Complex Structural Contribution of the Morphotropic Phase Boundary (MPB) in the (1-x)Na_0.5Bi_0.5TiO₃ – xCaTiO₃ system

Abstract

The correlation between structure and dielectric properties of lead-free (1-x)Na_0.5Bi_0.5TiO₃ – xCaTiO₃ ((1-x)NBT – xCT) (0 ≤ x ≤ 1.00) polycrystalline ceramics was investigated systematically by X-ray diffraction, combined with impedance spectroscopy for dielectric characterizations. The system shows high miscibility in the entire composition range. A morphotropic phase boundary (MPB), at 0.09 ≤ x < 0.15, has been identified using XRD data where the rhombohedral and orthorhombic (R3c + Pnma) symmetries coexist at room temperature, with increasing Ca²⁺ concentration.The fraction of orthorhombic phase increases gradually with x in the MPB region. Dielectric measurements reveal that the relative permittivity increase with addition of Ca²⁺.This behavior is unusual with this kind of doping (Ca²⁺). A thermal hysteresis was occurred only in the MPB composition (0.09 ≤ x < 0.15) which varies non-monotonically manner with x (%Ca), detected by dielectric properties. This phenomenon is related to the crystalline microstructure by a linear relationship between the fraction of each phase and dielectric properties, and, more precisely, to the strong interaction between the rhombohedral (R3c) phase and orthorhombic (Pnma) phase. The maximum interaction is obtained for the maximum thermal hysteresis at x = 0.11, where the two phases (R3c + Pnma) have equivalent proportions.

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I.                   Introduction

Lead oxide ferroelectric ceramics (such as PZT)  are widely used in various electronic devices such as transducers, actuators, MEMS, capacitors and Random Access Memory (RAM) [1].However, due to the toxic effect of lead, the development of alternative lead-free ferroelectric materials able to replace PZT in microelectronics is currently pursued worldwide.

Among the different varieties of lead-free materials, Na_0.5Bi_0.5TiO₃(NBT) is considered one of most promising   ferroelectric materials which has equivalent properties as PZT[2]. Although NBT system presents a complex behavior, it has shown interesting features: (i) good ferroelectric properties at room temperature with strong remanent polarization (Pr ~ 38 μC.cm-2) [3-5], (ii) high Curie temperature(T_C ~ 320 ˚C) [6], (iii) special sequence of phase transition as a function of temperature [7-9] and finally, (iv) it can form solid solutions with other perovskites which appears in phase diagrams as a biphasic domain called Morphotropic Phase Boundary (MPB). Aroundthis region, NBT and BaTiO₃ (BT) solid solution systems exhibit improved properties [10].In addition to NBT-BT, other families of NBT-based solid solutions have been developed in order to understand the MPB behavior of this material. Among these solutions, the (1-x)NBT – xCT system shows excellent piezoelectric and ferroelectric properties at the rhombohedral – tetragonal MPB [11, 12]. Despite the succession of structural changes obtained in this region, the exact behavior of the MPB remains unclear.

First of all, it is crucial to differentiate between a normal biphasic domain and a Morphotropic Phase Boundary (MPB).  A “MPB”is a biphasic zone constituted by a mixture of two phases with different crystal structures, with variable composition but always identical. In other words, the two phases of same compositions exist (NBT-BT rhombohedral + NBT-KBT tetragonal at x = 0.07[13] for example) at room temperature; the fraction of each phase and the lattice parameters change with x (% of doping).While, in a “normal biphasic domain”, the compositions of the two phases are different (x₁ ≠ x₂), and their proportion varies with x, but always have the same characteristics as that x₁ and x₂ and finally, the lattice parameters remain constant with x.

Several systems were studied in order to determine the compositional range of MPB [14, 15] and to establish the physical and structural properties. However, there are inconsistencies in its location. Despite the various techniques used, it is shown that the MPB locations varies with previously published work. In NBT – BT, the MPB was found around x = 6-7 %[16], where the maximum values of the piezoelectric and dielectric constants were obtained. Rout et al. [18] observed the MPB at x ≈ 5.5 %. Chen et al. [13] revealed the MPB between x = 6-10%, whereas Sung et al. [19] obtained this region around x = 5-7 %.In the other hand, Ge et al. [20] reported that the MPB was located between 5 and  8 %.Recently, Eerd et al. [21]found the MPB of NBT-BT at x = 5.5%. In  other system such as NBT – ST (SrTiO₃), a specific concentration is never determined; this leads eventually to different values of MPB [15, 22-24]. However, some studies have not obtained the MPB, regardless of the percentage of substitution [25]. Recently, few studies have been carried out on (1-x)NBT – xCT (CaTiO₃) system and the MPB region was found at x = 10 % [26].

