Morphotropic Phase Boundary in the Pb‐Free (1 − x)BiTi_3/8Fe_2/8Mg_3/8O₃–xCaTiO₃ System: Tetragonal Polarization and Enhanced Electromechanical Properties

Abstract

Lead‐free bismuth‐based perovskite oxides with polarization directed along the [001]_p primitive perovskite unit cell edge, analogous to tetragonal PbTiO₃, are synthesized at ambient pressure. Enhanced piezoelectric properties, large polarizations, and high depolarization temperatures are observed in the wide morphotropic phase boundary region formed with a rhombohedral phase, with up to 92.5% Bi on the perovskite A site.

The perovskite oxide lead zirconate titanate (PbZr_1−xTi_xO₃) (PZT) has extraordinary electromechanical properties at the morphotropic phase boundary (MPB),1 making modified PZT ceramics the basis for almost all actuators, sensors and related applications in use today. The MPB in the PZT solid solution occurs near x ≈ 0.481 between the ferroelectric rhombohedral (R3m, denoted as R_[111]) and tetragonal (P4mm, denoted as T_[001]) phases, with polarizations lying along the [111]_p body diagonal and [001]_p edge of the primitive ≈ 4 Å ABO₃ perovskite unit cell, respectively.1-3 The PZT phases are untilted and the R_[111] and T_[001] structures are described crystallographically, using a modified Glazer notation, as and , respectively, where the subscript indicates ferroelectric displacement and the superscript the nature of the octahedral tilting with respect to the primitive unit cell axes.4 It is challenging to create an MPB in a bismuth‐based lead‐free system as it has proved difficult to prepare phases with polarization directed along the [001]_p primitive cell edge in such materials. Several Pb‐free MPB systems based on K_0.5Na_0.5NbO₃, Na_0.5Bi_0.5TiO₃ (NBT), BaTiO₃ (BTO), and K_0.5Bi_0.5TiO₃ (KBT) are known but all have inferior properties to PZT.2, 3, 5 Bi³⁺ has a 6s² configuration with crystal chemistry similar to that of Pb^2+­, and bismuth‐based perovskites are attractive as they can offer high Curie and depolarization temperatures required for demanding application environments.5, 6 A phase with [001]_p polarization that is accessible at ambient pressure with a high (>50%) Bi³⁺ content is thus a significant target.

There are very few bismuth perovskites such as BiFeO₃ (R3c) which can be stabilized at ambient pressure. We have developed a strategy based on multiple B site cations to access such materials, e.g., antiferroelectric Bi₂Mn_4/3Ni_2/3O₆7 and the polar rhombohedral (R_[111]) phase BiTi_3/8Fe_2/8Mg_3/8O₃ (BTFM), which has a high Curie temperature of 730 °C.8 In BTFM, in addition to the long‐range ordered [111]_p displacements, the Bi cations have locally correlated [110]_p displacements9 which can be converted into a long‐range polarization along this direction by the introduction of LaFeO₃ (LFO) which itself has antiferrodistortive [110]_p displacements, although this orthorhombic O_[110] phase is separated from R_[111] BTFM by a non‐perovskite region of the phase diagram.10 We therefore explored solid solutions between BTFM and CaTiO₃ (CTO), motivated by the isostructural nature of LFO and CTO, but noting that the Ti cation in BTFM undergoes local displacements along multiple directions9 that are not correlated with the primary [111]_p A‐site displacement direction favored by the other two B site cations. This enhances the likelihood of locking in other long‐range polarization directions when Ti rather than Fe is the B site cation introduced by solid solution formation and may enable the two perovskite symmetries to directly neighbor each other in the phase diagram. We obtain a Bi‐based perovskite O_[001] phase with polarization along [001]_p and accessible at ambient pressure. Enhanced piezoelectric properties and high depolarization temperatures are observed in the wide MPB region formed with an R phase, with up to 92.5% Bi on the perovskite A site.

