Insights into the Early Size Effects of Lead‐Free Piezoelectric Ba0.85Ca0.15Zr0.1Ti0.9O3

Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT) stands out among lead‐free ferroelectric oxides under consideration to replace state‐of‐the‐art high‐sensitivity piezoelectric Pb(Zr,Ti)O3, for a range of energy conversion ceramic technologies. However, the best performances have been reported for very coarse‐grained materials, and attempts to refine microstructure below 10 µm grain size consistently result in significant property degradation. Here a comprehensive study of the grain size effects on the properties of BCZT across the micron scale is reported, down to the verge of the submicron one. Results show a distinctive early evolution of properties for grain sizes between 1 and 5 µm. For the larger sizes in this range, an opposite effect is found for the piezoelectric charge coefficient and electric field‐induced strain with respect to the very coarse‐grained material, while very good overall performance is maintained. For the lower sizes, relaxor features appear, yet materials can still be poled indicating their ferroelectric nature. This strongly resembles size effects in the Pb(Mg1/3Nb2/3)O3‐PbTiO3 system, driven by the slowing down of the relaxor to ferroelectric transition with size reduction, though kinetics seem to slow down across much larger grain sizes for BCZT. Concomitant changes in the polymorphic phase coexistence are described and discussed by synchrotron X‐ray diffraction.


Introduction
Piezoelectric ceramics are a mature and ubiquitous technology widely used in ultrasonic transduction, sensing and actuation applications, which also offers great prospects as energy harvesting DOI: 10.1002/aelm.202300556[3] They are smart materials that react to an electrical stimulus through a deformation or mechanical stress, and also give electrical answer under a mechanical stimulus.][10] In recent years, specific compositions of the BaTiO 3 -CaTiO 3 -BaZrO 3 ternary system have emerged as leading leadfree candidates to replace PZT, owing to the high piezoelectric charge coefficients (d 33 ) reported, [11][12][13][14] with figures approaching those of high-sensitivity soft PZTs.Specifically, most research has focused on the composition Ba 0.85 Ca 0.15 Zr 0.1 Ti 0.9 O 3 (hereinafter BCZT), which is placed at a region in the phase diagram where up to three ferroelectric polymorphs seems to converge, and that shows phase coexistence strongly dependent on temperature, unlike the case of the vertical MPB of PZT. [15]In this system, polar phases involved are the rhombohedral R3m, orthorhombic Amm2 and tetragonal P4mm perovskites, in addition to the cubic Pm-3m one above the Curie temperature (T C ). [15][16][17] The presence of Amm2 among the polymorphs of BCZT is controversial, [18] and the enhanced piezoelectric performance was first attributed to a nearly vanishing polarization anisotropy that facilitates polarization rotation in the proximity of a tricritical point that excluded the Amm2 phase. [11]However, subsequent reports signaled the polymorphic transition from Amm2 to P4mm near room temperature as the origin of the outstanding properties of BCZT. [19]It is worth recalling the very well established presence of the former polymorph between the tetragonal and rhombohedral ones in the polymorphic phase transition sequence of BaTiO 3 (and of KNbO 3 ) on cooling from the high-temperature cubic phase. [7,13][22][23][24] This is probably the most important parameter among material properties when performance for actuation is assessed, without forgetting the strain hysteresis Hs (ΔS/S max ).This parameter is determined from S-E curves as the strain difference at half of the maximum E-field divided by the maximum strain S max achieved.Despite the large d 33 * reported for BCZT, comparable to those of soft PZTs, strain responses are highly hysteretic (Hs ≈27% was reported in the seminal work by Liu and Ren [11] for a ceramic with d 33 of 620 pC N −1 ), as compared to values for, e.g., commercial PZT-5H (Navy type-VI) of ≈12%. [25]Indeed, large but hysteretic nonlinear strain response is typical of soft piezoceramics (usually higher than 10%), inherent to the increased piezoelectric activity when it results from the activation of extrinsic mechanisms like domain wall motion.This is an issue for actuation because it causes poor positioning accuracy. [26]otwithstanding the high piezoelectric response so far reported in BCZT ceramics, their possible transfer to the current piezoelectric technologies is being hindered by ceramic processing issues.In this sense, preparation of high-quality, reliable ceramic materials with tailored microstructure and controlled grain growth while performance is maintained remains a challenge.Like any other ceramic component for microelectronics; it is advantageous to have dense and homogeneous microstructures with fine grain sizes to optimize material performance and improve reliability.[22][23][24] This compromises mechanical and electrical strengths and offers poor reproducibility of materials properties, as extensively illustrated in literature. [13]here have been several attempts to refine the microstructure of BCZT ceramics, and dense materials with reduced grain size across the micron range have been obtained by two-step sintering [27,28] or using highly reactive powders synthesized by sol-gel. [29]Further refinement down the submicron range has been attained by spark plasma sintering (SPS). [30,31]However, these studies consistently showed a distinctive degradation of piezoelectric performance as soon as grain size entered the sub-10 μm range.This was somehow unexpected, and actually very different to the behavior of state-of-the-art PZT and other lead containing MPB materials, [32,33] such as BiScO 3 -PbTiO 3 that mostly maintain functionality all across the micron and submicron ranges, until the vicinity of the nanoscale. [34]It is thus essential to carry out a comprehensive investigation of the grain size effects on the electrical and electromechanical properties of BCZT and the underlying mechanisms, for which a series of high-quality ceramics with decreasing grain size across the micron range, down to the verge of the submicron-range is required.
Ideally, it is preferred to use a single-source powder and the same sintering procedure for obtaining the whole series of BCZT ceramics.This has been achieved here by SPS of nanocrystalline powders obtained by mechanosynthesis.SPS is an electricalcurrent-and pressure-assisted sintering procedure that makes possible the preparation of fully dense materials with controlled grain sizes in short times of only few minutes. [35]When combined with mechanosynthesized, highly-reactive nanocrystalline powders, it has allowed ceramic materials with refined microstructures down to the nanoscale to be obtained for a number of ferroelectric perovskite oxides among the most topical ones, [36,37] and the grain size effects comprehensively described for them. [38,39]This approach is applied here for BCZT, for which grain size effects on properties within the sub-10 μm range are disclosed.

