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Dielectric behavior of a lead-free electroceramics Ba1−xEr2x/3(Ti1−yZry)O3

  • F. Si-Ahmed
  • K. Taïbi
  • O. Bidault
  • N. Millot
Article
  • 64 Downloads

Abstract

Lead-free electroceramics samples of composition Ba1−xEr2x/3(Ti1−yZry)O3 (BETZ) with x = 0.01 and 0.02 and 0.20 ≤ y ≤ 0.35 have been elaborated by solid-state reaction technique. X-ray diffraction at room temperature discloses a single perovskite phase with a cubic symmetry. Dielectric measurements were carried out in the ranges (80–445 K) and (102–106 Hz) of temperature and frequencies respectively. The ceramics exhibited normal and/or relaxor ferroelectric properties then some of them have very interesting dielectric characteristics in the vicinity of room temperature. A wide dielectric anomaly combined to the dielectric maxima shift toward a higher temperature with increasing frequency denotes either a diffuse phase transition or relaxor behavior in some ceramics. For any erbium concentration, when titanium is substituted by zirconium, the temperature of the permittivity maximum TC (Tm) and the maximum permittivity (ε′rmax) decreases while ΔTm(f)= [Tm(106 Hz) − Tm(102 Hz)] and tan δ increase. The diffuse phase transition parameters were calculated from the modified Curie–Weiss law linear fit. Further a relaxor nature was confirmed and endorsed by a good fit to the Vogel–Fülcher relation.

1 Introduction

Due to their high solubility in BaTiO3 (BT), many dopants are used in the manufacture of materials such as positive temperature coefficient resistors and multi-layer capacitors [1]. These materials have a formulation involving the incorporation of rare earth cations to control conductivity and electrical degradation [2, 3]. The rare earth elements are also known for their ability to stabilize the thermal evolution of the permittivity and to reduce dielectric losses. Some of them (called amphoteric) maximize the lifetime of multi-layer capacitors.

Numerous reports indicate that ionic radii are a major factor affecting the rare earth ions incorporation in BT ceramics [4, 5, 6, 7, 8]. Among these, a study on the doping of BT ceramics by rare earth ions was made on the basis of the tolerance factor evolution as a function of the ionic radii [4]. For this purpose, the authors have defined tolerance factors for substituted ions at A (tA) and B (tB) sites of the ABO3 perovskite structure. Under these conditions, it is expected that the incorporation of small rare earth ions (rR3+ < 0.87 Å) occurs at B site, those of large size (rR3+ > 0.94 Å) at A site and the intermediate ions (0.87 ≤ rR3+ ≤ 0.94 Å) occupy the two sites with different proportions. The latter are called amphoteric dopants and according to the occupied site they are acceptors (B site) or donors (A site).This is the case of erbium which, introduced into the BT network, revealed different behaviors [9].

The effect of rare earths on the microstructure and the dielectric properties of BTZ type ceramics were also studied. However, very little work was reported about the erbium influence on BTZ [10, 11, 12]. Some experimental results showed that Er improves the dielectric properties of Ba(Ti0.8Zr0.2)O3 ceramics. High values of the dielectric constant (> 12,000) and low values of the dielectric losses (1%) were obtained when the Er content is 0.15 mol%. The frequency and temperature stability were also improved, which is appropriate for dielectric applications as capacitors [10].

To our knowledge, no systematic investigation was made on a series of solid solutions about the influence of the erbium incorporation on the BTZ compositions. It is precisely in this perspective that these new materials derived from BTZ (containing very little erbium) are presented. Thus, several compositions resulting from solid solutions Ba1−xEr2x/3(Ti1−yZry)O3 (abbreviated BETZ 100x/100y with x = 0.01 and 0.02 and 0.20 ≤ y ≤ 0.35) were elaborated. The characterizations are achieved by X-ray diffraction (XRD), scanning electron microscopy (SEM) and by dielectric measurements as function of temperature and frequency.

