Composition and grain size-driven ferroelectric-relaxor crossover in Ba ( Zr , Ti ) O 3 ceramics

First Ba(ZrxTi1-x)O3 (BZT) ceramics with various compositions prepared by solid state, with high density, homogeneous microstructures and grain sizes in the range (0.7–4) μm were studied. Besides the dielectric and ferroelectric investigations, First Order Reversal Curves method was employed to describe the changes of the switching properties induced by composition and grain size, related to the ferroelectric-relaxor crossover. The dielectric and ferroelectric data for ceramics with similar grain sizes demonstrated the expected ferroelectricrelaxor crossover induced by increasing x. For a given composition (x = 0.10), the relaxor character increases whit reduction of the grain size. The FORC distribution shows almost zero reversible contribution and wellseparated sharp irreversible component for larger grains, while more diffuse distribution with a continuous extension from Ec=0 (reversible) to Ec≠0 (irreversible, switching) is typical for fi ner grains.


I. Introduction
In recent years, a large number of Pb-free perovskite ceramics, mainly based on BaTiO 3 solid solutions, have been studied because of their potentials as environmentfriendly materials.Barium titanate (BaTiO 3 ) is one of the most used ferroelectrics in the electronic industry, fi nding extensive application as dielectric material in multilayer ceramic capacitors (MLCCs), piezoelectric actuators, electro-luminescent panels, pyroelectric detectors, embedded capacitance in printed circuit boards, positive temperature coeffi cient of resistivity (PTCR) sensors, controllers and pulse generating devices [1][2][3][4][5][6].
One of the BaTiO 3 solid solutions, BaZr x Ti 1-x O 3 (BZT), is one of the most important compositions used as dielectric in MLCCs.The presence of Zr in the BaTiO 3 unit cell results in a strong increase in the permittivity.At the same time, the temperature characteristic is smoothed due to the broadening of the permittivity-temperature dependence and the material can be adapted to meet the Z5U specifi cations for being used in MLCCs [1].The system Ba(Zr x Ti 1-x )O 3 started to be recently investigated also for more fundamental studies related to the solubility limits, phase diagrams and effects on the functional properties derived from the BaTiO 3 ones, induced by very low substitutions, various types of defects (like O-vacancy or others), different grain size or grain boundary phenomena.
The dielectric data of BaZr x Ti 1-x O 3 (BZT) ceramics suggests a normal ferroelectric behaviour for 0 < x < 0.1, a diffuse phase transition in the range 0.1 < x < 0.2 and a relaxor character for 0.2 < x < 0.5.The degree of diffuseness of the ferro-para phase transition increases with the Zr addition [7][8][9].For x > 0.5, the system does not present anymore a ferroelectric distortion.These limits are very sensitive to the preparation method, presence of possible secondary phases and microstructural characteristics.Recently, a detailed study concerning the dielectric and switching characteristics in BZT ceramics as a function of composition and grain size was performed, in the way to demonstrate a ferroelectric-relaxor crossover [10][11][12][13][14].The present work reports on the main dielectric and ferroelectric results related to the ferroelectric-relaxor crossover induced by composition in BaZr x Ti 1-x O 3 and by the grain size in BaZr 0.10 Ti 0.90 O 3 ceramics.

