3.3.1. BCTZ Characterization
The temperature dependence of the real ε
r’ and imaginary ε
r’’ parts of the complex dielectric permittivity (ε = ε
r’ +
j × ε
r’’) of BCTZ1 are displayed in
Figure 8, showing the whole frequency range between 1 kHz and 1 MHz. Both these parameters prove the usual trends of relaxor. ε
r’ and ε
r” are frequency-independent at high temperature and ε
r’ increases on cooling. Moreover, ε’
r undergoes a broad peak whose corresponding temperature
Tm increases, while the amplitude ε
rmax’ decreases with increasing frequency. At temperatures lower than this maximum, ε
r’ curves are dispersed and parallel. The imaginary part of the relative dielectric constant displays frequency dependent maxima whose amplitude increases with the operating frequency,
i.e., opposite to the real part. All these qualitative features are in perfect agreement with the archetype relaxor compound Pb(Mg
1/3Nb
2/3)O
3 (PMN) [
31,
32]. Referring to the systematic investigation of the BaTiO
3-CaTiO
3-BaZrO
3 phase diagram of powders and ceramics [
33], we find a good agreement between the Zr and Ba segregation in BCTZ single crystals and their relaxor features. Indeed, when the Zr content at B-sites of the perovskite exceeds 27 mol %, a shift from ferroelectric to relaxor state is observed. Thus, starting from the initial ferroelectric composition with Zr content = 15 mol %, we obtained a relaxor with Zr content of 57.3% In this work, we think that the substitution of barium (Ba
2+) by calcium (Ca
2+) stabilizes more and more the perovskite structure but it does not alter significantly functional properties of BCTZ solid solutions: relaxor characteristic signatures are solely governed by the Zr content in B-sites.
Figure 6.
X-rays diffraction patterns on crushed crystals of KNL20S14T07N (attempt 1), KNL34S91T40N (attempt 2), and KNL25S50T24N (attempt 3) exhibiting an orthorhombic structure.
Figure 6.
X-rays diffraction patterns on crushed crystals of KNL20S14T07N (attempt 1), KNL34S91T40N (attempt 2), and KNL25S50T24N (attempt 3) exhibiting an orthorhombic structure.
Figure 7.
XRD patterns on crushed crystals of (a) KNL23S38T37N (attempt 4) and KNL34S57T47N (attempt 5) exhibiting tetragonal structure; (b) XRD patterns with an intensity logarithm scale where no inclusions are detected (c) and zoom on (200) and (002) lines for KNL23S38T37N and KNL34S57T47N.
Figure 7.
XRD patterns on crushed crystals of (a) KNL23S38T37N (attempt 4) and KNL34S57T47N (attempt 5) exhibiting tetragonal structure; (b) XRD patterns with an intensity logarithm scale where no inclusions are detected (c) and zoom on (200) and (002) lines for KNL23S38T37N and KNL34S57T47N.
Figure 8.
Real (a) and imaginary (b) parts of the complex dielectric permittivity, εr’ and εr’’, respectively, as a function of temperature and frequency for BCTZ1 (arrows indicate the direction of increasing frequency).
Figure 8.
Real (a) and imaginary (b) parts of the complex dielectric permittivity, εr’ and εr’’, respectively, as a function of temperature and frequency for BCTZ1 (arrows indicate the direction of increasing frequency).
The dielectric behavior of the randomly oriented BCTZ2 sample of composition (Ba
0.857Ca
0.143)(Ti
0.928Zr
0.072)O
3, which contains a much higher Ti content, displays (
Figure 9a) dielectric constant and loss with a broad frequency-independent anomaly at 310 and 275 K. These two peaks are the signature of two successive phase transitions, which are in full agreement with what was reported in ceramics of similar composition.
Figure 9b shows the temperature dependence of the dielectric constant and loss at various frequencies for (001)
pc-oriented BCTZ3 single crystal. Dielectric parameters confirmed the chemical analysis displaying well defined anomalies at 366 and 265 K. The intermediate phase was thus much more extended than that depicted in BCTZ2, which was already ferroelectric.
Another feature, which was not observed in ceramics, is the very peculiar frequency behavior of the dielectric permittivity. While it is almost dispersion-less in the high-temperature cubic phase and in the low temperature phases, it shows a strong dispersion in the vicinity of dielectric anomalies. Even though the temperature at which the anomalies occur is not frequency dependent, a strong depletion of the permittivity is observed when the frequency increases. Such phenomena could be attributed to ferroelectric domain wall motions, which translate into an increasing of the dielectric loss with increasing frequency. In BCTZ solid solutions, we naturally expect compositional fluctuations and/or structural disordering of cations in one or more crystallographic sites of the perovskite structure. These microscopic characteristics will systematically disturb the long-range dipolar interactions and induce a diffuse behavior within the ferroelectric phase. Moreover, it cannot be excluded that this feature could be attributed to phase transitions as previously seen in literature [
2,
8,
34].