Results and Discussions
Ceramics obtained by SPS at temperatures between 1000 and 1350 °C systematically attained very high densifications (> 99% of the theoretical density) and homogeneous microstructures with hardly porosity, as shown in Figure 1.As the SPS temperature decreased, grain size was reduced from roughly 10 μm down to the submicron range.Largely refined microstructures were thus consistently obtained, as compared to the ceramic prepared by conventional means with a coarse-grained microstructure (Figure S1a of the Supporting Information).A typical bimodal microstructure with abnormally grown grains up to 35 μm in size resulted in the latter case, along with a lower densification (95% of the theoretical density). [40]rain size distributions were obtained by quantitative image analysis and results are given in Figure 2. The analysis showed lognormal unimodal size distributions that shifted to small sizes and narrowed with decreasing SPS temperature.Average grain size was reduced from 5.0 μm down to 1.0 μm when temperature was changed between 1350 °C and 1000 °C, while distribution width was decreased from 1.75 μm down to 0.3 μm.The temperature dependence of the average values can be fitted by using an Arrhenius-type curve, considering non-isothermal kinetics, [41] as shown in Figure 2b.This indicates that a single thermally activated grain growth mechanism is active in this temperature interval during SPS.Note that, the dominant densification mechanism (via grain boundary diffusion) has an activation energy much higher than that of the coarsening mechanism (via surface diffusion), which is quite beneficial to achieve full densification while controlling microstructure coarsening.
Achieved differences in microstructure are even more obvious when grain volume distributions are considered instead of the size ones (Figure 2c).They are relevant because ferro-/piezoelectric properties are mainly determined by the grains occupying most of the material volume.Note that for the sample SPS at 1000 °C, this corresponds to grains with diameter between 1 and 2 μm, whereas for the sample SPS at 1100 °C, most of the volume is occupied by grains between 2 and 4 μm in size, i.e., this is twice the previous values.As for samples SPS at 1250 °C and 1350 °C, respectively, most of the material is similarly formed by grains with diameters in the range between 4 and 8 μm.The difference in grain volume distributions of these two sets of samples, that is, samples SPS at 1000 °C and 1100 °C with most of the grains below 4 μm and those SPS at 1250 °C and 1350 °C with most of the grains above, will have strong implications on the ferro-/piezoelectric performance of this system.
[29][30][31] However, and before addressing the size effects, the possible presence of SPS effects on properties, either related to the low thermal budget or the involved reducing conditions must be ruled out.Besides, mechanosynthesis is known to result in significant levels of microstrain within the per-ovskite oxides, only sluggishly relaxed during the subsequent ceramic processing at high temperature. [42]The possibility of incomplete re-oxidation during the post-thermal treatment cannot be ignored either.The relevance of this effects was evaluated by comparing the properties of the material SPS at 1350 °C with those of a ceramic also conventionally sintered at 1450 °C but with hindered abnormal grain growth (fine-grained sample in Table 1 and Figure S1b of the Supporting Information), which showed a very similar grain size distribution. [40]he temperature dependence of dielectric permittivity and the RT ferroelectric hysteresis loops for these two materials with comparable microstructure are provided in Figure S2 of the Supporting Information.No significant differences were found between the two samples conventionally (fine-grained) and spark plasma sintered from the same source powder, except for the slightly higher polarization achieved in the latter, which demonstrates the absence of significant SPS effects, neither related to microstrain nor to incomplete re-oxidation.Indeed, these samples with average grain sizes of ≈5 μm show temperature dependences of dielectric permittivity and losses quite similar to those of largely coarsened materials, in which up to three dielectric anomalies can be identified, whose positions are not frequency dependent, as shown in Figure 3a for sample SPS at 1350 °C.These anomalies are associated with the successive structural phase transitions of BCZT, [15] namely, on heating, from Table 1.Correlation between SPS temperature and average grain size of the SPS samples, along with that of two samples obtained by conventional sintering. [40]Macroscopic properties of the ceramics: d 33 the linear piezoelectric charge coefficient, d 33 * the "effective" piezo-coefficient and Hs the strain hysteresis, obtained from the S-E curves.