Solid solutions (1 − x)BTFM–xCTO were synthesized successfully in the range 0.0 < x ≤ 0.40 (the perovskite structure is maintained over this entire composition range in contrast with BTFM–LFO10). The R_[111] powder X‐ray diffraction (PXRD) pattern of BTFM changes dramatically with increasing CTO content beyond x = 0.05, as shown in Figure 1 (also Figure S1, Supporting Information). A complex PXRD pattern emerges in the region 0.075 ≤ x ≤ 0.1625, followed by a second single‐phase region when x ≥ 0.175 which is indexed to an orthorhombic cell of dimensions √2a_p × √2a_p × 2a_p (where a_p is the pseudocubic lattice parameter). These materials are second harmonic generation (SHG) active, indicating a non‐centrosymmetric structure. A selected area electron diffraction (SAED) experiment performed on the single crystal grain (Figure S3, Supporting Information) on orthorhombic composition x = 0.20 along the [010] zone axis (Figure 1e) is consistent with the space groups Pnam and Pna2₁ and allows us to exclude the other polar subgroups of Pnam (Pn2₁m and P2₁am). SAED experiments cannot distinguish between nonpolar Pnam and polar Pna2₁ because they have the same reflection conditions: convergent beam electron diffraction (CBED), which is a powerful and definitive tool for point symmetry determination, was therefore employed to distinguish between their respective mmm and mm2 point symmetries. The CBED pattern corresponding to the SAED pattern along the [010] zone axis is shown in Figure 1f. In this zone axis, two mirror planes are expected for Pnam whereas only one mirror plane is expected for Pna2₁.11 Only one mirror plane is observed in the CBED pattern which confirms that the space group is Pna2₁; this absence of inversion symmetry is also confirmed by the non‐identical structures in the (200) and discs (Figure 1f). SAED and CBED experiments on the [130] zone axis are also consistent with the non‐centrosymmetric structure (see Figure S5, Supporting Information). Thus the structure of x = 0.20 is unambiguously confirmed to be Pna2₁, described in terms of tilts and displacements as ,4 and is denoted O_[001] hereafter, as the determined symmetry requires the polarization to lie along the [001]_p cell edge direction. All the compositions with the orthorhombic structure are SHG active and have PXRD patterns consistent with Pna2₁ symmetry (Figure S2, Supporting Information). We therefore conclude that the compositions 0.175 ≤ x ≤ 0.40 possess a polar orthorhombic structure (O_[001]) in space group Pna2₁ with the polarization along [001]_p. The polarization is thus in the same direction as for T_[001] PbTiO₃ with respect to the primitive perovskite cell, but the BO₆ octahedra are tilted to produce the expanded orthorhombic cell.

Figure 1

a–c) Lebail fits to x = 0.05 (R_[111]), x = 0.15 (R_[111]+ O_[001]), and x = 0.20 (O_[001]), respectively (the most intense [110]_p cubic perovskite peaks, where p subscript indicates that the Miller indices refer to the cubic perovskite sub cell, are shown for clarity) with corresponding schematic unit cell diagrams showing the polarization directions present in the R_[111], (R_[111] + O_[001]), and O_[001] structures in the cubic perovskite sub cell, where the arrows indicate the polarization directions of A‐site cations (blue atoms) and B‐site cations (orange atoms), with the oxide sublattice (red atoms) defining the shaded BO₆ octahedra. d) Room‐temperature lattice parameters obtained from Lebail fits to synchrotron PXRD data plotted against composition (x), showing the structural transition from R_[111] (area shaded in pink) to O_[001] (area shaded in green) with a region of phase coexistence at 0.075 ≤ x ≤ 0.1625. The red arrows indicate the compositions plotted in (a)–(c). e) SAED pattern from x = 0.20 (O_[001]) along the [010] zone axis, which is consistent with Pnam and Pna2₁. The red arrows indicate spots from double diffraction (see tilt experiment results in Figure S4, Supporting Information). f) Corresponding CBED pattern along the [010] zone axis showing the presence of a single mirror plane confirming the Pna2₁ space group. The arrows indicate the (200) and discs: the different appearances of these discs are consistent with non‐centrosymmetry.

In the compositional range 0.075 ≤ x ≤ 0.1625, the PXRD patterns could not be indexed with either R_[111] or O_[001] structures (Figure S6a,b, Supporting Information). Two‐phase Lebail fits based on (R_[111] + O_[001]) resulted in good fits to the data with all peaks indexed (Figure 1b and Figure S2 and S6c, Supporting Information), consistent with a mixed phase structure (R_[111] + O_[001]) containing both polarization directions (Figure 1b). All the (R_[111] + O_[001]) compositions are SHG active and lie between two polar phases, confirming that compounds in this region are polar at ambient temperature. Detailed structural characterization of this complex region will be the subject of future study and is expected to be challenging: e.g., the structure of PZT at and near the MPB remains the subject of controversy after many years of detailed study where both multiple and single phase models have been proposed.12-15

