In situ Raman scattering investigation of field-induced phase transition behavior in Na_1+xNbO₃ ceramics via nonstoichiometric regulation Open Access

In 1960, Megaw and co-workers systematically proposed the structural sequence of sodium niobate (NaNbO₃) during cooling with consecutive phase transitions, namely, U₂ (paraelectric, cubic Pm $3 ¯$m) $⟶ 640 ° C$ T₂ (paraelectric, tetragonal P4/mbm) $⟶ 575 ° C$ T₁ (paraelectric, orthorhombic Ccmm) $⟶ 520 ° C$ S (paraelectric orthorhombic Pnmm) $⟶ 480 ° C$ R (antiferroelectric, orthorhombic Pnmm) $⟶ 360 ° C$ P (antiferroelectric, orthorhombic Pbcm) $⟶ − 100 ° C$ N (ferroelectric, rhombohedral R3c).^1–3 This widely recognized sequence has established NaNbO₃ as the “most complex perovskite,” which is also considered to be an ideal model for understanding the evolution of lattice distortion in dielectrics.^4,5 However, the complexity of phase transition in NaNbO₃ is far more than this description. In particular, the presence of a ferroelectric Q phase with P2₁ma space group leads to a higher level of intricacy in both phase transition and electrical behavior under external fields. It is well known that NaNbO₃ possesses an antiferroelectric P phase at room temperature, while it generally fails to exhibit the characteristic double hysteresis loop associated with antiferroelectricity. Some studies have indicated that the approximate free energies between P and Q phases give rise to the minute electric field needed by the irreversible transition from the P phase to the Q phase.⁶ However, based on the previous work of Zhang et al. and our research group, in situ XRD and Raman results under varying electric fields demonstrate that the required electric field is relatively higher for the transition from the P phase to the Q phase.^7,8 Consequently, there is a discrepancy between macroscopic polarization measurement and microscopic structural characterization. In addition, the dielectric properties during the heating process manifest that most NaNbO₃ samples display dielectric anomaly with relaxation in the temperature range of ∼100–200 °C.⁹ The explanation for this phenomenon is still controversial. Considering that room-temperature NaNbO₃ samples usually contain an unavoidable Q phase component, some research studies propose that this anomaly arises from the incommensurate phase induced by a competition behavior during the transition from room-temperature Q phase component to P phase, while other references signify that the anomaly is just due to the transition process from the ferroelectric Q phase to the antiferroelectric P phase.^10,11 Therefore, there are still many unsolved mysteries about the intricate transition between the ferroelectric and antiferroelectric phases in NaNbO₃.

The phenomenological model of complex phase transition in NaNbO₃ can be attributed to the synergistic effect involving the displacement of Na atoms and the distortion of NbO₆ octahedra.¹² Numerous works have reported on the off-center of Nb atoms and the distortion of NbO₆ octahedra under external fields.^4,13 Meanwhile, the influence of Na atoms cannot be overlooked, particularly during the transition between P and Q phases. According to the crystallographic structure reported by Zhang et al., NaNbO₃ with the P phase exhibits two kinds of non-equivalent Na sites (denoted as Na1 and Na2), which are alternately arranged along the c axis accompanied by an antiparallel displacement between the adjacent Na1 atoms.⁷ This unique antiparallel displacement, in conjunction with the distortion of NbO₆ octahedra, collectively forms the fourfold superlattice structure of the P phase. For comparison, both the adjacent Na1 atoms and Nb atoms present a parallel displacement in the Q phase, leading to the characteristic 1/2 superlattice reflections in electron-diffraction patterns. Of course, it is important to note that the Na atoms show constrained displacement amplitudes, combined with their inherently low atomic mass. Consequently, the traditional microstructure characterization techniques, such as x-ray diffraction, generally struggle to effectively investigate the influence of Na atoms on the phase transition of NaNbO₃.¹² Currently, in situ Raman spectroscopy serves as a precise probe for exploring phase transition due to its ability to sensitively detect the evolution of various phonon vibrations in response to the external physical fields.¹⁴ For example, the Raman spectrum of NaNbO₃ can clearly display the splitting of phonon modes arising from two kinds of unequal Na sites, which is a hallmark feature of the P phase.¹⁵ Moreover, the ferroelectric and antiferroelectric phases, respectively, possess distinguishable characteristics in different phonon vibrations of NbO₆ octahedra.¹⁶ Therefore, it is expected to reveal the influence of Na sites on the modulation principles and the related physical mechanisms of the ferroelectric-antiferroelectric transition in NaNbO₃, utilizing in situ Raman spectroscopy. However, the current research in this area remains limited and requires further development.