II. Experimental
BaZr x Ti 1-x O 3 (BZT) ceramics with various compositions (x = 0, 0.10, 0.15 and 0.18) were prepared by solid-state reaction, as described in detail elsewhere [13,14].The microstructures were checked by scan ning electron microscopy (SEM, Philips, Model 515).The grain size was estimated by line intercept method.The phase formation after calcination and in bulk cera mics was analysed by X-ray diffraction (XRD, Philips, Model PW 1710).High density ceramics (relative density > 90%) were obtained by sintering the calcined powder at different temperatures (1350-1500°C) for 2 hours.By changing the sintering temperature, ceram ics with composition BaZr 0.10 Ti 0.90 O 3 with grain sizes in the range of 0.75 -3.3 μm were obtained, allowing the investigation of some features related to grain size effects.An impedance spectroscopy system (Solartron, SI 1260, 0.5V excitation voltage) was used to study the dielectric properties as a function of temperature and frequency in the range of (1-10 6 ) Hz.The P(E) loops and First Order Reversal Curves (FORC) were recorded under sinusoidal waveform by using a modifi ed Sawyer-Tower circuit.
The FORC diagrams method is a new tool for characterizing the switching process in ferroelectrics, considering the distribution of the elementary switchable units over their coercive and bias fi elds in relationship with classical Preisach model [15,16].The FORC measurements involve the recording of minor loops between saturation E sat and a variable reversal fi eld E r ∈ (-E sat , E sat ), the polarization along FORCs , where E c and E bias play the role of local coercive and bias fi elds respectively,

(
) becomes a distri bution of the switchable units over their coercive and interaction (bias) fi elds.The FORC method was used in this study to demonstrate the effect of composition and grain size in detecting changes of the switching parameters.

Dielectric properties of BaZr x Ti 1-x O 3 ceramics
The role of composition on the dielectric properties of BaZr x Ti 1-x O 3 ceramics sintered at the same temperature can be seen by comparing the dielectric data from the Fig. 1.As expected, the relaxor character is more evident when the Zr addition increases (Figs. 1 and 2).This was described with empirical equations, e.g. one proposed in the ref. [18]: (2) where ε is dielectric constant at a given temperature and ε m is its maximum value at the corresponding temperature T m .Equation ( 2) describes dielectric properties in relaxors, even in the dielectric dispersion region, with unique values of parameters δ and η for all frequencies [18].The coeffi cient η gives information on the character of the phase transition: for η = 1, normal Curie-Weiss law is obtained, η = 2 describes a full relaxor state with completely diffuse phase transition and η ∈ (1,2) a combined ferroelec tric/relaxor state with a certain degree of diffuseness in the phase transition.The parameter δ indicates the temperature extension for the diffuse phase transition, which is correlated with the dielectric permittivity broadening.The values of these parameters obtained by fi tting the dielectric data with the equation (2): η = 1.5 and δ = 20°C for x = 0.10, η = 1.65 and δ = 32°C for x = 0.15 and η = 1.7 and δ = 36°C for x = 0.18 [19].These values indicate a mixed ferroelectric-relaxor character for all compositions and an increased relaxor character with Zr addition.The parameter δ, correlated with the dielectric permittivity broadening, shows a gradual increase of the diffuse character of the phase transition with increased Zr concentration.It is worth to mention that when we increase the Zr content, a reduction of the average grain size takes place in ceramics sintered under the same conditions [11].Moreover, the grain size distribution in ceramics might also induce an increased character of the ferro-para phase transition.Therefore, the increased relaxor character observed with Zr addition is a combined effect of the increasing chemical heterogeneity, reducing grain size and broadening of the grain size distribution in the ceramics.
The composition-induced shift of the ferro-para phase transition at a fi xed frequency (f = 80 kHz) is visible in the Fig. 2, where the temperature-dependence of the dielectric constant of the BZT solid solutions in comparasion with a BaTiO 3 ceramics is reported.The difference between the sharp ferroelectric-paraelectric phase transition in BaTiO 3 (fully ferroelectric) and the diffuse phase transitions in the solid solutions is clearly shown in this fi gure.
[ ] The grain size induced changes of the dielectric properties were detected by comparatively analyzing BZT ceramics with x = 0.10 sintered at different temperatures and thus, having different grain sizes in the range of 0.7-4 μm.
The permittivity of all these ceramics at room temperature (Fig. 3a) assumes very high values, of around 3000-4000 for the fi nest ceramics sintered at 1350°C and of 5000-7500 for the coarser ones sintered at 1500°C.At the transition point, T m , the permittivity reaches 30000 for the coarse ceramics.This is a result of the combined large and homogeneous grain size and the highest densifi cation of this ceramics.Fig. 3a,b shows how the real and imaginary components of the complex permittivity are dependent on the grain size in a heating/cooling cycle.The transition is accompanied by a thermal hysteresis that raises with increasing of the grain size.For the coarse sample, the temperature dependence of the imaginary part of permittivity allows us to identify both the tetragonal-cubic (ferro-para) phase transition at ~90°C, and also the structural orthorhombic-tetragonal (ferroferro) transition at ~ 75°C by a small anomaly (Fig. 3b).For the fi nest ceramics these transitions are overlapped.The fact that the dielectric constant is so high in the temperature range of ~70-100°C is a result of proximity of the both structural phase transitions.
The results of the dielectric study showed that both by increasing the Zr content and reducing grain size, the relaxor character is increased.

