In situ electric field-dependent structural changes in (Ba,Ca)(Zr,Ti)O₃ with varying grain size

Piezoelectric materials are used for transduction applications due to their efficiency in converting electrical energy to mechanical energy and vice versa. Additionally, for emerging technologies, such as the Internet of Things and Micro-Electro-Mechanical-Systems (MEMS), materials are required to be low cost while displaying a high piezoelectric response even at small dimensions.^1,2 Piezoelectric materials with outstanding properties are often based on lead zirconate titanate [Pb(Zr,Ti)O₃, PZT] because of the high piezoelectric response at the morphotropic phase boundary (MPB), which is shown by the large signal piezoelectric coefficient, $d 33 ∗(≈700 pm / V)$⁠, for actuator applications.^3,4 However, lead toxicity presents an environmental and health problem, especially for biomedical applications.^5–7 For this reason, legal restrictions, such as the EU-Directive 2002/95/EC (RoHS), have been implemented and established a driving force for research toward lead-free alternatives.^4,8,9 Among other lead-free compositions, the solid solutions of (Ba,Ca)(Zr,Ti)O₃ (BCZT) can be a viable alternative to PZT for room temperature applications $d 33 ∗(≈900 pm / V)$⁠.^10,11

While considerable research has been presented on BCZT, the microscopic origins of its functional properties are not well understood.^12,13 Previous works claim that the high piezoelectric response is caused by a diffuse phase transition at a triple point of the cubic, tetragonal, and rhombohedral phases.^10,12–17 However, other reports propose that there is a temperature-dependent polymorphic phase boundary (PPB) between the orthorhombic and tetragonal phases.^18–24 Additionally, the coexistence of the tetragonal, orthorhombic, and rhombohedral phases is discussed.²⁵ Certainly, the emerging phases are dependent on the composition, and there remains a lack of consensus regarding the phase boundary associated with the highest piezoelectric response. Moreover, the preparation conditions can affect the piezoelectric response through the microstructure, which, in turn, influences the electromechanical properties and the crystallographic phases.^26–28 

Generally, grain size-dependent measurements of electromechanical properties can provide critical information for applications. For example, the $d 33 ∗$ for BCZT has been observed to increase with the grain size, especially up to an average grain size of approximately 10 μm.^11,16,29,30 Furthermore, investigating the small to intermediate grain size range (0.01–10 μm) is essential for techniques and applications with limited dimensions like thin films^31–33 or MEMS devices.^1,7 Additionally, some fabrication techniques can lead to samples with small grain size, such as the room-temperature powder aerosol deposition (AD) method, which is promising for ceramic thick films due to being a rapid deposition method.^34–36 However, AD provides samples with an intrinsically small grain size in the nanometer range that has been shown to reduce the electromechanical response.^37–39 

Studies on the grain size dependence of BaTiO₃ (BT) have revealed a maximum in the piezoelectric and dielectric responses at approximately 1 μm.^40–42 In general, the total piezoelectric response of a ferroelectric material can be divided into an intrinsic contribution due to lattice strain and an extrinsic contribution due to ferroelectric domain wall motion and/or phase transitions.^3,43 In addition to the impact of phase transitions, the extrinsic contributions scale directly with the grain size through domain wall mobility and domain wall density.^43,44 At low grain sizes below 1 μm, the domain wall mobility in BT is limited by grain boundaries and internal stress.⁴² This effect was illustrated in an in situ electric field-dependent synchrotron x-ray diffraction (XRD) study on BT samples with varying grain size between 0.3 and 3.5 μm by Ghosh et al.⁴⁵ Above 1 μm, the extrinsic contributions are reduced by an increasing domain width and, thus, decreasing domain density. Arlt et al.^28,40,44 described a decrease in the ferroelectric 90° domain width found in tetragonal BT proportional to the square root of the grain diameter for grains below 10 μm. Additionally, a variation in grain size can also be connected to a change in the crystal phase,^27,28 leading to the appearance of a combined tetragonal and an orthorhombic phase at about 1 μm for BT.²⁸ Therefore, a synergy of high-domain wall mobility connected to a multi-phase region and high-domain wall density can explain the maximum in extrinsic contributions for BT at a grain size of around 1 μm. The grain size dependence of the intrinsic contribution is related to the stability of the ferroelectric phases. Above the Curie point T_C, the ferroelectric tetragonal phase transitions into the paraelectric cubic phase.³ For BT, T_C decreases below a grain size of ≈4 μm,^41,46 as the tetragonal phase has a slightly higher volume compared to the cubic phase, and a driving force toward a lower tetragonality is established.⁴⁶ This decreases the intrinsic contribution, which in comparison does not vary significantly for grain sizes above approximately 4 μm.^40,47