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While many studies were carried out in order to improve the piezoelectric properties of these materials near the MPB compositions; studies concerning the MPB physical behavior were rarely investigated. As it is well known the solid solutions with compositions close to MPB exhibit interesting physical properties.

According to Glazer, rhombohedral (R3c) and orthorhombic (Pnma) phases are not related to group-subgroup relationship[27], however a strong relationship between these two phases in the MPB region was suggestedThis paper  proves that the orthorhombic phase (Pnma) contributes to the rhombohedral phase(R3c) as will be shown in dielectric response. This new result gives a proper understanding of the correlation between structure and dielectric properties of lead-free (1-x)Na_0.5Bi_0.5TiO₃ – xCaTiO₃ ((1-x)NBT – xCT)) polycrystalline ceramics. Thus, several compositions of (1-x)NBT –xCT (0 ≤ x ≤ 1.00) were prepared focusing on a specific range of Ca²⁺ concentration near the MPB region (0.07 ≤ x ≤ 0.15).The crystalline structure of the prepared ceramics was examined using X-ray diffraction at room temperature. A mixture of two phases (R3c + Pnma) is stabilized for (0.09 ≤ x < 0.15), indicating that rhombohedral phase of NBT is able to undergoes an orthorhombic distortion when increasing Ca²⁺ substitution.The dielectric and aging properties were measured as a function of temperature and frequency. Then, dielectric aspects and structural analysis obtained at room temperature were compared and discussed. These results enable a great comparison between the structural models at the MPB such as phase fraction, phase identify and the related dielectric properties.

II.               Experiment

(1-x)N_0.5B_0.5TiO₃ – xCaTiO₃powders and ceramics were prepared by a conventional solidstate synthesisroute. A stoichiometric amount of reagent grade powders of Na₂CO₃, CaCO₃, Bi₂O₃, and TiO₂ (purity greater than 99.6%) were mixed and milled in water with Zirconiaballs for 2 hours and then dried at 90°C. The mixture was homogenized in a dry mortar and calcined at 750°C for 4 hours. A second calcination at 950°C for 4 hours was required to complete the reaction. After this procedure, the calcined powders were pressed into pellets and sintered in the temperature range 1075 – 1350°C for 1 hour in a confined environment using alumina crucibles.This operation is necessary in order to prevent the exceed volatilization of Bi and Na. The sintering temperature was selected based on Ca²⁺ concentration in each composition. Note that all samples are pure and no secondary phase was observed in contrast to many other studies.

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Bulk densitiesof all the ceramics was measured by the Archimedes method. Despite the difficulty encountered during sintering; the average values are in a range between 96 – 99%. Sintered samples were polished in order to remove the thin layer of powders adhered to the surface ofpellets.

Powders and ceramics X-ray diffraction measurements were performed at room temperature, using a D8 advance X-ray diffractometer (Vantec detector) with CuKα₁α₂radiations in the 2θ range of 20° – 90°with a scanning step 0.017° and 2 s/step.Structural analysis and Rietveld refinement were carried out with the Topas(Brucker-AXS) software. For dielectric and aging properties, surfaces of the sintered pellets were coated with gold electrodes by PVD (physical vapor deposition) procedure. The permittivity (real part, imaginary part and loss tangents) and aging measurements were performed under multi-frequency (100 Hz – 1 MHz) with a precision LCR meter (4284A) in the temperature range of 77 – 450 K.

III.           Results and discussion

X-ray diffraction was used to highlight the change in crystal structure of (1-x)NBT-xCT samples as a function of CT concentration (0 ≤ x ≤ 1.00).Figure 1(a) shows XRD patterns of all (1-x)NBT – xCT systems at room temperature. All samples exhibit a pure ABO₃perovskite structure without any secondary or impurity phases. This implies that Ca²⁺ has diffused into the rhombohedral NBT lattice in order to form a solid solution with a perovskite structure. For all synthesized solid solutions, the XRD patterns obtained are either identical to pure NBT or to pure CT. The increase in Ca content shifts XRD peaks patterns towards higher angle (2θ),, indicating a decrease in cell volume. Figure 1(b) shows a scan XRD data taken around the 2θ range 66.8-72°. As known, pure NBT has a rhombohedral phase (R3c space group), while CT possesses orthorhombic structure (Pnma space group). The rhombohedral symmetry was characterized by (208)_R and (220)_R peaks splitting. Similarly to pure NBT (x = 0), the samples below  x = 0.07 exhibit a rhombohedral structure. With increasing x, the symmetry gradually changes from rhombohedral to orthorhombic. From x = 0.09, an additional peak appears, it corresponds to the (004)_O reflection (solid arrow) of the orthorhombic phase. The intensity of this reflection increases with x while the intensity of the rhombohedral peaks gradually decreases until disappearing completely for x = 0.15. The simultaneous presence of the (R+O) peaks in this composition range (0.09 ≤ x < 0.15) indicate that both orthorhombic and rhombohedral phases coexist. For x ≥ 0.15, pure orthorhombic phase was obtained, where the XRD patterns are all identical to those of Pnma of the pure CT (x = 1.00) phase. This was highlighted by the splitting of the double rhombohedral peak (208)_R, (220)_R to quadruplet peak (400)_O, (242)_O,(004)_O and (410)_O features of the orthorhombic phase. The inset in Figure 1(a) shows the variation of the integrated intensity ratio of (230)_O and (024)_R peaks as a function of x. The evolution of intensity ratio (I(230)_O/I(024)_R) reveals two anomalous as discontinuities at x = 0.09 and x = 0.15.

