Noncritical behavior in Pb(In_1/2Nb_1/2)O₃-Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ relaxor ferroelectric crystals detected by acoustic emission method

Abstract

[011]-oriented unpoled relaxor ferroelectric Pb(In_1/2Nb_1/2)O₃-Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ crystals are studied by means of acoustic emission and dielectric methods in dependence on both temperature and dc bias electric field. The rhombohedral-cubic ferroelectric phase transition and the dielectric maximum as well as the intermediate temperature are successfully detected. Both rhombohedral-cubic ferroelectric phase transition and the dielectric maximum are studied in dependence on dc bias electric field, too. No the critical end point, but the tricritical one is detected. Existence of the supercritical behavior is discussed in these crystals.

Keywords:

• Relaxor ferroelectrics
• phase transition
• critical end point
• tricritical point
• acoustic emission

1. Introduction

The Pb-based relaxor ferroelectrics (RFEs) are the objects of scrupulous study due to their fundamental intrinsic chemical chaos on their B-sites, in contrast to ordering ferroelectrics (FEs) [1]. Such a chemical chaos is known to be a reason to arise the quenched random electric fields [2], which in turn is a reason of nucleation of polar nanoregions (PNRs) [3]. It is well documented that the PNRs nucleate below high-lying Burns temperature, T_B, start to grow below the intermediate temperature, T*, provide a huge, smeared and frequency dependent maximum of a dielectric constant, ɛ, at temperature, T_m, [4–6], and freeze below the freezing temperature, T_f, [5, 6], as the temperature decreases, in case of canonical RFEs. While, in case of non-canonical RFEs with FE doping, T_f, is replaced by the Curie temperature, T_c, of a spontaneous FE phase transition, as the temperature decreases [1, 6].

During last decade the two effects, resulting from the application of a bias dc electric field, E, to RFEs, have been revealed.

The first effect consists in non-trivial behavior of T_m in dependence on E and is called the V-shape, i.e. in initial the T_m retains constant or slightly increases, then decreases and attains the minimum (turning point) at a some small threshold field, E_th, and then increases as happens in normal FEs with a 2^nd-order phase transition, as E enhances [7]. The V-shape effect is observed in PbMg_1/3Nb_2/3O₃-xPbTiO₃ (PMN-xPT) crystals with different orientations [7–9], and is concluded to be a competition between both the random fields and E when affecting the PNRs [7].

The second effect consists in the existence of a critical end point (CEP) of a liquid-vapor type, where the piezoelectric modulus is maximum due polarization rotation through a monoclinic phase, above which the supercritical behavior starts, instead of the tricritical point (TCP), in the bias electric field-temperature, E-T, phase diagram of [111]-oriented PMN-xPT crystals [10]. The existence of such a CEP is explained due to coincidence of both low-temperature rhombohedral phase and direction of E, resulting in merging the low-temperature rhombohedral and high-temperature cubic phases without a boundary in [111]-oriented crystals, whereas in crystals with other orientations are shown to exist several interim boundaries and no CEP would expected to be exist. However, in [110]-oriented crystals the situation is similar to that of [111]-oriented crystals and the CEP exists [11]. While, the CEP is observed in [111]-oriented pure PMN crystals [12, 13], no CEPs is observed in both [110]- and [100]-oriented pure PMN crystals in the vicinity of turning points of T_m and the TCP is not attained [13]. Later it is shown that the CEP (referred as CP) exists in the vicinity of the turning point of T_m in [100]-oriented PMN-xPT crystals [14] due to the observation of a piezoelectric modulus maximum similar to those observed in both [111]- and [110]-oriented PMN-xPT crystals [10, 11]. This statement is then discussed based on the observation of a pyroelectric current maximum, γ_m, in [100]-oriented PMN-xPT crystals, pointing out the CEP in a vicinity of the turning point of T_m, where a so-called Widom line presumably begins instead of 2^nd order FE transition [15]. It is stress to note that no words concerning the TCP are made.

Along with both piezoelectric and pyroelectric data, the CEP is presumably detected using an acoustic emission (AE) in [001]-oriented PMN-xPT crystals [9]. A justification for application of AE to detect the CEP is caused by an approximately proportional correspondence between the strains and its count rate values [16–18]. Worth noting that all the CEPs, determined in PMN-xPT by a maximum of piezoelectric modulus [14], pyroelectric current [15], and AE [9], are localized around the turning point of T_m.