According to the above discussion, a series of Na_1+xNbO₃ samples were synthesized by precisely controlling the different nonstoichiometric ratios of Na elements. The microstructure and electrical behavior could be deciphered in detail. Furthermore, the correlation between the Na atoms and the field-induced phase transition in NaNbO₃ is thoroughly analyzed, based on the in situ Raman spectroscopy technique under varying electric fields and temperatures. In this work, we aim to clarify the modulation effect of Na atoms on the physical properties of NaNbO₃, involving the transition from the room-temperature antiferroelectric component phase to the ferroelectric component phase and the dielectric relaxation process in the range of ∼100–200 °C. The relevant findings will provide an important foundation for further understanding the origin of electric polarization in NaNbO₃, as well as the design and development of NaNbO₃-based electronic devices.

Na_1+xNbO₃ (−0.02 ≤ x ≤ 0.02) samples were prepared by the traditional solid-state reaction method using analytical-grade Na₂CO₃ (99.8%) and Nb₂O₅ (99.9%) as starting materials. The raw materials were thoroughly dried at 150 °C and weighed according to the specified non-stoichiometric ratios. After adding anhydrous ethanol, the mixtures were ball-milled for 24 h at 200 r/min to achieve full mixing of the raw materials. Then, the resulting slurry was dried in a water bath, accompanied by transferring the powder to corundum crucibles. Calcination was conducted at 900 °C for 4 h to obtain the precursor powder. Subsequently, a secondary process under the same condition is necessary, including ball milling and drying. After adding 5 wt. % polyvinyl alcohol (PVA), the pellets were pressed at 200 MPa, with a diameter of ∼13 mm and a thickness of ∼0.5 mm. Finally, the Na_1+xNbO₃ ceramic series were obtained via sintering at 1300 °C for 2 h. For relevant electrical measurement, the sample thickness was reduced to ∼0.1 mm using a polishing machine, followed by high-temperature silver paste coated on both sides of the samples to form electrodes.

The crystal structure was characterized using an x-ray diffractometer with Cu Kα radiation (XRD, Rigaku Miniflex 600). Room-temperature ferroelectric hysteresis loops were measured with a Precision Premier II system (Radiant Technologies) at a frequency of 10 Hz. The dielectric properties were conducted by a polarization comprehensive measurement system (PEMS 6000, Partulab), in the temperature range of 27–627 °C. Here, the measurement frequencies are, respectively, 100 Hz, 1 kHz, 10 kHz, 50 kHz, 100 kHz, 500 kHz, and 1 MHz. In situ Raman spectra under varying electric fields and temperatures were evaluated through a high-speed and high-resolution micro-confocal Raman spectrometer using a 532 nm laser (LabRAM HR Evolution, Horiba Scientific), equipped with a temperature controller (Linkam Scientific Instruments Ltd, T96-S) and an electrometer (Keithley 6517B). The wavenumber range of Raman spectra is 50–1000 cm⁻¹ and the groove density of gratings is 1800 gr/mm. Specifically, for the measurement of in situ Raman spectra with varying electric fields, the ceramic samples were polished and coated with silver slurry to form electrodes, after which the samples were processed into narrow strips. The measurement was performed on the section cutting plane of the strips with a direct-current bias voltage which was provided by the electrometer.

