the perovskite-like blocks are typically occupied by lanthanide or group 2 ions. In contrast to the Ruddlesden–Popper and Aurivillius families, the perovskite-like blocks in DJ materials are eclipsed, giving ideal, high-symmetry structures of P4/mmm symmetry (Figure 1).

Figure 1.

Figure 1

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Illustration of crystal structures for n = 3 DJ phases including (a) ideal P4/mmm high symmetry model, (b) Imcm model for CsNd2Ti2NbO10 at 700 K (with disordered O(1) site) with A5+ rotations about in-plane axis, and (c) Pbnm structure for CsNd2Ti2NbO10 at 293 K with A5+ and M3+ rotations. Cs, Ln, and O sites are shown by purple, green, and red spheres, and Ti(1) and Ti/Nb(2) sites are within dark blue and light blue polyhedra, respectively.

Theoretical work has shown that for even-layer DJ phases, combinations of rotations of BO6 octahedra (e.g., about both an in-plane axis and about the tetragonal axis [001]t to give a–a–c+ tilts overall) can break inversion symmetry, stabilizing polar, noncentrosymmetric structures by hybrid-improper mechanisms.16 Zhu et al. have explored the role of A′ ions (Cs+, Rb+) in stabilizing different combinations of rotation modes and how these ions influence the sequence of phase transitions to the centrosymmetric, nonpolar high temperature phase.17,18

While combinations of equivalent rotation modes (i.e., involving rotation of all octahedra about both in-plane and out-of-plane axes) in odd-layered DJ systems do not break inversion symmetry,16 distortions involving rotation of only inner-layer octahedra, or only outer-layer octahedra about [001]t are possible,19−21 and can couple with rotations about an in-plane axis to break inversion symmetry.20 This means that odd-layer DJ phases can adopt polar structures stabilized by proper or hybrid-improper mechanisms. Recent work on CsBi2Ti2NbO10 showed that with 6s2 Bi3+ ions on the A sites (which favor asymmetric coordination environments22), the origin of its polar behavior is close to a proper mechanism.20 Experimental studies of RbBi2Ti2NbO10 and CsBi2Ti2TaO10 suggest these closely related materials behave analogously.23 However, the possibility of tuning between proper and hybrid-improper mechanisms and the role of A cations in these systems has not been explored.

We report here a combined experimental and computational study of the n = 3 DJ phases CsLn2Ti2NbO10 (Ln = La, Nd). Our structural characterization using neutron and electron diffraction gives an understanding of the crystal structure at long-range and shorter length scales. Density functional theory calculations reveal the very shallow energy landscape in these systems, and competing combinations of octahedral rotations can induce disorder and break inversion symmetry at a local level, as manifested in the second-harmonic generation behavior. These results indicate that DJ phases can be tuned between proper and hybrid-improper mechanisms but that the hybrid-improper behavior may be limited to effects at short length scales.

2. Methods

Polycrystalline samples of CsLa2Ti2NbO10 and CsNd2Ti2NbO10 were prepared by reacting stoichiometric quantities of Cs2CO3 (in 30% excess to account for volatility), La2O3, Nd2O3, TiO2, and Nb2O5 [these reagents were of ≥99.5% purity and were dried (at 800–1000 °C) prior to use]. These reagents were ground by hand in an agate mortar and pestle under an acetone slurry and pressed into 10 mm diameter pellet(s). The resulting mixture was placed in an alumina boat and heated at 550 °C for 6 h followed by 12 h at 1000 °C. After cooling to room temperature in the furnace, the sample was ground under acetone and reheated at 1000 °C for 12 h, with this process repeated several times. Finally, the powder was washed several times with cold, deionized water and recovered by vacuum filtration. Preliminary characterization was carried out using X-ray powder diffraction (XRPD) using a Bruker D8 Advance diffractometer operating in reflection mode with a Cu Kα source and a Vantec detector. (Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by NIST, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.)

Neutron powder diffraction data were collected on the BT1 diffractometer at the NIST Center for Neutron Research (NCNR). Data sets were collected at 20, 293, 400, and 700 K. Diffraction data were analyzed using the Rietveld method24 in the Topas Academic software.25,26 Distortions and group-subgroup relations were explored using the symmetry-adapted distortion mode approach and ISODISTORT.27 With the use of a global atomic displacement parameter for all sites, the distribution of Ti and Nb over the two B sites was refined (with a constraint to maintain stoichiometry). This suggested that the central B(1) site is fully occupied by Ti with the outer B(2) occupied equally by Ti and Nb. Ti and Nb have neutron scattering lengths of opposite signs [7.054(3) fm for Nb, −3.438(2) fm for Ti]28 which lead to low average scattering for the mixed sites; therefore, the atomic displacement parameters were constrained to be the average of those of the other sites in the structure. In subsequent refinements, the Ti/Nb distribution was fixed and again, average temperature factors were used for these sites.20 Separately from the Rietveld analysis described above, the diffuse scatter was fitted by a Warren-like function using the Profit software to estimate the size of sort-ranged correlated regions.

Samples for transmission electron microscopy were prepared by the mechanical grinding and polishing of sintered (1300 °C for 12 h) pellets followed by ion polishing at 100 K until perforation. Selected samples were prepared by grinding the crushed powder under acetone using an agate mortar and pestle and dispersing this suspension on copper grids coated with lacey carbon. Electron diffraction patterns and diffraction-contrast images were obtained in a conventional TEM operated at 200 kV.