The sharp break in the intensity ratio I(230)_O/I(024)_Rbelow can be interpreted as a detection of phase transition from rhombohedral tothe orthorhombic phase.

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it is very important to study the behavior of this mixture of two phases (R3c + Pnma) in order to know if it is a normal biphasic domain or Morphotropic Phase Boundary (MPB). For this reason, a Rietveld refinement was carried out with a two phase rhombohedral and orthorhombic model to check the variation of the phase fraction of two phases as well as the cell volume for each composition in this region (0.09 ≤ x < 0.15). The evolution of phase fraction (%)at room temperature as a function of x is plotted in Figure 2(a). While, the fraction of orthorhombic phase increases from 16% to 100% when x increased from x = 0.09 to 0.15, the fraction of rhombohedral phase decreases gradually (from 84% to 38%) in the composition range 0.09 ≤ x ≤ 0.13, and disappears completely (0%) at x ≥ 0.15. This evolution shows that in terms of phases proportions, a normal behavior of a heterogeneous mixture of two solid solutions in biphasic domain is observed. However, the variation in cell volume in this region (0.07≤ x < 0.15) at room temperature (Figure 2(b)) shows an “unusual” behavior of the two phases (R3c + Pnma) in the biphasic domain. It’s known that in a biphasic domain between two monophasic domains, the cell volume of each of the two phases is constant while the proportions (fraction) of the two phases change with x. However, in our case, the cell volume of the R3c and Pnma phases changes continuously with x. In the particular biphasic domain presented in the (1-x)NBT – xCT system (0.09 ≤ x < 0.15), it was shown that the solid is formed by a mixture of two phases (R3c + Pnma)where (i) the two phases present always equal compositions and (ii) the fraction of these two phases will vary with x. In view of this, a strong interaction could occur between these two phases based on their distribution.

Based on the properties mentioned in the introduction, this result confirm that the particular biphasic domain obtained in the (1-x)NBT – xCT between 0.09 ≤ x < 0.15, is a Morphotropic Phase Boundary (MPB).

The temperature dependence of the real part of the relative permittivity for the (1-x)NBT – xCT with x = 0.01,0.05, 0.11, 0.15 0.25, 0.35 and 0.85 at 1 kHz and 10 kHz is shown in Figure 3.  All the ceramics exhibit at least one dielectric anomaly. Phase transitions are observed clearly and the peaks become broader with increasing CT concentration. The relative permittivity for x = 0.01 and 0.05 exhibit frequency dispersion and appear as a shoulder which become broad taking the form of a curve at x = 0.11. The dielectric behavior totally changed for x ≥ 0.15, the permittivity exhibits strong frequency dependence at the maximum temperature (T_m) suggesting a diffuse phase transition. In this case, the temperature associated to each maximum of the dielectric constant shifts gradually to lower values with increasing x.

NBT – xCT with x = 0.01 and 0.05 present the same anomaly that occurred in pure NBT [10, 15, 28] in the ferroelectric state with the stabilization of the rhombohedral structure (R3c) at room temperature. In fact, the XRD analysis showed that the system between 0.09 ≤ x < 0.15 is not monophasic; in addition to R3c phase, a supplementary (230)_O peak proves the simultaneous presence of the orthorhombic phase (Pnma). The latter is non-polar (centrosymmetric) and hence is not anticipated to show any dielectric anomaly in the temperature range studied. Therefore, the dielectric anomalies obtained in this region are attributed to rhombohedral (R3c) phase.

