Phase Transitions and Local Polarity above T_C in a PbZr_0.87Ti_0.13O₃ Single Crystal

Abstract

Solid solutions of PbZr_1−xTi_xO₃ (PZT) are one of the most widely used piezoelectric materials with perovskite structure. Despite the decades of research, the phase diagram of PZT reported in 1971 has not been resolved yet. Recently, it turned out that single crystals of good quality of these solid solutions can be grown. By means of top-seeded solution growth (TSSG) technique, we succeeded to grow a single PbZr_0.87Ti_0.13O₃ crystal. Hence, a partial verification of the diagram could be performed through investigations of the optical, dielectric, pyroelectric and elastic properties of this crystal, in a wide temperature range. The obtained results confirmed that the PbZr_0.87Ti_0.13O₃ crystal undergoes a sequence of phase transitions, such as those observed in ceramics of similar chemical composition. However, additional anomalies of investigated physical properties were observed and discussed. Moreover, the influence of electric field on optical properties has been investigated for the first time and has proven the existence of local polar character of the phase above T_C in a limited temperature range.

1. Introduction

After more than six decades, solid solutions of PbZr_1−xTi_xO₃ (PZT) still continue to be intensively studied piezoelectric materials and are among the most interesting compounds from the application perspective. Recently, ferromagnetic properties were also found in a PZT crystal [1], which means that these materials can be classified as multiferroics and may find even wider application. For a long time, the PZT phase diagram developed by Jaffe et al. [2] has been accepted as the basic characterization of the PZT solid solution. However, many reports [3,4,5,6,7,8,9] show that the Jaffe’s diagram needs verification. One of the reasons for it is that it was developed on the basis of ceramics only, because PZT crystals growth process has been developed only recently. As early as 40 years ago, Whatmore et al. [10] found that the diagram for ceramics differs from that for crystals. Only a few reports described the properties of PZT single crystals [1,9,10,11,12,13,14,15,16], mainly due to above mentioned technological difficulties related to their growth. Our high quality single PbZr_0.87Ti_0.13O₃ crystal enabled investigations of phase transformations, domain structure, optical, dielectric, pyroelectric and elastic properties. One of the most important experimental results for this crystal is the proof for the existence of local polarity above Tc.

According to report [2], the PZT demonstrates a complex temperature-composition phase diagram, including the so-called morphotropic phase boundary (MPB) in the range of Ti content of x = 0.4 < x < 0.6. In this region, the values of piezoelectric coefficients reach maximum values e.g., [17]. In the PZT phase diagram, the Zr-rich rhombohedral (R) region consists of two ferroelectric phases: R3c (FE₁) and R3m (FE₂). At lower temperatures, the R3m space group is characterized by a crystalline structure with cation shifts along the pseudocubic direction [111], and with oxygen octahedral tilts of the a^-a^-a^- type [18]. At higher temperatures, the loss of the octahedral tilts causes the space group to become R3m [19]. Recent structural studies of the PZT crystal with Ti content of x = 0.13 have shown that in 300 K the monoclinic phase Cm fits the structure better than the rhombohedral (R) one [9]. This is in line with the diagram proposed by Zhang et al. (see figure 7 in [4]) for ceramics. In that report, it was ascertained that long-range average rhombohedral and both long- and short-range monoclinic regions coexist in all PZT compositions. Such significant changes in the PZT phase diagram prompted us to re-analyze the dielectric properties and phase transformations in a single PbZr_0.87Ti_0.13O₃ crystal.

The appearance of polar clusters in the paraelectric phase has already been observed in PZT ceramics [20,21] and even in the well-known ferroelectrics, such as BaTiO₃ (BT) crystal [22,23,24]. The existence of pertinent piezoelectric response far above T_C, accompanied by strong changes in the elastic properties, was attributed to the existence of, and interaction between, polar regions in paraelectric phase. Burns and Dacol [25] reported that the role of precursor in the paraelectric phase of BT is performed by randomly-oriented polar regions with local symmetry-breaking, while the macroscopic cubic phase is preserved. The substantial elastic anisotropy observed in the paraelectric phase of BT was attributed to temperature evolution of sizes of precursor polar clusters formed by correlated Ti motions [24,25]. Theoretical calculations reported in [26] have shown that these polar precursors, correlated with the interrelated softening of optic and acoustic modes, may appear even 80K above the phase transition temperature. From the measurements of birefringence, for the first time conducted under the action of d.c. electric field, we have proved the polar character of precursor in the paraelectric phase, in the single PbZr_0.87Ti_0.13O₃ crystal investigated. Moreover, we have shown that the existence of local polarity above T_C is consistent with the theoretically predicted temperature range.