Ferroelectric properties of BaZr x Ti 1-x O 3 ceramics
Fig. 4 represents the major hysteresis loops (MHLs) for the BaZr 0.1 Ti 0.9 O 3 samples sintered at 3 different temperatures (T s = 1350°C, 1400°C and 1500°C).The sample sintered at lower temperature T s = 1350°C (grain size of ∼ 0.75 μm), presents a very tilted P(E) loop, with a large reversible component, low rectangularity factor, small value of the remanent polarization (P r ≅ 2.4 μC/cm 2 ) and coercive fi eld of 0.17 kV/mm.A higher remanent polarization is obtained for the ceramics sintered at 1400°C and 1500°C, due to their larger grain size.The ceramics with the highest density and the largest grain size of ∼ 3.27 μm, sintered at 1500°C, has the most rectangular P(E) loop and the lowest coercivity (E c = 0.15 kV/mm), but its saturation polarization is slightly smaller than for the sample sintered at 1400°C having grain size of ∼1.1 μm (P s = 11.12 μC/ cm 2 ), while the remanent polarization is almost the same (P r ≅ 6.5 μC/cm 2 ).In any case the MHLs obtained in the present ceramics refl ect the tendency found by other authors in systems like BT, BZT, BST and PZT thin fi lms [20][21][22][23][24].When comparing the loops of these samples sintered at different temperatures, one should keep in mind the possible differences caused by extrinsic phe-nomena.These extrinsic contribution might be different for the samples sintered at 1400°C and 1500°C, and this might explain why a higher saturation polarization was found in the sample with grain size ∼ 1.1 μm and not in the one with higher grain size (∼ 3.27 μm), in spite its excellent dielectric properties and almost full densifi cation (99% relative density).A possible explanation is related to the anomaly of the dielectric and ferroelectric properties reported in the landmark paper of Arlt et al. [23] in the BaTiO 3 ceramics with grain size around ∼1μm that might take place also in the BZT ceramics.
At a given temperature in the ferroelectric phase, the grain size dependence of the permittivity of BaTiO 3 ceramics has a maximum value around this critical grain size of ∼ 1 μm.For this grain size, it was supposed that an optimum twinning of the domain walls within the ceramic grains takes place.Additional information on the switching properties is given by the FORC analysis.The FORC distributions for the BZT samples with x = 0.10 and extreme grain sizes are shown in Fig. 5a,b.Remanent polarization of ∼ 3.4 μC/cm 2 for BaZr 0.1 Ti 0.9 O 3 with small grains and ∼ 7 μC/cm 2 in BaZr 0.1 Ti 0.9 O 3 with large grain size and apparently similar coercivities of around 0.25 MV/m were obtained.The computed 3D-FORC distributions (Fig. 5a,b) show a small bias, i.e. the maximum of the FORC distribution is shifted towards negative bias fi elds: E bias = -2.19kV/mmfor the sample sintered at 1350°C and E bias = -2.16kV/mmfor the sample sintered at 1500°C.Dealing with bulk structures with symmetric electrodes, the possible origin of this bias as coming from the interfaces ceramics-electrodes is excluded.Since the negative bias is typical to all samples investigated, it results that this is an intrinsic effect caused either from the processing (one-directional pressing) or by dipolar defects contributions intrinsic to this type of material.The maximum is located at low coercivities of ∼ 5 kV/m for both samples, indicating low energy barriers for the large majority of irreversible domain walls movements.Only a small number of dipolar units is switchable under higher fi elds.Since there is no net separation along the bias axis between the reversible (E c = 0) and the irreversible (for E c ≠ 0) components of the polarization on the FORC distribution as in other ferroelectrics [25,26], it results that a continuous distribution of energy barriers from zero to non-zero values is characteristic for these BZT ceramics.A simi-lar behaviour was found for some BST compositions [27] and is related to the high degree of local compositional inhomogeneity of the solid solutions, giving rise to broad distributed Curie temperatures and coercivities.Therefore, the sample BaZr 0.1 Ti 0.9 O 3 sintered at T s = 1500°C is much homogeneous from the switching point of view, i.e. the large majority of the dipolar units are switchable at similar fi elds, giving rise to a very sharp FORC distribution with a peak maximum of ~ 45% (Fig. 5b) in comparison with a broad peak with maximum of ~ 15.5% for the fi ne grained ceramic (Fig. 5a).This is result of two effects: (i) larger grains and small non-ferroelectric grain boundary volume, resulting in switching characteristics closer to the single-crystal behavior; (ii) high density, causing similar boundary conditions for the overall dipolar units.The enlarged FORC distribution by porosity effects was also observed in PZT ceramics with high degree of porosity [27].
The role of composition on the FORC diagram can be observed by comparing the Figs.5b and 6, where the FORC distribution of BZT ceramics with x = 0.10 and x = 0.15, sintered at the same temperatu re, are shown.The maximum of the FORC distribution for the BaZr 0.1 Ti 0.9 O 3 ceramic is much sharper than in the case of the BaZr 0.15 Ti 0.85 O 3 sample (maximum of ~35%) and the irreversible component of the BaZr 0.1 Ti 0.9 O 3 sample is wider in comparison with BaZr 0.15 Ti 0.85 O 3 composition and it has a maximum located close to the second bisecting line at the coercivity E cM = 0.17 kV/mm and bias E bias = 0.13 kV/mm.Therefore, by analysing these 3D-FORC diagrams, a clear tendency towards the relaxor state with increased Zr content is observed, by