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Similar to pure NBT, for x = 0.01and 0.05 compositions, the first anomaly appears around 440K know as depolarization temperature (T_d) which is attributed to the transition from ferroelectric state to antiferroelectric state [29]. This transition is accompanied by a structural change resulting in the instability of the rhombohedral phase (R3c) which transits gradually to tetragonal phase (P4bm). Contrary to x = 0.07, the dielectric constant peak of x = 0.15 was depressed and broadened. The maximum of the dielectric anomaly moves toward lower temperature with increasing x, and exhibits a large maximum around the room temperature (T_m = 295 K). This is a characteristic of relaxor behavior, where the fitting by modified Curie-Weiss law (1/ε^’) – (1/ε_m) = (T – T_m)^γ/C gave a value of γ = 1.53 (degree of diffuseness). This value shows clearly that this ceramic is ferroelectric relaxor. This behavior may be related to the cations disorder at the A-site complex [30].

For a large temperature range and in the MPB compositions, the permittivity exhibits another anomaly between heating and cooling presented as two different values of the dielectric constant for the same temperature Ɛ’(T)_(Heating)< Ɛ’(T)_(Cooling). This anomaly appears as a large cycle called “thermal hysteresis” depending on x and situated in the temperature range between: 260 – 450 K (x = 0.09), 230 – 430 K (x = 0.10), 210 – 410 K (x = 0.11) and 180 – 360 K (x = 0.13) at 10 kHz. Figure 4 shows the thermal hysteresis of the (1-x)NBT – xCT in the MPB compositions during heating and cooling at 10 kHz. There is a remarkable characteristic that this cycle exhibits a non-monotonous evolution that didn’t exist for x ≤ 0.07and appears for x = 0.09. It gradually increases with increasing x up to a maximum and then decreases to disappear for x = 0.15.

Since NBT-CT composition is a heterogeneous mixture of two phases, relaxor ferroelectric phase (F/R-NBT) and paraelectric phase (P-CT). The total permittivity of biphasic domain decreases as x increases. Nevertheless, the permittivity increases with increasing CT (x) if T ≤ 220 K. In the MPB compositions (x = 0.09, 0.10, 0.11 and 0.13), the value of ε’ is very high compared with x = 0.07 and 0.15 for T > 300 K. As a result, increasing x,ε’ drastically increases from ~ 900 (x = 0.07) to ~ 1200 (x = 0.09), reaches a maximum of 1300 for x = 0.10 where the system is biphasic and then gradually decreases to 800 at x = 0.15 where the system becomes monophasic. These original observations can be related to the interaction between the two phases rhombohedral (R3c: F/R) and orthorhombic (Pnma: P) that leads to a nonlinear behavior as a function of x.

Figure 5 shows the difference Δε’(T) between the values of the permittivity obtained during heating and those revealed during cooling, as a function of temperature at 10 kHz. From the “full width at half maximum (FWHM)” of Δε’(T) curves, the degree of existence of the hysteresis and the maximum temperature of the hysteresis (T_mTH) were determined. Figure 5 confirms the particular evolution of thermal hysteresis in the MPB compositions. Each curve of Δε’ exhibits a maximum. The position of the maximum and their amplitude are highly dependent on x (%Ca). Therefore, there is a strong relationship between the evolution of the thermal hysteresis presented in these materials and its composition x (%Ca); in particular, the strong interaction between the two phases in the MPB compositions is confirmed.

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The width evolution of the thermal hysteresis for a given composition, as a function of temperature, is characterized by a peak through a maximum which the corresponding temperature is noted T_mTH. It represents the temperature at which the sample has a maximum thermal hysteresis magnitude. The T_mTH and the FWHM of Δε’(T) values are represented in the table 1. It is noted that, the T_mTH temperature strongly decreases with increasing x; and; even for a low degree of substitution (i.e. from 0.09 to 0.10, ΔT_mTH= 27 K). At the same time, the FWHM of Δε’(T) peak increases in with x.

In many ceramics, especially perovskites, the origin of such phenomenon is explained by the formation and detection of a modulated phase [31, 32]. The modulated phase is proposed to explain the thermal hysteresis behavior of pure NBT. In this study, (1-x)NBT – xCT system consists of a mixture of two phases: rhombohedral (R: R3c) and orthorhombic (O: Pnma). The behavior of pure NBT is very complicated, especially, in the MPB compositions and in the temperature range between 200°C – 320°C. It seems that the rhombohedral and tetragonal phases can coexist in the thermal hysteresis; which may be responsible for the appearance of this phenomenon [33]. Therefore, the resulting dielectric peak is a response to the electrical and mechanical interactions between polar and non-polar regions [34]. However, this remains a hypothesis and no experimental procedure was verified.