SPS
Grain size Conventional sintering [ 40] Fine-grained 4.7 270 ± 5 1300 6.5 Coarsegrained 20 a ) 480 ± 10 1000 13.0 a) Average size obtained from the grain volume distribution of a bimodal microstructure. [ 40]ombohedral to orthorhombic about 273 K, then to tetragonal about 300 K, and finally to the paraelectric phase at Tc of about 350 K (the ferroelectric phase transition), as also illustrated in Figure S3 of the Supporting Information for the largely coarsened materials. [40]here are not qualitative differences between the dielectric responses of the ceramics SPS at 1350 °C and 1250 °C, so that the three phase transitions can still be identified in the latter material with an average grain size of 3.5 μm, as shown in Figure 3b.Recall, that volume distributions were not so different in these cases.However, the temperature dependencies of permittivity and losses are drastically modified for the materials SPS at 1100 °C and 1000 °C with average grain size of 2 and 1 μm, respectively.In these cases, a single, largely widened and depleted dielectric anomaly is evidenced, as shown in Figure 4.This resembles the behavior of model ferroelectric BaTiO 3 , and it is generally associated with low-permittivity grain boundaries that exert an increasing dilution effect on the dielectric properties as grain size is reduced.However, this is usually observed for much smaller grain sizes, in the submicron range when approaching the nanoscale. [43]Besides, temperature data below 200 K has the opposite behavior, so that both permittivity and losses increase with decreasing grain size below RT.Curves at 1 MHz for all materials are compared in Figure 5 to highlight this trend.Therefore, this excludes a grain boundary effect, and suggests instead changes in the polymorphic phase coexistence and/or domain configurations with reducing grain size.Domain dynamics determines the extrinsic (non-lattice) contribution to the dielectric response, and configurations are known to evolve with microstructure. [44]roadening and depletion of the dielectric anomaly is accompanied with the appearance of a distinctive frequency dispersion at temperatures below the maximum.Actually, the dielectric response of these two samples with nearly all grains below 4 μm   strongly resembles that of ferroelectric relaxors (see Figure S4 of the Supporting Information).That is, the maximum permittivity shifts toward higher temperatures with increasing frequency, which fits a Vogel-Fulcher type relationship, as also illustrated in Figure S4 (Supporting Information) for both materials.
An evolution from conventional to relaxor ferroelectric with the decrease of grain size might then takes place, as that described for the (1-x)Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 (PMN-PT). [45]In this system, a high temperature relaxor state is known to exist for x ≤ 0.35, so that the dielectric anomaly is not related to a ferroelectric phase transition but to the dynamics of polar nanoregions (PNRs) nucleated at high temperature around chemically ordered regions. [46]Nonetheless, samples with x ≥ 0.1 spontaneously evolve (by growth and coalescence of the PNRs) toward a ferroelectric state on cooling.The kinetics of this transition has been shown to slow down as grain size is reduced across the submicron range. [47]Intermediate, very fine domains configurations are then quenched at room temperature for submicron structured materials. [48]An analogous behavior might occur for BCZT, though the slowing down would take place at significantly higher grain sizes, already in the micron range.Indeed, an evolu-tion from conventional to relaxor ferroelectric has been described for BaTi 1-x Zr x O 3 , [49] and relaxor behavior had already been reported for BCZT materials with grain size below 1 μm. [27,30]The origin of the relaxor state in B-site substituted BaTiO 3 has been discussed recently, and related to the disruption of the Ti-O-Ti chains by local random strain fields in the case of homovalent substitutions. [50]ielectric results indicate then a sharp decrease of the polar order scale for with grains below 4 μm in size, supported by the evolution of the ferroelectric hysteresis RT.Loops with grain size are shown in Figure 6.Samples with most of the grains above 4 μm showed similar polarization and current loops, characterized by saturation of polarization being slowly reached, P s approaching 18 μC cm −2 , and remnant polarization, P r , about 7 μC cm −2 which are similar to reported for the coarse-grained ceramic. [40]Note, however, the large difference with the hysteresis loops of samples with grain sizes well 4 μm, which are clearly far from approaching saturation (better seen in the derivative curves in Figure 6d).also the remarkably low mean coercive field E c ≈ 0.25 kV mm (as determined from maxima in the current density loops) samples most grains above μm, and the wide distribution of coercivity of samples with size below this value.This indicates exceptionally slow switching dynamics in the latter samples, for which difficult poling can be anticipated.