The reduced lattice parameters ( for R_[111] and a_O/√2, b_O/√2, c_O/2 for O_[001], where V_R is the volume of the rhombohedral unit cell and a_O, b_O, c_O are the lattice parameters of orthorhombic unit cell) correspond to pseudocubic cell dimensions and are plotted against CTO content x in Figure 1d. From the diffraction patterns and lattice parameter variation, the phase boundaries are clearly visible around 0.05 < x < 0.075 and 0.1625 < x < 0.175. The mixed phase region spans Δx ≈ 0.088 and is of comparable width to those reported for the MPB region of PZT (Δx ≈ 0.01–0.15)16, 17 and other Pb‐free MPB systems (0.08 for NBT–KBT,18 0.01 for NBT–BTO19).

To examine the piezoelectric behavior, discs were poled and longitudinal piezoelectric coefficients (d₃₃) were measured across the full range of compositions (0 ≤ x ≤ 0.40: Figure 2a). Compositions with the R_[111] structure show an increase in d₃₃ with increasing x. Compositions with the O_[001] structure showed small finite d₃₃ values consistent with their polar structures. The d₃₃ value increases with decreasing x in the “O_[001]” region, reaching a maximum of 2.8 pC N⁻¹ at x = 0.1875. Most interestingly, d₃₃ increases sharply near the phase boundaries and a maximum d₃₃ of 53 pC N⁻¹ is found for x = 0.1625. This is about two orders higher than found for the parent R phase BTFM (0.65 pC N⁻¹)20 and a quarter of that of PZT (223 pC N⁻¹).1 Despite being polar, the polarization–electric field (P(E)) measurements on single phase R_[111] (x = 0.05) and O_[001] (x = 0.20) materials did not result in saturated loops (Figure 2b,d). This indicates that the coercive field is much higher than the measurement fields (150–200 kV cm⁻¹) accessed here. In sharp contrast, all the mixed phase compositions showed saturated P(E) loops (Figure 2c shows data for x = 0.10). This agrees well with the maximized d₃₃ in the mixed phase region. Transverse piezoelectric coefficient (d₃₁), planar coupling coefficient (k_p), elastic compliance (), and mechanical quality factor (Q₃₁) were calculated from radial extensional resonance mode on poled discs as shown in Figure 2e. For x = 0.15 (R_[111] + O_[001]), d₃₁, k_p, , and Q₃₁ are 7 pC N⁻¹, 0.12, 8.25 × 10⁻¹² m² N⁻¹, and 360, respectively (see Table S2, Supporting Information for other compositions and comparison with PZT and other lead‐free MPB systems). In particular, the mechanical quality factor (Q₃₁) which is important for high power applications,21 reaches a maximum of 460 for x = 0.075, comparable to PZT (Q_M = 500)1 and considerably higher than several established Pb‐free MPB systems (see Table S2, Supporting Information).2, 3

Figure 2

a) Variation of longitudinal piezoelectric coefficient (d₃₃) with CTO content (x) on poled ceramic pellets. Compared to the low d₃₃ values (d₃₃< 4 pC N⁻¹) of single‐phase O_[001] and R_[111] materials, the mixed phase (R_[111]+ O_[001]) compositions show enhanced d₃₃ values (52 pC N⁻¹ for x = 0.15). b–d) P(E) loops under comparable measurement fields for R_[111] (x = 0.05), R_[111] + O_[001] (x = 0.10) and O_[001] (x = 0.20) materials, respectively (indicated by the red arrows). e) Impedance and phase plotted against frequency on a poled thin disc of x = 0.15 showing radial extensional resonance modes. The open symbols and lines represent measured and fitted data, respectively.