Therefore, two possible explanations for the observations obtained in this study were considered:

• Assuming that this would be based on the micro-domains model of relaxor ferroelectric, which is the cause of the thermal hysteresis phenomenon [35]. In this case, (1-x)NBT – xCT system with x ≥ 0.15 should be affected by this phenomenon. Hence, all ceramics appear to behave as relaxor. The same thing could be said for x ≤ 0.07 where the addition of Ca²⁺leads to the appearance of polar micro-domains[36]. However, in both cases, no thermal hysteresis is generated.
• A structural origin can also be invoked to explain the existence and evolution of thermal hysteresis as a function of x. In fact, the comparison between the evolution of the magnitude or the intensity of the cycle (normalized) to the percentage (fraction) evolution of the minority phase existing in the MPB compositions (Figure 6) at room temperature (300 K), shows that there is a strong correlation between the magnitude of the thermal hysteresis and the variation in the proportion of the two phases in the material.

Figure 6 showed that:

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• The amplitude of Δε’/ε’ cycle increases with x (%Ca²⁺) where the orthorhombic phase (O) is minority (x ≤ 0.11).
• While for x ≥ 0.13, the amplitude of the cycle Δε’/ε’ decreases with x and the minority phase become rhombohedral (O: majority). Then, this difference disappears when the system recovers its monophasic state.
• Another interesting feature is that the Δε’/ε’ reaches a maximum for an intermediate composition, where the two phases have an equivalent proportion (x = 0.11).

Such correlation between the coexistence of two phases and the presence of a dielectric hysteresis cycle in pure NBT was mentioned in the literature [32, 37]; previous studiesproposed this hypothesis to explain their experimental results but did not have the opportunity to provide the experimental proof. The results obtained in this study bring this confirmation. The correlation between the fractions of phase (proportion) and the width of the cycle is verified. Therefore, the strong interaction between the phases in the biphasic domain (between F/R (R3c) phase and P (Pnma) phase) with maximum interaction when the two phases are in equivalent proportions has been well demonstrated.

Mechanical and electrical interactions between various existing phases depend on the relative proportions (fraction) of the two phases; this leads to a wide change of the dielectric response which appears as a thermal hysteresis cycle. In this system, the coexistence of two phases (R+O) induces interactions between rhombohedral polar domains and orthorhombic non-polar matrix. At both extremities of MPB compositions, the system is monophasic; for x = 0.15, it is effectively non-polar single phase material (O:Pnma), with no thermal hysteresis. On the other hand, for x = 0.07, the system is also monophasic, with rhombohedral polar phase (R: R3c), but without thermal hysteresis too. The interaction between polar and non-polar domains is much stronger that the proportions (fraction) of two phases are equal; the maximum is obtained for x = 0.11. Hence, it seems that the main cause of this phenomenon is the coexistence of two phases in this material.

Therefore, it appears that the origin of thermal hysteresis is related to the crystal microstructure and, more specifically, the percentage of each phase existing in the MPB compositions.

In order to better understand the complex behavior of the MPB compositions materials, the evolution of the dielectric permittivity as a function of time, called aging was studied. It was carried out at different temperatures and for many ceramics in the MPB compositions.

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Figure 7.b shows the evolution of the dielectric permittivity(normalized over the permittivity at t = 0 s) as a function of time at 10 kHz for x = 0.10 ceramic, where different isothermal conditions were imposed inside the thermal hysteresis at T = 350 K, 380 K and 428 K (Figure 7.a).It is noted that the permittivity for x = 0.10 system evolved significantly as a function of time. Hence, this system undergoes an aging despite the imposed temperature with a maximum aging obtained at T = 380 K corresponding to the sharp decrease of the dielectric constant. It is remarkable that at T = 350 K, the system slightly evolves to reach a maximum at T= 380 K, then the aging decreases again as the temperature increases to T = 428 K. Figure 7 shows that the aging reaches a maximum concomitant with the maximum of thermal hysteresis reported in Figure 5.

Evolution of the thermal hysteresis, where the dotted line at T = 350 K represents an isothermal imposed at fixed temperature,

In order to study the aging for all compositions of the MPB, thermal hysteresis evolution was performed at 10 kHz with the application of an isotherm at T = 350 K (Figure 8.a).Figure 8.b shows the evolution of the permittivity (normalized over the permittivity at t = 0 s) as a function of time for different compositions (x = 0.10; 0.11 and 0.13). The aging phenomenon exists despite the value of x. its kinetics depending on x; the system exhibits a quick evolution for x = 0.10. This variation considerably increases for x = 0.11 where the system shows high aging kinetics. This kinetic abruptly decreases for x = 0.13 where the system undergoes slight changes at this temperature: the dielectric constant almost decreases. Note that, for x = 0.13, the majority phase is orthorhombic (62% Pnma, 38% R3c) and hence, this phase is centrosymmetric and does not show any dielectric anomaly. Therefore, there is no phase transition in the temperature range used in this study. This explains the slight variation of the permittivity as a function of time. However, the highest behavior in the aging curves (Figure 8.a) corresponds to the maximum of the thermal hysteresis phenomenon for x = 0.11 where the two phases (R3c + Pnma) have equivalent proportions. In view of this, the aging of these materials is probably due to the change in the relative proportions of the phases between rhombohedral (R3c) and orthorhombic (Pnma) structures; since the system is biphasic and provides a morphotropic phase boundary (MPB).

