Normal and relaxor ferroelectric behavior in the Ba1−xPbx(Ti1−yZry)O3 solid solutions

Journal of Alloys and Compounds 693 (2017) 245e256

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Normal and relaxor ferroelectric behavior in the Ba1
xPbx(Ti1
yZry)O3 solid solutions F. Si Ahmed a, b, K. Taïbi a, O. Bidault b, N. Geoffroy b, N. Millot b, * Laboratoire de Cristallographie-Thermodynamique, Facult e de Chimie, Universit e des Sciences et de la Technologie Houari Boumediene, BP32, Al Alia, 16111, Alger, Algeria b Laboratoire Interdisciplinaire Carnot de Bourgogne, Universit e de Bourgogne Franche Comt e /UMR 6303 CNRS, 9 Avenue Alain Savary, BP 47870, F-21078, Dijon Cedex, France a

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 July 2016 Received in revised form 15 September 2016 Accepted 16 September 2016 Available online 17 September 2016

Polycrystalline samples of Ba1
xPbx(Ti1
yZry)O3 (BPTZ) with x ¼ 0.025 & 0.1 and 0.10  y  0.50 have been synthesized by high-temperature solid-state reaction technique. X-ray diffraction reveals the formation of single phase with tetragonal or cubic structure. Dielectric investigations were carried out in the temperature range from 80 to 445 K with frequencies range from 102 to 106 Hz. A broad dielectric anomaly coupled with the shift of dielectric maxima toward a higher temperature with increasing frequency indicates either a diffuse phase transition or relaxor behavior in some of these ceramics. Whatever lead content, when zirconium is substituted by titanium, TC and ε’rmax decreases while DTm(f) ¼ [Tm(106 Hz)
Tm(102 Hz)] and tgd increase. The diffuse phase transition parameters were estimated from a linear fit of the modified CurieeWeiss law. A good fit to the VogeleFülcher relation further corroborates such a relaxor nature. © 2016 Elsevier B.V. All rights reserved.

Keywords: Ceramics Ferroelectrics Solid state reactions Dielectric response Impedance spectroscopy Scanning electron microscopy X-ray diffraction Low lead Diffuse phase transition

1. Introduction Among the lead-based ceramics with a perovskite structure, Pb(Ti1
yZry)O3 (PTZ) are the most widely used materials especially due to their excellent piezoelectric properties close to the morphotropic phase boundary (MPB) between rhombohedral and tetragonal phases [1]. On the other hand, the greater stability of Zr4þ ion as compared to Ti4þ ion favors the low dielectric losses and the diffuseness of the ferroelectric-paraelectric phase transition. Unfortunately, the use of the lead-based ceramics has caused serious environmental problems because of the high volatilization of lead oxide during the sintering process. Therefore, environmental friendly lead-free ceramic or low-lead content materials with equivalent properties, has become one of the main topics as an alternative to lead-based ceramics [2,3]. In this view, Ba(Ti1
yZry)O3

partement Nanosciences, Laboratoire Interdisciplin* Corresponding author. De  de Bourgogne Francheaire Carnot de Bourgogne, UMR 6303, CNRS/Universite , 9 av. Alain Savary, BP 47870, 21078, Dijon Cedex, France. Comte E-mail address: [email protected] (N. Millot). http://dx.doi.org/10.1016/j.jallcom.2016.09.166 0925-8388/© 2016 Elsevier B.V. All rights reserved.

(BTZ) constitutes one of the lead free ceramic family which is extensively investigated due to it interesting performances and potential applications in the field of environmental protection. According to the Zr/Ti ratio, BTZ exhibit normal or relaxor ferroelectric behavior. In fact, the substitution of Ti4þ by Zr4þ in BaTiO3 (BT) compounds leads to decrease greatly the temperature of the maximum of the relative permittivity and strengthens the relaxor character of the ceramics. Nevertheless, the large temperature dependence of the dielectric constant and a low Curie temperature observed for BTZ ceramics limit their practical applications. Otherwise, PbTiO3 (PT), with the tetragonal perovskite structure, is a well-known piezoelectric and ferroelectric material. Therefore, combination of BTZ with PT is expected to: - Decrease the sintering temperature of BTZ-based ceramics, a desirable move towards electrode of lower cost [4]. - Prepare ceramics without or with very low amount of undesirable pyrochlore phases, generally associated with lead-based system [5,6]. - Give a wide range of Curie temperature.