Loops as a function of temperature were also obtained to reflect the effect of the successive structural phase transitions on the hysteresis parameters, as shown in Figure Note again the remarkable difference in the evolution of the current density loops of samples SPS at 1350 °C and 1000 °C, both in the width of the current density curves, related with the distribution of coercivity, as well as the resulting P s values (Figure 7d).Note also that the successive phase transitions can be inferred from the evolution of E c for the samples with the largest grain sizes (Figure 7c), contrary to the sample at 1000 °C.The evolution from conto relaxor ferroelectric with the decrease of grain size is thus confirmed.
Poling experiments were finally accomplished, and the longitudinal piezoelectric coefficient d 33 obtained, and given in Table 1.Sample SPS at 1350 °C showed a high d 33 of 340 pC N −1 that stands out among highest values reported for a sub-10 μm grain BCZT ceramic, a value even comparable to those of undoped PZT ceramics.Despite the evident decrease of d 33 in the sample SPS at 1250 °C (220 pC N −1 ), it remains high and still suitable for target applications in microelectronics.Nonetheless, they are lower than typical ones for coarse grained BCZT materials.For samples SPS at lower temperatures (1100 °C and 1000 °C), d 33 drops considerably, as would be expected from the hysteresis Unipolar electric field-induced strain was measured on poled samples at RT, and curves are shown in Figure 8a.Large electroresponses were achieved in samples SPS at 1350 °C and 1250 °C, with strain values of up to 0.2% (S max ) at 2.5 kV mm −1 and very low strain hysteresis (Hs below 10% @1 kV mm −1 and of only 1.5% @2.5 kV mm −1 for sample SPS at 1350 °C), as obtained from the S-E loops.It is also remarkable the high "effective" piezo-coefficients d 33 *, determined from the ratio S max /E max at increasing electric fields and shown in Figure 8b.In these samples, a maximum d 33 * is achieved at moderate driving electric   fields below 1 kV mm −1 (at about 3 times E c ), where a value as high as 1400 pm V −1 is reached.[22][23] Indeed, the strain responses here reported are comparable to those of textured BCZT, which involve a complex processing and an abnormally grown microstructure that can pose a reliability challenge. [23]ote the unexpected, opposite grain size effects on the d 33 coefficient and the electric field induced strain of samples SPS at 1250 and 1350 °C with respect to a very coarse-grained ceramic conventionally sintered at 1450 °C (Table 1), included in Figure 8 for comparison.Actually, BCZT is characterized by large differences between direct charge coefficients and converse effective ones, which has been related to the selective activation of extrinsic contributions, such as polymorphic phase transformations and/or domain reorientations. [17,51]The improved electro-strain response of the SPS ceramics is likely related to the enhancement of reversible phase transformations by decreasing grain size and thereby domain wall density.
This does not occur for samples SPS at 1100 °C and 1000 °C, which showed significantly lower S max and d 33 *, which decreased with grain size like d 33 coefficients did.Note in this case the remarkable similarity between the d 33 *curves and derivative P s curves in Figure 6d.This suggests a different mechanism for the electrostrain response of these samples, bounded to the very wide distribution of coercive field and the sluggish domain switching.
