Perovskite B-Site Compositional Control of [110]p Polar Displacement Coupling in an Ambient-Pressure-Stable Bismuth-based Ferroelectric

Piezoelectrics are key functional materials in actuator and sensor applications.1 Current technology exploits lead-based materials displaying a morphotropic phase boundary (MPB) between two ferroelectric solid solutions of different symmetries and polarization directions. This is best exemplified by the PbZr1−xTixO3 (PZT) perovskite system where the distortions driving the piezo response are produced by the stereo-active electron lone pair of the Pb2+ cation on the A site of the ABO3 perovskite structure.2 Due to the environmental impact of lead, there is a considerable focus on the synthesis of lead-free electroceramics. It is not however clear if the complex crystal chemistry underlying the structural phase boundaries at the MPB in lead-based systems can be simply translated into lead-free analogues. In particular the balance between distortions driven by the A and B site cations and the role of octahedral tilting and tolerance factor considerations are expected to be quite different in non-lead systems, as Pb2+ is significantly larger than the more highly charged Bi3+ often considered as an alternative polarization-generating cation.3 However, the smaller size of bismuth ions generally requires high-pressure synthesis conditions to form a perovskite. Only a small group of known perovskites exist with A-site bismuth cations that are stable at ambient pressure, based on BiFeO3,4 Bi2Mn4/3Ni2/3O6,5 and Bi(Fe2/8Ti3/8Mg3/8)O3 (BFTM).6 Bi2Mn4/3Ni2/3O6 is antiferrodisplacive,5 while both BiFeO3 and BFTM adopt the R′ R3c structure where the [111]p displacements of untilted R (space group R3m in the PZT case) are coupled with octahedral rotation about the same axis (the prime symbol denotes the presence of tilts). In order to access MPBs, polar structures with distinct polarization directions away from [111]p in these Bi-based families are required.

Piezoelectrics are key functional materials in actuator and sensor applications. [1] Current technology exploits lead-based materials displaying a morphotropic phase boundary (MPB) between two ferroelectric solid solutions of different symmetries and polarization directions. This is best exemplified by the PbZr 1Àx Ti x O 3 (PZT) perovskite system where the distortions driving the piezo response are produced by the stereo-active electron lone pair of the Pb 2+ cation on the A site of the ABO 3 perovskite structure. [2] Due to the environmental impact of lead, there is a considerable focus on the synthesis of lead-free electroceramics. It is not however clear if the complex crystal chemistry underlying the structural phase boundaries at the MPB in lead-based systems can be simply translated into lead-free analogues. In particular the balance between distortions driven by the A and B site cations and the role of octahedral tilting and tolerance factor considerations are expected to be quite different in non-lead systems, as Pb 2+ is significantly larger than the more highly charged Bi 3+ often considered as an alternative polarizationgenerating cation. [3] However, the smaller size of bismuth ions generally requires high-pressure synthesis conditions to form a perovskite. Only a small group of known perovskites exist with A-site bismuth cations that are stable at ambient pressure, based on BiFeO 3 , [4] Bi 2 Mn 4/3 Ni 2/3 O 6 , [5] and Bi(Fe 2/8 -Ti 3/8 Mg 3/8 )O 3 (BFTM). [6] Bi 2 Mn 4/3 Ni 2/3 O 6 is antiferrodisplacive, [5] while both BiFeO 3 and BFTM adopt the R' R3c structure where the [111] p displacements of untilted R (space group R3m in the PZT case) are coupled with octahedral rotation about the same axis (the prime symbol denotes the presence of tilts). In order to access MPBs, polar structures with distinct polarization directions away from [111] p in these Bi-based families are required.