PMN is well-known to be a typical model of RFE exhibiting a large and smeared maximum of the real part of a dielectric constant, ɛ’, without undergoing any structural phase transition within a cubic phase and so is called a canonical RFE. Adding a ferroelectric PT to PMN transforms the canonical RFE PMN to non-canonical PMN-xPT one because of the spontaneous appearance of a ferroelectric rhombohedral phase, lying on some degrees below T_m, replacing a nonergodic state below T_f [1, 6]. Further addition an antiferroelectric Pb(In_1/2Nb_1/2)O₃ (PIN) to PMN-xPT provides an appearance of both orthorhombic and tetragonal phases along with both rhombohedral and cubic ones in the dependence on a PIN amount, especially of the poled crystals [19–22], demonstrating a sequence the FEs phase transitions, whereas the unpoled PIN-PMN-PT crystals undergo a rhombohedral-cubic FEs phase transition only [23].

Despite of such a number of the phase transitions in the PIN-PMN-PT system only some of them are studied in dependence on dc electric field E: temperatures of both rhombohedral-tetragonal, T_rt, and tetragonal-cubic, T_tc, phase transitions in [001]-oriented (0.25–0.35)PIN-(0.45–0.33)PMN-(0.30–0.32)PT crystals [24], of both T_rt and T_tc phase transitions, as well as T_m in [001]-oriented 0.34PIN-0.25PMN-0.41PT crystals [25], of rhombohedral-cubic, T_rc, and T_m in [111]-oriented 0.23PIN-0.52PMN-0.25PT crystals [26]. The reconstructed data of T_m in the dependence on E during heating from two latter works are shown in Fig. 1. It is clearly seen that both T_m exhibit the V-shape with E_th ≈ 1.5 kV/cm [25], E_th ≈ 2 kV/cm [26], respectively, as E enhances.

Figure 1. The reconstructed plots of the maximum temperatures, T_m, of the real part of a dielectric constant, ɛ’, in dependence on a bias dc field, E, of the PIN-PMN-PT crystals Refs. [25, 26].

T_B, estimated from Brillouin light scattering, is approximately 590 °C in [001]- and [011]-oriented 0.26PIN-0.46PMN-0.28PT crystals [27], whereas the T* is not detected in PIN-PMN-PT system at all. Also it would be interesting to detect the T*and study its dependence on a bias electric field as well as to detect the CEP because of its significance for applications, and the TCP in PIN-PMN-PT crystals, too. Over the past decade an AE has proven itself to be a very reliable method to detect all the phase transitions and characteristic points [28–31], as well as their behaviors under a bias electric field in some Pb-based RFEs [9, 30].

Based on our experience of detecting the phase transitions and characteristic points in RFEs, we have applied an AE method to detect phase transition temperatures and characteristic points as well as their behaviors under a bias electric field in [011]-oriented unpoled 0.26PIN-0.46PMN-0.28PT crystals.

2. Experiment

The ternary 0.26PIN–0.46PMN–0.28PT single crystals used in the current study were supplied by TRS Technologies Inc. They were grown by the modified Bridgman method. Samples were oriented along the [011] direction and the largest (011) surfaces were vacuum-sputtered by gold to apply a bias electric field [21].

The AE technique is described in great details elsewhere [9]. A crystal plate with the gold contacts is pasted with a silver epoxy to the polished side of a fused silica acoustic rod waveguide. A PZT-19 disk piezoelectric sensor is attached to the rear end of the waveguide. The sensor is electrically coupled to a 500 kHz band-pass low noise variable (up to 40 dB) preamplifier connected to a detector-amplifier (40 dB). A Ch-Al thermocouple junction is glued to the waveguide near the crystal. The higher part of the acoustic waveguide with the pasted sample is mounted in a resistance element tube furnace.

The dielectric data were measured using a HP4263A LCR meter wired to the sample. The thermocouple, amplifier, and LCR meter outputs were interfaced with a PC for coupled readout. The measurement of both the real part of a dielectric constant ɛ’ and AE count rate $\dot{N}$ (s⁻¹) was performed in the temperature range of 100 ÷ 300 °C with a rate of about 1–3 °C/min. When measuring the AE count rate $\dot{N}$ under a bias electric field, a high voltage supply was wired to the crystal instead of the LCR meter and the data were recorded by a step of 0.1 kV/cm and up to 0.9 kV/cm of the applied bias field E.

Before each cycle, the crystals are annealed at temperature of 400 °C for 15 min and then measure both dielectric and AE data during cooling and heating under the bias electric field E (field heating after field cooling regime (FHaFC)).