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In this way, a great number of investigations were achieved in the systems, based lead titanates zirconium, Pb1
xBax(Ti1
yZry)O3 (noted PBZT) [7e32]. It has been shown that the increase of Ba concentration in the ceramics with constant Zr/Ti ratio results in decrease of Tm temperature which is related to the maximum of the permittivity and favors the relaxor behavior [20,30]. It was also reported that Pb substituted BTZ ceramics exhibit improvements in dielectric losses, dielectric constant and ferroelectric properties [30]. However, in these systems a relatively high concentration of Pb was used and thus remains not suitable for environmental devices. Therefore, the aim of this present work is to investigate the behavior of the similar system, based barium titanates zirconium, but with very low lead-content and corresponding to the compositions Ba1
xPbx(Ti1
yZry)O3 (abbreviated BPTZ 100x/100y). This system is characterized by a substitution in the A site of Ba2þ by lower size ion Pb2þ (rPb2þ ¼ 1.49 Å and rBa2þ ¼ 1.61 Å in 12 Coordination Number (CN)) [33] and the substitution in the B site of Ti4þ 4þ by higher size ion Zr4þ (r4þ Zr ¼ 0.720 Å and rTi ¼ 0.605 Å in 6 CN) [33]. Thus, we have chosen to study the influence of low amount of lead on the BTZ composition in two regions associated respectively to: - x ¼ 0.025 and y ¼ 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50 (abbreviated respectively BPTZ 2.5/10; BPTZ 2.5/15; BPTZ 2.5/ 20; BPTZ 2.5/25; BPTZ 2.5/30; BPTZ 2.5/35; BPTZ 2.5/40; BPTZ 2.5/45; BPTZ 2.5/50) - x ¼ 0.100 and y ¼ 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50 (abbreviated respectively BPTZ 10/10; BPTZ 10/15; BPTZ 10/20; BPTZ 10/25; BPTZ 10/30; BPTZ 10/35; BPTZ 10/40; BPTZ 10/45; BPTZ 10/50). Also, we expect to reach a similar dielectric performances as PTZ and better than BTZ as well as to obtain a phase transition at Tm close to room temperature. For this purpose, structural and dielectric properties were investigated in Ba1
xPbx(Ti1
yZry)O3 (BPTZ) compositions and related to the previous results of BTZ and PBTZ ceramics. 2. Material and methods 2.1. Solid state synthesis The starting compounds were powders of BaCO3, TiO2, ZrO2 and PbO (all Sigma Aldrich, USA). Materials with compositions Ba1
xPbx(Ti1
yZry)O3 (BPTZ) with x ¼ 0.025 or 0.1 and 0.10  y  0.50 have been synthesized by the conventional mixed oxide method. They were obtained from carbonates (BaCO3), lead oxide (PbO) and dry oxides (TiO2, ZrO2) according to the following chemical reactions: (1
x) BaCO3 þ x PbO þ (1
y) TiO2 þ y ZrO2 / Ba1
xPbx(Ti1
yZry) O3 þ (1
x)CO2 The proper amounts of reagents: PbO, BaCO3, TiO2 and ZrO2 were weighed, mixed, and milled for 2 h in an agate mortar and calcined under air atmosphere at 900  C for 4 h. After new intimate and ground mixings, the mixture was then pressed under 200 MPa into a pellet of 8 mm diameter and about 1 mm thickness. The resulting disk shaped ceramics were sintered at 1360  C for 1 h under air atmosphere. It should be noticed that during the heat treatments, the ceramics were placed inside a crucible with some amount of PbO in order to preserve the predetermined composition, and especially to avoid the loss of PbO caused by its sublimation. Loss weight systematically determined before and after heat treatment was less than 1%. Diameter shrinkages DF/F were

determined as (Finitial - Ffinal)/Finitial. Their values were in the range 0.10e0.15 while the compactness (experimental density/theoretical density) was about 0.91 (BPTZ2.5/100y) and 0.92 (BPTZ10/ 100y). 2.2. Characterization The phase identification, symmetry and the unit-cell parameters were performed using a D8 Advance X-ray diffractometer (Vantack detector). The data were collected at room temperature using CuKa1þ2 radiation (l ¼ 1.541 Å) in the 2q range from 20 to 80 . The phase identification was done by comparison of the diffraction patterns with the reference cards of the JCPDS Powder Diffraction File. The lattice parameters were determined using the Rietveld method. Dielectric measurements were performed on the ceramic discs after DC sputtering of platinum electrodes on the circular faces. The real part of the permittivity ε’r and losses tgd were measured under nitrogen as a function of both temperature (80e445 K) and frequency (102e106 Hz) using an HP-4284A LCR meter. The microstructure observation, the particle size, morphology and chemical composition of the pellet, was performed using a Scanning Electron Microscope (SEM-JEOL 6360) combined with energy dispersive X-ray spectroscopy (EDS). 3. Results and discussion 3.1. XRD study The XRD patterns of BPTZ 100x/100y powders are shown in Fig. 1. The resulting unit cell parameters and volume are presented in Table 1. The XRD profiles of all the samples have revealed that no parasite phase exists. Only peaks corresponding to the perovskite phase are present and all the peaks may be indexed in cubic symmetry. However, the refinement of the lattice parameter highlights part of the samples may be refined in the tetragonal symmetry for ceramics low concentrate with zirconium (y  0.2) (Table 1). Indeed, a detailed study achieved on the BPZT10/15 composition, has shown the existence of widening peaks (200) in the XRD pattern of the sample which confirms that the sample has tetragonal structure (Fig. 2). Moreover, the asymmetry characteristic of tetragonal network that is visible to y  0.20 compositions disappears for compositions y > 0.20. Furthermore, the comparison of factors of agreement between experimental data collected and simulated data with high continuous background has revealed almost the same values either for refining tetragonal symmetry or cubic symmetry (Table 2). However, the goodness of fit (Gof) is slightly better in tetragonal symmetry in case of y  0.20. On the other hand, it is known that the ferroelectric-paraelectric transition of normal ferroelectric materials like BTZ was related to the structural transition from tetragonal to cubic symmetry. On the contrary, relaxor materials were illustrated by the absence of this macroscopic structural phase transition: the symmetry appears cubic regardless of the temperature. All these observations are in agreement of respectively the tetragonal and cubic symmetry determined for our BPTZ compositions (Table 1). Otherwise, the Fig. 1 reveals that as Zr content increased, the diffraction peaks (e.g., 110) were found to shift towards lower 2q values, suggesting an increase in lattice parameters due to the incorporation of Zr4þ (biggest ions) in the Ti4þ ion site (rTi4þ ¼ 0.605 Å and rZr4þ ¼ 0.720 Å) [33]. In fact, as the zirconium fraction increases, the unit cells parameters and the volume increase (Table 1). The same result has been observed for the Ba(TiyZr1-y)O3 solid solutions where the cubic symmetry appears for y > 0.1 [34], whereas in our case, doping the BTZ structure by