As a general result, dielectric behaviors of the three BCTZ crystals exhibit the same trend than that described by Ravez
et al. [
33] with ceramics of same compositions (
Figure 10).
Figure 9.
(a) Dielectric constant and loss tangent as a function of temperature and frequency of a randomly oriented BCTZ2 sample; and (b) temperature dependence of dielectric constant and loss tangent at various frequencies of [001]pc oriented BCTZ3 single crystal (arrows indicate the direction of increasing frequency).
Figure 9.
(a) Dielectric constant and loss tangent as a function of temperature and frequency of a randomly oriented BCTZ2 sample; and (b) temperature dependence of dielectric constant and loss tangent at various frequencies of [001]pc oriented BCTZ3 single crystal (arrows indicate the direction of increasing frequency).
Figure 10.
Molar pseudo-ternary phase diagram BaTiO
3-BaZrO
3-CaTiO
3 three different crystals compositions (yellow discs) are inserted in the relaxor-ferroelectric zones described by Ravez
et al. [
33]. Dielectric behaviors of the crystals are in accordance with ceramics of same compositions [
5,
33]. Red dashed line corresponds to the (1−
x)BaTi
0.8Zr
0.2O
3-
xBa
0.7Ca
0.3TiO
3 promising piezoelectric compositions above mentioned.
Figure 10.
Molar pseudo-ternary phase diagram BaTiO
3-BaZrO
3-CaTiO
3 three different crystals compositions (yellow discs) are inserted in the relaxor-ferroelectric zones described by Ravez
et al. [
33]. Dielectric behaviors of the crystals are in accordance with ceramics of same compositions [
5,
33]. Red dashed line corresponds to the (1−
x)BaTi
0.8Zr
0.2O
3-
xBa
0.7Ca
0.3TiO
3 promising piezoelectric compositions above mentioned.
Pyroelectric and piezoelectric measurements in BCTZ3 are depicted in
Figure 11 which illustrates the temperature dependence of the pyroelectric coefficient p along with the spontaneous polarization
Ps. Two anomalies are detected corresponding to cubic-tetragonal-rhombohedral phase transitions. Contrary to what has already been observed in BCTZ ceramic samples,
Ps shows less sensitivity to the temperature change in BCTZ3 single crystal. The maximum polarization remains; however, below 20 μC·cm
−2 (
Figure 11a). The piezoelectric response for the length thickness extensional mode is determined at different temperatures through frequency-dependent sweeps of the conductance G and the susceptance B (
Figure 11b).
Table 6 summarizes results obtained for three selected temperatures. It can be seen that the electromechanical response of BCTZ3 is smaller than that observed in BCTZ50 ceramic sample close to room temperature (
d31 (BCTZ50 ceramic disk) >
d31 (BCTZ3 single crystal plate) near room temperature).
Figure 11.
(a) Temperature dependence of the pyroelectric coefficient p and spontaneous polarization Ps of the [001]pc oriented BCTZ3 single crystal; and (b) resonance curves for the length thickness extensional mode measured at 337K for [001]pc oriented BCTZ3 single crystal. The plot shows a frequency dependent sweep of the conductance G and the susceptance B, which are the real and imaginary components of the admittance, respectively.
Figure 11.
(a) Temperature dependence of the pyroelectric coefficient p and spontaneous polarization Ps of the [001]pc oriented BCTZ3 single crystal; and (b) resonance curves for the length thickness extensional mode measured at 337K for [001]pc oriented BCTZ3 single crystal. The plot shows a frequency dependent sweep of the conductance G and the susceptance B, which are the real and imaginary components of the admittance, respectively.
Table 6.
Piezoelectric constants d31 and electromechanical coupling factors k31 calculated at three selected temperatures for BCTZ3 crystal elongated bar oriented along pseudo-cubic [001]pc direction.
Table 6.
Piezoelectric constants d31 and electromechanical coupling factors k31 calculated at three selected temperatures for BCTZ3 crystal elongated bar oriented along pseudo-cubic [001]pc direction.
T(K) | d31 (pC·N−1) | K31 |
---|
293 | 70 | 0.14 |
305 | 93 | 0.18 |
337 | 91 | 0.17 |
To achieve large piezoelectric coefficients, we applied poling field of about 5 kV/cm which is larger than the coercive field which is 2 kV·cm
−1 at most [
5]. The polarization of 20 μC·cm
−2 (
Figure 11a) confirmed that a saturated state was reached. However, it can be seen that the electromechanical response of BCTZ3 is smaller than that observed in BCTZ50 ceramic sample close to room temperature. Some possibilities can be suggested to understand such a difference:
Common resonance geometries along with recommended aspect ratios are usually used to characterize piezoelectric materials. In our case, the dimensions of BCTZ3 single crystal do not follow appropriately the metric conditions for length thickness extensional mode. Therefore, we may introduce a significant error when determining the electromechanical coefficients.