2 Materials and methods

2.1 Material elaboration

BaCO3, Er2O3, TiO2 and ZrO2 (all Sigma-Aldrich, USA, purity of 99.99%) powders were used as starting compounds. The conventional mixed oxide method were used to elaborate materials with compositions Ba1−xEr2x/3(Ti1−yZry)O3 (noted BETZ) as x = 0.01 or 0.02 and 0.20 ≤ y ≤ 0.35. They were produced according to the following chemical reaction:
$$(1 - {\text{x}}){\text{BaC}}{{\text{O}}_3}+\frac{{\text{x}}}{3}{\text{E}}{{\text{r}}_2}{{\text{O}}_3}+(1 - {\text{y}}){\text{Ti}}{{\text{O}}_2}+{\text{yZr}}{{\text{O}}_2} \to {\text{Ba}}(1 - {\text{x}}){\text{E}}{{\text{r}}_{\frac{{2{\text{x}}}}{3}}}({\text{T}}{{\text{i}}_{(1 - {\text{y}})}}{\text{Z}}{{\text{r}}_{\text{y}}}){{\text{O}}_3}+(1 - {\text{x}}){\text{C}}{{\text{O}}_2}$$

The proper amounts of reagents: (BaCO3, Er2O3, TiO2 and ZrO2) were weighed, mixed, and milled for 4 h (attrition milling with microballs of zirconium oxide) then calcined for 4 h at 1200 °C under air atmosphere (a temperature ramp of 5°C/min is applied before and after this treatment). Afterward a new intimate and ground mixing, the resulting powder mixture was pressed under 200 MPa into a pellet (of 8 mm diameter and about 1 mm thickness). The resulting disk shaped green ceramics were sintered under air atmosphere at 1375 °C for 2 h (a temperature ramp of 5°C/min is applied before and after this treatment). The weight losses systematically controlled before and after heat treatment were estimated less than 1%. Diameter shrinkages ΔΦ/Φ defined as [(Φinitial − Φfinal)/Φinitial] were about 17% while the relative density measured by using Archimedes principle, was about (0.96 ± 0.01) for all samples.

2.2 Characterization

The diffraction data were collected at room temperature, using a D8 Advance X-ray diffractometer (Vantack detector), in the 2θ range (20°–80°) applying CuKα(1+2) radiation (λ = 1.541 Å). The phase identification was established by comparison of the diffraction patterns to the ICDD powder diffraction file reference. Whereupon, a Rietveld method was applied to define the unit-cell parameters for each composition.

A scanning electron microscope (SEM-JEOL 7600 F) combined with energy dispersive X-ray spectroscopy (EDS SDD Oxford) was used to observe microstructure and particle size with a semi quantitative analysis of chemical composition of the pellet.

Dielectric measurements were carried out on the pellet afterwards a DC platinum electrodes sputtering on the circular faces. The complex dielectric permittivity were collected under primary vacuum as a function of both frequency (102–106 Hz) and temperature (80–445 K), using an HP-4284A LCR meter (with 1V as amplitude of the probing AC electric field).

3 Results and discussion

3.1 XRD analysis

The room temperature X-ray diffraction patterns of the BETZ 100x/100y compounds (x = 0.01 and 0.02; y = 0.20, 0.25, 0.30, 0.35) are shown in Fig. 1. It should be noted that for x(Er) content above 0.02, the patterns show a perovskite phase accompanied by a secondary phase (data not shown Fig. 2). This prompted us to limit the erbium content at 2 at.%.

Fig. 1

XRD patterns of BETZ 01/100y and BETZ 02/100y (0.20 ≤ y ≤ 0.35)

Fig. 2

XRD pattern of BETZ 03/20 exhibiting a secondary phase

The reflections of this perovskite phase are indexed as much as in tetragonal symmetry or in cubic symmetry. Indeed, the comparison of the concordance factor between the collected experimental data and the simulated data (Rietveld method) revealed practically similar values both for tetragonal symmetry and cubic symmetry refinement. It should be noted that we have observed the same behavior for the Ba1−xPbx(Ti1−yZry)O3 solid solutions [13]. In fact, the values of the c/a ratio observed in tetragonal symmetry are very close to one involving cubic symmetry for the BETZ phases. Moreover, this assertion is in agreement with the dielectric measurements results which will be presented in Sect. 3.2. Indeed, dielectric measurements of BETZ compositions show that the highest ferroelectric–paraelectric transition temperature is 290 K (~ 17 °C). Since, XRD measurements were carried out beyond this temperature (room temperature > 290 K), the symmetry is that of the paraelectric phase which is cubic.

