Revealing the mechanism of electric-field-induced phase transition in antiferroelectric NaNbO₃ by in situ high-energy x-ray diffraction

Antiferroelectric (AFE) materials are characterized by a phase transition from an antiferroelectric (AFE) to a ferroelectric (FE) state induced by the application of an external electric field. This transition is often accompanied by the appearance of double polarization hysteresis loops, depending on whether the transition is reversible^1–4 or irreversible.^5,6 Reversible AFE–FE transitions enable potential application of AFE materials in a wide range of devices, including high energy density capacitors,^7–10 nonvolatile random access memory,¹¹ and electrocaloric refrigerators.^12,13

Double polarization hysteresis loops were observed in PbZrO₃-based,^1,14 PbHfO₃-based,^15,16 and AgNbO₃^17,18 AFE systems. However, in pure NaNbO₃, one of the prototype lead-free AFE materials, double polarization loops were only verified in certain single crystals.^6,19 Instead, the electric field-induced phase transition was reported to be irreversible,^5,20 resulting in characteristic FE polarization loops after the first electric field cycle. The nature of the irreversibility remains unclear, but may be related to the small energy difference between the AFE and FE phases (about 2 meV/f.u.),^21,22 which is much smaller than the 20 meV/f.u. difference reported for PbZrO₃.²³ This irreversible transition was recently investigated ex situ by comparing the sample's states before and after the application of electric fields.⁵ The field-induced transformation of the nonpolar P phase (AFE, orthorhombic Pbcm)²⁴ into the polar Q phase (FE, orthorhombic P2₁ma)²⁵ is accompanied by a large longitudinal strain of 0.64%, drop in the permittivity, disappearance of the translational AFE domain structure, and changes of the local Na environment.⁵ The transition was previously suggested to be of the first order nature.⁶ 

However, the mechanism of AFE–FE transitions, which includes interactions between the structural transformations, induced lattice strain, and FE domain formation and reorientation, remains poorly understood. Park et al. reported that the tetragonal (AFE)–rhombohedral (FE) transition in polycrystalline Pb_0.98La_0.02(Zr_0.66Ti_0.10Sn_0.24)_0.995O₃ occurs by orientation of the AFE phase, AFE–FE transition, and subsequent poling of the FE phase.²⁶ This transition is also accompanied by an unusual auxetic behavior.²⁷ While macroscopic polarization and strain measurements can be used to detect the transition, they do not provide detailed insight into the underlying structural changes. This problem can be overcome by in situ x-ray diffraction (XRD), which has been utilized to study domain dynamics and lattice strain in ferroelectrics.^28–30 Recently, this approach has also been applied to study the electric-field-induced transitions in PbZrO₃-based AFEs.^31–34 Ciuchi et al. reported that the transition in (Pb_1−xLa_x)(Zr_0.90Ti_0.10)_1–x/4O₃ includes an irreversible orientation of the domain structure and a reversible/irreversible change in the lattice, depending on the composition.³¹ Indications for irreversible processes during AFE–FE transition were also previously reported by Lu et al., investigating Pb_0.97La_0.02(Zr_0.56Sn_0.33Ti_0.11)O₃ using in situ neutron diffraction.³² Liu et al. found that the large strain during the reversible AFE–FE transition in Pb_0.99(Nb_0.02[(Zr_0.57Sn_0.43)_0.94Ti_0.06]_0.98)O₃ arises from the anisotropic lattice strain and preferential domain reorientation.³³ A revised schematic of the AFE–FE transformation sequence was proposed.³³ However, similar studies of the lead-free NaNbO₃-based compositions, exhibiting predominantly orthorhombic phases, are still missing.

Here, we utilize in situ high-energy diffraction measurements to simultaneously study the macroscopic changes in polarization/strain and the structural/microstructural evolution during the AFE–FE transition in the lead-free prototype antiferroelectric NaNbO₃. Three stages were observed with the sequence: AFE (P phase) → FE (Q phase) without macroscopic polarization and strain → FE (Q phase) with macroscopic polarization and strain, whereby the phase transition was found to be clearly decoupled from the polarization switching process.