CsLa2Ti2NbO10 and CsNd2Ti2NbO10 were tested for a second harmonic generation (SHG) signal using the experimental setup described in reference;29 pellets of CsLn2Ti2NbO10 were ground and sieved into distinct particle size ranges (<20, 20–45, 45–63, 63–75, 75–90, and 90–125 μm). Relevant comparisons with known SHG materials were made by grinding and sieving crystalline KH2PO4 (KDP) into the same particle size ranges. SHG intensity was recorded for each particle size range.

Diffuse reflectance spectra were recorded by placing sample ground with dry sodium chloride (∼10% w/w) in an optical cuvette and illuminating it with a halogen lamp (Ocean Optics DH-2000-S). Nonspecular scattered light was collected, and the spectrum was recorded using an OceanOptics spectrometer (Mayer2000 Pro). A cuvette of ground sodium chloride was used as a reference. The data were used to calculate the reflectance spectra R(I) and Kubelka–Munk spectra F(R).30

Pellets of CsLa2Ti2NbO10, 5 mm in diameter, were heated at 2 °C min–1 to 1000 °C and held at this temperature for 4 h. During this sintering process, the pellets were embedded in a sacrificial powder of the same composition. This gave pellets of density ∼71% of their theoretical density. Gold electrodes were attached to sintered pellets of CsLn2Ti2NbO10 (Ln = La, Nd) using gold paste (annealed at 800 °C for 2 h). The dielectric response of these pellets was measured at 10, 100, and 250 kHz using an HP inductance–capacitance–resistance (LCR) meter. Measurements were carried out in a tube furnace, heating the sample at 1 °C min–1 to 800 °C.

We performed Density Functional Theory (DFT) calculations using the ABINIT package31,32 and norm-conserving pseudopotentials from the pseudodojo project (v.3)33 and generated with the ONCVPSP code.34 The following orbitals were treated as valence electrons in the pseudopotentials: 2s and 2p for O; 3s, 3p, 3d and 4s for Ti; 4s, 4p, 4d and 5s for Nb; 5s, 5p and 6s for Cs and 5d; and 6s and 6p for La and Nd (the f-electrons are treated as core electrons for Nd such that they do not participate as valence electrons). As in our previous work,20 we used the virtual crystal approximation (VCA)35 for the outer B(2) site (2g in the P4/mmm model, see Figure 3a) with an “alchemical” virtual atom made of 50% of Nb and 50% of Ti for this site. We kept a regular Ti atom for the central B(1) site (1a in the P4/mmm model, see Figure 3a). We used the GGA-PBE functional and converged the calculations up to 1 meV/f.u. on energy differences between structural phases and up to 2 cm–1 on phonon frequencies by setting the cutoff energy at 50 Hartree for the plane wave expansion and the k-point grid at 6 × 6 × 2 for the integration in the Brillouin zone of the P4/mmm phase and at 3 × 3 × 2 for phases having a doubling of the unit cell with respect to the P4/mmm. The phonon frequencies, Born effective charges, dielectric constants, and piezoelectric coefficients were computed through the density functional perturbation theory (DFPT)36−38 and the polarization through the Berry phase method.39

Figure 3.

Figure 3

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NPD data collected for CsLa2Ti2NbO10 at 20 (blue, bottom), 293 (green), 400 (orange), 600 (red), and 700 K (brown), showing positions of extra reflections indexed by A, M, and Z-point distortions highlighted by arrows.

3. Results

3.1. Consideration of Possible Distortions for n = 3 DJ Phases

Perovskite-related materials are well-known to undergo distortions including those involving rotations of BX6 (X=anion) octahedra and polar or antipolar displacements of ions. The lower-symmetry structures resulting from these distortions have been thoroughly investigated for three-dimensional perovskites.40−42 The layered nature of the Ruddlesden–Popper and Aurivillius families of materials (with high symmetry structures of I4/mmm symmetry) gives distorted structures of different symmetries depending on whether the perovskite-blocks contain an odd or an even number of layers n of corner-linked BX6 octahedra.43−46 Likewise, these distortions have also been explored for DJ phases (with high symmetry structures of P4/mmm symmetry).47 An added complexity for n = 3 materials of these families (in contrast to n = 1 and n = 2 phases) is the possibility of decoupling rotations of inner and outer BX6 octahedra about [001]t (the long, pseudotetragonal axis), i.e., only inner B(1)X6 octahedra (as in Bi4Ti3O1219) or only outer B(2)X6 octahedra (as in CsBi2Ti2NbO1020) might rotate about [001]t. Table 1 summarizes the distortions involving octahedral rotations considered for n = 3 DJ phases using Aleksandrov’s notation and Glazer notation, as well as irreps as described by ISODISTORT, and these are illustrated in the Supporting Information.

