Phase Transition Behavior of the Layered Perovskite CsBi_0.6La_0.4Nb₂O₇: A Hybrid Improper Ferroelectric

Abstract

The phase behavior of the layered perovskite CsBi_0.6La_0.4Nb₂O₇, of the Dion-Jacobson family, has been studied by high-resolution powder neutron diffraction between the temperatures of 25 < T < 850 °C. At ambient temperature, this material adopts the polar space group P2₁am; this represents an example of hybrid improper ferroelectricity caused by the interaction of two distinct octahedral tilt modes. Within the limits of our data resolution, the thermal evolution of the crystal structure is consistent with a first-order transition between 700 and 750 °C, with both tilt modes vanishing simultaneously, leading to the aristotype space group P4/mmm. This apparent “avalanche transition” behavior resembles that seen in the related Aurivillius phase SrBi₂Nb₂O₉.

1. Introduction

Recent theoretical work has revealed novel mechanisms for designing non-centrosymmetric, polar and potentially ferroelectric materials, based on the coupling of two or more distinct structural distortions (“modes”) [1,2,3,4]. So-called “hybrid improper ferroelectrics” (HIFs) have now been postulated for several families of layered perovskites, by the coupling of two distinct “octahedral tilt” modes with a polar mode. Although octahedral tilting has been a well-established phenomenon in perovskite crystallography for many years [5,6,7], in simple three-dimensional ABX₃ perovskites all the simple octahedral tilt schemes (as classified by Howard and Stokes [7]) give rise to strictly centrosymmetric crystals. It is now recognized that in more complex cases, for example cation-ordered or layered perovskites, inversion symmetry may be broken directly by particular combinations of octahedral tilt modes. The concept of HIFs has been typically applied by theorists to mean the imposition of a stable polar ground state in a crystal via the coupling of two or more intrinsically non-polar modes with a polar mode (“tri-linear coupling”), with no requirement for an experimentally-realized polarization reversal. However, such experimental demonstrations of polarization-field hysteresis have now been reported, for example in the Ruddlesden-Popper (RP) phase Ca₃Ti₂O₇ [8] and the Dion-Jacobson (DJ) phase RbBiNb₂O₇ [9].

Prior to the recent flurry of work from the theoretical standpoint, it was known that ferroelectricity, or at least polarity, co-existed with octahedral tilting in several layered perovskites, the most well-established being the Aurivillius family, exemplified by SrBi₂Ta₂O₉ and Bi₄Ti₃O₁₂ [10]. Snedden et al. [11] later made the intuitive link between the nature of octahedral tilting in the DJ phase CsBiNb₂O₇ and that in SrBi₂Ta₂O₉; both have a tilt system analogous to that described by the Glazer notation a⁻a⁻c⁺ in ABX₃ perovskites. This leads to related superlattices and space groups in both SrBi₂Ta₂O₉ and CsBiNb₂O₇, viz. superlattices of ~√2a_t x √2a_t x c_t relative to the aristotype tetragonal phase in each case, and polar space groups A2₁am and P2₁am in SrBi₂Ta₂O₉ and CsBiNb₂O₇, respectively. The nature of these superlattices and the allowed space groups of the possible distorted structures may be systematized by considering which particular distortion modes give rise to the specific tilts within each family of layered perovskites. So, for example, the “out-of-phase tilt”, a⁻a⁻c⁰, and the “in-phase tilt”, a⁰a⁰c⁺, correspond to the modes with irreducible representations M₅⁻ and M₂⁺, respectively, for the DJ phases of the type AA’B₂O₇, for which the parent phase is described in space group P4/mmm (these are “n = 2” examples of the generic DJ composition AA’_n−1B_nO_3n+1, with n representing the number of octahedral layers per perovskite-like block). The coupling of the two modes leads naturally to the polar space group P2₁am for CsBiNb₂O₇ and, in principle, permits ferroelectricity. These ideas have been described in more detail by Benedek et al. [3,4].