Figure 1(a) presents the XRD patterns of Na_1+xNbO₃ samples at room temperature, demonstrating well crystallinity with low background noise and sharp diffraction peaks. Comparison with the standard PDF card (space group Pbcm No. 01-073-0803) confirms that all samples are pure without any secondary phases, which indicates that the slight nonstoichiometric ratio of Na sites in the range of −0.02 ≤ x ≤ 0.02 does not significantly disrupt the lattice structure of parent NaNbO₃. Of course, the relative intensity of the diffraction peaks varies with different Na contents. For instance, Fig. 1(b) illustrates the ratio of relative intensity between the (110) and the (100) peak (I₍₁₁₀₎/I₍₁₀₀₎), as a function of Na content. It is evident that the ratio initially rises rapidly before gradually approaching saturation, with the monotonic increase of x. This suggests that the variation of the Na content induces a regular distortion in the NaNbO₃ lattice. To further investigate the detailed microstructure evolution, Figs. 1(c) and 1(d) provide the local enlargement of the diffraction patterns at ∼36.6° and ∼55.2°. It denotes the peaks of the fourfold superlattice in NaNbO₃, as the fingerprint evidence for the presence of the antiferroelectric P phase.¹⁷ Clearly, the relative intensity of the superlattice diffraction peaks is enhanced in the Na-rich state (x > 0), indicating a preferred fourfold superlattice P phase. Conversely, the intensity of the superlattice diffraction peaks gradually weakens due to the lack of Na content, which means that the Na-deficient state (x < 0) will be unfavorable for the stability of the antiferroelectric structure in NaNbO₃.

In order to quantify the influence of Na-occupancy content on the lattice structure of NaNbO₃ in detail, the XRD patterns of Na_1+xNbO₃ samples are refined using Fullprof software based on the Rietveld method. As shown in Fig. S1 (see in the supplementary material), the excellent agreement between experimental data and fitting results confirms the reliability of refinement analysis. Accordingly, the crystallographic parameters obtained from the refinement process are subsequently utilized for lattice visualization via VESTA software. Figure 2 depicts the lattice projection of all samples along the c axis. For P-phase NaNbO₃, the adjacent Na1 and Na2 atoms, as well as the neighboring Nb atoms along the c axis, exhibit a relatively off-center displacement of projection on the ab plane in lattices. It is also one of the important reasons for the typical fourfold superlattice of the P phase. As can be seen from Fig. 2, the gradual decrease of Na occupancy leads to an enhanced tendency of the relatively off-center displacement of the adjacent Na atoms. Notably, the projections of the adjacent Na atoms do not overlap at all in the sample with x = −0.02. However, as the Na content decreases, the adjacent Nb atoms display an opposite trend with the weakening of the relatively off-center displacement, accompanied by a nearly complete overlapping in the sample of x = −0.02. The relevant parameters are provided in Table I. Quantitative analysis of the relatively off-center displacement of the adjacent atoms is obtained by calculating the Wyckoff position of the corresponding atoms. As a result, the displacement of the adjacent Na atoms gradually increases from 0.030 30 of x = 0.02 to 0.354 04 of x = −0.02, while that of the adjacent Nb atoms decreases from 0.029 44 of x = 0.02 to 0.005 62 of x = −0.02. Combined with the discussion of Fig. 1, the weakening of the antiferroelectric structure in Na-deficient samples can be attributed to the greater displacement of the adjacent Na atoms and the reduced displacement of the adjacent Nb atoms.

Distinct from the conventional antiferroelectrics, NaNbO₃ is characterized by its irreversible transition from the antiferroelectric P phase to the ferroelectric Q phase under electric fields, which typically manifests as square-shaped ferroelectric-like hysteresis loops.²⁴ To investigate the modulating effect of Na-site occupancy on field-induced phase transition, the room-temperature polarization-electric field hysteresis loops of Na_1+xNbO₃ are presented in Fig. 4. Previous studies have revealed that the synthesis of polycrystalline NaNbO₃ would inevitably introduce substantial vacancy defects, mainly involving Na vacancies and oxygen vacancies with traces of Nb vacancies.^25,26 Notably, the pronounced volatility of Na at high temperatures leads to that the vacancy effect cannot be negligible in NaNbO₃.²⁷ This inherent limitation has historically constrained the maximum of the applicable electric field during the polarization measurement of NaNbO₃.²⁸ Consistent with these observations, the parent NaNbO₃ in this work exhibits a breakdown field of ∼90 kV/cm. Intriguingly, controlled deviations from Na-site stoichiometry, including both Na-rich and Na-deficient compositions, result in a significant enhancement of the breakdown electric field reaching ∼140 kV/cm. This counterintuitive phenomenon, particularly the improved breakdown field observed in Na-deficient Na_1 + xNbO₃ samples, suggests that the low breakdown field in general NaNbO₃ may not originate solely from vacancy effects. It could also potentially correlate with the intrinsic structural characteristics, such as the crystal distortion in NbO₆ octahedra. Of course, the underlying mechanism requires further elucidation. As shown in Fig. 4, the shape of hysteresis loops still demonstrates a regular trend despite the disparity in the maximum applicable field between the parent NaNbO₃ and the modified samples. The Na-rich samples tend to display an enhanced squareness of hysteresis loops at room temperature, indicative of the preferred ferroelectric feature. Conversely, a progressive weakening of the ferroelectric response is observed with decreasing Na content, as evidenced by the gradual reduction in loop rectangularity.