Table 1 presents the cell parameters, volume and crystallite size in cubic symmetry. For instance, the volume evolution as a function of the zirconium content is represented in Fig. 3. These results reveal the following observations:

Table 1

Unit cell parameters, volume and crystal size of some BETZ 100x/100y solid solutions

BETZ

BETZ 01/20

BETZ 01/25

BETZ 01/30

BETZ 01/35

BETZ 02/20

BETZ 02/25

BETZ 02/30

BETZ 02/35

V(Å3)

66.19

66.70

67.17

67.60

66.26

66.74

67.16

67.61

a (Å)

± 0.001

4.045

4.055

4.065

4.074

4.046

4.056

4.065

4.074

CS nm

130

800

330

375

365

410

430

310

CS crystal size, ΔCS < 4 nm

Fig. 3

Evolution of the cell volume as a function of the zirconium content for the compositions BETZ 01/100y (filled circle) and BETZ 02/100y (filled square)

  • For a constant Zr/Ti ratio, the increase in erbium content leads to a small change in volume. This result is certainly related to the low proportion of erbium involved in its Ba2+ substitution. Moreover, since Er3+ is amphoteric, a part could be fixed at the B sites in place of Ti4+ or Zr4+. Thus, if we neglect the vacancies influence, we would have two antagonistic phenomena:
    • As Er3+ has an ionic radius upper than that of both Ti4+ and Zr4+, during the substitution the volume of the lattice tends to increase (rEr3+ = 0.89 Å; rTi4+ = 0.605 Å ; rZr4+ = 0.72 Å, in six coordination number) [14].

    • As Er3+ has an ionic radius lower than that of Ba2+, during the substitution, the volume of the lattice tends to decrease. (rEr3+ = 1.00 Å ; rBa2+ = 1.42 Å, in eight coordination number) [14].

      These two competitive effects make the volume virtually constant when incorporating erbium into the crystal lattice of our BETZ samples.

  • For a constant Er/Ba ratio, the progressive substitutions in the octahedral sites of Ti4+ by Zr4+ cause the increase in volume and the unit cell parameter. This variation is undoubtedly related to the bigger size of Zr4+ than that of Ti4+.

3.2 SEM observations

The thermal evolution of the permittivity depends on grain size in the ferroelectric state whereas it is practically independent of grain size in the paraelectric state. For instance, in the case of BaTiO3, it has been noticed that as the grain size decreases, the permittivity in the vicinity of the room temperature (εRT) increase (to reach a maximum for an optimal grain size in accordance with the size of ferroelectric domains) while the maximum permittivity at Curie temperature (εrmax) decreases slightly [15, 16].

The gain size influence on the BETZ ceramics sintered at 1375 °C were investigated by scanning electron microscopy (SEM) combined with EDS analysis. The SEM observations have shown that these materials are constituted of grains with sizes ranging between 4 and 24 µm; they are distributed heterogeneously. For instance, Fig. 4 shows the SEM microstructure of BETZ 01/30 ceramic. SEM coupled with XRD results (Table 1) allow to conclude that these grains are in polycrystalline state (crystallites size around 330 nm, which was determined by a Rietveld refinement). This state of the samples could be related to their ferroelectric behavior (see Sect. 3.3). Indeed, according to X. Tang et al. [17], for a similar system (Ba(Zr0.2Ti0.8)O3 ceramics), materials with high grain size undergoes a structural phase transition, behave like normal ferroelectric and were characterized by a tetragonal symmetry. Nevertheless, materials with lower grain size showed diffuse phase transition, disclosed relaxor behavior with a cubic symmetry. This assertion also appears to be consistent with the small size of the crystallites of the various samples obtained (0.130 ≤CS≤ 0.800 μm) (Table 1).

Fig. 4

SEM microstructure of ceramic BETZ 01/30

On the other hand, EDS analysis confirms the expected composition. As an example, the proportions of the elements determined by the EDS analysis for the BETZ 02/30 sample are in good agreement with the expected stoichiometry (Table 2).