Nonetheless, highly reversible electric field induced strain with very low hysteresis Hs (well below 5% even at 1 kV mm −1 ) and remnant strain were found, which might be favorable for highprecision actuation applications.Actually, relaxor ferroelectrics are usually considered for this niche application making use of its high electrostriction. [52]t is worth highlighting that the fine-grained BCZT ceramics with average grain sizes of 3.5 and 5 μm processed in this work are clearly competitive candidates for actuation, for they show electro-strain responses among best ones ever reported, while providing improved mechanical performance and enhanced dielectric strength, well above typical ones for BCZT very coarsegrained materials.This refers to the large effective piezoelectric coefficient, but also to the low hysteresis.Indeed, Hs values of most lead-based and lead-free piezoceramics are above 10%, such as coarse-grained BCZT ceramics that typically show high d 33 * values (1000 pC N −1 ), but accompanied with very large Hs (up to 27%). [11,14]The Hs values reported here are in the range required for high precision actuation. [23]eyond the very good response, the presence of opposite grain size effects in piezoelectric charge coefficients and electric field induced strain requires clarification.Polymorphic phases present at the MPB of PMN-PT have been shown to change with reduction of grain size. [53]Therefore, the actual room temperature polymorphic phase coexistence of the BCZT samples under study was investigated by highly-brilliant, high-resolution SXRD in order to gain a deeper understanding of the grain size effects on the structure of this material.Specifically, we report here the temperature evolution of perovskite (400)c reflection (referred to the parent cubic perovskite) for the reference material with a largely coarsened microstructure (20 μm grain size), compared with that for the ceramic SPS at 1250 °C (3.5 μm grain size).
Results are shown in Figures 9 and 10, respectively (data is given in d-spacing).In the first case, peak splitting is observed at 50 °C but almost disappears at 100 °C, indicating the ferroelectric transition to the high temperature cubic Pm-3m phase.The intensity ratio of the doublet at 50 °C, as well as peak widths, are the expected ones for the P4mm tetragonal phase.This polymorph is still the major phase at RT, but a third peak is necessary between the tetragonal ones to obtain a good fit.Note the large width of this peak, which strongly suggests it to likely be formed by the convolution of two ones.[17] Peak keeps evolving on further cooling down to −50 °C, for which the tetragonal phase has disappeared.This is indicated by the evolution of the apparent tetragonality (marked in the figure) that would unphysically decrease between RT and −50 °C.However, three peaks are still necessary to obtain a good fit, which is consistent with the coexistence of the orthorhombic polymorph with the rhombohedral R3m one.This is the expected evolution of BCZT on cooling, which is also consistent with the three dielectric anomalies observed in the electrical characterization.
This evolution is slightly modified in the ceramic SPS at 1250 °C (Figure 10).The ferroelectric transition is also observed   between 100 °C and 50 °C, but the splitting of the peak at the latter temperature does not indicate P4mm only phase, but its coexistence with a second polymorph that should be the Amm2 one, as for the splitting at RT, while coexistence of Amm2 and R3m phases is again suggested at −50 °C, yet with an enhanced R3m fraction.Phase sequence is thus not modified by the microstructure refinement, but phase coexistence at RT is, so that the tetragonal component is largely reduced.
These results correspond to the unpoled samples, but poled ceramics were also studied.Figure 11 shows SXRD patterns across the (400)c reflection on the same two samples before and after poling.Note the configuration used in these experiments, for which the poling field is applied perpendicularly to the Bragg reflections measured.In this case, and for the tetragonal polymorph, an increase of the intensity ratio I(400)/I(004) should be observed if domain reorientation results from poling.Indeed, this is the case for the coarse-grained ceramic, which is predominantly P4mm and clearly shows an increase of I(400)/I(004) after poling, indicating irreversible 90°domain wall motion.The situation is very different for the fine-grained ceramic, which was mostly Amm2.No changes were found between the poled and unpoled samples, which indicated that any domain reorientation within the orthorhombic phase fully relaxes once the field is removed.Actually, this might be behind the opposite size effects on the direct piezoelectric charge coefficient and converse high-field effective one.Ferroelectric/ferroelastic domain relaxation must cause a reduction of the charge coefficients after poling, while extensive ferroelectric/ferroelastic domain reorientation under high field must result in very high strain under field.This effect seems to be amplified in the orthorhombic phase that is favored for fine grained microstructures.