F. Si Ahmed et al. / Journal of Alloys and Compounds 693 (2017) 245e256

247

Fig. 1. XRD patterns of BPTZ 2.5/100y (a) and BPTZ 10/100y (b) (0.1  y  0.5).

Table 1 Unit cell parameters, volume and crystal size of some compositions belonging to BPTZ 100x/100y solid solutions. (CS: Crystal Size, with an incertitude < 4 nm). (a) BPTZ 2.5/100y (0.1  y  0.5) Tetragonal BPTZ 2.5/100y 3

V(Å ) a (Å) c (Å) c/a C.S (nm)

Cubic BPTZ 2.5/10

BPTZ 2.5/15

BPTZ 2.5/20

BPTZ 2.5/25

BPTZ 2.5/30

BPTZ 2.5/35

BPTZ 2.5/40

BPTZ 2.5/45

BPTZ 2.5/50

65.42 4.022 4.043 1.005 88

65.85 4.031 4.053 1.005 76

66.31 4.042 4.059 1.004 69

66.63 4.054

67.10 4.064

67.49 4.071

67.08 4.063

68.40 4.090

68.8 4.098

93

99

81

82

124

141

(b) BPTZ 10/100y (0.1  y  0.5) Tetragonal

Cubic

BPTZ 10/100y

BPTZ 10/10

BPTZ 10/15

BPTZ 10/20

BPTZ 10/25

BPTZ 10/30

BPTZ 10/35

BPTZ 10/40

BPTZ 10/45

BPTZ 10/50

V(Å3) a (Å) c (Å) c/a C.S (nm)

65.29 4.018 4.044 1.007 81

66.02 4.033 4.059 1.006 64

66.49 4.043 4.067 1.006 61

66.87 4.052

67.07 4.057

67.32 4.063

67.79 4.073

68.20 4.086

68.61 4.094

84

84

69

76

122

153

Fig. 2. XRD pattern of BPTZ10/15 with a detailed view of (200) peak.

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F. Si Ahmed et al. / Journal of Alloys and Compounds 693 (2017) 245e256

Table 2 Comparison of mean values agreement factors acquired with a refinement using tetragonal and cubic symmetry respectively. Factors of agreement

Tetragonal

Cubic

Rexp Rwp Rp Gof

7.01 8.18 6.39 1.17

7.00 8.54 6.61 1.22

Rexp: Experimental reliability factor, Rwp: Weighted reliability factor, Rp: Reliability factor, Gof: Goodness of fit.