Table 2

EDS results of BETZ 02/30

 

Ti

Zr

Ba

Er

Experimental atomic %

35.2

15

49.3

0.5

Theoretical atomic %

35.12

15.05

49.17

0.66

3.3 Dielectric study

The thermal and frequency variations of the permittivity and the dielectric losses show different behaviors which depend on the substitution rate x and y of the ceramics BETZ 100x/100y (Fig. 5). Moreover, this study also allowed us to reach different parameters characteristics of these dielectric materials (Table 3). From these results, the following observations can be reported:

Fig. 5

Dielectric permittivity (ε′r) and dielectric loss (tan δ) as a function of temperature at various frequencies for ceramics BETZ 100x/100y

Table 3

Dielectric characteristics of some BETZ 100x/100y solid solutions

 

BETZ 01/100y

BETZ 02/100y

Type I

Type II

Type I

Type II

BETZ 01/20

BETZ 01/25

BETZ 01/30

BETZ 01/35

BETZ 02/20

BETZ 02/25

BETZ 02/30

BETZ 02/35

Tc = Tm (K)

290

249

204

167

285

238

196

155

T0 (K)

325

290

274

241

320

288

263

229

Tdev (K)

370

347

364

335

372

361

341

329

ΔTm (K)

80

98

160

168

87

123

145

174

ΔTm(f) (K)

2

2

20

34

1

10

25

41

ε′rmax (1khz)

22,118

9308

11,301

6366

14,772

9429

8096

7234

Δε′r/ε′r

0.2785

0.4171

0.3458

0.3461

0.1915

0.1916

0.2908

0.4238

tanδmax (1khz)

0.0198

0.04201

0.03485

0.09617

0.02673

0.03577

0.03415

0.04582

γ

1.83

1.89

1.85

1.75

1.84

1.98

1.88

1.81

C. 10− 5 (K)

1.3641

0.9564

1.2609

1.0548

2.1532

1.0951

1.1070

1.3618

Tc = Tm Curie temperature (at 1 kHz)

T0 Curie–Weiss temperature

Tdev deviation temperature from Curie–Weiss law

\(\Delta {{\text{T}}_{\text{m}}}={{\text{T}}_{{\text{dev}}}} - {{\text{T}}_{\text{m}}}\)

ΔTm(f) = Tm(106 Hz) − Tm(102 Hz)

γ diffuseness exponent

C Curie Weiss constant

\(\frac{{\Delta {{\varepsilon ^{\prime}}_{\text{r}}}}}{{{{\varepsilon ^{\prime}}_{\text{r}}}}}=\frac{{{{\varepsilon ^{\prime}}_{\text{r}}}{\text{(1}}{{\text{0}}^{\text{2}}}\;{\text{Hz)}} - {{\varepsilon ^{\prime}}_{\text{r}}}{\text{(1}}{{\text{0}}^{\text{6}}}\;{\text{Hz)}}}}{{{{\varepsilon ^{\prime}}_{\text{r}}}{\text{(1}}{{\text{0}}^{\text{2}}}\;{\text{Hz)}}}}\)

  1. (i)
    For a constant x(Er) ratio, an increase in the y(Zr) content leads to:
    • a decline in both of the maximum permittivity (ε′rmax) and the maximum temperature (Tm),

    • an increase in the deviation from Curie–Weiss’s law and in losses (tanδ).

     
  2. (ii)
    For a constant y(Zr) content, an increase in the x(Er) ratio leads to:
    • a minor decrease in the maximum permittivity temperature (Tm),

    • a minor increase in the deviation from Curie–Weiss’s law, while losses (tanδ) remain practically constant.

     

3.3.1 The two types behavior in Ba1−xE2x/3(Ti1−yZry)O3 solid solutions

According to x and y values, two types behaviors have been noticed in Ba1−xE2x/3(Ti1−yZry)O3 solid solutions:

  1. (i)

    The first kind (type I) involves the compositions BETZ 01/20, BETZ 01/25 and BETZ 02/20. For instance, Fig. 5a illustrate this dielectric behavior characterized by a single peak in the thermal variation of the permittivity (ε′r). Moreover, the temperatures of the permittivity maximum (TC) are almost independent of frequency. We observe also the highest values of the permittivity maximum (ε′rmax). This behavior is typical of normal ferroelectric materials.