Microstructural analysis reveals that the Na-rich samples possess enhanced stabilization of the antiferroelectric structure while the Na-deficient state leads to a progressive degradation of the antiferroelectric structure. However, hysteresis loop measurement indicates that those samples with reinforced antiferroelectric structures (x > 0) are easier for triggering the transition to the ferroelectric state, while those with weakened antiferroelectric stability show suppressed trigger response to the electric field. This behavior is interesting but seems to be counterintuitive. To elucidate this anomaly, as well as the relating origin, the room-temperature in situ Raman spectra are measured under varying electric fields, as shown in Fig. 5. For clarity, the two samples with x = −0.02 and 0.02 are, respectively, chosen due to the most obvious differences in their structure and performance. Both samples present distinct three-stage structural evolution of the phonon modes under the applied electric field. During the initial stage with lower electric field (E < E₁), all vibration modes are insensitive to the field without any detectable response, corresponding to the stable antiferroelectric state (AFE). Upon reaching the first critical field (E₁), abrupt variations in different phonon modes mainly manifest through three concurrent aspects, including the merging of phonon modes for two kinds of different Na sites, the dramatic intensity inversion between $ν 5 2$ (sharp decrease) and $ν 5 1$ (rapid enhancement), as well as the complete disappearance of the ν₂ mode accompanied by a significant intensity reduction and a wavenumber shift of the ν₁ mode. These collective evolution indicate the partial breakdown of the fourfold superlattice configuration of P-phase NaNbO₃ in the second stage after the electric field exceeds E₁ (E₁ < E < E₂), marking the trend of transition to the Q phase. Notably, residual signatures of the P phase persist during this stage, suggesting a superposition of the antiferroelectric and ferroelectric states (AFE + FE) in NaNbO₃. When exceeding the second critical field (E₂), the samples undergo further crystal evolution, involving the complete merging of two kinds of Na-site phonon modes, the gradual stabilization of $ν 5 2$ intensity, and the secondary wavenumber shift in ν₅ and ν₁ modes. Therefore, a full transition to the ferroelectric (FE) Q state is completed of NaNbO₃ in the third stage (E > E₂), evidenced by field-saturated phonon responses beyond E₂.

Moreover, a comparative analysis of in situ Raman spectra with varying electric fields between the samples with x = −0.02 and 0.02 reveals a markedly improved critical fields in the Na-deficient state, which is consistent with the polarization hysteresis characteristics in Fig. 4. This correlation reaffirms that NaNbO₃ with an optimized antiferroelectric P phase structure will be more easily triggered to the Q phase driven by an electric field. These findings conclusively demonstrate the critical modulatory role of Na-site occupancy in governing the field-induced phase transition behavior of NaNbO₃ systems. Crystallographic analysis indicates that the antiferroelectric structure collectively arises from the antiparallel displacement of the adjacent Na1 atoms and the distorted NbO₆ octahedra, in the prototypical P phase.²⁹ However, both polarization hysteresis and in situ spectra suggest that this “ideal” P phase exhibits intrinsic metastability under electric fields, readily transitioning to the ferroelectric Q state. Na deficiency results in the increase of the relatively off-center displacement of the adjacent Na atoms, coupled with the concomitant crystal distortion of NbO₆ octahedra, to a certain extent. The electric field-induced transition from the P phase to the Q phase involves transforming the antiparallel displacement of the adjacent Na1 atoms into parallel displacement. Consequently, the increase of the relatively off-center displacement of the adjacent Na atoms necessarily demands higher energy provided by the electric field to realize this phase transition process, thereby increasing the difficulty of the field-induced phase transition. Thus, it is a remarkable phenomenon that enhanced antiferroelectric structure facilitates to stronger ferroelectric characteristics at room temperature, from the macroscopic perspective.