Polycrystalline NaNbO₃ was prepared by the solid-state reaction.⁵ In situ XRD measurements were carried out on bars (0.5 × 1× 5 mm³) and sputter-coated with platinum (1 × 5 mm² surfaces). All samples were annealed at 600 °C for 2 h prior to the measurement. The diffraction patterns were collected at the DESY PETRA III P02.1 beamline in transmission geometry using a Pilatus CdTe 2M area detector (Dectris Ltd., Switzerland). The beam energy and spot size were 60 keV (λ = 0.20673 Å) and 0.3 × 0.3 mm², respectively. During the measurement, the samples were loaded with an unipolar electric field with a frequency of 0.05 Hz, while the frame exposure time was 415 ms. The two-dimensional XRD patterns were converted into one-dimensional patterns by integrating the intensity in different azimuthal ranges using Fit2D,³⁵ while LeBail fitting was conducted using the GSAS program.³⁶ The polarization and strain were simultaneously measured using a modified Sawyer-Tower circuit and an optical displacement sensor, respectively. The sample exhibited a piezoelectric coefficient of d₃₃ = 40 pC/N after the measurement, confirming the irreversible inducement of the FE phase. Electric field-induced longitudinal and transverse strains were additionally obtained using linear variable differential transformers.³⁷ 

Both, P and Q phases, exhibit orthorhombic symmetry with rhombic primitive cells (a = b ≠ c, γ ≠ 90°; Fig. 1). However, they differ in the arrangement of successive layers along the [001]_PC axis. In the Q phase, a repeating unit is constituted by two successive primitive cells along the [001]_PC axis, as indicated by the green dashed squares in Fig. 1(b). Within the repeating unit, all the atoms are mirrored across the (002) plane. The Nb displacements (yellow arrows) are the same and close to the [110]_PC direction, as indicated by blue arrows. The Na(1) displacement is also close to [110]_PC, but larger than that of Nb. The tilt system in the Q phase is a⁻a⁻b⁺ [Fig. 1(f)]. In the P phase, the repeating unit of the Q phase is operated by a screw diad along the [001]_PC direction, constituting a new repeating unit with antiparallel arrays of Nb and Na(1) displacements, as indicated by Nb/Nb′ and Na(1)/Na(1) ′, respectively [Fig. 1(a)]. The tilt system is different in successive octahedra layers, i.e., a⁻a⁻b⁺ for layers 1 and 2 and layers 3 and 4, and a⁻a⁻b⁻ for layers 2 and 3 [Figs. 1(c)–1(e)]. The primitive cell in the Q and P phases is multiplied by 2 and 4 in the [001]_PC direction, respectively. Therefore, their superlattice reflections are characterized by half-integer indices and quarter-integer indices, respectively.³⁸ In the following, all lattice parameters will be presented based on one primitive cell with a pseudocubic configuration.

The evolution of the main and the superlattice reflections upon application of an electric field to a virgin NaNbO₃ sample is displayed in Figs. 2(a) and 2(b) (full-range diffractograms are provided in the supplementary material, Fig. S1), while the simultaneous changes in polarization and strain are given in Fig. 2(c). The ¼{843}_PC peak is a characteristic reflection of the AFE P phase, which is the only phase present in virgin NaNbO₃.⁵ The integrated area of this peak was, thus, used to quantify the P phase fraction [Fig. 2(c)]. Single-phase models with the Pbcm or P2₁ma space groups were adopted. The structure of the sample during the application of the field does not meet the isotropic average assumption, which prevents quantification by Rietveld refinement. Therefore, LeBail fitting³⁹ was performed to track the changes in the lattice parameters, as shown in Fig. 3. The evolution of the d-spacings during individual stages, extracted from the diffraction data, is presented in Fig. 4.

The results presented in Figs. 2–4 reveal that the behavior is divided into three main stages. During stage I, between 0 and 8 kV/mm, the sample consists of the AFE P phase, as evident by the quarter-index superlattice reflections [Fig. 2(b)]. No structural changes can be observed, and the macroscopic strain is absent. The minor polarization increase could be related to the dielectric displacement and a minor leakage current contribution. The strain increase has a linear correlation with the square of polarization, indicating purely electrostrictive contribution with an electrostrictive coefficient of 0.012 m⁴/C². Interestingly, toward the end of this stage (at ∼6 kV/mm), the P phase fraction starts to decrease and the cell parameter c_PC slightly increases, which is reflected in a small increase in the cell volume.

This increase indicates the initiation of stage II (8–12 kV/mm). At 8 kV/mm, significant changes in main reflections are observed, e.g., {100}_PC and {200}_PC shift to lower 2θ values, and exhibit a strong increase in intensities, while {110}_PC shifts to lower 2θ values and reduces in intensity. Moreover, the ¼{843}_PC superlattice reflection disappears, ½{312}_PC appears, and the superlattice reflections ½{310}_PC and ½{311}_PC show changes in their intensities and positions. The parameters a_PC, b_PC, and γ_PC increase, while c_PC slightly decreases [Fig. 3(a)]. These changes clearly indicate the disappearance of the AFE P phase and the appearance of the FE Q phase at 8 kV/mm [Fig. 2(c)], which is accompanied by a large increase in the cell volume [Fig. 3(b)]. The d-spacings of 220, 200/020, and 002 reflections parallel to the electric field increase, while the d-spacings of 220 and 002 reflections perpendicular to the electric field decrease (Fig. 4). Interestingly, although the strain curve exhibits a minor continuous nonlinear increase, no other changes are observed in the macroscopic behavior at 8 kV/mm [Fig. 2(c)].