     
  2. (ii)
    The second (type II) involves the compositions BETZ 01/30, BETZ 01/35, BETZ 02/25, BETZ 02/30 and BETZ 02/35. As examples, Fig. 5b–d display the permittivity (ε′r) and losses (tanδ) dependences on the temperature and frequency for different compositions. The temperature and frequency variations of the permittivity demonstrated a very wide peak. Moreover, the temperature Tm of the permittivity maximum (ε′rmax) was raised to higher values as the frequency amplified. Frequency dispersion locates near Tm, the ε′r value decreases when frequency amplifies. All these dielectric properties corroborate ferroelectric relaxor behavior. Furthermore, the results obtained for the different compositions of the BETZ solid solutions are comparable to those of Ravez et al. relating to BTZ solid solutions [18]. As noted by the authors, the peak of permittivity as function of temperature is even thinner than it approaches the classic ferroelectric composition (content of Zr4+ inferior to 0.26) and become more broader for content of Zr4+ higher than 0.26 (i.e., when the behavior is of relaxor ferroelectric type). Otherwise, the difference between these two ferroelectric behaviors can be distinguished in Table 3 by the following remarks:
    • The TC (or Tm) temperatures are close to 300 K for the type I and substantially less than 300 K for the type II,

    • ΔTm are lower than 100 K (type I) or higher than 100 K (type II).

     

3.3.2 TC (or Tm) evolution in Ba1−xEr2x/3(Ti1−yZry)O3 solid solutions

3.3.2.1 Variations depending on the Zr/Ti ratio

The values reported in Table 3 show clearly a decrease in the Curie temperature TC (Tm) when the zirconium composition (y) increases. This result was expected for a substitution Ti4+/Zr4+. Undeniably, this behavior is in agreement with the normal ferroelectric theories established on the ions size located at the B site of the ABO3 perovskite structure. It is acknowledged that the non-polar to the polar phase transition, generates low atomic alterations amplitude Δz of the B cation along the polar axis. This is expressed by the S.C. Abrahams et al. empirical relationship: TC (K) = 2 × 104 Δz2 (Å) [19]. Therefore, an increase in the cation size located at the B site lead to the decrease of Δz and TC consequently. Taking into consideration the substitution Ti4+/Zr4+, it is the Zr4+ largest size that restrains the Δz shift. Since TC is directly linked to Δz in the empirical relation above, we stated its diminution.

3.3.2.2 Variations depending on the Er/Ba ratio

Table 3 displays that, for a fixed value of the ratio Zr/Ti, TC (Tm) decreases slightly when the amount of erbium (x) increases. For example, at fixed zirconium composition y = 0.20, Tm slightly decreased from 290 K (x = 0.01) to 285 K (x = 0.02). It should be noted that this evolution becomes greater when the zirconium content increases. In general, and regardless of the type of solid solution, the Tm value decreases as x increases. This result is related to the substituted ions nature in the cub-octahedral site (A). Indeed, the reduction in the ions size An+ reduces Tm on condition that the environment stays spherical and the coordination is not changed [20]. Moreover, it is acknowledged that the ferroelectric characteristics are mainly influenced by the substitutions occurring at the octahedral site. As for a fixed value of the ratio Zr/Ti, there is no change in the nature of the ions located at the octahedral site (Ti4+, Zr4+), this is the increases of x (Er3+) which leads to small Δz displacements in the non-polar phase. Thus, the Tm value decreases slightly when x increases, in agreement with the empirical relation of Abrahams et al. [19]. Otherwise, knowing that Er3+/Ba2+ substitution is of heterovalent type, the decrease of Tm could be attributed not only to the decrease in ion size but also to the increase of the charge of Erbium (rEr3+ = 1.00 Å and rBa+2 = 1.42 Å in coordination 8 [14]) leading to the appearance of defects during the Ba2+/Er3+ substitution.

3.3.3 Diffuse phase transition parameters

In relation to the transition temperature, the ferroelectrics permittivity can be expressed by the Curie–Weiss’s law as follows:
$$\frac{1}{{{{\varepsilon ^{\prime}}_{\text{r}}}}}=\frac{{{\text{T}} - {{\text{T}}_0}}}{{\text{C}}}({\text{T}}>{{\text{T}}_{\text{C}}})$$
(1)
where C is the Curie constant and T0 the Curie–Weiss temperature.