Although the a⁻a⁻c⁺ tilt system is predicted to be a stable option for DJ phases of the type AA’B₂O₇, recent experimental work has shown that other related polymorphs are possible, and a tilt system a⁻b⁰c⁺, in polar space group Amm2, has been reported in CsLaNb₂O₇ in the range 350 < T < 550 K [12] (curiously an earlier single crystal X-ray study of CsLaNb₂O₇ reported the adoption of the aristotype tetragonal structure, P4/mmm at 296 K [13]). Moreover, a recent experimental and theoretical study of the triple-layer DJ phase CsBi₂Ti₂NbO₁₀ has suggested that a proper rather than improper mechanism drives the polarity of the ambient temperature phase [14]. It is therefore of interest to explore more fully the phase behavior of further examples of the DJ family in order to map out the occurrence of the possible tilt systems, especially those giving rise to polarity, and also the nature of phase transitions in these systems as a function of T.

In our earlier work [11], it was established that both CsBiNb₂O₇ and CsNdNb₂O₇ adopted the polar P2₁am space group at ambient temperature, with the latter composition displaying a much reduced orthorhombic distortion relative to the former. Later, Fennie and Rabe predicted ferroelectricity in CsBiNb₂O₇ from a first-principles DFT study [15]. Our follow-up experimental studies [16] on CsBiNb₂O₇ suggested that ferroelectricity was hindered by moisture uptake, leading to proton conductivity and leakage. Nevertheless, a more recent work by Chen et al. [17] did provide experimental evidence for ferroelectricity in this compound. Goff et al. [16], attempted to determine any high temperature phase transitions in CsBiNb₂O₇ using powder neutron diffraction: no evidence for phase transitions was identified up to 900 °C, above which sample deterioration precluded further study. By analogy with CsNdNb₂O₇, we speculated that La-doping of CsBiNb₂O₇ would reduce the orthorhombic distortion such that any phase transition to higher symmetry might be brought down in temperature relative to that of CsBiNb₂O₇, and make this transition more amenable to experimental study.

In this paper, we report the phase behavior of CsBi_0.6La_0.4Nb₂O₇; this composition was chosen since CsBiNb₂O₇ and CsLaNb₂O₇ have been shown to adopt different phases at ambient temperature, and it was anticipated that a phase transition(s) might be observable within a reasonable temperature regime.

2. Results

Ambient temperature structure: Preliminary studies focused on the solid solution CsBi_1−xLa_xNb₂O₇ (see Supplementary Information), which is confirmed to exist for all compositions, 0 < x < 1. The x = 0.4 composition, i.e., CsBi_0.6La_0.4Nb₂O₇, was chosen for further study by high-resolution powder neutron diffraction. Initial analysis of the room-temperature powder neutron diffraction (PND) data assumed the P2₁am model previously identified for CsBiNb₂O₇ [11]. Rietveld refinement suggested this model to be correct, with an excellent fit, accounting for all observed peak splittings and superlattice peaks (Figure 1). However, in order for this assignment to be unambiguous, other options need to be considered. There are two aspects to this: first, the unit cell metrics need to be determined and second, the nature of any characteristic superlattice peaks (especially those arising from octahedral tilting) needs to be established.

Considering the unit cell metrics first: the possible superlattice options to be considered are either an approximate doubling or quadrupling of the unit cell in the ab plane; i.e., a ~ b ~ √2a_t or a ~ b ~ 2a_t. Superlattices along the c-axis are not considered in the simplest scheme (and are not necessary in this case). These two options can easily be distinguished based on related peak splittings observed in the experimental PND data: the √2a_t metric splits peaks of the type (hhl) in the parent tetragonal phase, whereas the 2a_t metric splits peaks of the type (h0l/0kl). Specific peaks labelled in Figure 1 confirm unambiguously that an orthorhombic (or lower) symmetry unit cell of metrics a ~ b ~ √2a_t, c ~ c_t, is required to account for all the observed peak splittings.

