High-temperature dielectric properties and impedance spectroscopy of PbHf 1− Sn 3 ceramics

: PbHf 1− x Sn x O 3 (PSH) ceramics were synthesised by a conventional solid-state reaction method. Dielectric properties were investigated in the temperature range of 20–650°C. As the Sn 4+ content goes up, the phase transition temperatures of an antiferroelectric (AFE1) to another intermediate antiferroelectric (AFE2) phase and AFE2 to the paraelectric (PE) phase decrease gradually. When x ≥0.1 for PSH ceramics, the ferroelectric (FE) phase appears around 225°C, and phase transition temperature from FE phase to PE phase goes up with the increasing concentration of Sn 4+ . Moreover, high-temperature dielectric relaxation (HTDR) phenomenon can be seen from all samples. Mechanism of HTDR was discussed from impedance spectroscopy and conductivity for PSH ceramics. It was found that three dielectric responses were observed in complex impedance plots and HTDR was involved with the movement of oxygen vacancies. Activation energy calculated from dielectric data suggested that the HTDR was governed by the hopping conduction process.

Recently, the most studied form of lead hafnate is PbHfO 3 single crystal, whereas PbHfO 3 ceramic is rarely reported. It is reported that PbHfO 3 single crystal undergoes two structural transformations in broad frequency and temperature range: at about 163°C from the antiferroelectric (AFE1) to another intermediate antiferroelectric phase (AFE2) and at about 209°C from the AFE2 to the paraelectric (PE) phase [5,12]. For more profound research, researchers are usually doping different ions to improve the dielectric properties of PbHfO 3 , such as Ti-doped PbHfO 3 antiferroelectric crystals [13], (1−x)PbSc 0.5 Ta 0.5 O 3 -(x)PbHfO 3 ceramics [14], PbHfO 3 -BaHfO 3 and PbHfO 3 -SrHfO 3 [15] and so on. In comparison with PbHfO 3 single crystal, phase-transition temperatures of PbHf 1−x Sn x O 3 (PSH, with x = 0.025) single crystal showed a slight decrease and reached about 153 and 201°C, respectively, for AFE1 to AFE2 phase and AFE2 to PE phase [5]. Considering the excellent characteristics of PSH single crystal, we conducted PSH ceramics as our research. In previous work, both Ti-doped [13] and Sn-doped [6] PbHfO 3 crystals show excellent FE and antiferroelectric properties due to Sn or Ti doping plays a crucial role in changing properties of PbHfO 3 , especially in structural phase transitions. Fan et al. reported a new cloverleaf AFE domain structure in PbHfO 3 ceramics. However, the high-temperature dielectric relaxation (HTDR) is rarely involved and studied.
Unlike antiferroelectric performance of perovskites ceramics, dielectric relaxation has been well-verified in both theoretically and experimentally. According to previous research, Bidault et al. showed that the amplitude of the diffuse anomaly might be increased with the density of oxygen vacancies (OVs) raising [16]. Dielectric relaxation is an essential property of perovskite-type ABO 3 . There are numerous research papers about its characteristic and origin. At high temperatures, OV is a critical factor to analyse dielectric properties in ABO 3 perovskite-type materials, such as dielectric relaxations and electrical conduction [17,18]. Lee et al. reported that the low-frequency dielectric relaxation in BaTiO 3 thin films was related to the ionised space-charge carriers such as OVs with the thermal activation energy of 0.72 eV [19]. Also, in SrTiO 3 ceramic, the same conclusion was gained. The clustering and hopping of OVs are the causes of dielectric relaxations at high temperatures [20]. Li et al. found that the HTDR in Ba 0.85 S 0.15 TO 3 ceramics was also involved with the hopping localised OVs, which was in agreement with the Polaron theory [2]. Based on the critical role in ABO 3 perovskite FE materials played by OVs, in this work, we mainly report the phase transition and oxygen-vacancy-related HTDR in PSH ceramics.