Table 1. Summary of Symmetry analysis for n = 3 DJ Phases (With Parent High Symmetry Structure of P4/mmm Symmetry) based on Analysis by Aleksandrov47 and Using ISODISTORT,27 Expressed with ψ and φ Representing In-phase and Out-of-phase Rotations, Respectively, and Using Glazer Notation40.

irrep Aleksandrov notation glazer notation symmetry unit cell
A5+ φ00 -φ00 a–b0c0 -(a–b0c0) Fmmm 2at × 2at × 2ct
  φφ0 -φ -φ0 a–a–c0 -(a–a–c0) Imcm √2at × √2at × 2ct
M5+ φ00 φ00 a–b0c0a–b0c0 Cmma 2at × 2at × ct
  φφ0 φφ0 a–a–c0a–a–c0 Pmna √2at × ct × √2at
A3+ 00φ 00-φ a0a0c– -(a0a0c–) I4/mcm √2at × √2at × 2ct
M3+ 00φ 00φ or 00ψ 00ψ a0a0c–a0a0c– P4/mbm √2at × √2at × ct
A1– 00φ 00φ (outer only) a0a0c–a0a0c– (outer only) I4/mcm √2at × √2at × 2ct
M1– 00ψ 00ψ (outer only) a0a0c+a0a0c+ (outer only) P4/nbm √2at × √2at × ct
A5+ + A3+ φφφ -φ-φ-φ a–a–c– -(a–a–c–) C2/c 2ct × √2at × √2at
A5+ + M3+ φφφ -φ-φφ or φφψ -φ-φ ψ a–a–c– -(a–a–)c– Pbnm √2at × √2at × 2ct
A5+ + A1– (+Γ5–) φφφ -φ-φφ (outer only) a–a–c– -(a–a–)c– (outer only) I2 cm √2at × √2at × 2ct
A5+ + M1– φφψ -φ-φψ (outer only) a–a–c+ -(a–a–)c+ (outer only) Pnna √2at × 2ct × √2at
M5+ + A3+ φφφ φφ-φ a–a–c–a–a–-c– Pbcn √2at × √2at × 2ct
M5+ + M3+ φφφ φφφ a–a–c–a–a–c– C2/m 2at × 2at × ct
M5+ + A1– φφφ φφφ (outer only) a–a–c–a–a–c– (outer only) Pbcn √2at × √2at × 2ct
M5+ + M1– (+Γ5–) Φ0ψ φ0ψ (outer only) a–b0c+a–b0c+ (outer only) Abm2 ct × 2at × 2at
  φφψ φφψ (outer only) a–a–c+a–a–c+ (outer only) Pnc2 ct × √2at × √2at
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3.2. Neutron Powder Diffraction

3.2.1. CsLa2Ti2NbO10

Neutron powder diffraction data collected for CsLa2Ti2NbO10 at 30, 293, 400, and 700 K could be indexed by the aristotype P4/mmm unit cell. Although no additional reflections are observed, diffuse scattering was observed (e.g., ∼37–40° 2θ and 72–74° 2θ) (Figure 2c and Supporting Information). Attempts to fit these NPD data with a model of P4/mmm symmetry gave an unreasonably high atomic displacement parameter (ADP) for the central equatorial oxygen site O(1). Allowing anisotropy of this ADP suggested significant disorder (either static or dynamic) within the xy plane, consistent with rotations of BO6 octahedra about their axes parallel to the [001]t direction (see the Supporting Information). Moving this O(1) site from the ideal 2f (0 1/2 0) Wyckoff position to a half-occupied 4n site (x 1/2 0) improved the fit significantly (Rwp decreased from 13% (26 parameters) to 9.9% (27 parameters) and gave reasonable ADP values for all sites. Although other lower-symmetry models were considered, including noncentrosymmetric models (see the Supporting Information), our NPD data suggest that the average, long-range structure of CsLa2Ti2NbO10 as probed by NPD between 30 and 700 K is best described by this disordered model of P4/mmm symmetry. Refinement profiles and refined parameters for 293 K Rietveld refinement are summarized in Figure 2 and Table 2; those for other temperatures are given in the Supporting Information, along with variable-temperature results. Bond valence sum calculations48 indicate that while the bonding environments around Cs, Ti(1), and Nb(2) are close to optimal (apparent valences of 1.1, 4.1, and 5.0, respectively), La is slightly overbonded (3.4) while Ti(2) is slightly underbonded (3.8). This illustrates the preference of the slightly larger Nb5+ cation (6-coordinate ionic radius 0.64 Å) for the larger outer B(2) site, in which the smaller Ti4+ cation (6-coordinate ionic radius 0.605 Å) is slightly underbonded.49

Figure 2.

Figure 2

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Rietveld refinement profiles for CsLa2Ti2NbO10 293 K NPD data fitted with arisotype P4/mmm model. Observed, calculated, and difference profiles are shown in blue, red, and gray with tick marks for the main phase shown in blue. Upper panel (a) shows whole 2θ range while lower panel (b) shows an enlarged high 2θ region; (c) shows the region of diffuse scatter as a function of temperature with data collected at 30, 293, 400, and 700 K shown by blue open points, green line, orange line, and brown points, respectively.