After exploring the modulation influence of Na-site occupancy on the field-induced phase transition in NaNbO₃, the effect on temperature-dependent phase evolution will be further investigated. Figures 6(a)–6(e) present the temperature dependence of the dielectric constant (ε) of Na_1 + xNbO₃ ceramics in the temperature range of 27–627 °C. All samples display a frequency-independent peak near 400 °C, corresponding to the transition from the P phase to the R phase in NaNbO₃. It is well consistent with the previous report.³⁰  Figure 6(f) shows the temperature-dependent dielectric loss for all samples, accompanied by a pronounced abrupt variation at ∼400 °C, which provides additional compelling evidence for the first-order phase transition. Furthermore, dielectric characterization reveals another anomaly (∼100 °C) with a diffuse behavior in the dielectric constant, which indicates dielectric relaxation. For clarity, the corresponding local enlargements are plotted in the insets of Figs. 6(a)–6(e). The relaxation is gradually prominent with the increasing Na content. It typically arises from the presence of the disordered state rather than first-order phase transitions.^31,32

The different relaxations at ∼100 °C for Na_1+xNbO₃ samples may potentially correlate with the different structural evolution tendency during heat processing, due to the slight difference in room-temperature microstructure. Thus, it is a primary issue to clarify. According to the curves in Fig. 6, the relaxation process for all samples has completely finished upon reaching ∼200 °C. Consequently, the Raman spectra at 200 °C are conducted and presented in Fig. 7(a). It is evident that all spectra exhibit negligible difference in both mode shape and relative intensity, suggesting that the phase transition pathway during the heating process is fundamentally consistent for the Na_1+xNbO₃ samples, despite the subtle structural discrepancy at room temperature. In addition, it should be noted that the difference is significant in phonon vibration, respectively, at room temperature and 200 °C, though extensive studies have demonstrated the P phase of NaNbO₃ at 200 °C during the whole phase transition sequence.³³ That is, the P-phase lattice at room temperature will inevitably undergo a gradual lattice expansion and bond distortion with increasing temperature, in spite of the same space group and crystal symmetry. Hence, for Na_1+xNbO₃ series, the lattice structure at 200 °C can be regarded as a distorted P phase. For clarity, in subsequent discussion, the structure state at 200 °C is designated as the P_h state (P phase at high temperatures). The phonon vibration of Na_1+xNbO₃ samples evolves from a distinguishable mode characteristic of room-temperature P phase to a nearly identical feature of the P_h state at 200 °C. The discrepancy of structure evolution under varying temperatures is likely the essential reason for the relaxation behavior during the process from the P state to the P_h state.

In order to further analyze this evolution discrepancy, the two samples with x = −0.02 and 0.02 are selected to measure the temperature-dependent Raman spectra from room temperature to 200 °C, due to their most different behaviors of relaxation. As shown in Figs. 7(b) and 7(c), all phonon modes exhibit a slight redshift with increasing temperature due to the lattice expansion under the thermal effect.³⁴ Moreover, the distinct response of various phonon vibrations to varying temperatures can be directly observed, involving the gradual disappearance of splitting behavior for Na-site phonon modes, the progressive merging of NbO₆ rotation (denoted as NbO₆ rot in Fig. 3) mode, and the intensity redistribution of different ν₅ modes. The increasing temperature provides additional energy to lattices, leading to structural distortion compared to that at room temperature. The comparison between Figs. 7(b) and 6(c) reveals that the corresponding characteristic temperatures associated with different mode evolution are clearly lower in the sample with x = −0.02 than those in the sample with x = 0.02, during the heating process. This indicates the lower energy needed by the sample with x = −0.02 for the structural evolution from the P state to the P_h state. Relevant study has demonstrated that the gradual decrease of temperature will enhance the relatively off-center displacement of the Na atoms as well as the Nb atoms in NaNbO₃, which reflects that the lattice structure can present more pronounced symmetry breaking at lower temperatures.¹³ Thus, compared with the room-temperature P phase, the P_h state at 200 °C should exhibit weaker displacement including both Na and Nb atoms. The analysis related to the above figures indicates that the Na deficiency in NaNbO₃, indeed, induces the distortion of the P phase. Namely, Na-deficient Na_1+xNbO₃ samples possess stronger displacement of the adjacent Na atoms but weaker displacement of the adjacent Nb atoms, compared to the perfect P phase. Hence, it is clear that the Na-deficient P phase at room temperature and the P_h state at 200 °C display consistent behavior of weak displacement for Nb atoms, accompanied by a significant difference in the displacement of Na atoms. Accordingly, for the sample with x = −0.02, a lower energy requirement during the evolution from the room-temperature P phase to the P_h state signifies that, the Na-deficient P phase at room temperature and the P_h state originate from the same mechanism during the phase evolution process from the perfect room-temperature P phase. That is, the variation of displacement behavior in the Nb atoms plays a dominating role during the phase transition from room temperature to 200 °C. Correspondingly, the Na-rich samples demonstrate a more stable P phase at room temperature accompanied by a stronger displacement of the Nb atoms, thereby requiring higher energy to evolve into the P_h state.