Conclusions
The combination of SPS and highly reactive nanocrystalline powders obtained by mechanosynthesis is capable of providing high-quality ceramics of Ba 0.85 Ca 0.15 Zr 0.1 Ti 0.9 O 3 with refined microstructures and tailored grain size across the micron range, down to the verge of the submicron scale.Distinctive grain size effects on properties occur in this range, where an evolution from conventional to relaxor ferroelectricity is revealed when size is decreased below 2 μm, approximately.This behavior quite resembles that of Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 , and suggests the occurrence of relaxor to ferroelectric transition in Ba 0.85 Ca 0.15 Zr 0.1 Ti 0.9 O 3 , whose kinetics slow down at quite large sizes as compared with the former system.Polymorphic phase coexistence responsible of the high electro-strain response is modified below 10 μm, so that the tetragonal fraction is significantly reduced, and basically orthorhombic single-phase materials are obtained.Reversible ferroelectric/ferroelastic domain reorientations take place under high electric field in the latter polymorph, so opposite grain size effects result for the direct piezoelectric charge coefficient after poling and for the electric field induced strain.As a result, large, low-hysteresis actuation characteristics are obtained for the fine-grained materials, also expected to have an improved mechanical performance compared with very coarse-grained materials.

Experimental Section
Sample Preparation: Perovskite Ba 0.85 Ca 0.15 Zr 0.1 Ti 0.9 O 3 nanocrystalline powders were obtained by mechanosynthesis in a high-energy planetary mill (Fritsch Pulverisette 6) operating at 300 rpm, using tungsten carbide milling media, from stoichiometric mixtures of analytical grade BaO 2 (Fluka, ≥ 95% peroxide basis), TiO 2 (Cerac, 99.9% pure anatase), CaTiO 3 and BaZrO 3 (both Alfa Aesar, 99% metals basis).Milling conditions were tailored to produce 10 g of perovskite single-phase BCZT nanopowder after only 12 h of milling, so that negligible contamination levels resulted.Details of the procedures and mechanisms taking place during mechanical treatments can be found elsewhere. [40]Ceramic materials with progressively refined microstructures were prepared by SPS in a Dr. Sinter Lab apparatus (model 212Lx, Fuji), using an 8 mm diameter cylindrical graphite die with graphite pistons and vacuum conditions.An uniaxial pressure of 80 MPa and sintering temperatures between 1000 °C and 1350 °C with 5 min soaking time were used (100 °C min −1 heating/cooling rates), with a total processing time of 15 min.Perovskite decomposition was observed above 1350 °C, while incomplete densification resulted below 1000 °C.Densification levels were assessed by Archimedes' method after ceramics polishing to remove the graphite.Finally, re-oxidation thermal treatments at 800 °C for 12 h in O 2 atmosphere were necessary to limit oxygen vacancies caused by the reducing conditions of SPS experiments. [30,54]he same nanopowder was used to prepare reference ceramics by conventional sintering at 1450 °C for 4 h.Abnormal grain growth processes were selectively activated to obtain either a largely coarsened microstructure or a fine grained one, to be used for comparative purposes. [40]tructural and Microstructural Characterization: Perovskite phase stability during SPS was controlled by lab-scale X-ray