Table 2. Structural Parameters and Selected Bond Lengths for Refinement for CsLa2Ti2NbO10 Using 293 K NPD Dataa.
structural parameters
 selected bond lengths (Å)
atom site Uiso × 100 (Å2) Cs – O(4) 8 × 3.161(2)
Cs 1d 1.3(1) La–O(3) 4 × 2.552(2)
La 2h; z = 0.1410(2) 0.46(6) La–O(1) 4 × 2.642(2)
Ti(1) 1a 0.85(3) La–O(2) 4 × 2.7358(4)
Ti/Nb(2) 2g; z = 0.2806(9) 0.85(3) Ti(1)–O(2) 2 × 1.914(3)
O(1) 4n; x = 0.118(1) 0.6(1) Ti(1)–O(1) 4 × 1.979(1)
O(2) 2g; z = 0.1242(2) 1.10(9) Ti/Nb(2)–O(4) 1 × 1.78(1)
O(3) 4i; z = 0.2497(1) 0.61(4) Ti/Nb(2)–O(3) 4 × 1.984(3)
O(4) 2g; z = 0.3959(2) 1.06(9) Ti/Nb(2)–O(2) 1 × 2.41(1)
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a

Refinement carried out in the space group P4/mmm, a = 3.85179(8) Å, c = 15.4054(6) Å; Rwp = 9.921%, Rp = 7.969%, χ2 = 1.88; for P4/mmm, 1a is at (0 0 0), 1d is at (1/2 1/2 1/2), 2g is at (0 0 z), 2h is at (1/2 1/2 z), 4i is at (0 1/2 z), and 4n is at (x 1/2 0).

The diffuse scattering observed in NPD data changes little with temperature and can be fitted with a Warren-like peak (see Supporting Information), indicative of short-range, two-dimensional correlations.50 The Warren peak maximum coincided with the approximate position of superstructure reflections due to M-type distortions such as octahedral rotations [k vector = (1/2 1/2 0)] [38.2(1)° 2θ at 700 K; 38.1(1)° 2θ at 30 K, Supporting Information] and suggested correlation lengths within the ab plane of ∼6 × the in-plane lattice parameter [22(1) Å at 700 K; 24(1) Å at 30 K].

3.2.2. CsNd2Ti2NbO10

3.2.2.1. 700 K

In contrast to CsLa2Ti2NbO10, NPD data collected at 700 K for CsNd2Ti2NbO10 could not be indexed by the aristotype P4/mmm unit cell and, instead, a larger body-centered √2at × √2at × 2ct unit cell was required. Pawley refinements using this tetragonal cell were promising, and models of I4/mcm symmetry (allowing either A3+, A2+, or A1– rotations of BO6 octahedra around [001]t, see the Supporting Information) were considered. However, the c glide perpendicular to [100] (along with the body-centring, giving reflection condition 0kl k, l = 2n) precludes, for example, 0 1 11, 0 1 13, 0 3 3, and 0 3 5 reflections, and therefore, these models were inconsistent with our 700 K data (see the Supporting Information). Although no clear orthorhombic splitting was observed, an orthorhombic model of Imcm (bca setting of Imma, 74) symmetry (√2at × √2at × 2ct) allowing A5+ rotations of BO6 octahedra around [110]t (see the Supporting Information) gave an excellent fit to the data but an unfeasibly high ADP for the equatorial O(1) site. Allowing this to refine anisotropically suggested disorder in the ab plane (consistent with rotation of Ti(1)O6 octahedra about [001]t). Moving O(1) from the high symmetry 8f site to the general 16i site, consistent with static or dynamic displacement of O(1) in the ab plane, gave a chemically reasonable model. Refinement profiles and details are given in the Supporting Information, with selected bond lengths and angles. We note that this model has a metrically tetragonal unit cell, but an orthorhombic symmetry, and it is likely that at length scales shorter than those probed by NPD, the structure may differ from the Imcm model as discussed below.

3.2.2.2. 20–600 K

Additional superstructure reflections were observed in 600 K NPD data that were inconsistent with the body-centered Imcm symmetry, suggesting a change in structure on cooling (see Figure 3). Various models, allowing combinations of octahedral tilts (see the Supporting Information), were considered and the model of Pbnm symmetry (cab setting of Pnma, 62) gave a good fit to the data. This model allows rotations about the [110]t and [001]t axes (A5+ and M3+ modes, giving a–a–c– tilts; see the Supporting Information).

NPD data collected at 20, 293, and 400 K were also consistent with similar Pbnm models, and refinement profiles and refinement details for 293 K data are given in Figure 4 (and in the Supporting Information for other temperatures); selected bond lengths and angles are tabulated in the Supporting Information. The orthorhombic unit cells of Imcm and Pbnm symmetry proposed to describe the average, long-range structure of CsNd2Ti2Nb10 are metrically close to being tetragonal, but the orthorhombic symmetry is confirmed (at room temperature) by electron diffraction studies (see below).

Figure 4.

Figure 4

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Rietveld refinement profiles for CsNd2Ti2NbO10 293 K NPD data fitted with the Pbnm model. Observed, calculated, and difference profiles are shown in black, red, and gray with tick marks for the main phase shown in blue. Upper panel (a) shows a whole 2θ range, while the lower panel (b) shows an enlarged high 2θ region.

Bond valence sum calculations for the 293 K structure give values of 4.3, 3.9, and 5.1 for Ti(1), Ti(2), and Nb(2) sites and 3.0 and 1.1 for Nd3+ and Cs+ sites, respectively. The surprisingly short Ti/Nb(2)–O(5) bond length and overbonding for Ti(1) sites may reflect distortions at a more local length scale to optimize bonding within the perovskite blocks (as discussed further below).