In our investigations, all the samples show a greater or lesser deviation from Curie–Weiss’s law. These observations are illustrated in the Fig. 6 showing the thermal evolution of the permittivity’s inverse (set at 1 kHz) along with the experimental data adjusted by Eq. (1). The Curie–Weiss temperature is defined from the plot by extrapolating the permittivity’s inverse in the paraelectric area. The calculated parameters (C et T0) are provided in Table 3. The values of T0 > Tm confirm the deviation from Curie–Weiss law. This behavior is specific to the ferroelectric materials with a diffuse phase transition (type I) and relaxor ferroelectric (type II). Moreover, the ΔTm parameter which expresses the deviation degree from Curie–Weiss’s law is defined as ΔTm= Tdev − Tm. Tdev allude to the temperature where the dielectric permittivity starts to deflect from the Curie–Weiss law and Tm is the temperature of the dielectric permittivity’s maximum [21]. For a constant x (Er) content, ΔTm increases with increasing of y (Zr). However, the values of ∆Tm become larger with increasing x (Er3+). This implies that the erbium also promotes a diffuse phase. We also used the modified Curie–Weiss law [22] to express the diffuse character of our compositions broadened peaks :

Fig. 6

Thermal variation of 1/εr at 1 kHz for ceramics BETZ 100x/100y

$$\frac{1}{{{{\varepsilon}_{\text{r}}}}} - \frac{1}{{{\varepsilon _{\text{m}}}}}=\frac{{{{({\text{T}} - {{\text{T}}_{\text{m}}})}^\gamma }}}{{\text{C}}}$$
(2)

Thus, we have plotted the curves ln(1/εr − 1/εm) as function of ln(T − Tm) at 1 kHz. The Fig. 7 show almost linear variations. The diffusivity γ mean value has been extracted from these curves by a linear regression. For all compositions, fairly high values were stated (Table 3). We note that the highest γ were obtained for compositions rich in zirconium. This implies that these compositions are distinguished by a diffuse phase and confirm, for some of them, the relaxor ferroelectric behavior.

Fig. 7

Plots of ln(1/εr − 1/εm) vs. ln(T − Tm) at 1 kHz for compositions BETZ 01/100y (a) and BETZ 02/100y (b) (0.20 ≤y ≤0.35)

All the characterizations carried out on the the Curie–Weiss law basis as well as the values of the empirical parameters such as ΔTm have confirmed that type I ceramics behave like conventional ferroelectrics with a slightly diffuse phase transition, while those of type II are distinguished by their relaxor effect.

3.3.4 Relaxor characteristics

The relaxor effect is marked by the frequency dependence of Tm and ε′r. Thus, we can evaluate the deviation at the Curie–Weiss law from the parameters noted ΔTm(f) and Δε′r/ε′r (see Table 3). The relaxor effect is more important as the frequency dispersion (ΔTm(f) and Δε′r/ε′r) are important. Table 3 highlights small values of ΔTm(f)≤ 2 and Δε′r/ε′r< 0.30 for type I BETZ compositions. This suggests that these compositions behave like conventional ferroelectrics. On the other hand, ΔTm(f) > > 10 and of Δε′r/ε′r > 0.30 values for type II BETZ compositions confirm their significant relaxor behavior. Certain of these compositions show temperatures Tm close to 300 K. This is the case of the conventional ferroelectric compositions (BETZ 01/20 and BETZ 02/20). For compositions exhibiting a relaxor ferroelectric behavior, they are distinguished by high frequency dispersion and high values of the permittivity maxima which appear towards low temperature values (Tm<240 K). Nevertheless, we observe appreciable values of the permittivities (close to 2000) in the vicinity of the room temperature showing the interest of these relaxor materials.

The relaxor ferroelectric behavior could also be defined by the Vogel–Fülcher relation [23, 24, 25]:
$${\text{f}}={{\text{f}}_0}\;\exp \frac{{{{\text{E}}_{\text{a}}}}}{{{{\text{k}}_{\text{b}}}({\text{T}} - {{\text{T}}_{{\text{VF}}}})}}$$
(3)
where f0 is the attempt frequency, Ea is the average activation energy measure, kB is the Boltzmann’s constant and TVF is the freezing temperature.

Figure 8 shows the plot of ln(f) vesrus T for the sample BETZ 01/30 and BETZ 02/30. The experimental curve (Fig. 8) was fitted applying the above Vogel–Fülcher formula. The Tm shift to lower values for decreasing frequencies follows to the Vogel–Fülcher law. This is known to be one of the relaxor systems properties. The Vogel–Fülcher relation fitting parameters were:

  • TVF = (169.5 ± 0.5) K f0 = (1.63 ± 0.4).1012 Hz Ea = (0.144 ± 0.004) eV for BETZ 01/30.