Experimental procedure
The PSH (x = 0, 0.05, 0.1, 0.15, 0.2 and 0.25, respectively) ceramics were prepared by the conventional solid-state method. According to the stoichiometric ratios, the raw materials from PbO (99%, Aladdin Industrial Corporation, China), HfO 2  850°C for 2 h in an alumina crucible. After that, the received powders were mixed with 5 wt% PVA and pressed into disk. Then the discs were sintering at 1250°C for 5 h. Besides, in order to reduce the Pb vaporisation, small amount of PbO powders were covered on the surface of samples during sintering.
The X-ray diffractometer (XRD, Philips XD-2) was engaged in distinguishing the phase structure in ceramics. The scanning electron microscope (SEM, HitachiS-3400N-II) was consumed to observe the surface topography for samples. Before the performance measurement, ceramics were polished to thickness of 0.5 mm, and then both sides of samples were coated with silver electrodes and sintered at 650°C for 2 h. Dielectric properties were detected by Agilent E4980A with various frequencies from 1 to 10 5 Hz and temperature rising of 2°C/min. The same machine was used to measure impedance spectroscopy under full frequencies, with temperature heating of 1°C/min and 1 V ac bias voltage.

Result and discussion
The XRD patterns of PSH ceramics at room temperature (RT) are shown in Fig. 1. The stable perovskite phases are achieved in these samples. By comparing the PDF cards, the principal phase presents orthorhombic phase (corresponding to PDF card #97-017-4109), which belongs to symmetric Pbam space group. Distinct impure phase is not observed in this pattern, indicating the Sn 4+ cation has been permeated into PbHfO 3 lattices to form a good solid solution. With the concentration of Sn 4+ goes up, the 2θ corresponding to diffraction peaks does not deviate greatly. This situation suggests doping of Sn 4+ cation almost possesses no significant influence for phase structure of PbHfO 3 ceramics. That may be ascribed to Sn 4+ replacing Hf 4+ , owing to two cations have similar ionic radii (Hf 4+ ∼69 pm, Sn 4+ ∼71 pm). Fig. 2 displays the SEM photos of PSH ceramics. From these graphs, it can be found that the distribution of grain size is uniform. While, for pure PbHfO 3 ceramics, a few voids are found on the surface of ceramic samples. As the increase of Sn 4+ doping content, the voids gradually disappear, indicating Sn 4+ doping is beneficial to enhance the dense of PSH ceramics. Fig. 3 presents the permittivity ɛ r and loss tanδ as a function of temperature (20-650°C) under different frequencies (1-100 kHz). With regard to pure PbHfO 3 ceramic sample, it can be observed that ɛ r -T curves, measured at different frequencies and low temperature range (T ≤ 275°C), gradually merge together and the ɛ r values reach maximum value ɛ m . However, the T m (temperature corresponding to ɛ m ) does not change with increasing frequency. When x ≤ 0.1, there exist two apparent peaks in the temperature range of 100-225°C. According to relevant literature reports, the dielectric peak at low temperature means the phase transition from antiferroelectric1 (AFE1) phase to another antiferroelectric 2 (AFE2); the dielectric peak at high temperature expresses the phase transition from antiferroelectric (AFE2) phase to PE phase [4][5][6]21]. Among them, the phase structure of AFE1 is an orthorhombic phase, while, the AFE2 phase is relatively complex and remains many controversies [6]. At present, there are many kinds of phases considered AFE2, such as tetragonal phase, pseudo-tetragonal phase and rhombohedral phase. When x ≥ 0.1, a new weak dielectric peak, which is related to FE phase, appears in a higher temperature area (225-275°C). Furthermore, as the measured temperature increase, HTDR is found in temperature range of 300-600°C. The value of permittivity ɛ r exhibits an apparent frequency dispersion phenomenon and decreases with increasing frequency. According to previous reports for the relaxation mechanism of FE materials, the relaxation phenomenon may come from the following mechanisms: dipole polarisation, Maxwell-Wagner, domain relaxation, space charge and so on. Among them, space charge model is also related to electrical conduction [22], so OVs play a crucial role in HTDR [23][24][25][26][27][28]. From the loss patterns, it can be found that values of loss tanδ for all samples are <1 in the temperature range of RT to 275°C. However, at high-temperature range (300-600°C), the tanδ value suddenly increase and this situation is line with the HTDR of ɛ r -T curves. This phenomenon   = 0.0, (b) x = 0.05, (c) x = 0.1, (d) x = 0.15, (e) x = 0.2, (f)  results from the enhancement of space charge or conductivity of ceramics with the rising temperature [9,16]. Besides, according to the change of phase transition temperature, the phase diagram for PSH ceramics is recorded in Fig. 4. As the amount of Sn4 + increases, T 0 (phase transition temperature from AFE1 to AFE2) and T 1 (phase transition temperature from AFE2 to PE or FE) decrease gradually. When x ≥ 0.1, the T 2 (phase transition temperature from FE to PE) increases with increase of Sn 4+ content. From this diagram, we can see in which phase the different components will be at different temperatures. In order to analyse the mechanism of HTDR, complex impedance spectroscopy was measured for the PSH ceramics under different temperature. It is an effective method and has been widely employed to investigate the relaxation behaviour and conduction characteristics of dielectric ceramics. Fig. 5 shows the Nyquist plots of real part impedance (Z ) versus imaginary part impedance (Z ) for PSH ceramics under the temperature range of 500-600°C. A distinct circle arc appears in the complex impedance plots for all samples at different temperature and this may be attributed to the grain boundary response caused by a higher barrier [29]. Furthermore, as the temperature rises up, the radius of arc for each impedance plot decreases. Maybe the increased temperature makes it easier for space charges to move, and some carriers gathered around the grain boundary can gain enough energy to cross the boundary, showing a negative temperature effect [8]. Fig. 5g presents the impedance spectroscopy of different component for PSH ceramics at 550°C. With Sn 4+ doping concentration increases, the radius of arc decreases and maybe because the increase of Sn 4+ reduces the height of grain boundary barrier at this temperature, thus leading to the change of impedance [30]. Besides, a small tail appears on the periphery of the arc in low-frequency range of some graphs (such as x = 0, 0.1, 0.2 and 0.25), which may be related to the electrode effect [31]. Following discussion will ignore it, due to the limit of measurement frequency. Generally, the contribution source of an ideal semicircle can be represented by an equivalent circuit comprised of resistance (R) and capacitance (C) in parallel [32,33]. Whereas, the experimental data presents a non-Debye model and it is preferred to choose the constant phase element (CPE), instead of standard capacitance C, to gain an appropriate fitting result for complex impedance plots. We use the Z-view software to fit the arcs of complex impedance plots at 550°C and three series R-CPE components can fit the data well. The fitting result and the element model are shown in Fig. 5i, and the received parameters are recorded in Table 1.