Ferroelectric materials, such as PZT and BCZT, are often compositionally engineered to utilize the enhanced electromechanical properties at the MPB or PPB, respectively, which relies on the phase coexistence observed in this region. The coexisting phases facilitate the formation of additional domain walls compared to those allowed in a single crystal phase. This varies the grain size dependence of their functional properties, which depends on the composition and is often influenced by non-180° domains from multiple phases, such as the tetragonal and rhombohedral phases in the case of PZT.^43,48 Therefore, the grain size dependence of the functional properties changes with doping and composition similar to the crystallographic phases and domain wall mobility.^47,49 This is especially relevant for a composition like BCZT where a multitude of phases are discussed regarding the piezoelectric behavior as described above. In general, the piezoelectric response of BCZT often increases with grain size, especially up to approximately 10 μm.^{11,17,22,24,29,30,50}

The influence of ultra-fine grain sizes of 1 μm and below for BCZT bulk ceramics has been previously investigated, and it is understood that the low grain size limits the ferroelectric properties.^11,29,30,51 For example, Bharathi et al.²⁹ have shown an increase in $d 33 ∗$ by one order of magnitude with a grain size increase from 0.5 to 7 μm. This is in agreement with results reported by Hao et al.,¹¹ where spark plasma sintering (SPS) was used to densify BCZT with grain sizes down to 0.4 μm. Amorín et al.³⁰ investigated BCZT samples with average grain sizes between 1.0 and 5.0 μm using temperature-dependent synchrotron XRD, where a shift in the crystallographic phase toward the orthorhombic was observed. In addition, the influence of internal stress can be significant with decreasing grain size. For example, as described by Arlt²⁸ for polycrystalline BT, larger grain sizes lead to twinning of domain walls, whereas domain wall clamping and a subsequent reduction in domain wall motion can be observed with reducing grain sizes. Additionally, stress and grain size reduction can lead to phase transitions, further impacting the extrinsic contributions to the piezoelectric response.^27,28,52 Similar observations were also made in PZT, where Picht et al.²⁷ used in situ electric field-dependent XRD data to observe the increased stress at smaller grain sizes, the resulting lower domain wall mobility, and the overall lowered tetragonality.

One of the earliest in situ electric field-dependent synchrotron XRD studies is the work performed by Endriss et al.,^53,54 who investigated PZT bulk ceramics in 1999, and Lee et al.,⁵⁵ who investigated PZT thin films in 2001. Since then, among others, Hall et al.⁵⁶ and Jones et al.⁵⁷ have used this method to investigate the intrinsic and extrinsic contributions to the macroscopic strain response of bulk ceramic samples.^{45,53,54,56–65} The method can also deliver insights into the variation of the piezoelectric response down to sub-micrometer grain size. For example, Ghosh et al.⁴⁵ used it to measure BT samples with average grain sizes of approximately 0.2–3.5 μm, as discussed above. Following this, in situ electric field-dependent synchrotron XRD measurements of BCZT were performed on intermediate to large average grain size samples.^59,65,66 Ehmke et al.,⁵⁹ for example, identified extrinsic contributions as the main mechanism behind the large piezoelectric response of BCZT for samples with a grain size of ≈19 μm. This is in agreement with the results of Tutuncu et al.⁶⁵ for 20 μm grain size. Meanwhile, Sanz et al.⁶⁶ combined in situ synchrotron x-ray diffraction and total scattering measurements while varying the composition, reporting that the maximum piezoelectric response occurs at a minimum relative contribution of lattice strain. However, neither of these authors investigated the influence of grain size on the properties of BCZT.