In addition, compared with the sample with x = 0.02, the evolution behavior of various phonons in the sample with x = −0.02 is relatively smoother during the whole temperature range. This is another manifestation of the lower energy required in the evolution of the sample with x = −0.02. Thus, it can be concluded that the relatively off-center displacement of the adjacent Nb atoms is the critical factor during the phase evolution in NaNbO₃ from room temperature to 200 °C. The distorted NaNbO₃ at ∼200 °C exhibits a more similar displacement of the Nb atoms to that of room-temperature NaNbO₃ with Na-deficient state, which belongs to a metastable antiferroelectric structure. Of course, although the direct influence of Na atoms on this phase evolution is relatively minor, the variation of Na content can indirectly have an impact on the displacement behavior of Nb atoms, thereby significantly modulating the relaxation behavior at ∼100 °C. It can be attributed to the evolution of the typical antiferroelectric P phase at room temperature to the metastable distorted P phase at higher temperatures.

In summary, a series of nonstoichiometric Na_1+xNbO₃ ceramics are successfully synthesized to investigate the regulation mechanism of Na-site ions on the field-induced phase transition in NaNbO₃. On the basis of the superior capability of the Raman spectroscopy technique in detecting phase transition details, the microstructure characterization of Na_1+xNbO₃ is systematically analyzed via in situ Raman spectra under varying temperatures and electric fields. The modulation of Na-site occupancy on field-induced phase transition is reflected by easier triggering to the Q phase of NaNbO₃ with an ideal antiferroelectric P phase. Combined with the related ferroelectric and dielectric properties, in situ Raman results confirm that the Na-rich Na_1+xNbO₃ samples tend to stabilize a more perfect P phase at room temperature, whereas the Na-deficient samples will develop an octahedral distortion in the preserved P-phase matrix. The distorted NaNbO₃ at ∼200 °C exhibits a more similar displacement of Nb atoms to that of room-temperature NaNbO₃ with a Na-deficient state, which belongs to a metastable antiferroelectric structure. Moreover, the regulation of Na-site atoms on the relaxation behavior at ∼100 °C should be attributed to the evolution of the typical antiferroelectric P phase at room temperature to the the distorted P phase at higher temperatures, through indirectly having impact on the displacement behavior of the Nb atoms. The findings in this work provide an additional design methodology for the structure–activity relationship of NaNbO₃-based materials.

See the supplementary material for the refinement of Na_1+xNbO₃ ceramics.

This work was supported by the Natural Science Foundation of Guangxi Province (No. 2024GXNSFAA010295), Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi (Nos. 2024KY1887 and 2023KY0065), and Innovation Project of Guangxi Graduate Education (No. YCSW2024156).

The authors have no conflict of interest.

H. Cui and X.X.H. have contributed equally to this work.

H. Cui: Investigation (equal); Writing – original draft (equal). X. X. Huang: Funding acquisition (equal); Investigation (equal); Writing – original draft (equal). X. L. Jiang: Investigation (equal); Project administration (equal). C. M. Zhu: Conceptualization (equal); Writing – review & editing (equal). L. G. Wang: Funding acquisition (equal); Writing – review & editing (equal). R. Wang: Validation (equal). S. Lu: Validation (equal). G. B. Yu: Funding acquisition (equal); Software (lead).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.