IV.            Conclusion

A combined structural and dielectric property of Ca²⁺ modified NBT [(1-x)Na_0.5Bi_0.5TiO₃ – xCaTiO₃] revealed that the system undergoes a phase transition as a function of the substitution composition x (%Ca) at room temperature. XRD analysis shows the formation of continuous solid solution. Two different single phases were obtained for the lowest values of x (R3c) and for the higher values of x (Pnma). These two phases are separated by an intermediate biphasic domain proved as Morphotropic Phase Boundary (MPB). This MPB exists around 0.09 ≤ x < 0.15 where two phases coexist: rhombohedral (R3c) and orthorhombic (Pnma). The system shows the following sequence of structural evolution at room temperature:

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R3c → R3c + Pnma→Pnma

 

This study confirms that the cationic substitution in the A-site of NBT perovskite strongly changes the dielectric properties of the material. By changing the doping concentration, a gradual transition from the normal ferroelectric state to relaxor behavior was highlighted. The maximum temperature of the dielectric anomaly is close to room temperature (or lower).

In summary, the results obtained in this study revolve around the position of MPB composition as a function of x (%Ca) and its relation to dielectric properties. In addition, dielectric behavior is highly pertinent. The structural properties of different compositions were discussed in combination with dielectric properties. Four interesting points can be concluded:

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• Only in the MPB composition, this study revealed the occurrence of thermal hysteresis whose magnitude evolves in non-monotonically manner with the amount of Ca²⁺ doped.
• The origin of this phenomenon is attributed to a relationship between the crystalline microstructure and dielectric properties. In fact, the interaction between the orthorhombic (Pnma) and rhombohedral (R3c) phases is responsible of the appearance of this phenomenon; the highest magnitude of the hysteresis thermal occurs when the two phases have almost equal proportions (x = 0.11).
• Another important feature, in the MPB composition, is the aging as a function of time; which was revealed by a continuous decrease in the permittivity. The maximum of aging is obtained when the two phases present equivalent proportions (x = 0.11). This probably corresponds to the gradual transformation of the rhombohedral phase to the orthorhombic phase.
• Finally, phase coexistence alone is not sufficient to provide excellent dielectric properties but it is necessary to combined with structural properties such as domain orientation and repartition of two phases.

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5. Yuan, Y., et al., High-temperature stable dielectrics in Mn-modified (1-x) Bi_0.5Na_0.5TiO₃-xCaTiO₃ ceramics. Journal of Electroceramics, 2010. 25(2-4): p. 212-217.

6. Yu, H. and Z.-G. Ye, Dielectric, ferroelectric, and piezoelectric properties of the lead-free (1−x)(Na_0.5Bi_0.5)TiO₃-xBiAlO₃ solid solution. Applied Physics Letters, 2008. 93(11): p. 112902.

7. Jones, G.O. and P.A. Thomas, The tetragonal phase of Na_0.5Bi_0.5TiO₃ – a new variant of the perovskite structure. Acta Crystallographica Section B, 2000. 56(3): p. 426-430.

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8. Jones, G.O. and P.A. Thomas, Investigation of the structure and phase transitions in the novel A-site substituted distorted perovskite compound Na_0.5Bi_0.5TiO₃. Acta Crystallographica Section B, 2002. 58(2): p. 168-178.

9. Luo, L., et al., Raman spectroscopic study of Na_1/2Bi_1/2TiO₃-x%BaTiO₃ single crystals as a function of temperature and composition. Journal of Applied Physics, 2011. 109(11): p. 113507-6.

10. Xu, C., D. Lin, and K.W. Kwok, Structure, electrical properties and depolarization temperature of (Bi_0.5Na_0.5)TiO₃-BaTiO₃ lead-free piezoelectric ceramics. Solid State Sciences, 2008. 10(7): p. 934-940.

11. Watanabe, Y., et al., Phase transition temperatures and electrical properties of divalent ions (Ca²⁺, Sr²⁺ and Ba²⁺) substituted (Bi_1/2Na_1/2)TiO₃ ceramics. Ceramics International, 2008. 34(4): p. 761-764.