At lower grain sizes, the piezoelectric response of BCZT is limited.^11,29,30,51 However, there remains a lack of understanding for this limitation as former grain size-dependent studies on BCZT only investigated grain sizes down to approximately 0.5 μm.^11,30 Therefore, this study combines the hydrothermal powder preparation method and spark plasma sintering to conduct large electric field-dependent electromechanical measurements on samples with a grain size down to below 0.08 μm. Furthermore, in situ electric field-dependent synchrotron XRD experiments are utilized to distinguish between extrinsic and intrinsic contributions to the piezoelectric response.

To prepare samples with a varying range of different average grain size, lead-free polycrystalline Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ powder with an average particle size of 0.075 μm was prepared using the hydrothermal method. The starting materials BaCl₂⋅H₂O (99%), CaCl₂ (97%), and ZrOCl₂⋅8H₂O (98%) were dissolved and mixed in de-ionized water through stirring. The precursors were obtained via a drop-wise addition of tetrabutyl orthotitanate (97%). NaOH was utilized to control the pH value for a molar ratio of 1–5 between Ba²⁺ and OH⁻. The precursor was stirred for 1 h and then put into a Teflon-lined autoclave, which was heated to 190 °C for 24 h and afterward naturally cooled.

Following this, the resulting powder was densified using spark plasma sintering (SPS) in a commercial setup (Dr. Sinter Lab SPS-515S, Fuji Electronic Industry Co., Ltd., Japan). For every sample, 0.75 g of powder was filled in a graphite die with an inner diameter of 10.4 mm. Graphite sheets were placed between the powder and graphite die to prevent adhesion during the sintering process. The powder was pre-pressed uniaxially under approximately 7.4 MPa before densification. Under a vacuum, the temperature was increased by applying a current within 1 min up to a temperature of 600 °C as determined with a pyrometer. The temperature was held for 8 min to stabilize until the temperature was increased further to a sintering temperature of 1100, 1125, 1150, 1175, 1200, 1300, and 1400 °C. The pressure was continuously increased, and upon reaching the sintering temperature, a maximum pressure of 75 MPa was applied. The respective sintering temperature was held for 5 min before cooling down to room temperature, while the pressure was released. Heating and cooling rates were approximately 100 K/min. Additionally, all samples were annealed at 950 °C for 12 h to remove residual stress and re-introduce oxygen.

Microstructure analysis was performed on polished samples (1 μm diamond and oxide-polishing suspension) with a scanning electron microscope (Helios NanoLab 600i FIB Workstation, FEI Company, USA). For each sample, three images and about 100 grains each were analyzed with the linear intercept method utilizing software tool ImageJ.⁶⁷ The results were used to determine a grain size distribution, with the median representing the average grain size.

Before macroscopic measurements, the samples were ground to a thickness of 1 mm and annealed at 600 °C for 1 h to avoid grinding-induced stress. Platinum layers were sputtered on both sides of the samples as electrodes. The polarization and the strain against the electric field were measured with a commercially available piezoelectric test setup (TFAnalyzer 2000, aixACCT Systems GmbH, Germany). The measurement frequency was 10 Hz with a maximum electric field of 3 kV/mm supplied by a high voltage amplifier (20/20C, Trek Inc., USA).

In situ electric field-dependent measurements were conducted on beamline I15 of the Diamond Light Source Synchrotron Facility (DLS, Oxfordshire, UK) with a 72 keV (λ = 0.1722 Å) high-energy monochromatic x-ray beam. The incident beam size was 76 × 120 μm² (vertical × horizontal), and calibration was carried out using a LaB₆ sample. The sample-to-detector distance was 824.71 mm. BCZT samples sintered at 1100, 1300, and 1400 °C were cut into bars (4 × 1 × 0.5 mm³) and annealed at 600 °C for 1 h, and the opposing 4 × 1 mm² surfaces were coated with silver paste as electrodes. During measurement, the electrodes were connected with a custom-built sample holder as used by Hall et al.^56,61 A bipolar electric field loop up to 3 kV/mm with a frequency of about 10 mHz was applied using a Matsusada EC-10 high-voltage amplifier. Data acquisition was performed with a Pilatus3 X CdTe 2M large area detector. Two-dimensional diffraction patterns were caked (15° per slice) along the azimuthal angle (ψ) with DLS facilities DAWN software (version 2.29).⁶⁸ 