lead promotes a low temperature phase and it is maintained for higher concentration of zirconium (until y  0.2). 3.2. SEM observations Typical microstructures of BPTZ ceramics were obtained by SEM combined with EDS after the sintering treatment. The EDS mapping analysis revealed and confirmed a single phase perovskite with the elemental composition of our ceramics where the stoichiometry is maintained which was a goal to reach, despite of the difficulty that the system present in avoiding the lead losses caused by its sublimation (Table 3). The SEM observations (Fig. 3) shows two antagonist behaviors in the evolution of the BPTZ grain size with increasing Pb concentration: - The first is related to the Ti-rich ceramics (Zr/Ti  0.10). In this case, the increase of Pb lead to the reduction of the grain size of BPTZ compositions from approximately 2 to 1 mm as observed between BPTZ2.5/10 and BPTZ10/10 compositions (Fig. 3 a and b) - The second corresponds to the relative Zr-rich ceramics (Zr/ Ti  0.30). Here, the increase of Pb leads to the rise of the grain size of BPTZ compositions from approximately 2 to 3 mm as observed between BPTZ2.5/30 and BPTZ10/30 compositions (Fig. 3 c and d). These results are in good agreement with the assertions of X.G. Tang et al. [35] who showed that for a same system, materials with low grain size behave like normal ferroelectric and were in tetragonal symmetry. However, materials with higher grain size revealed relaxor ferroelectric behavior and were characterized by cubic symmetry. Indeed, BPTZ2.5/10 and BPTZ10/10 compositions which belong to the normal ferroelectric ceramics (type I) were characterized by lower grain size (<2 mm) while BPTZ2.5/30 and BPTZ10/30 samples which belong to relaxor nature (type II) were distinguished by higher grain size (>2 mm) (Fig. 3). Furthermore, other authors have reported that the tetragonality decreases with diminishing of the crystallites sizes [36,37]. These findings are also consistent with the values of the crystal size (CS) determined for our materials (Table 1). In fact, CS varies between 61 and 88 nm for the samples in tetragonal symmetry and between 84 and 153 nm for the samples in cubic symmetry. From Table 1, it is clear that whatever the Pb content, as the Zr/Ti ratio increases, the crystallites size (CS) decreases for y  0.2, the tetragonality (c/a) decreases and the sample shift from tetragonal to cubic symmetry.

Table 3 EDS results of BPTZ 10/20.

Atomic % experimental Atomic % theoretical

Ti

Zr

Ba

Pb

38.96 40

9.03 10

47.69 45

4.32 5

3.3. Dielectric study The dielectric permittivity (ε0 r) and loss (tgd) of the BPTZ 100x/ 100y solid solutions were measured as function of both temperature and frequency. The thermal and frequency variations of the dielectric permittivity and dielectric losses as well as the temperature variation of the inverse of the permittivity (1/ε0 r) at 1 kHz exhibited different behaviors depending upon the substitution rate. As an example, Figs. 4 and 5 show these variations for various compositions. Furthermore, Table 4 shows some dielectric parameters characteristics of BPTZ 100x/100y solid solutions. From these results we can make the following preliminary findings: i) For x (Pb) constant, increasing y (Zr) lead to - a decrease of both the maximum of permittivity (ε0 rmax) and the temperature of this maximum (Tm) (see respectively the 6th and 1st line of Table 4 (a and b), - a slight increase of the Curie-Weiss law deviation (DTm) and the losses (tgd) (see respectively the 4th and 8th line of Table 4 (a and b), ii) For y (Zr) constant, increasing x (Pb) leads to: - a slight decrease of the temperature of the permittivity maximum (Tm) between 2.5 and 10% Pb, - a slight increase of the Curie-Weiss law deviation (DTm) whereas losses (tgd) were practically constant) (see Table 4 (a and b)).

3.3.1. The two types of behavior in Ba1
xPbx(Ti1
yZry)O3 solid solutions According to the x and y values, two types of behavior have been observed: i) The first one (appointed type I) concerns the compositions ceramics BPTZ 2.5/10 to BPTZ 2.5/20 (x ¼ 0.025; 0.10  y  0.20) and BPTZ 10/10 to BPTZ 10/20 (x ¼ 0.10; 0.10  y  0.20). The Fig. 4 illustrate the dielectric behavior for some of these compositions characterized by only one broad peak in the thermal variation of the permittivity (ε’r) involving a diffuse phase transition. In addition, the temperatures of the maximum of the permittivity (TC) were nearly frequency independent. Likewise, we observed that the dielectric losses decreased with increasing temperature. In particular, the loss tangent values were smaller at temperatures above Tm and decreases quickly at high temperature (T < 445 K). ii) The second solid solution (appointed type II) concerns the compositions ceramics BPTZ 2.5/25 to BPTZ 2.5/50 (x ¼ 0.025; 0.25  y  0.50) and BPTZ 10/25 to BPTZ 10/50 (x ¼ 0.10; 0.25  y  0.50). The Fig. 5 shows the dielectric behavior for some of these compositions which are also characterized by only one broad peak in the thermal variation of the permittivity (ε0 r) leading to a relaxor behavior. In addition, these variations show at temperature Tm a relative low dielectric losses and the temperature Tm of ε0 rmax was shifted to higher values as the frequency increases. Slight frequency dispersion sets near Tm,: the value of ε0 r decreases when the frequency increases. All these dielectric characteristics are typical of ferroelectric relaxor behavior. Moreover, the difference between these two ferroelectric types can mainly distinguished in Table 4 by the values of: - TC (or Tm) which are generally higher (type I) or lower (type II) than 300 K.

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249

Fig. 3. SEM microstructures of typical BPTZ ceramics, at the same scale, of type I (a, b) normal ferroelectric and type II (c, d) relaxor ferroelectric.

Fig. 4. Dielectric permittivity (ε0 r) and dielectric loss (tan d) as a function of temperature at various frequencies for some BPTZ 100x/100y ceramics (type I).