We investigated the pseudoternary phase field BFTM-LaFeO 3 (LFO)-La 2 MgTiO 6 (LMT) where the introduction of LFO (tolerance factor t = 0.95) would alter the average structural asymmetry on the A site by combining the aspherical Bi 3+ and spherical La 3+ cations, and the addition of Mg 2+ and Ti 4+ from LMT (t = 0.95) on the B site would reduce the dielectric loss caused by the increase in Fe 3+ content. LFO adopts the Pmnb structure of GdFeO 3 with an a + b À b À tilt system and 0.18 antiferrodistortive La 3+ displacements along the [110] p direction. LMT (P2 1 /a) has the same A-site displacement pattern and tilt system plus rock salt ordered B-site cations. [7] Phases in the BFTM-LMT-LFO (BLFTM) field (Figure 1 a) were prepared according to the protocol set out in Section 1 of the Supporting Information. Four distinct classes of powder diffraction patterns are observed. BFTM (t = 0.96) is the only material with the rhombohedral R3c space group, and is surrounded by a two-phase region. At low LFO content and along the BFTM-LMT line, an orthorhombic perovskite phase and an Aurivillius phase coexist (XRD data Figure S1, Supporting Information). However, single phases emerge at higher substitution levels. These phases adopt the nonpolar Pmnb structure at high LFO/LMT content, but a new orthorhombic phase emerges between the Pmnb and multiphase regions, as shown by the evolution of the lattice parameters along the (1Àx)BFTM-xLFO line in Figure 1 b. Powder second harmonic generation (SHG) measurements [8] show that the non-Pmnb BLFTM samples are non-centric (x = 0.28, 0.37, 0.40, 0.42), whereas the Pmnb materials (x = 0.5, 0.67) are centric as expected. Thin films can be grown by pulsed laser deposition (Section 5, Supporting Information).
The The Pmc2 1 structure of 0.72BFTM-0.28LFO (Section 3.1, Supporting Information) is adopted at low temperature by the high-pressure form of the B-site-driven CdTiO 3 ferroelectric, [9] (though more recent neutron diffraction studies have cast doubt on this [10] ), the high field form of NaNbO 3 [11] and sol-gel synthesized NaNbO 3 . [12] There are one B site and two A sites in the asymmetric unit, with the Rietveld refinement showing no indication of Bi/La cation ordering. The two A sites are arranged in alternating layers along a (Figure 3  There are also small (< 0.05 ) antiferrodistortive displacements at both A sites along b and c and at the B site along a (Figure 3 d). The ionic polarization calculated [13] from the refined structure is 30.6 mC cm À2 .
Measurement of the synchrotron X-ray and neutron powder diffraction patterns as a function of temperature reveals a structural phase transition from Pmc2 1 to Pmnb above 650 AE 5 8C ( Figure S6). This structure (Section 3.2, Supporting Information) maintains the a + b À b À tilt system of Pmc2 1 . There is only one crystallographically distinct A site, which is displaced 0.08 antiferrodistortively along [110] p and no B-site displacement.
The atomic displacements for the polar Pmc2 1 BLFTM structure and the high-temperature (HT) Pmnb phase can be understood in terms of distortion modes derived from the  Pm " 3m a p aristotype cell, evaluated with the Isodisplace [14] and Amplimodes [15] programs (for further details and mode amplitudes see Section 3.3, Supporting Information). Pmnb (basis = {(2,0,0),(0,1,À1)(0,1,1)}, origin = (0,0,0)) is produced by the R 4 + (Figure 4 b) antiphase a 0 b À b À and in-phase M 3 + ( Figure S8a) a + b 0 b 0 octahedral tilts which are the most significant modes. The associated antiferrodistortive A-site displacements along c, 0.08 from the centroids of their coordinating oxygens, are from the X 5 + mode [16] (Figure 4 c), giving the observed single A-site structure. The Pmc2 1 phase (basis = {(2,0,0),(0,1,À1)(0,1,1)}, origin = ( 1 = 2 , 1 = 2 ,0)) is driven by the onset of the dominant G 4 À polar displacement at the A and B sites (Figure 4 a). This ferroelectric displacement is along [110] p , as in the Amm2 (O) phase of BaTiO 3 [17] and the high-field form of PbZrO 3 . [18] In-phase combination of this ca. 0.22 magnitude polar displacement with the 0.08 antiferrodistortive displacement (X 5 + mode) present in the Pmnb precursor affords the 0.31 displacement at the A1 site, while the out-of-phase combination gives the 0.14 polar displacement at the A2 site along the [110] p direction. The small A-site antiferrodisplacive R 5 + mode ( Figure S8b) along b is unchanged between Pmnb and Pmc2 1 . There is a single B site in Pmc2 1 with the G 4 À -driven polar displacement along c accompanied by a smaller antiferroelectric displacement along a from the X 3 À mode (Figure 4 d). Only one B site results because the ferroelectric and antiferroelectric displacement directions are perpendicular.