The x-ray diffraction (XRD) data of the unpoled samples were analyzed by full pattern refinement with TOPAS (version 5, Bruker),⁶⁹ while selected area fitting was used for analysis of the data obtained from in situ experiments. For the latter, a custom Python script (version 3.10.10) was used to fit lmfit's (version 1.2.1)⁷⁰ skewed Gaussian and Pseudo Voigt models at every reflection identified with the scipy.signal.find_peaks method (version 1.10.1).⁷¹ The skewed Gaussian model was utilized to identify reflection asymmetry and the Pseudo Voigt model to identify reflection position. Error margins were directly determined by the model and used for error propagation calculations.

BCZT samples with varying grain sizes between 0.08 and 7.35 μm were prepared with the SPS method using different maximum sintering temperatures between 1100 and 1400 °C. Representative microstructures of the samples prepared at 1100, 1300, and 1400 °C are shown in Figs. 1(a)–1(c). It is important to mention that all samples were annealed after SPS and after grinding, but before image acquisition, at a maximum temperature of 950 °C in air. No significant influence of annealing on the grain size at this temperature is expected.⁷² Density measurements following the Archimedes' principle revealed that samples prepared at 1300 or 1400 °C both have 99 ± 1% of their theoretical density, whereas samples sintered at 1100 °C display 95 ± 1% theoretical density. It appears that an increase in SPS temperature from 1100 to 1300 °C primarily leads to densification, while an increase to 1400 °C also leads to coarsening. This is supported by the grain size distributions shown in Fig. 1(d). The average grain size, here defined as the median of the grain size distribution, increases from 0.08 to 0.18 μm with a temperature increase from 1100 to 1300 °C. Increasing the temperature to 1400 °C increases the average grain size to 7.35 μm. In the following sections, the samples will be referenced according to their average grain size.

BCZT ceramics with different grain sizes were investigated to identify the differences in their electromechanical behavior. In Fig. 2, the macroscopic polarization- and strain-electric field hysteresis is plotted against an applied bipolar electric field loop up to 3 kV/mm. It is evident that the maximum polarization increases from approximately 4 to 17 μC/cm² with increasing grain size, while the maximum strain exhibits a similar trend. The 0.08 μm grain size sample demonstrates a nearly linear response to the applied electric field without polarization or strain saturation and limited hysteresis, indicating an approximately linear dielectric behavior. With increasing grain size, the 0.18 μm sample displays an increase in the electromechanical response, which corresponds to the onset of an apparent polarization saturation and an increase in hysteresis. Despite the shift toward a more ferroelectric response in regard to the polarization behavior, the 0.18 μm sample shows an electrostrictive response. This suggests that the piezoelectric character is not fully developed at these grain sizes and below as shown in a similar response in the 0.08 μm sample. The sample with 7.35 μm grain size shows a more pronounced hysteresis with an apparent saturation in the polarization-electric field hysteresis curve and corresponding enhanced remanent polarization as well as significantly increased maximum polarization and strain values. These data demonstrate that BCZT shows a transition from linear dielectric to ferroelectric behavior with increasing grain size within the applied electric field range used in this study.

This transition has not been described in literature before as other studies focused on higher average grain sizes. For a direct comparison with the available literature,^11,16,29,30 Fig. 3 shows the previously observed large field piezoelectric coefficient $d 33 ∗$⁠, which is in the referenced literature defined as the maximum strain divided by the maximum electric field as a function of the average grain size. Although $d 33 ∗$ is an indicator for the large field electromechanical response, it is important to note that $d 33 ∗$ varies with the amplitude of the applied electric field.³⁰ It was previously observed that $d 33 ∗$ values in BCZT become saturated at an electric field above approximately 2 kV/mm for average grain sizes of about 2 and 1 μm.³⁰ Therefore, only results with applied electric fields above 2 kV/mm are included in Fig. 3. For the samples analyzed in this study with average grain sizes below 1 μm, the polarization-electric field hysteresis loops are not saturated. It is possible that this is because the coercive field has not been reached, meaning that a ferroelectric response might be observed at larger applied electric fields. However, as the samples do not display ferroelectricity and have a cubic symmetry as described below the general trend is supposed to remain the same. Besides the general decrease, a significant reduction in $d 33 ∗$ is observed between 0.18 and 0.12 μm grain size.