2. Materials and Methods

Powder diffraction measurements executed on crushed transparent single PbZr_0.87Ti_0.13O₃ crystal grown by top-seeded solution growth (TSSG) technique had been performed at room temperature [9]. The concentrations of elements were examined by SEM technique, using JSM-5410 electron microscope by Jeol with energy dispersion x-ray spectrometer EDS by Oxford Instruments. It was verified that the distribution of all elements was homogenous within the accuracy of the method used. The PZT single crystal was cut perpendicular to [001] pseudo-cubic perovskite axis and polished to the thickness of 0.3 mm.

A single PbZr_0.87Ti_0.13O₃ crystal was electroded with silver paste and rejuvenated at 600 K for half an hour. The Agilent 4192A Impedance Analyzer that was used registered the capacity C and the conductance G for selected frequencies on heating and cooling, with the rate of 1K/min. The real ε’, and imaginary ε’’ part of the permittivity were calculated from the following formulas: ε’ = C/C₀; ε’’ = G/(2πf C₀) with C₀ = (ε₀S)/d, where S is the electrode surface, d is sample thickness (0.3 mm) and f stands for frequency. In dielectric measurements, the intensity of electric field was of the order of 0.01 kV/cm. Additionally, the real ε’ part of permittivity for crystal poled in d.c. electric field was determined on heating. The sample was poled at d.c. electric field having the strength of 7 kV/cm, applied for 20 min at 350 K and subsequently cooled in this field to 300 K, at which temperature the field was switched off. Then, the crystal was heated, applying the rate of 1K/min, to 670 K.

The pyroelectric current of the sample was registered by means of Keithley 6514 System Electrometer on heating and cooling, with the constant rate of 3 K/min. The measurements were performed in the temperature range from 300 K to 600 K, which covered the points of phase transitions. The pyroelectric current was also measured on heating of polarized single PbZr_0.87Ti_0.13O₃ crystal. Prior to measurement, the sample was poled in d.c. external electric field having the strength of 7 kV/cm, applied for 20 min in 350 K and subsequently cooled in this field to 300 K, at which temperature the field was switched off. Then the sample was heated applying the rate of 3 K/min, to 600 K, with pyroelectric current registered.

The elastic properties, as a function of temperature, were determined through the measurement of piezoelectric resonance. Prior to the experiments, the sample in the shape of a bar 2 mm × 0.6 mm × 0.3 mm (thickness), fulfilling the conditions for determination of d₃₁ piezoelectric coefficient, was poled in d.c. electric field. The poling conditions were the same as in dielectric and pyroelectric measurements. For certain temperatures, the complex admittance Y = ?Y?e^iθ as a function of frequency f was measured by means of Agilent 4192A Impedance Analyzer. The model of forced harmonic oscillator [27] was applied to find piezoelectric resonance frequency f_o and damping coefficient γ. These data permitted to calculate the real s₁₁’ and imaginary s₁₁’’ part of complex elastic coefficients s₁₁:

$$s_{11}=s_{11}^{\prime }+i{s}_{11}^{″}=\frac{1}{4\rho l^2{f}_o^2}+i\frac{\gamma }{f_o}\frac{1}{4\rho l^2{f}_o^2}$$

(1)

where l is the length of sample (2 mm) and ρ the density of crystal (7990 kg/m³).

The measurements of birefringence were performed by means of Oxford Cryosystems Metripol Birefringence Imaging System (Metripol). The details of the technique have been described elsewhere [28]. The sample was heated in a high-precision Linkam TMSG600 temperature stage, and the temperature ramps were performed at the rates of 0.2 K min⁻¹.

The technique used for birefringence measurement allowed us to determine the values of ∆n in two ways. In the first way, for temperature range below T_C, we measured the change in the optical retardation Γ = Δn*d, where d is the crystal thickness of 0.3 mm, thus allowing the variation of Γ with temperature to be determined, for temperatures at which the maxima occurring for the periodic output signal, obtained from the rotating-analyzer apparatus, provided Γ=0.25 × (2N + 1)λ, where N is an integer. Secondly, for temperatures above T_C, in which birefringence is very small, it is based on the measurement of the phase difference δ = (2πd × Δn)/λ between the polarized light components for the same crystal, where λ is the wavelength of the light. Linkam THMS600E temperature microscope stage allowed also to observe changes in the domain structure and perform birefringence measurements in the external electric field. The birefringence measurements of a transparent single PbZr_0.87Ti_0.13O₃ crystal were carried out in a wide temperature range, from 300 K to 673 K. Before starting each experiment the crystal was heated to 673 K and left for several minutes, in order to release any strain. Each run was carried out with a constant temperature rate, and the images of birefringence were taken at constant time intervals. The temperature runs were performed at the rates of 1 K/min. The direction of the electric field applied, having the intensity of 7 kV/cm was parallel to [001] direction. The crystal was placed in glass plate capacitor coated with transparent electrodes.