diffraction (XRD) with a Bruker AXS D8 Advance diffractometer (Cu-K radiation) in steps of 0.05°(2) with counting time of 1 s per step.Patterns for ceramics processed at 1000 and 1250 °C are given in the Figure S5 of the Supporting Information.No peak splitting is evident, so that symmetries lower than pseudo-cubic (on average) cannot be distinguished in fine grained BCZT samples, even if the compound is well known to be ferroelectric.Indeed, peak splitting is observed in the coarse-grained material (also given in Figure S5, Supporting Information).Therefore, synchrotron x-ray diffraction (SXRD) was carried out at the SpLine BM25 beamline of the European Synchrotron Radiation Facility (ESRF).The X-ray beam wavelength was set to 0.7293 Å (≈17 keV) with an energy resolution ΔE/E of ≈10 −4 and the beam spot size was adjusted to 300 μm x 80 μm (horizontal x vertical dimensions).For temperature-dependent measurements, samples were placed in an ultra-high vacuum chamber designed for multipurpose experiments which is attached to a six-circle diffractometer in vertical configuration. [55]High-resolution SXRD was performed in grazing incidence mode using a 2D photon-counting X-ray MAXIPIX detector [56] and the data were processed with the BINoculars software. [57]Quantitative microstructural analysis was carried out for which ceramic microstructures were recorded with a field-emission scanning electron microscope FE-SEM (FEI Nova NanoSEM 230).The surface of the samples was polished in alumina suspensions down to 1 μm.Micrographs were taken using a backscattered electron detector that provides strong crystallographic contrast, so that individual grains can be distinguished by a gray scale map associated to the different crystal orientations.Feret diameters of 1500 grains were measured to obtain reliable grain size distributions.
Electrical Characterization: Ferroelectric and piezoelectric properties were measured on ceramic disks, on which Ag electrodes were painted and annealed at 700 °C for 1 h.The temperature dependencies of the dielectric permittivity and losses were obtained using a HP4284A precision LCR Meter (Agilent) under heating at 1.5 K min −1 at frequencies between 100 Hz and 1 MHz.Measurements were carried out between 77 and 500 K, for which a Janis VPF-700 Cryostat coupled to a temperature controller (Lakeshore model 331) was used.Ferroelectric hysteresis loops were obtained at room temperature (RT) under low frequency (0.1 Hz) and highvoltage sine waves, by the combination of a synthesizer/function generator (HP3325B) and a high-voltage amplifier (Trek Model 10/40A), while charge was measured with a homebuilt charge to voltage converter.Loops are presented after compensation for subtracting linear polarization and conduction contributions, assuming a resistance and a capacitance in parallel.Finally, ceramics were poled at RT in oil bath at 5 kV mm −1 for 20 min and Berlincourt d 33 piezoelectric coefficients determined (Channel Products Inc).Values reported are those measured 24 h after poling process.Actuation performance was also characterized at RT by measuring the direct longitudinal deformation of ceramic discs under unipolar sine wave driving voltages (0.1 Hz) by combination of a digital signal generator (NI-SCXI 1302) and a power supply/amplifier (Kepco BOP-1000 M), while deformation was measured with a linear variable differential transducer.