IV. Conclusions
The dielectric and ferroelectric analysis of the BZT ceramics with similar grain size demonstrated the expected ferroelectric-relaxor crossover induced by increased Zr content.For the BaZr 0.1 Ti 0.9 O 3 ceramics sintered at different temperatures, the relaxor character is increased with the reduction of the grain size.The FORC distribution shows almost zero reversible contribution and well-separated sharp irreversible component for larger grains, while more diffuse distribution with a continuous extension from E c = 0 (reversible) to E c ≠ 0 (irreversible, switching) is typical for fi ner grains.
of the actual, E, and reversal fi elds, E r , respectively.The FORC distribution is defi ned as the mixed second derivative of polarization with respect to E r and E [17]: of polarization in a given sample with respect to changes of the reversal fi eld E r and actual electric fi eld E. By changing the coordinates of the FORC distribution from

Figure 2 .
Figure 2. Real part of the dielectric constant vs. tempera ture for the BaZr x Ti 1-x O 3 ceramics with x = 0, 0.10, 0.15 and 0.18 at a fi xed frequency, illustrating the compositionally-induced shift of the Curie temperature.

Figure 3 .Figure 4
Figure 3. Grain size dependence of the real (a) and imaginary (b) part of the dielectric constant vs. temperature for the BaZr 0.1 Ti 0.9 O 3 ceramics, sintered at: 1350°C, 1400°C, 1450°C and 1500°C