Electrical properties of BLFTM were measured on 97 + % dense ceramics, with dielectric loss reduced by the addition of 0.2 wt % MnO 2 , [19] which lowers tan d from 0.036 to 0.025 at 1 kHz and from 0.589 to 0.034 at 1 Hz for 0.72BFTM-0.28 LFO. The low-frequency loss (Figure 5 a) is comparable to other shared A-site Bi-based ferroelectrics for example, Na 0.5 Bi 0.5 TiO 3 (> 0.05 at 1 kHz). [20] 0.625BFTM-0.25LFO-0.125LMT has the lowest tan d, suggesting that LMT is particularly effective in reducing the loss. All the Pmc2 1 [110] p displaced materials have higher permittivities than [111] p displaced rhombohedral BFTM, and the broad step-like decrease in permittivity for BFTM above 1 kHz, suggestive of a relaxation phenomenon, is not observed in the new polar phase. The magnitude of the relative permittivity rules out the possibility of contributions from extrinsic charge carriers at grain boundaries or electrode-sample interfaces. [21]  . Displacement components (0, À0.09 , 0.31 ) in the unit cell reference frame. f) Coordination environment of the A2 cation. This site has three short contacts (blue) and nine which are less distinctly separated than for A1, divided here into six bonds between 2.6 and 3 (green) and three bonds longer than 3 (black). Displacement components (0, À0.03 , 0.17 ). g) B-site octahedral environment. Displacement components: (À0.06 , 0.009 , 0.14 ). The polarity shown in the structure and SHG measurements was confirmed by measurements of piezoelectric behavior. Strain-field measurement on Pmc2 1 0.72BFTM-0.28LFO (Figure 5 d) shows a butterfly loop, with a negative strain component. This negative strain is related to domain back-switching during the bipolar cycles and demonstrates typical ferroelectric behavior. [22] The coercive field, calculated from the minimum in the strain field plot, is equal to 62 kV cm À1 . The calculated strain is 0.003 % and the high-field d 33 value obtained from the strain-field measurements is 1.68 pC N À1 . The measured piezoelectric coefficient is 0.25 pC N À1 .
It was not possible to obtain a saturated P(E) (P = polarization, E = electric field) hysteresis loop before dielectric breakdown, which is a common problem in BiFeO 3 ceramics. [23] This can be attributed to a high Curie temperature and coercive field. The best P(E) loop came from the Pmc2 1 structure composition 0.625BFTM-0.25LFO-0.125LMT (Figure 5 b). Although the loop is not saturated, electrical polarization does not evolve as a linear function of the driving-field amplitude indicating nonlinearity (a necessity for ferroelectrics) and therefore domain wall motion. [24] P(E) for 0.72BFTM-0.28LFO (Figure 5 c) is not saturated but shows non-linearity, indicating the presence of domain wall motion, consistent with the strain-field measurement on this composition. Figure 6 represents the A-site displacements in polar structures derived from the ideal perovskite, with the effect of octahedral tilting in systems containing smaller A cations than Pb 2+ evident. The O' Pmc2 1 structure found here corresponds to the polarization direction changing from [111] p in the R' parent phase BFTM to [110] p , driven by the substitution of La 3+ onto the A site, because of the tilts and displacements in this direction in LaFeO 3 . La 3+ substitution into R' BiFeO 3 also induces [110] p A-and B-site displacements, but in this case the displacements are coupled antiferrodistortively to produce the antiferroelectric PbZrO 3 structure (Figure 6; O A ' denotes a tilted antiferroelectric structure). [25] The striking difference in the coupling of the [110] p displacements in the present BLFTM case may arise from the presence of Mg 2+ and particularly Ti 4+ on the B site in the BFTM parent, as Ti 4+ produces ferroelectric [110] p displacements in O BaTiO 3 . [17] The O' structure features two A sites with distinct polarizations because of the competition between La-driven [110] p antiferrodisplacive motions and the dominant ferroelectric displacements along the same direction driven by Bi 3+ and Ti 4+ , reflecting structural frustration between the bonding preferences of the two A-site cations. In the present BLFTM system, the O' structure is separated by two-phase regions involving non-perovskite impurities from the R' structure, and bridging this phase gap is important in the search for enhanced functionality associated with potential phase boundaries differing in polarization direction.