The ferroelectric and piezoelectric responses possess anisotropic behaviors in single crystals and optimized crystallographic orientation is required to increase the piezoelectric efficiency [
35,
36,
37].
Although the BCTZ3 composition is close to the targeted BCTZ50 from the chemical point of view, both of them behave differently from the crystallographic point of view. Based on recent studies of Keeble
et al. [
8]; the orthorhombic O-phase found in BCTZ50 close to ambient temperature seems to be absent in BCTZ3 (from dielectric and pyroelectric measurements). Consequently, BCTZ3 is far away from the phase convergence region already reported for BTZ-BCT pseudo-binary phase diagram and no instability gradient could then be attained. This situation may explain the relatively low piezoelectric response in BCTZ3 compared to BCTZ50 ceramics composition. Finally, it is perhaps interesting to state that electromechanical properties of BCTZ3 single crystal presented, in this work, are consistent with those reported for BTZ (BaTiO
3-BaZrO
3) and BCT (BaTiO
3-CaTiO
3) single crystals synthesized by laser heated pedestal growth and floating zone techniques, respectively [
29,
38].
3.3.2. KNLSTN Characterization
The dielectric measurements carried out on all KNLSTN samples displayed no dielectric anomaly on the samples one to three from room temperature up to 420 °C. The results of KNL23S38T37N and KNL34S57T47N exhibit ferroelectric properties. The temperature dependence of the dielectric constant is shown in
Figure 12. While two peaks are observed at 370 and 160 °C for KNL23S38T37N, only one single ferroelectric transition was recorded on KNL34S57T47N at 250 °C. All these anomalies can be ascribed to ferroelectric transitions because they are frequency independent. In KNL34S57T47N, the extrapolated Curie temperature was found to be 248 °C, close to the temperature of the dielectric maximum of 250 °C. This confirms that the ferroelectric transition is of a second order type. KNLSTN ceramics of composition close to our single crystals exhibit two phase transition temperatures, an orthorhombic (O) to tetragonal (T) transition temperature
T(O–T) at around 200 °C and a tetragonal to cubic (C) transition temperature
T(T–C) at 400 °C [
38]. These are close to our reported transition temperatures in KNL23S38T37N where
T(O–T) = 160 °C and
T(T–C) = 370 °C and for which a deficit of lithium has been observed. We, thus, confirm that KNLSTN single crystals have the same succession of phase transition than ceramics of the same composition.
We next compare the ferroelectric transition temperature of KNL23S38T37N and KNL34S57T47N. We see a down-shift of the first transition temperature
T(T–C) of more than 100 °C in KNL34S57T47N. From the chemical analysis reported above, the main trend is that KNL34S57T47N includes more Li than KNL23S38T37N (3.4 mol % instead of 2.3 mol %). Such strong depression of ferroelectric transition temperature upon increasing Li substitution was also reported by Jimenez
et al. [
39] in ceramics where larger amount of Li in the starting reagents was needed in order to get such a large transition temperature shift. In addition, Hollenstein
et al. [
40] and Ochoa
et al. [
41] found that the addition of Li in the A site and Ta, Sb in the B site in ceramics decrease this temperature. As we discussed, from the powder XRD patterns of KNL23S38T37N and KNL34S57T47N, for which ferroelectric measurements were made, we noticed that KNL23S38T37N and KNL34S57T47N are close to the switching between orthorhombic and tetragonal symmetry at room temperature and, as a consequence, the ferroelectric behaviors of KNL23S38T37N and KNL34S57T47N are drastically different, as can be seen from the sizable differences in transition temperatures (
Figure 12).
Figure 12.
Variation of dielectric properties with temperature for KNL23S38T37N and KNL34S57T47N. (Reproduced from [
6]. Copyright © 2012 Elsevier Masson SAS. All rights reserved).
Figure 12.
Variation of dielectric properties with temperature for KNL23S38T37N and KNL34S57T47N. (Reproduced from [
6]. Copyright © 2012 Elsevier Masson SAS. All rights reserved).
The large change of ferroelectric transition temperature with minute change of composition is similar to what is observed in the MPB region of lead containing materials like PZT [
31] or lead-free BCTZ [
2] solid solutions. This similarity is an indication for possible large piezoelectric coefficients of KNLSTN single crystals, but this still remains an open question.
Piezoelectric constant for KNL34S57T47N was measured by the Berlincourt method and gave, at room temperature, around
d33 = 39 pC·N
−1 on a randomly-orientated crystal. This is a smaller value than that expected and mentioned by Fu
et al. [
4], which, as well as the Curie temperature, could be attributed to the elements stoichiometry differences between our composition and theirs as well as slight chemical inhomogeneities in the bulk crystal. Moreover, the low value of this direct piezoelectric effect measurement could be due to inhomogeneity of the applied stress caused by the non-optimal shape of the contact between the sensor and the sample.