3. Results and Discussion

The dielectric properties of the investigated crystal are collected and presented in Figure 1. The temperature dependence of the real part of the permittivity ε’(T) for five arbitrarily chosen frequencies is shown in Figure 1a. The maximum of ε’ associated with phase transition from ferroelectric (FE) to paraelectric (PE) phase was observed at about 540 K, showing no thermal hysteresis between the maximum of ε’(T) on heating and cooling (Figure 1b). However, transition between two ferroelectric phases (inset in Figure 1b) is of diffused character and with significant thermal hysteresis. It should be noted that not every experimental technique is sensitive enough to register it. Earlier studies have shown that this transition is difficult to be registered in PZT ceramics (e.g., [29]). It is worth mentioning that there is clear dispersion in permittivity values around Tc, while temperature points are independent on the measuring field frequency. This is connected mainly with domains and domain wall movements in the electric field. The transition from FE to PE phase is accompanied by the maximum of the imaginary ε’’ part of the complex permittivity (Figure 1c). It appeared that the most interesting results, presented in Figure 1d, are connected with temperature dependence of the inverse of the real part of the complex permittivity at 500 kHz. We have found that the Curie–Weiss law ε’^-1 ~(T-T₀), where T₀ is the Curie–Weiss temperature, is obeyed above 600 K only. Moreover, the best fit to this law, shown in Figure 1d, was obtained for T₀ = 555 K, which is higher than T_C. This unusual relation of T₀ > T_C will be discussed further in the text, although it can be said immediately that the phase above T_C is certainly not of pure paraelectric character. However, it is interesting that in the vicinity of T₀ the permittivity dispersion vanishes (Figure 1a).

The ε’(T) measured after poling in the electric field having the strength of 7 kV/cm revealed a shift of T_C of the order of 1 K, which most probably is the result of the influence of pyroelectric effect on permittivity while approaching the transition point (Figure 1e), rather than a change of symmetry under electric field action, as observed for PZTs from morphotropic phase boundary [30].

Another proof for polar phase transition occurrence is the observation of pyroelectric phenomena associated with flowing current due to changes of temperature only. In the case of ferroelectric materials, the total pyroelectric current consists of two parts. The first one is connected with temperature changes of spontaneous polarization (P_S), while the second one is produced due to mutual interactions between the thermal expansion, elastic and piezoelectric properties. The faster the changes of temperature and P_S, the higher the changes of total pyroelectric current. P_S quickly disappears while approaching transition point, therefore the pyroelectric current is of the highest intensity. Such changes of the pyroelectric current that are associated with transition in T_C point and between two ferroelectric phases in virgin PbZr_0.87Ti_0.13O₃ crystal are presented in Figure 2. Changes in the sign of current registered, when passing transition point on heating and then on cooling, are the direct proof that the current is induced due to the pyroelectric phenomenon. The observed anomalies correspond to changes of complex permittivity in the same temperature ranges (Figure 1). For virgin sample, the pyroelectric current is an effect of partially ordered domain structure that may take place due to pinning of domains on lattice defects or internal stresses. Local current peaks (jumps) seen in I_pyro (T) run below T_C (Figure 2) represent Barkhausen pulses connected with domain appearance or disappearance, depending on the direction of temperature changes.

To determine the temperature-dependent changes of polarization, the investigated crystal had to be poled in d.c. electric field. The pyroelectric currents are shown in Figure 3 as a function of temperature for such polarized crystal. As was expected, the changes on I_pyro near transitions at 380 K and 540 K are much stronger than for virgin crystal, and correspond to changes of polarization of the of order of 2.6 and 13 µC/cm², respectively. However, these values are smaller than P_S observed earlier in standard Tower-Sawyer system [11]. It means that poling of PZT crystals in d.c. electric field is not an easy process. One of the reasons is dielectric breakdown, which already appears for fields stronger than 7 kV/cm at the temperature of 350 K. In both transitions irregular runs of the pyroelectric current, like the two clear peaks recorded near the T_C, testify for creep movements of domains close to the transition point.