  • TVF = (154 ± 1) K f0 = (1.97 ± 0.5).1012 Hz Ea = (0.174 ± 0.007) eV for BETZ 02/30.

Fig. 8

Plots of log (f) as a function of Tm for BETZ 01/30 (a) and BETZ 02/30 (b) (the symbols: experimental data; the solid curve: fitting to the Vogel–Fülcher relation)

These values are comparable to those obtained by Badapanda et al. for the compositions Ba1−xY2x/3(Ti0.75Zr0.25)O3 [26]. We also find that the highest values of the frequency f0 and activation energy were reached for compositions containing more erbium. Furthermore, the freezing temperature becomes lower when the rare earth concentration increases.

Moreover, the concordance of these data based on the Vogel–Fülcher relation implies that these relaxors behavior is comparable to that of dipolar glasses with polarization fluctuations above the freezing temperature TVF. Our compositions have similarities with Ba(Ti1−xZrx)O3 relaxor compositions (0.26 ≤ x ≤ 0.40). For these latter, the study of the local structure was carried out by combining the X-rays absorption and neutron scattering [27]. This study showed that the octahedrons of ZrO6 and TiO6 were deformed with a particular impact on the local dipole moments direction conducted by the Ti4+ cations. An aleatory cations distribution leads to a local polarization state which would be the cause of the frequency dispersion observed experimentally.

4 Conclusion

New lead-free compositions of formula Ba1−xEr2x/3(Ti1−yZry)O3 (BETZ) with x = 0.01 and 0.02 and 0.20 ≤ y ≤0 .35 have been prepared using high-temperature solid state route.

The room temperature XRD patterns revealed a cubic symmetry perovskite phase. The variations in the lattice parameters, the volume and the crystallites size were discussed according to the Zr/Ti ratio (B site) and Er/Ba ratio (A site).

According to the Zr/Ti ratio, two sorts of behavior have been highlighted by dielectric measurements on ceramics. The first kind (type I) relates to compounds characterized by a single peak of ε′r with a slightly diffuse but frequency independent phase transition. These materials of compositions BETZ 01/20, BETZ 01/25 and BETZ 02/20 are distinguished by a low Zr/Ti ratio (y ≤ 0.25) and belong to the class of conventional ferroelectric compounds. The second (type II) also relates to compounds characterized by a single but relatively broad peak involving a diffuse phase transition and frequency dispersion. These ceramics of compositions BETZ 01/30, BETZ 01/35, BETZ 02/25, BETZ 02/30 and BETZ 02/35 belong to relaxor ferroelectric class and are distinguished by higher values of the Zr/Ti ratio (y ≥ 0.25). In addition, quantitative analysis based on the empirical parameters endorsed the diffuse nature phase behavior within BETZ ceramics and the relaxor effect for compositions with relatively higher values of Zr/Ti ratio. Furthermore, the experimental Tm data disclosed a good conformity with the Vogel–Fülcher equation implying that these phases can be described using the dipolar glasses model. On the other hand, compared to BTZ, comparable dielectric properties have been highlighted. Moreover, for certain of the studied samples, the permittivity maximum temperature (TC or Tm) were found in the vicinity of room temperature: BETZ 01/20 (290 K), BETZ 0.2/20 (285 K). This is very valuable for applications as dielectrics capacitor. Moreover, although they have low Tm temperature, the relaxor compositions (BETZ 01/30, BETZ 01/35, BETZ 02/25, BETZ 02/30 and BETZ 02/35) have also appreciable values of the permittivities (close to 2000) in the vicinity of the room temperature showing the interest of these relaxor materials for applications (i.e., as capacitor dielectrics). These lead-free materials have further advantages like the environmental friendliness.

Notes

Acknowledgements

The authors are grateful to N. Geoffroy for his help in XRD experiments and helpful discussion and to Dr. F. Herbst for SEM and EDX observations.

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Authors and Affiliations

  1. 1.Laboratoire de Cristallographie-Thermodynamique, Faculté de ChimieUniversité des Sciences et de la Technologie Houari BoumedieneAlgiersAlgeria
  2. 2.Laboratoire Interdisciplinaire Carnot de BourgogneUniversité Bourgogne Franche-Comté /UMR 6303 CNRSDijon CedexFrance

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