12. Jo, W., et al., Evolving morphotropic phase boundary in lead-free (Bi_1/2Na_1/2)TiO₃-BaTiO₃ piezoceramics. Journal of Applied Physics, 2011. 109(1): p. 014110-7.

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13. Chen, M., et al., Structure and electrical properties of (Na_0.5Bi_0.5)_1−xBa_xTiO₃ piezoelectric ceramics. Journal of the European Ceramic Society, 2008. 28(4): p. 843-849.

14. Otonicar, M., et al., Compositional range and electrical properties of the morphotropic phase boundary in the Na_0.5Bi_0.5TiO₃-K_0.5Bi_0.5TiO₃ system. Journal of the European Ceramic Society, 2010. 30(4): p. 971-979.

15. Rout, D., et al., Dielectric and Raman scattering studies of phase transitions in the (100 – x)Na_0.5Bi_0.5TiO₃–xSrTiO₃ system. Journal of Applied Physics, 2010. 108(8): p. 084102-7.

16. Tadashi, T., M. Kei-ichi, and S. Koichiro, (Bi_1/2Na_1/2)TiO₃ – BaTiO₃ System for Lead-Free Piezoelectric Ceramics. Japanese Journal of Applied Physics, 1991. 30(9S): p. 2236.

17. Chu, B.-J., et al., Electrical properties of Na_1/2Bi_1/2TiO₃–BaTiO₃ ceramics. Journal of the European Ceramic Society, 2002. 22(13): p. 2115-2121.

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18. Rout, D., et al., Study of the morphotropic phase boundary in the lead-free Na_1/2Bi_1/2TiO₃-BaTiO₃ system by Raman spectroscopy. Journal of the Ceramic Society of Japan, 2009. 117(1367): p. 797-800.

19. Sung, Y.S., et al., notRoles of lattice distortion in (1-x)(Bi_0.5Na_0.5)TiO₃ – xBaTiO₃ ceramics. Applied Physics Letters, 2010. 96(20): p. 202901-202901-3.

20. Ge, W., et al., Electric field dependent phase stability and structurally bridging orthorhombic phase in Na_0.5Bi_0.5TiO₃ – x%BaTiO₃ crystals near the MPB. Solid State Communications, 2011. 151(1): p. 71-74.

21. Wylie-van Eerd, B., et al., Structural complexity of (Na_0.5Bi_0.5)TiO₃-BaTiO₃ as revealed by Raman spectroscopy. Physical Review B, 2010. 82(10): p. 104112.

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22. Gomah-Pettry, J.-R., et al., Sodium-bismuth titanate based lead-free ferroelectric materials. Journal of the European Ceramic Society, 2004. 24(6): p. 1165-1169.

23. Gomah-Pettry, J.R., et al., Ferroelectric relaxor behaviour of Na_0.5Bi_0.5TiO₃–SrTiO₃ ceramics. physica status solidi (b), 2004. 241(8): p. 1949-1956.

24. Hiruma, Y., et al., Large electrostrain near the phase transition temperature of (Bi_0.5Na_0.5)TiO₃–SrTiO₃ ferroelectric ceramics. Applied Physics Letters, 2008. 92(26): p. 262904-3.

25. Krauss, W., et al., Piezoelectric properties and phase transition temperatures of the solid solution of (1 – x)(Bi_0.5Na_0.5)TiO₃-xSrTiO₃. Journal of the European Ceramic Society, 2010. 30(8): p. 1827-1832.

26. Rajeev, R., et al., Phases in the (1 − x)Na_0.5Bi_0.5TiO₃ – (x)CaTiO₃ system. Journal of Physics: Condensed Matter, 2010. 22(7): p. 075901.

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27. Glazer, A.M., The classification of tilted octahedra in perovskites. Acta Crystallographica Section B, 1972. 28(11): p. 3384-3392.

28. Chu, B.-J., et al., Electrical properties of Na_1/2Bi_1/2TiO₃-BaTiO₃ ceramics. Journal of the European Ceramic Society, 2002. 22(13): p. 2115-2121.

29. Ting, W., D. Huiling, and S. Xiang, Dielectric and ferroelectric properties of (1-x)Na_0.5Bi_0.5TiO₃-xSrTiO₃ lead-free piezoceramics system. Journal of Physics: Conference Series, 2009. 152(1): p. 012065.

30. Li, Y., et al., Dielectric and ferroelectric properties of lead-free Na_0.5Bi_0.5TiO₃-K_0.5Bi_0.5TiO₃ ferroelectric ceramics. Ceramics International, 2005. 31(1): p. 139-142.