3. Results and discussion

Figure 2 presents both the real part of a dielectric constant, ɛ’, and the AE count rate, $\dot{N},$ data in absence of an applied bias field E. ɛ’ ≈ 4.5·10⁴ exhibits a relatively sharp, or relatively smeared, maximum, at T_m ≈ 150 °C. Inset presents a gradually decrease of ɛ’ and gradually increase of T_m with increasing the measuring frequency, characteristic for RFEs [1, 2]. No temperature hysteresis of T_m is observed in agreement with those observed in PMN-xPT (x = 0.13 and 0.24) [14], and [111]- and [001]-oriented PMN-0.2PT crystals [15]. Both ɛ’ and T_m shift in dependence on frequency are in good accordance with the previously measured data for the PIN-PMN-PT crystals with close compositions but different orientations [19–22, 26, 32, 33]. Another low-temperature slightly seen and very smeared ɛ’ dielectric anomaly around 125 °C resembles that clearly seen in [011]-oriented unpoled 0.26PIN–0.46PMN–0.28PT crystals, which is obviously corresponds to a rhombohedral-cubic phase transition at T_rc [21].

Figure 2. The plot of a temperature dependence of both the real part of a dielectric constant, ɛ’, and the AE count rate, $\dot{N},$ in absence of a bias dc field, E. Inset shows the frequency dependence of the real part of a dielectric constant, ɛ’.

AE points out the T_rc ≈ 120 °C during FC and ≈ 130 °C during FH, T_m ≈ 150 °C, i.e. AE does clearly distinguishes both these temperatures, as well as the T* ≈ 264 °C during FC and ≈ 270 °C during FH. The temperature hysteresis of T_rc is known to be intrinsic for a 1^st order phase transition. The temperature hysteresis of T* is earlier observed in Pb_0.78Ba_0.22Sc_0.5Ta_0.5O₃ crystals and is explained by taking place of a 1^st order local phase transition inside PNRs [34]. All these temperatures of both T_rc and T_m are in reasonably accordance with the ones determined in the [011]-oriented crystals with close compositions [21, 22], though the some non-coincidence of these temperatures might be explained due to small variation of the compositions of the crystals.

AE of T* ≈ 270 and 264 °C points out a temperature range where the FWHM of the LA mode starts to increase steeply below approximately 320 °C upon cooling [19, 21]. Such the increase of the FWHM curve was earlier proved to correspond to T* in some well-known RFEs [35–37], but the AE provides a more precise value of T* due to its sharp bursts in comparison with a smooth change of a FWHM curve. True, recently the 320 °C is ascribed to be the T_B, below which the relaxation time rapidly increases [19]. Again the T_B is known to be determined by a deviation of the Brillouin frequency shift from a straight line upon cooling in both [001]- and [011]-oriented 0.26PIN-0.46PMN-0.28PT crystals [27], and such a rule was proved for [001]-oriented PMN-xPT crystals [38]. So we believe that the T_B is really equal to be of about 590 °C [27].

Figure 3 presents the dependence of all the T_rc, T_m and T* on a bias electric field E. Both T* and T_m exhibit the clearly seen a V-shape form, characteristic for PMN-xPT crystals [7–9]. Initially the T_m slightly increases in the vicinity of E ≈ 0.15 kV/cm, then decreases. It attains the turning point of T_m at E_th ≈ 0.3 kV/cm and then increases again in accordance with theoretical model [7], as E enhances. The V-shape of T_m is similar that observed in [111]-oriented 0.23PIN-0.52PMN-0.25PT crystals [26], (Fig. 1). T_rc exhibits no V-shape and its thermal hysteresis reduces gradually up to E_th, but do not vanishes, as it is shown in Fig. 2(a) [15], and continues up to E ≈ 0.5 kV/cm, above which it vanishes and the T_rc(E) dependence is a single line. A hysteresis vanishing point is known to occur at TCP, where a 1^st order phase transition line meets a 2^nd order phase transition line, and, consequently, E_TCP ≈ 0.5 kV/cm. This data resembles that observed in [110]-oriented pure PMN crystals in Fig. 7(b) [13]: a thermal hysteresis steep reduces at E_th ≈ 5 kV/cm (do not marked there), corresponding to a turning point of T_m, but a TCP is not attained. Surprisingly that the T* thermal hysteresis do not vanishes and remains approximately constant of about 6 °C, despite of presumably taking place a 1^st order phase transition inside PNRs [34].

Figure 3. The plot of all dependences of the intermediate temperature, T*, the maximum temperature, T_m, of the real part of a dielectric constant, ɛ’, the rhombohedral-cubic phase transition temperature, T_rc, in dependence on a bias dc field, E.