To investigate the initial crystallographic structure without an applied electric field, Fig. 4 shows a 2θ diffraction scan at room temperature for samples sintered at 1100, 1300, and 1400 °C. First, reflection broadening can be identified with decreasing grain size. This can be caused by the smaller grain size itself, which is correlated with a smaller crystallite size leading to peak broadening according to Scherrer's equation.⁷³ Additionally, a peak shift toward lower diffraction angles was observed with reducing grain size below 7.35 μm. This is most likely connected to the processing conditions, for example, due to the presence of defects such as oxygen vacancies, however, as the following analysis focuses on the relative changes in the peak position with the applied electric field, the initial peak positions are not considered to be a significant factor in the data analysis.

Two phases can be distinguished for each sample, a pseudocubic BCZT phase (P4mm) and a secondary CaTiO₃-like phase (Pbnm). Full pattern refinement reveals that the phase fraction of the CaTiO₃ phase is about 3 ± 3%, where the resulting phase fraction is generally lower for higher grain size samples. The low overall phase fraction and the high error margin led to the assumption that the secondary phase cannot be correctly determined for this data with full pattern refinement. Overall, the crystallographic phases of BCZT are difficult to determine. There is no clear consensus about which phases are expected for this composition at room temperature following the phase diagram proposed by Keeble et al.;¹⁸ there should be a tetragonal and an orthorhombic phase. However, the low grain size of the investigated samples leads to peak broadening and thereby overlapping of peaks. Hao et al.¹¹ also describe this in their work, where a shift from overlapping to distinct double peaks can be seen with increasing grain size of BCZT samples. Without visible peak splitting, full pattern refinement did not result in fits sufficient to analyze (Figure S1 in the supplementary material). Therefore, these data will be treated as pseudocubic with a selected area single fitting method.

Without an applied electric field, the diffraction patterns of samples with different grain sizes all display same pseudocubic reflections, where the primary differences are caused by extrinsic defects like the secondary phase or intrinsic defects like grain boundaries. Both types of defects seem to be more relevant for the lower grain size sample. When applying an electric field, the impact on the diffraction peak shape and position is more apparent for higher grain sizes. This can be observed in the plots of diffraction data (Fig. 5) parallel to the applied electric field direction (ψ = 0 or ψ = 180°). The lowest 0.08 μm grain size sample shows nearly no response to the applied electric field for the pseudocubic 111 or the 200 reflection. For the 0.18 μm grain size sample, there is a slight peak shift toward a lower angle for the 200 reflection at maximum electric field (E_max; Fig. 5). In contrast, the 7.35 μm grain size BCZT is significantly impacted by the applied field. There is an irreversible reflection shift toward lower diffraction angles accompanied by slight narrowing of the peak widths. Furthermore, significant changes in the peak profile of the 200 reflection are recognizable for the 7.35 μm grain size sample, which could indicate the presence of a tetragonal or orthorhombic phase. However, as mentioned above without clear peak splitting, it is difficult to identify the occurrence of any extrinsic electric field-induced domain switching or phase transformation mechanisms.

For further analysis, each reflection is fitted with a Pseudo Voigt function. The fit is used to determine the center of the reflection, which can be utilized to calculate the pseudocubic lattice parameter with the Bragg equation. The relative change of this lattice parameter resembles the lattice strain that represents the intrinsic contribution to the piezoelectric response. For the pseudocubic 200 reflection, the lattice strain is plotted against the applied electric field in Figs. 6(a) and 6(c). The 0.08 μm grain size sample displays no significant response to the applied field. The existence of a critical grain size d_C below which ferroelectric properties vanish was proposed for BT by Zhao et al.⁴⁶ First, the grain boundaries limit the domain wall mobility and, thereby, extrinsic contributions.⁴² Furthermore, there is a diminishing of non-cubic phases with slightly higher volume than the cubic phase as the limited dimensions result in a stress-associated driving force toward the cubic phase with decreasing grain size.⁴⁶ This reduces T_C to room temperature and below when d_C is reached. For BCZT, the d_C could be reached or approached at 0.08 μm, leading to the observed suppression of ferroelectric properties, i.e., both intrinsic and extrinsic contributions. This result confirms the macroscopic strain-electric field data obtained for the ultra-fine grained BCZT ceramic.