- DTm (K) which are generally lower (type I) or higher (type II) than 100 K.

3.3.2. The nature of structural phase transition in Ba1
xPbx(Ti1
yZry)O3 solid solutions The Ba1
xPbx(Ti1
yZry)O3 solid solutions are characterized by one phase transition. This evolution with only one phase transition was reported previously for numerous compositions derived from BaTiO3 (BT) as it was the case of BPTZ solid solutions: - For compositions close to BT, there were three dielectric anomalies corresponding to the phase transitions: rhombohedral / orthorhombic / tetragonal / cubic. The

phase transition, which is first order for BT, moves progressively to the second order as the composition shifts from BT. It should be noted also in the case of PBZT, that the substitution Pb2þ-Ba2þ leads to a unique tetragonalecubic transition from a relatively low substitution rate [21e23]. These physical properties are distinctive of normal ferroelectric with diffuse phase transition, as found in our compositions of type I. In this case, the ferroelectric phase appears macroscopically tetragonal (Table 1). - When the composition deviates from BT, the progressive replacement of Ti4þ by the larger cation Zr4þ causes the disappearance of both orthorhombic and tetragonal distortions, thus leading to a unique rhombohedralecubic transition. The same result was observed in the BaTiO3-BaZrO3-CaTiO3 system where an X-ray diffraction study has shown that the rhombohedral a-

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Fig. 5. Dielectric permittivity (ε0 r) and dielectric loss (tan d) as a function of temperature at various frequencies for some BPTZ 100x/100y ceramics (type II).

angle increases with temperature and reaches 90 at TC [38,39]. This evolution is typical of ferroelectric relaxor compositions in which the relaxor phase appears macroscopically cubic (Table 1) although there is probably a local rhombohedral distortion as it was probably the case for our compositions of type II.

3.3.3. Evolution of TC (or Tm) in Ba1
xPbx(Ti1
yZry)O3 solid solutions 3.3.3.1. Changes depending on the Zr/Ti ratio. Table 4 (a & b) shows that TC (or Tm) shifts towards lower temperature when y increases, which is an expected result of Ti4þ/Zr4þ substitution. Indeed, this behavior is in accordance with the normal ferroelectric theories based on the size of ions located at the B site of the ABO3 perovskite structure. It is known that a transition from the non-polar to the polar form induces low atomic shifts amplitude Dz of the B cation along the polar axis. This is formulated by an empirical relationship of S.C. Abrahams et al.: TC (K) ¼ 2  104 Dz2 (Å) [40]. So, an increase in the size of the cation located at the B site lead to the decrease of Dz and consequently of TC. Considering the substitution Zr-Ti, it is the largest size of Zr4þ which limits the shift Dz. As TC is directly correlated to Dz by the empirical relation above, we observed its decrease. Furthermore, it is possible to explain the variation of TC from the relationship of Goldschmidt tolerance factor (t) [41].

r þ ro t ¼ pffiffiffi A 2ðrB þ ro Þ Where rA, rB and rO are the ionic radius of the respective ions located in the A site, B site and oxygen site of the ABO3 perovskite structure. In fact, the plot of Curie temperature TC as a function of tolerance factor t (Fig. 6) for the ceramics BPTZ2.5/100y and BPTZ10/100y shows that TC decreases with decreasing of t. According to the relationship of Goldschmidt, the decrease of t is favored by the high values of rB (ionic radius of element located in the B site). Therefore, the decrease of TC is increasingly important as the B ion is higher. That's what we got for our compositions.

3.3.3.2. Changes depending on the Pb/Ba ratio. Table 4 (a & b) shows that TC (or Tm) decreases when x increases. For instance, for y ¼ 0.10, Tm decreases slightly from 371 K (x ¼ 0.025) to 368 K (x ¼ 0.100). This decrease becomes more important when the zirconium content increases. This evolution seems in contradiction with the results reported previously concerning the cation (A) located outside of octahedron in the ABO3 compositions [42]. In this hypothesis, a decrease in the size of A leads to an increase in TC when the concerning cation possess a lone pair which leads to the non-spherical and strongly polarized cation. This is the case when Pb2þ replaces Ba2þ: an increase in the distortion of the octahedron and of the TC shift occurs, although the cation Pb2þ is smaller than

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251

Table 4 Dielectric characteristics of some compositions belonging to BPTZ 100x/100y solid solutions. a- BPTZ 2.5/100y (0.1  y  0.5) Type I BPTZ 2.5/10