The (R_[111] + O_[001]) composition x = 0.15 was selected for a detailed study of electromechanical properties in the MPB region. Room temperature P(E) loops at a frequency of 1 Hz (preset delay = 1 s) under different measurement fields are shown in Figure 3a. Well saturated loops are obtained with the maximum polarization (P_max), remanent polarization (P_rem) and coercive field (E_C) of 49 μC cm⁻², 44 μC cm⁻², and 110 kV cm⁻¹, respectively. The remanent polarization observed is higher than that of PZT ceramics (P_rem = 35 μC cm⁻²) and other lead‐free ceramics at the MPB.2, 3 To verify the large observed polarization, PUND (positive‐up‐negative‐down) measurements were performed with square pulses (pulse width = 1000 ms and pulse delay = 1000 ms). A switchable polarization of P ≈ 49 μC cm⁻² is obtained (Figure 3c) and this confirms that large polarization is intrinsic. Room temperature strain‐field measurement on the same composition at 1 Hz exhibited the classic butterfly loop (Figure 3b). The saturated P(E) loops and the butterfly strain‐field data demonstrate the ferroelectric nature of this material. The observed bipolar strain of 0.16% is of the same order as PZT (0.30%).3 Saturated P(E) and butterfly strain‐field loops are observed for all (R_[111] + O_[001]) compositions. The discs have low dielectric loss (tanδ ≈ 0.03 at 1 Hz) that supports measurements up to fields of 200 kV cm⁻¹.

Figure 3

Room temperature electromechanical properties of an (R_[111] + O_[001]) composition x = 0.15. a) Saturated P(E) hysteresis loops and b) butterfly strain‐field loop at 1 Hz confirming ferroelectricity. c) PUND measurement confirming the polarization value. P* contains remanent and non‐remanent polarizations whereas P^{^} contains non‐remanent polarization contributions. dP (= P* − P^) represents the remanent polarization. d) Unipolar strain‐field loop showing d₃₃ (calculated from the low field slope as shown by the black line) and effective (=S_max/E_max, where S_max is the strain observed at the maximum field E_max) and finite hysteresis h (= ΔS/S_max; where ΔS is the width of the widest part of the loop). e,f) PXRD patterns, plotted over the 2θ range which contains the most intense [110]_p cubic perovskite subcell reflections (similar to Figure 1a–c), from unpoled (bottom panels) and poled (top panels) pellets of x = 0.175 (O_[001]) and x = 0.15 (R_[111] + O_[001]), respectively. The increase in the intensity of the rhombohedral [104] peak, which is clearly resolved, indicates that an electric field‐induced change in polarization direction occurs in the MPB region. Incident wavelengths are 0.45018 and 0.499953(9) Å for x = 0.175 and x = 0.15, respectively.

To correlate the Berlincourt d₃₃ value with the direct piezoelectric coefficient, unipolar strain‐field loops were measured (Figure 3d). The piezoelectric coefficient calculated from the low field slope is 46 pC N⁻¹ which is close to the Berlincourt value of 52 pC N⁻¹. The effective piezoelectric coefficient ( = 77 pC N⁻¹) is slightly higher than the observed d₃₃. The unipolar loop exhibited non‐linearity with a hysteresis (h) of 27%. The finite hysteresis and mismatch of d₃₃ and may indicate an irreversible contribution from domain wall motion.2, 3

The composition x = 0.175 (single phase O_[001] before poling) showed a d₃₃ (49 pC N⁻¹) close to the mixed phase compositions (Figure 2a). X‐ray diffraction on a poled disc of x = 0.175 shows the appearance of peaks corresponding to the R_[111] phase, indicating a change in polarization direction under electric field (Figure 3e).22 This is also evident from the change in the relative intensities of the R_[111] and O_[001] components of the x = 0.15 composition after poling (Figure 3f).

For practical applications, temperature stability of piezoelectric properties and high Curie temperature (T_C) are advantageous. Recently, it has been suggested that the depolarization temperature (T_d) is more relevant since in many systems partial or complete loss of polarization occurs at T_d which can be well below T_C.2, 5 T_d has been estimated from the temperature dependence of d₃₃ measured ex situ. For x = 0.10 (R_[111] + O_[001]), d₃₃ drops sharply to a low value (≈1 pC N⁻¹) at T_d = 650 °C and becomes zero at T_C ≈ 840 °C (Figure S7, Supporting Information). Changes in the diffraction patterns support the depolarization at T_d whereas the Curie temperature is supported by differential scanning calorimetry (DSC) and dielectric permittivity data (Figure S7, Supporting Information). These experiments indicated that depolarization occurs below T_C in all the (R_[111] + O_[001]) compositions (Table S2, Supporting Information). The composition x = 0.10, with a room temperature d₃₃ of 50 pC N⁻¹ and T_d of 650 °C, which is high for a Pb‐free MPB system (Table S2, Supporting Information),2, 5 is therefore of interest for high temperature piezoelectric applications. The origin of the depolarization and the detailed phase diagram versus temperature is the subject of further study.