Strayer et al. [12] listed all models corresponding to the simple combinations of octahedral tilts for this structural family (see Supplementary information in Reference [12]). Specifically, the definition of simple combinations here means that there are four distinct octahedral tilts modes to be considered, viz. in-phase and out-of-phase tilts of two adjacent octahedra along the a (and/or b) and c axes of the parent tetragonal unit cell. These four modes are given the Glazer-like symbols a⁺ (or b⁺) and c⁺ for the respective in-phase tilts and a⁻ (b⁻) and c⁻ for the out-of-phase tilts. In turn, these distortions give rise to superlattice peaks in the diffraction pattern at characteristic points, labelled M (k = ½, ½, 0) or X (k = 0, ½, 0) relative to the parent tetragonal reciprocal lattice. The specific modes corresponding to each of the four possible tilts are X₁⁺ (a⁺), M₅⁻ (a⁻) M₂⁺ (c⁺) and M₄⁻ (c⁻). The nature of these modes and their effect on the diffraction pattern can be probed using the on-line software ISODISTORT [18]. The X-point mode can be easily ruled out (no peaks are visible at the relevant positions), but the M-point modes provide some ambiguity, as they may contribute to many of the same superlattice peaks. In fact, closer inspection of the allowed superlattice intensities from each of the M-point modes reveals that the M₄⁻ mode can also be ruled out: we also note that neither the X₁⁺ nor the M₄⁻ modes were considered in the earlier theoretical studies [3,15]. The M₅⁻ mode is certainly required, as it is the only contributor to certain peaks (for example the one near d ~ 2.5 Å). The M₂⁺ mode contributes to several observed peaks (for example those near d ~ 2.4 Å), but the M₅⁻ mode may also contribute to those.

Table 1. Example models based on combinations of octahedral tilt modes (adapted from Strayer et al. [12].)

Glazer Notation	Active Modes	Space Group	Metrics
a0a0c0	None	P4/mmm	at x at x ct
a0a0c+	M2+	P4/mbm	√2at x √2at x ct
a0a0c−	M4−	P4/nbm	√2at x √2at x ct
a+a+c0	X1+	P4/mmm	2at x 2at x ct
a−a−c0	M5−	Pmam	√2at x √2at x ct
a−a−c+	M2+ $⨂$ M5−	P21am	√2at x √2at x ct
a−b0c0	M5−	Cmmm	2at x 2at x ct
a−b0c+	M2+ $⨂$ M5−	Amm2 *	ct x 2at x 2at
a−b−c0	M5−	P2/m	√2at x ct x √2at
a−b−c+	M2+ $⨂$ M5−	Pm	√2at x ct x √2at

* C2mm setting for c corresponding to c_t.

lists an abbreviated selection of the possible octahedral-rotation-induced superlattices of Strayer et al. Taking into account the requirement of a √2a_t x √2a_t x c_t orthorhombic metric and the presence of at least the M₅⁻ mode (and also possibly the M₂⁺ mode) reveals the only plausible models are the P2₁am and Pmam ones, as suggested by Snedden et al. [11] for CsBiNb₂O₇. In particular, the Amm2 model observed for CsLaNb₂O₇ can be ruled out in the present case. In order to confirm P2₁am as the correct model for CsBi_0.6La_0.4Nb₂O₇ at ambient temperature, a comparative refinement against the Pmam model was carried out. This led to agreement factors of χ² ~ 5.870 and 9.081, for the P2₁am and Pmam models. P2₁am is therefore selected as the best model at ambient T. The corresponding crystal structure is shown in Figure 2, refined atomic parameters are given in

Table 2. Refined structural model for CsBi_0.6La_0.4Nb₂O₇ at 25 °C. Space group P2₁am, a = 5.49618 (14), b = 5.46012 (14), c = 11.3254 (3) Å.