BPTZ 2.5/15

BPTZ 2.5/20

BPTZ 2.5/25

BPTZ 2.5/30

BPTZ 2.5/35

BPTZ 2.5/40

BPTZ 2.5/45

BPTZ 2.5/50

371 379 429 58 3 4558 0.046 0.0100 nd 0.807

350 363 419 69 1 4620 0.044 0.0086 nd 0.854

311 326 394 83 1 3567 0.045 0.0069 1.46 0.832

284 317 389 105 10 3256 0.196 0.0132 1.95 1.047

256 305 372 117 10 3302 0.141 0.0083 1.73 1.143

212 273 356 104 25 3102 0.279 0.0183 1.85 1.157

212 147 332 120 23 658 0.075 0.0116 1.74 1.103

130 nd 202 nd 44 523 0.136 0.0208 1.63 0.952

123 138 320 197 49 861 0.196 0.0346 1.90 1.704

BPTZ 10/10

BPTZ 10/15

BPTZ 10/20

BPTZ 10/25

BPTZ 10/30

BPTZ 10/35

BPTZ 10/40

BPTZ 10/45

BPTZ 10/50

368 376 440 64 4 3352 0.039 0.0081 1.85 0.455

332 352 426 94 2 3594 0.071 0.0118 1.89 0.604

293 325 408 115 8 3954 0.077 0.0097 1.81 0.637

257 299 405 148 22 2335 0.088 0.0083 1.97 0.858

242 287 386 144 17 1151 0.351 0.0131 1.79 1.140

204 175 335 131 28 711 0.069 0.0101 2.02 1.960

150 161 340 190 40 962 0.138 0.1699 1.75 0.963

135 nd 268 133 40 326 0.072 0.0109 1.87 0.707

124 nd 286 162 45 243 0.068 0.0110 1.64 1.196

Tc ¼ Tm(1khz) (K)1khz T0 (K) Tdev (K) DTm (K) DTm(f) (K) ε0 rmax 1khz Dε0 r/ε0 r tgdmax (1khz)

g C.10
5 (K)

Type II

b- BPTZ 10/100y (0.1  y  0.5) Type I

Tc ¼ Tm(1khz) T0 (K) Tdev (K) DTm (K) DTm(f) (K) ε0 rmax (1khz) Dε0 r/ε0 r tgdmax (1khz)

g C. 10
5 (K)

Type II

nd ¼ not determined, Tc ¼ Tm: Curie temperature, T0: Curie-Weiss temperature, Tdev: Deviation temperature from Curie-Weiss law, DTm ¼ Tdev
Tm, DTm(f) ¼ Tm(106 Hz)
Tm(102 Hz), g: diffuseness exponent, C: Curie Weiss constant.

Fig. 6. Curie temperature plotted against tolerance factor for the compositions BPTZ 2.5/100y and BPTZ 10/100y. The lines are a least squares fit to the data.

Ba2þ [42]. So, in our case, instead of increasing, TC decreases slightly when Pb2þ increases. It should be noted that same results were obtained for the low compositions of Pb2þ: - by W. Chaisan et al. [13] during the study of the (1
x) Pb(Zr0.52Ti0.48)O3-xBaTiO3 system. It has been found that TC

increases from 129  C (xBa ¼ 1; (1
x)Pb ¼ 0) to 155  C (xBa ¼ 0.9; (1
x)Pb ¼ 0.1) and then decreases to 146  C (xBa ¼ 0.7; (1
x)Pb ¼ 0.3). - by Dipti et al. [30] during the investigation of the Pb1
xBax (Zr0.55Ti0.45)O3 compositions: TC increases slightly from 461  C (xBa ¼ 0.02; (1
x)Pb ¼ 0.98) to 464  C (xBa ¼ 0.01;

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(1
x)Pb ¼ 0.99) and then decreases to 430  C (xBa ¼ 0; (1
x)Pb ¼ 1) - by P. Kumar et al. [27] which have also indicated a very slight diminution of TC when Pb2þ increases from xBa ¼ 0 to (1
x)Pb ¼ 0.05. Similar high permittivity response with a shift to lower temperatures was also observed during the dielectric study of (1
x) BaTiO3 e x BiGdO3 system [43]. Indeed, normal ferroelectric behavior was observed with a maximum of permittivity moving toward low temperatures as x increases (up to x ¼ 0.06). Beyond, the system has a relaxor ferroelectric behavior to x ¼ 0.10. 3.3.4. Diffuse phase transition parameters The diffuseness is corroborated by the deviation from the CurieWeiss law within these compositions. It is known that the thermal variation of dielectric constant above the Curie temperature (in the paraelectric phase region) can be described generally by a CurieeWeiss law; Eq. (1):

1 T
T0 ðT > T0 Þ ¼ ε0r C

(1)