3.3. Electron Diffraction and Dark-Field Imaging

3.3.1. CsLa2Ti2NbO10

The fundamental reflections in the selected-area electron diffraction (SAED) patterns (Figure 5) for this material can all be indexed by the a × c unit cell suggested by NPD. However, SAED reveals additional superlattice reflections at the 1/2 hkl (h,k,l = odd) position, suggesting ordering (presumably displacive) in the a-b plane. These reflections exhibited diffuse streaking along the c-axis, and the corresponding dark-field images confirmed that the streaks originate from planar defects on the c-planes. In some regions, the superlattice spots appeared sharp with the dark-field images highlighting large antiphase domains, while in others, they were very diffuse, indicating that the ordering in such regions is limited to the nanoscale. These observations are consistent with the diffuse-scattering features encountered in the NPD patterns.

Figure 5.

Figure 5

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SAED patterns and dark-field imaging for CsLa2Ti2NbO10 indexed according to the at × ct (P4/mmm) unit cell. Superlattice reflections (e.g., highlighted within red ellipses) indicate displacive ordering in the a-b plane and dark-field imaging indicates different length scales of this displacive ordering.

3.3.2. CsNd2Ti2NbO10

The SAED patterns (Figure 6) appear to be inconsistent with the (long-range) √2at × √2at × 2ctPbnm structure inferred from NPD. For example, sharp spots at 1/2 310 (in Pbnm indexes) cannot be accounted for by the √2at × √2at × 2ct unit cell. At the same time, the h0l or 0kl spots with l odd (which are allowed by Pbnm symmetry and typically serve as a signature of the coexisting in-phase and out-of-phase rotations) are missing. In fact, all the sharp spots can be indexed by a 2at × 2at × 2ct unit cell. The convergent-beam diffraction and parallel-beam microdiffraction patterns (Figure 7) recorded with the electron beam parallel to the c-axis also support the orthorhombic 2at × 2at × 2ct unit cell with the (001) diffraction group 2mm. Dark-field images recorded with the 212-type spots highlight antiphase boundaries separating domains a few hundred nanometers in size. In addition to the sharp spots, the SAED patterns contain sets of diffuse reflections near 100-type locations which appear as doublets split along the c-axis. Dark-field imaging using these doublets reveals a high number density of planar defects on the c-planes. Conceivably, these defects represent antiphase boundaries and/or twins associated with rotations of octahedra along the c-axis which form a sequence with a periodicity that is incommensurate with the fundamental lattice parameter thus giving rise to the doublets of spots in SAED. A consistent set of reflection conditions for the sharp spots can only be defined by assuming that the extra spots in the (001) patterns originate from the intersections of the diffuse rods associated with the incommensurate reflections with the (001) reciprocal lattice section. In this case, the reflection conditions are h0l: h,l = 2n; hkl: h + l = 2n; hk0: h,k = 2n, which would correspond to a B-centered cell. However, possible combinations of low-energy tilts identified from DFT calculations (see below) were considered but did not give models consistent with these reflection conditions. This may indicate combinations of more complex tilts occurring at shorter length scales.

Figure 6.

Figure 6

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SAED patterns collected at room temperature for CsNd2Ti2NbO10; superstructure reflections requiring a 2at × 2at × 2ct are highlighted by red ellipses.

Figure 7.

Figure 7

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(a) Electron microdiffraction and (b) convergent beam electron diffraction along [001]t for CsNd2Ti2NbO10, confirming an orthorhombic and not tetragonal structure and a 2at × 2at × 2ct unit cell with reflection condition h + k = 2n.

3.4. First-Principles Calculations

Following a similar procedure to that used to study CsBi2Ti2NbO10,20 we explored the energy landscape of CsLa2Ti2NbO10 and CsNd2Ti2NbO10 by condensing the main unstable phonons and their combinations. To identify instabilities in these systems, we computed the phonon dispersion curves of the high symmetry P4/mmm phase (Figure 8). Comparison with our previous study on CsBi2Ti2NbO1020 reveals similar dispersions for these La and Nd analogues, although fewer unstable modes are present. In addition, the polar branch (Γ5– → Z5–) is much less unstable for CsLn2Ti2NbO10 (Ln = La, Nd) than for the Bi analogue. This confirms that the nonspherical Bi3+ ion is a driving force to enhance ferroelectricity in the Dion-Jacobson systems.

Figure 8.

Figure 8

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Calculated phonon dispersion curves of CsLa2Ti2NbO10 (a) and CsNdTi2NbO10 (b) in their high-symmetry phase with space group P4/mmm. Negative frequencies correspond to imaginary eigenvalues of the dynamical matrix (unstable modes). The label of the unstable modes at zone center and zone boundary points (Γ5–, X3+, M5+, M3+, A5+, A3+, R3+, and Z5–) is represented on the plots close to their position. The lowest frequency X2+ and R2+ mode label positions are also shown.

However, the unstable modes of the P4/mmm phase cannot indicate which distortions will be dominant. To determine this, we performed single and coupled mode condensations to find which distortions gave the biggest energy gains. The results are reported in the Supporting Information and illustrated in Figure 9.

Figure 9.

Figure 9

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Schematic showing energy gains from different distortion modes and combinations of modes for CsNd2Ti2NbO10 from DFT calculations.

In general, the gains of energy for Nd and La analogues are noticeably smaller than those for CsBi2Ti2NbO10 for all distortions (octahedra rotations or in-plane polar/antipolar displacements), giving a much more shallow energy landscape for these two lanthanide analogues.