Atom	Wyckoff Position	x	y	z	100 * Uiso (Å2)
Cs1	2b	0.3349 (17)	0.2579 (12)	0.5	2.08 (10)
Bi/La1 *	2a	0.367	0.2692 (8)	0.0	2.91 (11)
Nb1	4c	0.3334 (10)	0.7540 (6)	0.20533 (14)	0.56 (7)
O1	2a	0.321 (2)	0.6892 (9)	0.0	2.83 (15)
O2	4c	0.3272 (12)	0.7812 (7)	0.3574 (2)	1.66 (9)
O3	4c	0.0869 (15)	0.0104 (12)	0.1589 (3)	3.10 (13)
O4	4c	0.5290 (11)	0.4590 (8)	0.1840 (3)	2.25 (13)

* fixed occupancy Bi_0.6La_0.4; the x-coordinate is fixed to define the origin of the polar axis.

and selected bond lengths in

Table 3. Selected bond lengths (Å) for CsBi_0.6La_0.4Nb₂O₇ at 25 °C in the P2₁am model.

Cs-O	Bond Length (Å)	Bi/La-O	Bond Length (Å)	Nb-O	Bond Length (Å)
Cs1-O2 × 2	3.063 (7)	Bi1-O1	2.307 (7)	Nb1-O1	2.3531 (19)
Cs1-O2 × 2	3.158 (10)	Bi1-O1	2.508 (12)	Nb1-O2	1.730 (3)
Cs1-O2 × 2	3.231 (10)	Bi1-O3 × 2	2.651 (6)	Nb1-O3	1.968 (9)
Cs1-O2 × 2	3.282 (7)	Bi1-O3 × 2	2.758 (6)	Nb1-O3	2.018 (8)
		Bi1-O4 × 2	2.492 (4)	Nb1-O4	1.952 (6)
				Nb1-O4	2.052 (6)

.

Structural Evolution Versus T: The continued presence of orthorhombic distortion can easily be determined on raising the temperature, by tracking the O peak splittings highlighted in Figure 1. However, since the M-point superlattice peaks are very weak, even at ambient temperature, it is problematic to use a simple qualitative visual observation of these as a single reliable measure of the structural distortions versus T. Instead, full comparative Rietveld refinement of the structure in both P2₁am and Pmam models is the preferred method of discrimination (since the tilts significantly affect the intensities of the subcell peaks, in addition to the supercell peaks). Both models were therefore refined against each data set up to 725 °C, taking care to use a consistent set of parameters throughout (see Experimental). At 700 °C the orthorhombic splitting is still clearly seen in the raw data, but at 725 °C the splitting disappears, and the unit cell becomes metrically tetragonal (Figure 3). The parent P4/mmm model was therefore trialed at 725 °C and above, with a further check on the alternative possible tetragonal model, P4/mbm (a⁰a⁰c⁺, Table 1) at 725 °C only. In addition to tracking the comparative fit quality for the two orthorhombic models, ISODISTORT was used to derive the mode amplitudes versus T. Thermal evolution of the unit cell parameters is given in Figure 4, and for the distortion modes in Figure 5. Comparative goodness-of-fit parameters (χ²) for the P2₁am and Pmam models are given in Figure 6.

The difference in χ² values clearly supports the assignment of the P2₁am rather than the Pmam model up to 700 °C (χ² values are 2.055 and 2.273 for P2₁am and Pmam, respectively, at 700 °C). In addition, the tilt mode amplitudes (Figure 5) tend towards zero, but do not become zero, at 700 °C. The negligible difference in fit quality between the four models tested at 725 °C (χ² values 2.065, 2.054, 2.041 and 1.883 for P4/mmm, P4/mbm, Pmam and P2₁am, respectively) supports the absence of both tilt modes at this temperature (we note that the refinement in the P2₁am model was unstable to the refinement of thermal parameters, thus a direct comparison is not possible). Although the unit cell volume has no clear discontinuity within the temperature resolution of our datasets, the fact that the polar mode Γ₅⁻ seems to have a step-like change at the transition may indicate the existence of a first-order component.