Figure 2 .
Figure 2. a) Grain size distributions of BCZT ceramics obtained by SPS at different temperatures, b) evolution of the average grain size with SPS temperature and c) cumulative grain volume distributions of all samples.

Figure 3 .
Figure 3. Temperature dependence of the real (K') and imaginary (K") permittivity for BCZT samples SPS at a) 1350 °C and b) 1250 °C (arrows indicate increasing frequency).Transitions from R3m to Amm2 (T R-O ), then to P4mm (T O-T ) and finally to the paraelectric phase (T C ) are indicated with dashed lines.

Figure 4 .
Figure 4. Temperature dependence of the real (K') and imaginary (K") permittivity for BCZT samples SPS at a) 1100 °C and b) 1000 °C (arrows indicate increasing frequency).

Figure 5 .
Figure 5. Permittivity curves at 1 MHz for samples SPS at different temperatures.

Figure 6 .
Figure 6.a) Ferroelectric hysteresis and b) current density loops, along with the evolution of the c) spontaneous polarization (P s ) and d) derivative of P s with the applied electric field, for the BCZT samples SPS at different temperatures.

Figure 7 .
Figure 7. Current density loops as a function of temperature for samples SPS at a) 1350 °C and b) 1000 °C, along with the temperature evolution of the c) coercive field (E c ) and d) spontaneous polarization (P s ) for BCZT samples SPS at different temperatures.

Figure 8 .
Figure 8. a) Unipolar strain versus electric field curves and b) effective piezoelectric coefficient d 33 * (S max /E max ) at increasing electric fields for BCZT samples SPS at different temperatures.The data for a ceramic conventionally sintered (CS) at 1450 °C is included for comparison.

Figure 9 .
Figure 9. Temperature evolution of the perovskite (400)c reflection from SXRD patterns for a BCZT sample conventionally sintered (CS) at 1450 °C with large coarsened microstructure and average grain size of 20 μm.

Figure 10 .
Figure 10.Temperature evolution of the perovskite (400)c reflection from SXRD patterns for a BCZT sample SPS at 1250 °C with refined microstructure and grain size of 3.5 μm.

Figure 11 .
Figure 11.SXRD patterns across the (400)c reflection on BCZT samples a) conventionally sintered at 1450 °C and largely coarsened microstructure, and the ceramics SPS at b) 1350 °C and c) 1250 °C, before and after poling in all cases.