where T0 is the Curie-Weiss temperature and C is the Curie Weiss

constant. Regarding the normal ferroelectric, the decreasing part of the curve located in the paraelectric region follows a CurieeWeiss law. On the other hand, the curves 1/ε0 r ¼ f (T) also make it possible to determine the order of transition; it is first order if T0 < TC and second order if T0 ¼ TC. For instance, Fig. 7 shows the plot of 1/ε0 r as a function of temperature at 1 kHz and the fit according to CurieWeiss law of the experimental data by Eq. (1). The curves presented in this figure correspond to the comparables compositions belonging to type I (BPTZ 2.5/15 and BPTZ 10/15) and to type II (BPTZ 2.5/30 and BPTZ 10/30). The Curie temperature is determined from the graph by the extrapolation of the reciprocal dielectric constant in the paraelectric region. For all the compositions studied, the fitting parameters (C and T0) are displayed in Table 4. The values of T0 > Tm confirm the deviation from the Curie-Weiss law which is a typical behavior of ferroelectric materials with diffuse phase transition (type I) and ferroelectric relaxors (type II). On the other hand, the parameter DTm which describes the degree of deviation from CurieeWeiss law is defined as DTm ¼ Tdev
Tm. Tdev denotes the temperature where the dielectric permittivity starts to deviate from the CurieeWeiss law and Tm is the temperature of the dielectric maximum [44]. For x (i.e. Pb) constant, DTm increases as y increases. However, the values of DTm (i.e. the diffuseness) are more important with the rise of x (i.e. when

Fig. 7. Thermal variation of 1/εr at 1 kHz for some BPTZ 100x/100y ceramics of type I: [(a) & (b)] and type II [(c) & (d)].

F. Si Ahmed et al. / Journal of Alloys and Compounds 693 (2017) 245e256

the Pb content increases). Otherwise, a modified CurieeWeiss law (Eq. (2)) has been proposed to describe the diffuseness in a phase transition [45]:

1 1 ðT
Tm Þg
¼ εr εm c

(2)

where εm is the peak value of ε0 r, C is a constant and g is the diffuseness exponent. The parameter g gives information about the phase transition character (g ¼ 1 corresponds to a typical normal

253

ferroelectric and g ¼ 2 corresponds to a typical relaxor transition with a complete diffuse phase [18] [46]). Thus, to describe the diffuseness of the broadened peaks in the paraelectric phase, the plots of ln(1/εr
1/εm) vs. ln(T-Tm) at 1 kHz for some compositions BPTZ 100x/100y of type I (a) type II (b) showed nearly linear variation (Fig. 8). The mean value of the diffusivity g was extracted from these plots by fitting a straight-line equation. For all the compositions, relatively high values of g (>1) were observed (Table 2). This involve that these compositions are characterized by a diffuse phase transitions with a predisposition of relaxor behavior.

Fig. 8. Plots of ln(1/εr
1/εm) vs. ln(T
Tm) at 1 kHz for some compositions BPTZ 100x/100y of type I (a) type II (b).

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F. Si Ahmed et al. / Journal of Alloys and Compounds 693 (2017) 245e256

However, we noticed that the higher values of g were obtained for zirconium-rich compositions. All the characterizations done above on the basis of the Curie-Weiss law and the value of the empirical parameters like DTm and g confirmed that the ceramics of type I were normal ferroelectrics with a diffuse phase transition while

those of type II were relaxor type. On the other hand, it has been observed the increase of DTm and consequently the relaxor effect was amplified when the composition deviated from BaTiO3. Such result was also obtained for other lead-free perovskite relaxors [47,48].

Fig. 9. Plot of log (f) as a function of Tm for BPTZ 2.5/35 (a) and BPTZ 10/35 (b) [the symbols: experimental data; the solid curve: fitting to the VogeleFülcher relation].

F. Si Ahmed et al. / Journal of Alloys and Compounds 693 (2017) 245e256

3.3.5. Relaxor characteristics As for all the diffuse phase transition, the relaxor behavior is characterized by the Curie-Weiss law deviation DTm ¼ Tdev
Tm. Furthermore, the relaxor effect give rise to the frequency dependency of Tm and ε0 r which can be estimated respectively from the parameters noted by DTm(f) and Dε0 r/ε0 r as:









DTmðfÞ ¼ Tm 106 Hz
Tm 102 Hz Dε0r ε0r

    ε0r 102 Hz
ε0r 106 Hz   ¼ ε0r 102 Hz

The relaxor effect is even more significant that the frequency dispersion (i.e. DTm(f) and Dε0r =ε0r ) is important. Table 4 shows low values of DTm(f) (<10) and Dε0r =ε0r (<0.10) for the BPTZ type I compositions. This implies that these compositions do not have a significant relaxor effect. In contrast, the values of DTm(f) [ 10 and Dε0r =ε0r > 0:10 for the BPTZ type II compositions with low concentration of Pb (x ¼ 0.025) indicates their better relaxor behavior. Some of these compositions are of great interest for obtaining relaxor effect at temperatures close to 300 K for use as low lead capacitor dielectrics or actuators. As an example, the value of Tm corresponding to BPTZ2.5/25 is 284 K (at 103 Hz), which can be compared to the well-known but lead-containing PMN (Tm ¼ 265 K) [49]. The relaxor ferroelectric behavior could be also described by the Vogel-Fülcher relation (Eq. (3)) [50e52]:

f ¼ f 0 exp

Ea kb ðT
TVF Þ

(3)