Considering first in-plane displacements (Γ5– and Z5–), it is striking that condensing these modes individually gives almost no energy gain in the case of CsLa2Ti2NbO10 (<3 meV/f.u.) and only a few tens of meV/f.u. in the case of CsNd2Ti2NbO10, while it is close to 800 meV/f.u. for CsBi2Ti2NbO10. This difference with Bi can be explained by the fact that polar structures are often favored by the presence of inert-pair Bi3+ ions, illustrated by BiFeO351 and Bi4Ti3O12,19,52 for example. The difference between La and Nd analogues (Nd favoring ferroelectricity more strongly than La) can be ascribed to steric (or geometric) ferroelectricity as reported in strongly ionic perovskites53 where small cation sizes enhance ferroelectricity (in contrast to conventional charge transfer ferroelectricity as in BaTiO3).53 This is confirmed by the computer experiment for the smaller Ln cation analogue where the energy gains of Γ5– and Z5– distortions are stronger than for Nd (but still smaller than for Bi, see data table in the Supporting Information), similar to results of calculations on the n = 2 DJ phases.16 In all these cases, the polarization is strongly dominated by Ln-O motions and not by the central B-cation of perovskite-like blocks, consistent with the optimization of the A cation coordination environment (in terms of sterics or electronic factors) driving these cation-displacement distortions.

The octahedral rotations (A5+, M5+, A3+, M3+, A1–, A2+; see the Supporting Information for illustrations) are the dominant distortions governing the crystal phases for Ln = La and Nd. The other Ln cases indicate that, as for bulk perovskites, smaller A-cations enhance the octahedral rotations such that the energy gain for these rotations increases with decreasing A cation size (i.e., it increases for La → Lu, see Figure 10 for the A5+ and A3+ modes) in the n = 3 DJ systems. The octahedra rotations are the dominant distortions in these n = 3 lanthanide systems, but when in-plane and out-of-plane rotations are present (such as A5+ with A1–, or M5+ with M1– for example), (hybrid)-improper ferroelectricity may be allowed by symmetry. However, this is in contrast with the Bi case where polar displacements (ferroelectricity) drive larger energy gains than octahedral rotations such that CsBi2Ti2NbO10 is much closer to a proper ferroelectric, while any polar nature of Ln = La and Nd analogues is mostly driven by an improper origin. (All the lowest energy phases found for La and Nd analogues from DFT calculations are predicted to be improper ferroelectrics.) We also note that the X3+ and R3+ modes (more complex rotations about an in-plane axis) give less energy gain than similar modes at M and A points. Likewise, the X2+ and R2+ modes (modes involving rotations of only outer octahedra about the out-of-plane axis) are low frequency modes in the DFT calculations but are not unstable. In all cases (Ln = Pm–Yb) but specifically for Ln = La, Pr, and Nd, rotations about an in-plane axis (A5+ and M5+ modes) give stronger energy gains than rotations about the out-of-plane axis (A3+ and M3+). The energy gain from A5+ rotations increases more dramatically than that for A3+ rotations with decreasing Ln size (Figure 10), so that A3+ dominates for larger La and Nd, while A5+ dominates for smaller ions. These rotations of octahedra occur to optimize cation coordination environments (particularly for the A cation in the perovskite layers) and to relieve strain in stacking the perovskite and A′ layers of different widths. A5+ modes might relieve stacking strain to a greater extent than A3+ modes and so become more significant as A cations decrease in size, in the presence of the large Cs+ ion on A′ sites. The low-energy phase of Pnma symmetry predicted by DFT calculations for CsNd2Ti2NbO10 (Figure 9) is consistent with the long-range, average structure proposed above from 20–600 K NDP data for CsNd2Ti2NbO10. It would be interesting to see the effect of smaller Rb+ ions of the A′ on the relative energies of the A3+ and A5+ modes.

Figure 10.

Figure 10

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Schematic showing calculated energy gains for A5+ (a–a–c0) and A3+ (a0a0c–) rotation modes and Γ5– (in-plane polar displacements) for CsLn2Ti2NbO10 for different Ln analogues from DFT calculations.

Consideration of the phonon dispersion for these n = 3 DJ phases indicates that there is a lack of dispersion between M (1/2 1/2 0) and A (1/2 1/2 1/2) points and between Γ (0 0 0) and Z (0 0 1/2). This highlights the limited structural connectivity along [001]t between successive perovskite-like blocks. As a consequence, often very similar energy gains are observed for different distortions, i.e., rotation modes that are in-phase from block to block (M modes) and those that are out-of-phase from block to block (A modes) give similar energy gains. (M modes are very slightly more stable for Ln = La, Nd, while A modes are slightly favored for Ln = Y, Bi, but these differences are very subtle.) This suggests that such DJ phases show similar behavior to the Srn+1TinO3n+1 Ruddlesden–Popper phases investigated by Birol et al. in which the rocksalt-like SrO layers break the connectivity between perovskite-like layers, reducing the out-of-plane correlation length of (polar) distortions and giving rise to a large number of degenerate, uncorrelated polar regions.15

3.5. Physical Properties

3.5.1. Dielectric Measurements

The dielectric response of CsLa2Ti2NbO10 and CsNd2Ti2NbO10 was measured (see the Supporting Information) and indicated that both ceramics are leaky (with frequency dispersion of tan δ). The permittivity measured was fairly low but increased with temperature as the ceramics became increasingly conducting. Within the temperature range measured (300–800 K), no maximum in permittivity was observed, and there was close agreement between data collected on warming and on cooling.