Changes in elastic properties taking place with temperature were determined for the crystal poled in strong electric field and are presented in Figure 4. The imaginary part of the elastic compliance s₁₁’’ has anomalies at about 390 K and 448 K. Starting from 520 K, the s₁₁’’ value fluctuates and reaches its maximum value around 555 K. Similarly, the real part of the elastic compliance s₁₁’ reveals abnormal behavior at 390 K, 448 K and 554 K. What is interesting is that both coefficients, determined based on piezoelectric resonances, vanished at the temperature that well corresponds to the T₀ obtained from linear fit of high temperature run of reciprocal permittivity (Figure 1d). Except for transition between two ferroelectric phases, other local anomalies have been observed at different temperatures (Figure 3 and Figure 4). The reason is that the pyroelectric current and elastic compliance were measured with different heating rates. It should be noted that the temperature of 448 K is related to a transition associated with lattice instability, reported by Cordero et al. and Lazar et al. [7,8,9].

It has already been proven that PZT single crystals have complex domain structures over a wide temperature range [11]. In spite of that, the method we used for birefringence measurement permitted to determine the birefringence ∆n for a region of 25 × 30 μm² inside a domain. The results presented in Figure 5 confirmed that at least two phase transitions occur in investigated single PbZ_0.87Ti_0.13O₃ crystal. The transition between two ferroelectric phases has been identified as a kink on the ∆n(T) dependence, while at T_C point the birefringence disappeared almost completely. In those studies, we did not observe an anomaly connected with additional phase transition appearing due to suggested distinct lattice instability between 377 K and 540 K. Since in studies concerning elastic properties this transition was clearly observed, and these properties were encountered for crystal poled in d.c, field, the birefringence measurements were conducted in d.c. electric field.

Figure 6 shows the influence of this field on ∆n(T) function for a single PbZ_0.87Ti_0.13O₃ crystal. The calculations of birefringence were carried out for a region inside the domain, having the surface area of 25 × 30 μm². The electric field slightly reduced the ∆n value, but shifted the temperature at which birefringence disappears towards higher values. In a crystal subjected to d.c. field having the strength of 7 kV/cm, the birefringence disappeared at 548 K, i.e., distinctly higher than T_C, as expected for ferroelectric transition. It should be remembered that the strongest changes of elastic coefficients s₁₁’ and s₁₁’’ were also observed near T₀ (Figure 4).

As in other perovskites [22,23,24], birefringence was observed far above T_C = 540 K. Figure 7a shows an example of ∆n(T) run above T_C and the influence of electric field on this dependence. As in the case of dielectric and elastic measurements, the temperature of 555 K has been distinguished with clear anomaly in the ∆n(T). Birefringence finally disappears near 600 K. While birefringence was measured under action of d.c. electric field applied inside ferroelectric field, the point of T_C and anomaly near T₀ were shifted towards higher temperatures (Figure 7b). Additionally, the anomaly near T₀ became more diffuse, with a small thermal hysteresis. However, the electric field almost did not shift the temperature at which ∆n disappeared. According to the theory reported in [26], below the temperature T=1.1*T_C, i.e., starting inside the paraelectric phase, polar regions with the size of some 10–15 lattice units appear. In the investigated crystal, this temperature is equal to T = 1.1 × 540 K = 594 K. The fact that in d.c. electric field the anomaly near T₀ becomes diffused and moves to higher temperatures proves the existence of polar regions above T _C in a wide temperature range. To the best of our knowledge, this is the first proof of local polarity existence in PZT single crystal. At the same time, we exclude the induction of local polarity due to change in symmetry while d.c. is acting. On the other hand, it is known that ∆n ~q², where q is an order parameter [31]. In the investigated crystal, the P _S is the order parameter, therefore, the presence of birefringence above T_C indicates once again that the phase is polar. It is worth mentioning that polar nano-regions in a macroscopically centrosymmetric lattice appear well above T_C in other oxide perovskites, such as BaTiO₃, SrTiO₃, PbTiO₃ or PbZrO₃:Nb (e.g., [22,23,24,26,32]).

4. Conclusions

PbZr_0.87Ti_0.13O₃ single crystal undergoes transition of diffused character between two ferroelectric phases around 380 K, and transition at T_C= 540 K. The fact that there is no thermal hysteresis of transition at T_C allows to state that this phase transition is of continuous character. Only the temperature dependence of elastic properties confirms the presence of a transition associated with lattice instability around 448 K. The measurements of dielectric, pyroelectric, elastic and optical properties of virgin crystal proved that an anomaly of these properties near 555 K is sensitive to the action of d.c. electric field. It is the direct proof that there are polar regions in the investigated crystal, and those regions can exist far above T_C. The polar regions vanish, and the crystal becomes isotropic, only above around 600 K.