We attempted to fit the thermal evolution of the tilt modes, M₂⁺ and M₅⁻, to critical behavior of the form: amplitude = A (T_c − T)^β. This produced the fit parameters of A = 0.0292, 0.227; T_C = 749, 742 °C; β = 0.401, 0.127 for the M₂⁺ and M₅⁻ modes, respectively. The key observation here is that the derived value of T_C is approximately equal for the two modes, implying that they condense simultaneously. Unfortunately, the paucity of data in the vicinity of T_C prohibits a definitive conclusion about the exact T_C and β values, and also the specific mode which drives the transition. However, further support for our crystallographic model comes from a measurement of dielectric properties versus T. Figure 7 shows a single dielectric maximum just below 750 °C, with no evidence of any lower temperature anomalies. This supports an abrupt, single phase transition, as was observed crystallographically.

Taken together, these observations suggest a direct to transition from P2₁am to P4/mmm in the vicinity of 700–750 °C; we note that Landau theory requires the direct P2₁am to P4/mmm transition to be first-order, whereas the Pmam to P4/mmm transition is allowed to be continuous. Hence, the most likely scenario, which is also compatible with the present data, is that both tilt modes are lost simultaneously, with no substantial evidence for an intermediate phase of symmetry Pmam or P4/mbm (Table 1). The final refined model in P4/mmm at 750 °C is given in

Table 4. Refined structural model for CsBi_0.6La_0.4Nb₂O₇ at 750 °C. Space group P4/mmm, a = 3.92282 (16), c = 11.4138 (5) Å.

Atom	Wyckoff Position	x	y	z	100 * Uiso (Å2)
Cs1	1b	0.0	0.0	0.5	7.09 (13)
Bi/La1 *	1a	0.0	0.0	0.0	7.17 (16)
Nb1	2h	0.5	0.5	0.20414 (16)	2.13 (9)
O1	4i	0.0	0.5	0.17054 (17)	5.56 (10)
O2	2h	0.5	0.5	0.3555 (3)	6.44 (13)
O3	1c	0.5	0.5	0.0	7.20 (17)

* fixed occupancy Bi_0.6La_0.4.

and

Table 5. Selected bond lengths (Å) for CsBi_0.6La_0.4Nb₂O₇ at 750 °C in the P4/mmm model.

Cs-O	Bond Length (Å)	Bi/La-O	Bond Length (Å)	Nb-O	Bond Length (Å)
Cs1-O2 × 8	3.2273 (14)	Bi1-O1 × 8	2.7634 (14)	Nb1-O1 × 4	1.9985 (5)
		Bi1-O3 × 4	2.77385 (11)	Nb1-O2	1.727 (4)
				Nb1-O3	2.3300 (18)

.