Where f0 is the attempt frequency, Ea is a measure of average activation energy, kB is the Boltzmann's constant and T VF is the freezing temperature. Fig. 9 shows the plot of ln(f) vs Tm for the sample BPTZ 2.5/35 and BPTZ 10/35. The experimental curve was fitted using the above VogeleFülcher formula. The shift of Tm to lower values for decreasing frequencies obeys to the Vogel-Fülcher law. This is own to be one of the characteristics of relaxor systems. The fitting parameters of VogeleFülcher relation were: - T VF ¼ 176.5 K, f0 ¼ 2.1011 Hz; Ea ¼ 0.058 e.V for BPZT 2.5/35 and - T VF ¼ 139 K, f0 ¼ 6.5.1014 Hz; Ea ¼ 0.150 e.V for BPTZ 10/35. It should be noted that the higher values of the attempt frequency and the activation energy were obtained for compositions containing more lead. This corroborates the weak relaxor effect of these compositions and confirms that this behavior is influenced by the substitution in the A site (i.e when Pb2þ replace Ba2þ). Nevertheless, in our compositions, relaxor behavior could be explained mainly on the basis of compositional fluctuation due to Zr4þand Ti4þ ions distributed randomly in the B-site. This model suggests also that the relaxor behavior in the present composition is similar to a spin glass model with polarization fluctuations beyond the static freezing temperature. One of the characteristics of the dipolar glass system as well as relaxor ferroelectrics is the appearance at low frequency dielectric loss peak below T VF. The loss peaks shift to lower frequencies on decreasing the temperature, indicating the thermally activated nature of the dielectric relaxation [53].

4. Conclusion Ba1
xPbx(ZryTi1
y)O3 (BPTZ) with x ¼ 0.025 & 0.1 and 0.10  y  0.50 have been synthesized by high-temperature solid-

255

state route. The refinement of the lattice parameter determined by XRD at room temperature gave values corresponding to the tetragonal (y  0.2) or cubic (y > 0.2) system. However, it is to highlight that the tetragonal unit cell parameters (a and c) have very similar values and therefore the c/a ratio is close to 1 involving tetragonal symmetry. According to the Zr/Ti ratio, two types of behavior have been observed by dielectric measurements. The type I (low Zr/Ti ratio) characterized by only one peak of ε’r with a diffuse phase transition and frequency independent. Such compounds belong to the normal ferroelectric having a single diffuse phase transition. The type II (higher Zr/Ti ratio) characterized by only one broad peak, but with frequency dispersion and therefore relaxor behavior. Some of these compositions present the values of Tm close to room temperature which allows the use of relaxor properties in normal conditions. Otherwise, the quantitative analysis based on the empirical parameters confirmed the diffuse phase transition in Ba1
xPbx(Ti1
yZry)O3 ceramics and the relaxor effect for low Pb and Zr rich compositions. In addition, the experimental Tm data revealed a good agreement with the VogeleFülcher equation implying similarities of a spin glass model with polarization fluctuations beyond the static freezing temperature. Compared to BTZ, similar dielectric characteristics have been evidenced. However, for some of the explored samples, the temperatures of the permittivity maximum (TC or Tm) were found close to room temperature: BPTZ2.5/20 (311 K), BPTZ2.5/25 (284 K) and BPTZ10/20 (293 K). This is a very useful parameter for applications. In addition, the BPTZ relaxor domain (0.25  y  0.50) appears more expanded comparatively to the one of BTZ (0.26  y  0.40). Compared to PBTZ, besides the appearance of ferroelectricparaelectric transition around the room temperature, the BPZT compositions are characterized by low-lead content (2.5%  Pb  10%). This is a very valuable parameter for environmental protection. Moreover, this class of materials with very small amount of lead has further advantages like the environmental friendliness. References [1] B. Jaffe, W.R. Cook, H. Jaffe, Piezoelectric Ceramics, Academic Press, London, 1971. [2] Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nsagaya, M. Nakamura, Lead free piezoceramics, Nature 432 (2004) 84e87. [3] L.-E. Cross, Materials science: lead-free at last, Nature 432 (2004) 24e25. [4] J.-F. Chen, Z.-G. Shen, F.-T. Liu, X.-L. Liu, J. Yun, Preparation and properties of barium titanate nanopowder by conventional and high-gravity reactive precipitation methods, Scr. Mater 49 (2003) 509e514. [5] B.-K. Gan, J.-M. Xue, D.-M. Wan, J. Wang, Lead zirconate titanateebarium titanate by mechanical activation of mixed oxides, Appl. Phys. A 69 (1999) 433e436. [6] W. Chaisan, S. Ananta, T. Tunkasiri, Synthesis of barium titanate-lead zirconate titanate solid solutions by a modified mixed-oxide synthetic route, Curr. Appl. Phys. 4 (2004) 182e185. [7] T. Ikeda, Studies in (Ba,Pb)(Zr,Ti)O3 system, J. Phys. Soc. Jpn. 14 (1959) 168e174. [8] G. Li, G. Haertling, Dielectric, ferroelectric and electric field-induced strain properties of (Pb1
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