The sample enters stage III at about 12 kV/mm. Reflections {100}_PC and {200}_PC shift slightly to higher 2θ values, and their intensities decrease. The changes in superlattice reflections are negligible, which indicates that the phase composition remains almost unchanged and the behavior in stages II and III is mostly related to microstructural changes. A slight decrease in a_PC, b_PC, and γ_PC and a slight increase in c_PC are observed near 12 kV/mm. Note that the values of γ_PC, a_PC, and b_PC in stage III are still larger than those in stage I. These structural changes correspond to the onset of the macroscopic polarization and strain increase, which reaches the inflection point at 13.3 kV/mm. The small delay of the macroscopic response can be partially ascribed to the limited time resolution of the measurement (patterns were collected over a time of 415 ms, during which the field increased by 0.67 kV/mm). The critical electric fields for the transitions between individual stages are also expected to be frequency⁵ and grain size⁴⁰ dependent. Structural and microstructural changes during the stages will be discussed in more detail below.

To gain further insight into the transition mechanism, the electric field-induced longitudinal (S₃₃), transverse (S₁₁), and volumetric (S_V) strains were recorded simultaneously [Fig. 3(c)]. For reference, the same measurement was conducted on a lead-based AFE with an irreversible phase transition (Pb_0.97La_0.02)(Zr_0.75Sn_0.13Ti_0.12)O₃ (PLZST) and on a classical ferroelectric Pb(Zr,Ti)O₃ (PZT), as displayed in the supplementary material, Fig. S2. The large increase in S₃₃ in NaNbO₃ at about 13 kV/mm is accompanied by a small decrease in S₁₁. Note that the strain ratio $−S11/S33$ remains positive throughout the process [inset in Fig. 3(c)]. This reveals that NaNbO₃ does not exhibit the same auxetic behavior as PLZST, i.e., simultaneous expansion in longitudinal and transverse directions [Fig. S2(a) and Refs. 27 and 41]. The corresponding macroscopic volume strain (S_V) in NaNbO₃ reaches a value of 0.26% at 16 kV/mm [Fig. 3(c)], which is comparable to the volume change obtained by diffraction [0.29%; Fig. 3(b)]. No changes in S₁₁ and S_V could be detected below 12 kV/mm (stages I and II), confirming the macroscopic measurement in Fig. 2(c). However, the large change in S_V at about 13.3 kV/mm is accompanied by a pulse-like behavior [small decrease and increase just before and after the large change, respectively; see Fig. 3(c)]. Such behavior has not been observed in PLZST, despite the larger S_V; however, similar features can be seen in the vicinity of the coercive field in PZT [supplementary material, Fig. S2(b)], which supports our conclusion that the polarization and strain increase at 13.3 kV/mm (stage II→III) are related to polarization reorientation, rather than a phase transition.

Based on the results of combined structural analysis and macroscopic measurements, we propose a three-stage phase transition mechanism. The virgin sample (AFE P phase) exhibits Na(1) displacements in a direction close to ⟨110⟩_PC, whereby the sequence of these displacements is antiparallel in consecutive cells along the [001]_PC axis⁴² (Fig. 1). The domain structure consists of orientational domains with antipolarization.^43,44 During stage I, the E-field is not strong enough to induce the AFE–FE phase transition and electrostatically neutral domains are not affected. No change in the diffraction patterns was observed at this stage, which is consistent with an in situ neutron diffraction study by Lu et al.³² These results are different from the model of Park et al., which observed the formation of preferred orientation within the AFE state as soon as the E-field was applied.