3. Discussion and Conclusions

The present study indicates, within the temperature resolution of our data, a direct first-order transition from the parent, untilted phase, P4/mmm, to the observed ambient temperature phase, P2₁am (tilt system a⁻a⁻c⁺). This requires the simultaneous condensation of the two tilt modes M₅⁻ (a⁻a⁻c⁰) and M₂⁺ (a⁰a⁰c⁺), which couple with the polar mode, Γ₅⁻. This special case of tri-linear coupling has been termed an “avalanche transition” [19]. Due to the temperature increments used in this experiment, we cannot fully rule out a possible intermediate phase of symmetry Pmam or P4/mbm but, if present, this must only exist in a narrow temperature interval around 700 to 750 °C. Avalanche transitions are rare, but such a transition has been confirmed in the Aurivillius phase ferroelectric, SrBi₂Nb₂O₉ [20,21], which also displays the tilt system a⁻a⁻c⁺. It has been suggested that SrBi₂Nb₂O₉ differs from its analogue SrBi₂Ta₂O₉, which does display an intermediate phase (tilt system a⁻a⁻c⁰), because the magnitudes of the three necessary distortion modes in the ground state (i.e., ambient temperature) polar phase are relatively similar, rather than one tilt mode being dominant [21]. In their detailed study of CsLaNb₂O₇, Strayer et al. [12], reported a tilt system a⁻b⁰c⁺ (space group Amm2, Table 1) between 550 and 350 K. This phase also requires the condensation of both the M₂⁺ and M₅⁻ tilt modes, but differs from the present P2₁am phase in the direction of the M₅⁻ mode. It might also be expected that an intermediate phase would be observed in the P4/mmm to Amm2 pathway seen in CsLaNb₂O₇; i.e., via the sequential loss of either M₅⁻ then M₂⁺, or vice versa. The corresponding intermediate phases (Table 1) in that case would be a⁰a⁰c⁺ (P4/mbm) or a⁻b⁰c⁰ (Cmmm). Strayer et al. ruled out these pathways by the observation of a clear SHG signal, signifying non-centrosymmetricity, and thus implying an avalanche transition in this composition also. As the present study represents the only detailed crystallographic study so far of the tilt transitions concerning a verified P2₁am phase (a⁻a⁻c⁺) in the n = 2 DJ family, it remains to be seen whether such avalanche transitions are common in the DJ family.

4. Experimental Section

4.1 Synthesis

A phase pure sample of CsBi_0.6La_0.4Nb₂O₇ was prepared using traditional ceramic methods. Stoichiometric amounts of La₂O₃ (99.9% Sigma-Aldrich, Dorset, UK, Nb₂O₅ (99.9% Alfa Aesar, Lancashire, UK) and a 20% excess of Cs₂CO₃ (99% Alfa Aesar, Lancashire, UK) were dried at 100 °C for 24 h. The loose powders were ground for a period of 30 min and pressed into pellets of approximately 10 mm diameter and 5 mm thickness. The pellets were annealed at 1000 °C for a period of 24 h with a cooling rate of 10 min⁻¹.

4.2 Powder Diffraction

Sample purity was gauged by preliminary X-ray diffraction using a PANalytical Empyrean (Cu K_α1 radiation).

Neutron powder diffraction (NPD) was performed at beamline HRPD (High resolution powder diffractometer), ISIS facility, Oxfordshire, UK. A sample of approximately 5 g was placed in an 8-mm cylindrical vanadium can before loading into the diffractometer vacuum furnace. Patterns were collected at room temperature, and then at 100 intervals between 200–800 °C with a final data collection at 850 °C, each data collection lasting approximately 3.5 h, with the exception of the data collections at 600 and 700 °C (which lasted approximately 2 h). Intermediate patterns were collected at intervals of 10 between 810 and 840 °C, and 25 intervals between 725 and 775 °C, each data collection lasting approximately 25 min.

Rietveld refinement was performed using GSAS [22] and the EXPGUI interface [23]. The same set of standard parameters were used, including 3, 3, 21 and 5 parameters to model instrumental variables, scale factors, background and peak-shape for each dataset in the region of RT to 700 °C. The same refinement strategy was employed for the remaining high temperature datasets, except that the number of background terms was decreased from 21 to 18. A significant contribution from the vanadium sample can was seen throughout and this was fitted as a secondary phase at each temperature.

4.3 Dielectric Measurements

Pellets were electroded with sputtered Au before being coated with Ag paste (RS components). Dielectric measurements were made using a Wayne Kerr 6500B impedance analyzer with the sample mounted in a tube furnace. Capacitance and loss data were recorded in the frequency range of 100–10 MHz at a heating and cooling at a rate of 2 K min⁻¹ over the temperature range of 50 to approximately 750 °C. Data collected on the cooling cycle are described here, since the heating cycle showed an additional anomaly due to the failure of the Ag paste (which is used to protect the Au electrode). Nevertheless, there was no evidence for hysteresis during the heating/cooling cycle.