We have stabilized a perovskite with polarization directed along the [001]_p primitive cell edge that has a high bismuth content (up to 92.5% bismuth on the A‐site cf., KBT23) and is accessible at ambient pressure (cf., BiInO₃24). The mixed phase region with the polar R_[111] phase generates an MPB reminiscent of that in PZT, based on Bi‐rich R_[111] and O_[001] structures. A piezoelectric coefficient d₃₃ of 52 pC N⁻¹, mechanical quality factor Q₃₁ of 460, a switchable polarization of 49 μC cm⁻², and a depolarization temperature T_d of up to 650 °C were observed for bulk ceramics in the MPB‐like composition range. The new Pb‐free MPB system offers the opportunity for further electromechanical property improvement by chemical substitution and strain optimization.

Experimental Section

High quality powder samples were synthesized by a conventional solid‐state reaction of binary oxide and carbonate precursors heated at temperatures of 900–950 °C for 12 h (described in detail in Table S1, Supporting Information). Phase purity was confirmed using a PANalytical X'pert Pro diffractometer (Co K_α1, λ = 1.78896 Å). High resolution PXRD data were collected on beamline BL44B225 at SPring‐8 with an incident wavelength λ = 0.499953(9) Å in Debye–Scherrer geometry with samples contained in spinning glass capillaries. This instrument was also used to collect data from poled and unpoled pellets of approximate thickness 180 μm (x = 0.15) and 80 μm (x = 0.175), which were contained in a rocking sample holder. Lattice parameters were extracted from Lebail fits in the 2θ range 3 ≤ 2θ ≤ 74°. For synchrotron diffraction experiments at high temperature (30–700 °C), powder samples were packed in a 0.1 mm quartz capillary and data were collected from the I11 powder diffractometer at the Diamond Light Source, with an incident wavelength of 0.825725 Å.26 Electron diffraction experiments (SAED and CBED) were conducted using a JEOL 2000FX electron microscope operating at 200 kV. Analysis was performed on a single crystal grain (Figure S3, Supporting Information) in a thin lamella specimen prepared by the lift out method27 using a dual beam FEI focused ion beam instrument; final milling steps were performed using an 8 kV Ga ion beam. Powder second‐harmonic generation (SHG) measurements were performed on a modified Kurtz‐non‐linear optical system using a pulsed Nd:YAG laser with a wavelength of 1064 nm.28

Physical property measurements were performed on pellets with densities greater than 95% of the crystallographic values, which were produced from high quality powders by ball‐milling, isostatic pressing, and a final sintering step (these processing conditions are described in detail in the Supporting Information). Pellet densities were measured using an Archimedes balance and their phase purity was confirmed by laboratory PXRD. Thin discs (100–200 μm) electroded with silver paint or sputtered gold were poled at 150–200 °C for 10 min under 100 kV cm⁻¹ field. Piezoelectric coefficients (d₃₃) were measured using a d₃₃ piezometer and other electromechanical properties (d₃₁, k_p, , Q₃₁) were measured using resonance–antiresonance method. Impedance and phase angle were measured using an Agilent E4980 inductance–capacitance–resistance (LCR) meter and HP4294A impedance analyzer. Polarization and strain‐field loops were collected at 1 Hz using a Radiant ferroelectric tester system coupled with Fotonic sensor MTI‐2100. Short‐circuited poled pellets were depoled at a selected temperature and d₃₃ was measured ex situ using the piezometer. DSC experiments were performed using an SDT Q600 instrument with a heating and cooling rate of 10 °C min⁻¹. Further details on sample preparation, ceramic processing, SHG experiments, and characterizations are provided in the Supporting Information.

Acknowledgements

The authors thank the European Research Council (ERC Grant agreement 227987 RLUCIM), the European Union (SOPRANO project Grant No. PITN‐GA‐2008‐214040) and the Engineering and Physical Sciences Research Council (EP/H000925) for support. A.M.‐S., E.N., and M.T. thank RIKEN International Program Associate (IPA) for support and Dr. Kato for experimental help at SPring‐8 BL44B2. The synchrotron radiation experiments were performed at BL44B2 in SPring‐8 with the approval of RIKEN. The authors thank Dr. C. Murray and Dr. C. Tang for assistance on beamline I11 (Diamond Light Source, UK). L.F.H. thanks the European Union (NANOMOTION project Grant No. 290158). T.T.T. and P.S.H. thank the Welch Foundation (Grant E‐1457) for support.