3.5.2. Second Harmonic Generation (SHG)

Second harmonic generation (SHG) measurements using 1064 nm radiation gave a phase-matcheable signal for CsLa2Ti2NbO10 (about 0.7 times that of KDP), while the SHG signal for CsNd2Ti2NbO10 was lower ∼0.2 times that of KDP) and is not phase matcheable (Figure 11). No laser damage was observed for either sample. These results indicate that both materials must adopt acentric structures, at least at the length scale probed by SHG measurements.

Figure 11.

Figure 11

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SHG signal as a function of particle size for (a) CsLa2Ti2NbO10 and compared with KDP and (b) for CsLa2Ti2NbO10 and CsNd2Ti2NbO10.

3.5.3. Optical Characterization

Diffuse reflectance measurements for CsLn2Ti2NbO10 (Ln = La, Nd) diluted in NaCl show a decrease in reflectance from ∼500 nm, although spectra recorded for CsNd2Ti2NbO10 are complicated by f-f transitions associated with Nd3+ (see spectra in the Supporting Information). The signal for both samples are relatively weak, and its hard to detect a sharp decrease in reflectance. However, after the Kubelka-Monk treatment, the spectra suggest an optical bandgap of ∼2.6(2) eV, similar to optical bandgaps reported for CsBi2Ti2NbO10 and for CsBiNb2O7 [3.0(1) eV and ∼3.4 eV, respectively].20,54

4. Discussion

The long-range, average structures described above for CsLn2Ti2NbO10 (Ln = La, Nd) share similarities with those reported for A′Bi2Ti2NbO10 (A′ = Cs, Rb),20,23 with the same B-site cation ordering and similar out-of-center displacements for these ions. For CsLn2Ti2NbO10, Ti4+ preferentially occupies the smaller and higher-symmetry central B(1) site, consistent with its size (six-coordinate ionic radii of 0.605 and 0.64 Å for Ti4+ and Nb5+, respectively).49 In common with many n = 3 layered perovskite-related materials, the B cations in the outer layers of the perovskite blocks in CsLn2Ti2NbO10 are displaced out-of-center toward the interblock layers, giving shorter B–O apical bond lengths, as reported previously for CsBi2Ti2NbO1020 and for n = 3 Aurivillius phases such as Bi2Sr1.4La0.6Nb2MnO12,55 Bi2Sr2Nb2.5Fe0.5O12,56 and Bi4Ti3O12.19 However, the noncentrosymmetric, polar structures reported for A′Bi2Ti2NbO10 (A′ = Cs, Rb)20,23 differ from the results of NPD analysis described here for CsLn2Ti2NbO10 (Ln = La, Nd). We will consider first the average structures for CsLn2Ti2NbO10 (Ln = La, Nd) and distortions that give rise to lower symmetry (polar) regions at shorter length scales, as well as the factors that give rise to the differing origins of polar behavior.

The most striking observation from our DFT calculations for CsLn2Ti2NbO10 (Ln = La, Nd) is the shallow energy landscape dominated by tilt distortions (Figure 9 and DFT results in the Supporting Information). That tilts are the most significant structural distortions is born out by the average structures determined from NPD analysis (with a disordered oxide sublattice observed for CsLa2Ti2NbO10 and longer-range correlations for CsNd2Ti2NbO10). In terms of the shallow energy landscape, Figure 9 illustrates that several tilt modes (including those about in-plane axes and those about [001]t) give similar energy gains, and the structural disorder observed experimentally likely arises from combinations of different tilts occurring in different regions and over different length scales. Our electron diffraction and dark field images show clear evidence of this.

Figure 10 also suggests that with decreasing Ln size, rotations about an in-plane axis (A5+ rotations) are increasingly favored, presumably to optimize Ln coordination without significant changes to the interlayer A′ cation coordination environment. A simple consideration of the packing of ions within the perovskite blocks can be quantified using the Goldschmidt tolerance factor t.57 (We note that for the DJ phases, this approach neglects their layered nature and any relaxations that might occur at the edges of the perovskite blocks). Values calculated for CsLn2Ti2NbO10 (t = 0.974 and 0.942 for Ln = La and Nd, respectively, assuming 3D perovskites of hypothetical composition Ln[Ti0.667Nd0.333)O3] suggest that distortions, such as octahedral rotations, are likely to occur to optimize bonding around the small Ln3+ ions.

The significance of octahedral rotations in CsLn2Ti2NbO10 (Ln = La, Nd) compared with displacive distortions contrasts with CsBi2Ti2NbO10. For the proper ferroelectric CsBi2Ti2NbO10, in-plane polar cation displacements form the primary order parameter for the paraelectric–ferroelectric phase transition at ∼820 K, giving the largest energy gains and are clear in the long-range average structure. For CsLn2Ti2NbO10 (Ln = La, Nd), octahedral rotations give the larger energy gains and are likely to drive any phase transitions and so are key to understanding physical properties.58

The lack of dispersion along [001]t in the DJ phases (see Figure 8 and similar results for CsBi2Ti2NbO1020) is more significant than in other layered perovskite-related systems (e.g., Ruddlesden–Popper12,15 and Aurivillius families), presumably due to the relatively weakly bound A′ ions between the perovskite-like blocks (giving the intercalation chemistry these phases are well-known for). This disrupts the correlation in octahedral rotations between blocks; with the similar energies of possible tilts, this gives increased structural disorder. For example, the disordered structure described above for CsLa2Ti2NbO10 and broad superstructure reflections (incompatible with the c glide present in models with A3+, A2+, and A1– tilts) at 700 K data for CsNd2Ti2NbO10 are consistent with disorder and shorter-range translational symmetry along [001]t within the oxide sublattice.