31. Kiat, J.M., G. Calvarin, and J. Schneck, Coexistence of the 1q and 2q incommensurate phases and memory effect in barium sodium niobate. Physical Review B, 1994. 49(2): p. 776-785.

32. Zhao, M.-L., et al., Grain-Size Effect on the Dielectric Properties of Bi_0.5Na_0.5TiO₃. Chinese Physics Letters, 2003. 20(2): p. 290.

33. Suchanicz, J. and J. Kwapulinski, X-ray diffraction study of the phase transitions in Na_0.5Bi_0.5TiO₃. Ferroelectrics, 1995. 165(1): p. 249-253.

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34. Siny, I.G., C.S. Tu, and V.H. Schmidt, Critical acoustic behavior of the relaxor ferroelectric Na_1/2Bi_1/2TiO₃ in the intertransition region. Physical Review B, 1995. 51(9): p. 5659-5665.

35. Fousek, J. and L.E. Cross, Domain-related problems of ferroelectric ceramics. Ceramics International, 2004. 30(7): p. 1169-1173.

36. Yuan, Y., et al., Effects of Ca and Mn Additions on the Microstructure and Dielectric Properties of (Bi_0.5Na_0.5)TiO₃ Ceramics. Journal of Electronic Materials, 2011. 40(11): p. 2234-2239.

37. Smolenskii, G.A., et al., New ferroelectrics of complex composition Soviet Physics – Solid State, 1961. 2(11): p. 2651-2654.

Figure1. (a)X-ray diffraction patterns of (1-x)NBT – xCT(0 ≤ x ≤ 1.00) at room temperature as a function of x (%Ca) and (b) detailed scan of X-ray reflections showing the evolution of XRD peaks at room temperature of the samples near the MPB (without the contribution of CuKα₂) in a limited 2θ range 67 – 72°. The inset in Figure 1.(a) shows the variation of the ratio of the integrated intensity of the (230)_O/(024)_R with composition.

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Figure2. (a) Evolution of the phase fraction of each phase (R3c) and (Pnma)in the (1-x)NBT – xCT system as a function of CT composition at room temperature. (b) The dependence of the perovskite unit-cell volume of the compositional fraction in the MPB region at room temperature.

Figure3.Temperature dependence of the real (ɛ’) parts of dielectric constant for NBT ceramics containing different concentration of CT at 1 and 10 kHz during heating. The two symbols “C” and “H” represent the Cooling (continuous line) and the Heating (dotted line) respectively for x = 0.11 ceramic.

Figure4.Comparison of the evolution of the thermal hysteresis from the dielectric constant at 10 kHz as a function of temperature for the ceramics (1-x)NBT – xCT(x = 0.07 and 0.15) in the MPB composition (x = 0.09, 0.10. 0.11 and 0.13).

Figure5.Variation of the magnitude of the thermal hysteresis as a function of x (%Ca) for (1-x)NBT – x(0.07, 0.09, 0.10, 0.11, 0.13 and 0.15)CT at 10 kHz.

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	MPB composition
x	TmTH (K)	FWHM (+/-1 K)
0.09	390	60
0.10	363	71
0.11	332	91
0.13	271	104

Table1. T_mTH and FWHM values of Δε’(T) at MPB composition (x = 0.09, 0.10, 0.11 and 0.13) at 10 kHz.

Figure6.Comparison between the evolution,as a function of composition CT (x), on the first side, the magnitude of the thermal hysteresis at 300 K, at a frequency of 10 kHz, and, on the other side, the variation of the percentage (fraction) of the minority phase founded in the ceramics of the MPB composition (coexistence of two-phases: R3c + Pnma). Note that the Δɛ’ values are normalized over the permittivity ɛ’ on heating.

Figure7. (a) thermal hysteresis of x = 0.10 ceramics at 10 kHz, where the dotted lines represent the isotherm imposed on the either side of the maximum of thermal hysteresis. (b) Evolution of the permittivity (ɛ’ normalized over ɛ’(t = 0)) at 10 kHz as a function of time (s) for 3 isotherms: T = 350, 380 and 428 K imposed within the thermal hysteresis for x = 0.10. The solid line represents the refinement obtained from the equation ofcapacitor discharge:

y = A + B.exp(-

(t-t0τ)γ).

Figure 8. (a) Evolution of the thermal hysteresis for different compositions in the MPB, where the dotted line at T = 350 K represents an isothermal imposed at fixed temperature, in order to studythe aging for all compositions of the MPB. (b) Variation of the permittivity (ɛ’ normalized over ɛ’(t = 0)) at 10 kHz of (1-x)NBT – xCT for x = 0.10, 0.11 and 0.13 as a function of time (s).

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