The 0.18 μm grain size sample shows a non-hysteretic strain response to the applied electric field comparable to the macroscopic measurements. To evaluate the total macroscopic strain from in situ XRD data, both intrinsic and extrinsic contributions need to be taken into account. Ehmke et al.⁵⁹ and Tutuncu et al.⁶⁵ determined the extrinsic contributions in similar experiments with the ferroelectric domain texture defined by the change in peak intensity ratio for BCZT samples. However, they both utilized a significantly larger grain size of ≈20 μm. Because no peak splitting is observed for the obtained data, this approach cannot be used here to discuss the electric field-induced ferroelectric domain texture. Nevertheless, a change in peak intensity ratio can also lead to a change in reflection shape when multiple peaks overlap. Therefore, the reflection asymmetry is used as an indicator for the intensity ratio of the underlying peaks. To define the reflection asymmetry, a skewed Gaussian function is fitted on the pseudocubic reflections to determine the asymmetry factor γ.^70,74 Exemplary skewed Gaussian fits are shown in Fig. 7 for the 7.35 μm average grain size sample. Assuming two underlying peaks for tetragonal crystal symmetry, a negative γ resembles an increased intensity of the peak at the higher diffraction angle, as shown for 200 reflection before in Fig. 7(b). As an electric field is applied, a remanent shift toward a negative γ can be observed parallel to the applied electric field, which could be associated with a phase transition from tetragonal to orthorhombic. However, the mechanisms that contribute to the evident variations in γ are not discussed further here due to issues in identifying the specific phases involved, as discussed above.

To discuss the reversible extrinsic contributions to the strain, the asymmetry factor γ against the applied electric field is displayed in Figs. 6(b) and 6(d) for the pseudocubic 200 reflection, which shows a more pronounced change compared to the 111 reflection. In contrast to the lattice strain, there is no significant change in the reflection shape with the applied field for the 0.08 and 0.18 μm grain size samples. Furthermore, compared to the 7.35 μm grain size sample, the peak shape is similar parallel and perpendicular to the applied field. Consequently, it is proposed that both samples show no significant domain wall motion under an applied electric field. The 0.08 μm sample has no significant polarization or strain response under the applied field of 3 kV/mm as they are below the critical grain size. In contrast, the 0.18 μm sample displays significant intrinsic contribution, but no apparent extrinsic contributions (hysteresis) because of limited domain wall mobility, similar to fine-grained BT.⁴⁵ This has not been seen in other grain size-dependent studies on BCZT as they do not reach this grain size. For example, in the work of Bharathi et al.,²⁹ the sample with the smallest average grain size of 0.5 μm was found to exhibit a ferroelectric response.

The 7.35 μm grain size sample shows a reflection shape change with the applied electric field, indicating extrinsic contributions and a partly irreversible or remnant lattice strain. Importantly, the ferroelectric behavior of this sample corresponds well to previous studies for BCZT.^59,66,75 However, the contribution to the total strain can still not be quantified with sufficient accuracy due to the pseudocubic reflections. Nevertheless, it is expected that the extrinsic contributions provide the major part when the grain size is closer to an optimal value, similar to the results of Ehmke et al.⁶⁵ and Tutuncu et al.⁶⁵ It is proposed that the intrinsic contribution also increases from d_C up to an intermediate grain size, similar to BT.^40,47

With decreasing grain size a stress-associated driving force limits the tetragonality as dicussed above.⁴⁶ Additionally, stress has been observed to lead to phase transitions;⁵² therefore, the electromechanical properties are discussed in terms of internal stress in the following. To analyze the stress with XRD data, the lattice spacing, d₂₀₀, is plotted against the square sine of the azimuthal angle, ψ. The change in the dependency on the square sinus shown in Fig. 8 can be used to discuss the residual stress, where the changing slope of the linear fits is an indicator of a relative change in stress. The slopes for the different grain sizes and at different applied electric fields are shown in Table I. The total stress values are not calculated as the texture and phase fraction cannot be determined.