Figure 4 presents the behavior of ${\dot{N}}_{rc},$ during FH regime, accompanying the T_rc, in dependence on a bias electric field E. Both ${\dot{N}}_{T_m}$ and ${\dot{N}}_{T^{*}}$ are essentially weaker in comparing with ${\dot{N}}_{rc},$ because the former is caused by PNRs interaction, whereas the latter is caused by a structural phase transition. By this reason, there is no possibility to plot both ${\dot{N}}_{T_m}$ (E) and ${\dot{N}}_{T^{*}}$ (E) dependencies truthfully enough. ${\dot{N}}_{rc}$ exhibits a smeared maximum toward the E_tcp and then steeply decreases, pointing out the E_th in vicinity of turning point of T_m in good agreement with that detected in PMN-0.33PT crystals [9]. This pronounced peak of ${\dot{N}}_{rc}$ means a large strain, which in turn proportional the piezoelectric modulus maximum in the vicinity of a turning point of T_m, measured in both [111]- and [100]-oriented PMN-xPT crystals [10, 14]. When E exceeds E_TCP, the ${\dot{N}}_{rc}$ gradually weakens, as E enhances, due to minimization of strain when occurring a 2^nd order phase transition.

Figure 4. The plot of all dependences of the maximum temperature, T_m, of the real part of a dielectric constant, ɛ’, the rhombohedral-cubic phase transition temperature, T_rc, as well as the AE count rate $\dot{N}$ in dependence on a bias dc field, E.

The similar relationship between T_m(E) and $\dot{N}$ (E) dependencies has recently been observed in [100]-oriented PMN-0.30PT crystals [39]. It is clearly seen that the ${\dot{N}}_{rc}$ (E) dependence in Fig. 4 is similar to ${\dot{N}}_{mt}$ (E) in Fig. 3 [39] for the monoclinic-tetragonal, T_mt, phase transition.

In Ref. [39] the behavior of ${\dot{N}}_{mt}$ (E) is found to be similar to the pyroelectric coefficient γ_m(E) dependence in [100]-oriented PMN-xPT crystals in Fig. 2(b) [15]. γ_m exhibits a maximum in the vicinity of a turning point of T_m and then steeply weakens, presumably manifesting a beginning a so-called Widom line (the continuation of the 1^st order phase transition line above the CEP) [11]. On the other hand, the γ_m(E) dependence in Fig. 2(b) [15] is similar to that obtained in [001]-oriented pure BaTiO₃ crystals in Fig. 8 [40]. γ_m exhibits a maximum, too, and then steeply weakens toward the TCP, where a 1^st order phase transition line meets a 2^nd order phase transition one, as E enhances, i.e. the γ_m(E) becomes to maximum in the absence of any monoclinic phase when the T_tc closing to TCP. Based on similarity of ${\dot{N}}_{mt}$ (E), d₃₃(E) and γ_m(E) dependencies, it is concluded that there is TCP instead of CEP in [100]-oriented PMN-xPT crystals [15, 16], and, consequently, no CEP observed in [100]-oriented PMN-0.30PT crystals.

By an analogy due to similarity of both ${\dot{N}}_{mt}$ (E) [39] and ${\dot{N}}_{rc}$ (E) in Fig. 4, we concluded that no CEP but TCP exists in [011]-oriented 0.26PIN-0.46PMN-0.28PT crystals as well as in [100]-oriented PMN-xPT ones, and, consequently, no supercritical behavior observed in these crystals, but observed in [111]-oriented ones only.

Meanwhile, the mechanism of a d₃₃ maximum in [111]-oriented PMN-0.295PT crystals [10] in a vicinity of CEP seems to be confuse. Indeed, x = 0.295 lies below the morphotropic phase boundary of about 0.30 ÷ 0.35 for PMN-xPT system [41]. By this reason there is no enough amount of a monoclinic phase to provide the polarization rotations when applied the dc field E to decrease an energy of the crystals so strong, as it is explained in Ref. [10]. From this point of view, we believe that the d₃₃ maximum occurs when a 1^st order T_tc closing to the CEP and then steeply weakens when it crossing the CEP and meets the Widom line within the supercritical state, as E enhances.

4. Conclusions

We have studied the unpoled [011]-oriented 0.26PIN-0.46PMN-0.28PT relaxor ferroelectric crystals by means of acoustic emission and dielectric measurements. We have detected the Curie temperatures of the 1^st order rhombohedral-cubic ferroelectric phase transition, the dielectric maximum temperature as well as the intermediate temperature and studied their dependences on a dc bias electric field. We have observed a V-shape form in a vicinity of the turning point of temperature of a dielectric maximum at the threshold field and a tricritical point lying at several higher field, as well. We have detected a smeared maximum of acoustic emission in a vicinity of the V-shape form closer to a tricritical point, meaning the maximum of piezoelectric modulus in it, what is important for applications. We have detected no critical end point and concluded that there is no supercritical behavior in these crystals.

Acknowledgments

One of authors (SK) is thankful to TRS technologies, Inc. for providing Pb(In_1/2Nb_1/2)O₃-Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ crystal plates.

Additional information

Funding

This study was supported in part by JSPS KAKENHI Grant Number JP17K05030.