In order to identify the origin of contributions for complex impedance plots, the Bode plots (frequency dependence) of imaginary part impedance (Z ) and electric modulus (M ) for all PSH samples at 550°C are exhibited in Fig. 6. The value of M can be calculated by the equation [32] M′′ = 2π f C 0 Z′ (1) where f is the measurement frequency and C 0 is the vacuum capacitance. Generally, modulus plots emphasise these elements with the small capacitances, whereas impedance plots highlight the high resistance components [32,33]. The Z Z max plots possess two peaks and the curves can be fitted by Lorentzian multi-peak function, as shown in Fig. 5h. The low-frequency peaks may result from grain boundary and high-frequency peaks attribute to the contribution of grain. From M plots, there exist a peak in highfrequency range, indicating a low-capacitance component contributes to dielectric response [34]. Unfortunately, the peak has not been found in the M data of x = 0.25, which is limited by the measured frequency range. According to the equivalent circuit fitting results and combined Z and M plots, the dielectric response mainly comes from three aspects: grain core, grain shell and grain boundary. Combined with the R and C values, the lowfrequency responses are related to grain boundary (R 3 , C 3 , n 3 ), and the high frequency responses are involved with the grain core (R 1 , C 1 , n 1 ) and grain shell (R 2 , C 2 , n 2 ) [31,33]. The insets in Fig. 5 show the normalisation impedance spectra of imaginary part. As the temperature increases, the characteristic peak frequency (f max ) moves towards high frequency gradually. This phenomenon indicates the relaxation time reduces with the increased temperature, suggesting a thermal activation relaxation process. As for the current PSH ceramics, the investigated HTDR may result from the concentration of OVs and OVs may come from lead volatilisation and ion substitution. Due to the low melting point of PbO, lead will be volatilised during high-temperature sintering, thus OVs generate. The whole process can be described as the Kroger-Vink formulation [22]: In order to maintain electrical neutrality, Pb 2+ loss will lead oxygen ions to ionise two electrons, resulting in OVs V Ö . Besides, the ion radius of Sn 4+ is different from that of Hf 4+ . After the Sn 4+ replacement of Hf 4+ occurs, dislocation defects appear in the lattices, which will induce the generation of OVs in the process of movement. It may be the high carrier concentration that results in small R values in Table 1. As the Sn 4+ content increases, the concentrations of OVs increase, thus the decreased R values exist in PSH ceramics. From combined Z and M plots, the mismatch between Z and M peaks indicates the charge carrier migration are not mainly long range, and the short-range movements also exist in dielectric response process. In order to understand the mechanism of HTDR and ion conduction, we can calculate the relaxation activation energy (E a ) and conductance activation energy (E c ) by Arrhenius equations [35][36][37]: where ω, and τ 0 are characteristic angular frequency (τω = 1, ω = 2π f max , f max refers to the frequency corresponding to the peak values in the Z /Z max -log f plots), relaxation time and pre-factor or the relaxation time at infinite temperature; T, and k β are absolute temperature, ac conductivity and Boltzmann's constant, respectively; the ɛ o , o are constant. Through the formula (3) and insets of Fig. 5, the values of E a can be computed. As for the ac conductivity , we can use the permittivity data and (4) and (5) to receive the values of E c .
It is reported that the removal of OVs is not only confined in a cell, but also spread into whole sample to obtain ionic conductivity [16,38]. HTDR is involved with the thermal activation process.
After the temperature rise, the migration rate of oxygen ions became faster, resulting in the OVs induced conduction mode become the leading position [39]. This is why the permittivity and loss increase abruptly at high-temperature range. Fig. 7 shows Arrhenius plots for E a (a) and E c (b), and the values of E a and E c are recorded in Table 2. Generally, E a is involved with the free energy of charge carriers and the hopping of these charge carriers between adjacent lattice positions, while E c presents all the generation and migration of charge carriers or the free energy of long-distance hopping charge carriers. If the relaxation mechanism is a dipolar conduction process, E a should be greater than E c . If relaxation mechanism is a trap-controlled or hopping conduction process, E a should be equal to E c. Therefore, from the comparison of calculated activation energy, it is evident that the relaxation process of all samples is controlled by the dipolar conduction. OVs promote the generation of dipoles formed with a neighbouring host ion and expand the vibration space for dipoles, which leads to short-range hopping and HTDR [38,40,41].

Conclusions
In this work, we investigated the effect of Sn 4+ doping on the structure, dielectric and HTDR of PbHfO 3 ceramics. It can be found that as the content of Sn 4+ goes up, the T 0 and T 1 decrease, while the T 2 increases. Moreover, mechanism of HTDR was discussed from the impedance spectroscopy and ac conduction, presenting that it was involved with the concentration of OVs. The calculated activation energies were compared and found that the lowest OVs existed in PSH (x = 0.15) ceramic samples. As the temperature rise, OVs conduction became the main mode of conduction and then HTDR appeared in high-temperature range. By comparing the value of E a and E c , the relaxation process was controlled by the dipolar conduction. OVs promoted the generation of dipoles formed with a neighbouring host ion and expand the vibration space for dipoles, which lead to short-range hopping of iron and relaxation process.