Before applying an electric field (E₀), the difference between the slopes is insignificant and most likely caused by a calibration error. However, as no type I residual stresses are expected for unpoled samples, these lines can function as calibration lines to discuss the electric field response.^76,77 With the application of a maximum electric field of 3 kV/mm (E_max), the slope changes depending on the grain size. For the 0.08 μm sample, no significant response can be observed, which corresponds well with the previous results. Here, the stress-associated driving force limiting the tetragonality is not apparent as it is not dependent on an applied electric field and can only be observed on the local scale.^46,76,77 There is a small and reversible decrease in the slope for the 0.18 μm grain size sample, which could be due to a small tensile stress in the electric field direction connected to the non-hysteretic behavior discussed above. However, this shift is insignificant, especially, compared to the 7.35 μm grain size sample that shows an irreversible contribution. This remnant change in the slope is connected either to residual tensile stress or more likely to domain or phase switching, which is also hinted at by the systematic change in peak shape as discussed above and seen in the literature.⁵⁹ Overall, this analysis further confirms the transition from linear to hysteretic behavior from 0.08 to 7.35 μm.

Spark plasma sintering was used to prepare lead-free polycrystalline BCZT samples with grain sizes ranging from 0.08 to 7.35 μm. In situ electric field-dependent synchrotron x-ray diffraction measurements reveal a transition from paraelectric to ferroelectric behavior with increasing grain size. This transition is proposed to be connected to the grain size as the minor impurities and defects observed in this study are not sufficient as an explanation. For instance, BCZT is considered ferroelectric at room temperature for a wide compositional range. Importantly, all samples were produced using the same starting powder in the same processing conditions, where only the sintering temperature was varied. Therefore, significant changes in the stoichiometry and defects are not expected between the different samples. The 0.08 μm grain size sample demonstrates no significant response to the applied electric field, which is suggested to be connected to a critical grain size between 0.08 and 0.18 μm, similar to that observed in BT. Below this critical grain size, a combination of a reduced tetragonality associated with the limited grain volume and an increased grain boundary volume limiting domain wall mobility is suggested to suppress the electromechanical properties. Samples with an average grain size of 0.18 μm displayed intrinsic contribution to the total lattice strain but no extrinsic contributions, explaining the observed reduced ferroelectric response and limited electric field-dependent polarization and strain hysteresis.

See the supplementary material for a figure (Fig. S1) to display a comparison of different full pattern refinement approaches on the synchrotron x-ray diffraction data. It can be seen that the pseudocubic reflections can either be fitted assuming multiple phases (a), an apparent texture (b), or assuming a different peak shape as due to peak broadening (c). Therefore, and due to the lack of peak splitting, the electric field-dependent data are not further analyzed with full pattern refinement.

M.K., J.G.M., N.H.K., and K.G.W. gratefully acknowledge the financial support for this work from the Deutsche Forschungsgemeinschaft (DFG) under No. GRK2495/F. A.M. and K.K. acknowledge the financial support by the JSPS Japanese-German Graduate Externship (Grant No. 2019/R1). The authors thank Diamond Light Source for access to beamline I15 (Proposal No. CY31704) that contributed to the results presented here.

The authors have no conflicts to disclose.

Michel Kuhfuß: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Juliana G. Maier: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). David A. Hall: Formal analysis (equal); Investigation (equal); Resources (equal); Writing – review & editing (equal). Bingying Xie: Investigation (equal); Writing – review & editing (supporting). Annette K. Kleppe: Investigation (equal); Resources (equal); Writing – review & editing (supporting). Alexander Martin: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Ken-ichi Kakimoto: Project administration (equal); Resources (equal); Writing – review & editing (equal). Neamul H. Khansur: Conceptualization (equal); Data curation (supporting); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). Kyle G. Webber: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

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