The transition from the P phase to the Q phase occurs when the critical electric field of about 8 kV/mm is reached, which marks the beginning of stage II (onset at ∼6 kV/mm; Fig. 2). This induces the displacement of Na(1)′ in the same direction as Na(1) (Fig. 1) and the disappearance of the quarter-index superlattice reflections. The transition to stage II is accompanied by a significant increase in the d-spacings of 220, 200/020, and 002 reflections parallel to the electric field and a simultaneous decrease in the d-spacings of 220 and 002 reflections perpendicular to the electric field (Fig. 4). The primitive cells oriented in the ⟨110⟩ direction exhibit a tensile stress in the direction parallel to the field and a compressive stress in the direction perpendicular to the field. The presence and the previously predicted first order nature of the transition⁶ were additionally confirmed by detecting slight cooling of the sample between 6 and 8 kV/mm, indicative of the absorbed latent heat (Fig. S3). Due to the first order nature of this transition, both phases coexist over a certain period (certain E-field range). In addition, a distribution of critical fields is expected due to polycrystallinity.^45,46 These two phenomena induce mechanical stress at the phase boundary, related to the crystal lattice adaptation in the phase boundary vicinity.^47,48 This stress influences the phase transition and the orientation of the phase boundary. Note that a unit cell expansion was observed during the phase transition [Fig. 3(b)]. In addition, a reorientation of the primitive cells occurs. The cells with their [110]_PC axes [long face diagonal of the (110) plane] are parallel to the field. Hence, texturing is induced, as evident from the azimuthal dependence of the {220}_PC and {200}_PC reflections in XRD patterns (Fig. S4). The primitive cell expansion observed at 8 kV/mm (Fig. 3) and texturing are expected to induce straining of the grains [Fig. 3(c)]; however, the absence of the macroscopic strain suggests that this effect is compensated by the randomly oriented grains. This includes compensation by grain boundaries and pores, twinning, and intragranular stress buildup. Although polarization variants with the direction closer to the applied electric field are energetically favored, their reorientation in stage II is prevented by the mechanical stress, and thus, the macroscopic polarization does not exhibit a sudden change.

At about 13 kV/mm (stage II→III), the electric field is strong enough to counteract the internal mechanical stresses and polarization switching takes place, accompanied by the significant increase in macroscopic polarization and strain. Na(1) is displaced along the [110]_PC direction, while the primitive cells are elongated in the [110]_PC direction and contracted in the [$11¯0$]_PC direction. The mechanical energy accumulated in stage II gets released, and a significant change in d-spacings is observed (Fig. 4). The cells with the orientation of 220, 200/020, and 002 exhibited tensile stress in the direction parallel to the electric field in stage II, and thus, the corresponding d-spacings of 220, 200/020, and 002 reflections parallel to the electric field decreased at the stress release from stage II to stage III. On the other hand, the cells with the orientation of 220 were compressed in the direction that is perpendicular to the electric field in stage II, and correspondingly, their d-spacings increase. Polarization switching also results in a 0.24% volumetric dilatation, which does not relate to the very small decrease in the unit cell volume observed at this field. This additional volume is suggested to be due to microcracking stemming from large intragranular strain incompatibility. Evidence for microcracks has been found in the polished microstructures (see Fig. S5). The microcrack volume can be estimated by⁴⁹ 

where $ν$ is the Poisson ratio, E the Young's modulus, and a the size of the microcrack. Taking crack tip toughness of related (K,Na)NbO₃⁵⁰ and penny-shaped microcracks of diameter a equal to half of the average grain size yields a microcrack volume of 0.27% of the grain volume. This is in agreement with the measured volumetric strain [Fig. 3(c)] and would also rationalize the tendency of NaNbO₃-based compositions to exhibit slanted polarization hysteresis curves (related to the field-drop across the microcracks and broader distribution of switching fields) and dielectric breakdown after electric field cycling. As a result, the primitive cell volume decreases in stage III [Fig. 3(b)] and reaches the value of 59.59 ų, which closely matches previous reports for the Q phase.⁵¹ 

In summary, we investigated the electric field-induced phase transition in the prototype lead-free AFE material NaNbO₃. Three stages were observed, whereby the structural AFE–FE transition takes place much before macroscopic changes in polarization and strain are observed, with the latter being related to polarization reorientation in the FE phase. These results show that the AFE–FE phase transition sequence in NaNbO₃ is distinctively different from PZ-based AFEs. Moreover, insight into the mechanism of this irreversible transition may facilitate further design of AFE materials with reversible transitions, which are desired for applications.

See the supplementary material for details on the collected XRD patterns (Fig. S1), unipolar strain and polarization hysteresis loops of the reference materials PLZST and PZT (Fig. S2), temperature change of the sample during E-field loading (Fig. S3), texturing indications following (220)_PC and (200)_PC reflections in the directions with 0°, 45°, and 90° to the electric field (Fig. S4), and micrographs of polished samples before and after E-field loading (Fig. S5).

This work was supported by the Hessian State Ministry for Higher Education, Research and the Arts under the LOEWE collaborative project FLAME (Fermi level engineering of antiferroelectric materials for energy storage and insulation systems). N.N. additionally thanks the Slovenian research agency (No. P1-0125). Parts of the work were supported by the DAAD through funds from the Bundesministerium für Bildung und Forschung (BMBF) Grant No. 57570962 and the Slovenian Research Agency through the bilateral project. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at the beamline P02.1, PETRA III. The authors would like to thank Professor Nan Zhang for useful discussions on the diffraction data.