The average centrosymmetric structures determined from NPD analysis are inconsistent with the observed SHG activity for both samples. However, the lower symmetry structures suggested at shorter length scales by SAED (Figures 5–7), resulting from competition between similar energy tilts, could well include local noncentrosymmetric regions that are SHG active. The shallow energy landscape dominated by octahedral tilts that is revealed by our DFT calculations suggests the presence of short-range noncentrosymmetric regions (giving SHG activity) of a hybrid-improper nature (i.e., resulting from different combinations of octahedral rotations as the primary order parameter). We note that there have been reports of localized regions with polarization and octahedral tilts not observed on NPD length scales in Aurivillius phases,59−61 suggesting that disorder of the anion sublattice may be a factor in other families of layered perovskite-related materials.

Relaxor ferroelectrics, with frequency dispersion of their permittivity,62 are usually described in terms of polar nanoregions caused by modulations on the cation sublattice.63 Experimental and theoretical work on other layered materials has suggested a new class of relaxor ferroelectrics, “digital relaxors”.15,64 In these systems, it is the disorder on the oxide sublattice due to the relatively shallow energy landscape (giving several structures of similar energies due to the 2D nature of these materials with perovskite blocks relatively decoupled) that gives rise to short-range polar regions. The DJ family of materials have potential to display such behavior, and the implications for tuning properties are worth further study. Similarly shallow energy landscapes have been reported for hybrid-improper Ruddlesden–Popper systems and are suggested to influence phase-transition pathways between models with different combinations of tilts.65

Contrasting the behavior and structures of CsLn2Ti2NbO10 (Ln = La, Nd) with A′Bi2Ti2NbO10 (A′ = Cs, Rb)20,23 indicates that it is possible to tune between proper and hybrid-improper mechanisms in n = 3 Dion-Jacobson phases. The hybrid-improper mechanism in these n = 3 systems relies on more complex tilts that rotate only some octahedra in the perovskite blocks (such as A1– or M1– modes which rotate only octahedra in the outer layers) and can couple with rotations about an in-plane axis (such as A5+ or M5+ modes) to break inversion symmetry. Such tilt modes are not physical for n = 2 DJ phases, but a similar balance between mechanisms should still be possible and is hinted at in the relative energies of tilts versus displacements as a function of composition across the series A′ANb2O7 (A′ = Rb, Cs and A = Y, Nd, La, Bi).16 Recent high-resolution work on the Aurivillius phase Bi4Ti3O1219 highlights the importance of these more complex tilt modes and structures.

5. Conclusions

This combined experimental and computational study on the n = 3 DJ phases CsLn2Ti2Nb10 (Ln = La, Nd) highlights the hybrid-improper character of their polar nature, in contrast to CsBi2Ti2NbO10.20 This illustrates the ability to tune between proper and hybrid-improper mechanisms in this family of materials as the relative energies of tilt and displacement distortions are changed by composition. The shallow energy landscape revealed by DFT calculations, with little difference in energy between competing structures, is consistent with the structural disorder revealed by neutron and electron diffraction. These disorder and short-range noncentrosymmetric regions are key to understanding the properties (including second-harmonic generation) and have implications for designing functional materials with properties reliant on competing low energy phases such as relaxors and antiferroelectrics.

Acknowledgments

We are grateful to the NIST visiting researcher scheme and to the NCNR instrument scientists and support laboratories team for provision of beamtime, expertise, and assistance, and to Dr. P. Zajdel for assistance collecting NPD data. We thank funding agencies including the Royal Society (equipment grant RG130844, international exchange scheme IES\R3\170112), The Leverhulme Trust (RPG-2017-362), and EU Cost Action “Towards oxide-based electronics”. P.S.H. and W.Z. thank the Welch Foundation (grant E-1457) for support. Computational resources are provided by the Consortium des Equipements de Calcul Intensif (CECI) funded by the F.R.S-FNRS (Grant 2.5020.11) and the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles funded by the Walloon region (Grant 1117545). This research was supported by the HADES/MIDAS facility at the University of Sheffield established with financial support from EPSRC and BEIS, under Grant EP/T011424/1.66

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.0c03326.

  • Summary of distortions considered for n = 3 DJ phases, details of variable temperature NPD analysis for CsLa2Ti2NbO10, Pawley and Rietveld refinements using variable temperature NPD data for CsNd2Ti2NbO10, relative energies of distorted structures for CsLn2Ti2NbO10 (Ln = La, Nd, Y, Bi) calculated by DFT, dielectric measurements on CsLn2Ti2NbO10 (Ln = La, Nd), and optical characterization of CsLn2Ti2NbO10 (Ln = La, Nd) (PDF)

The authors declare no competing financial interest.

Supplementary Material

cm0c03326_si_001.pdf (993.3KB, pdf)

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